ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 The complete diffraction pattern including the effects of gravitational lensing is given in black., The complete diffraction pattern including the effects of gravitational lensing is given in black.3 The diffraction pattern with f=0 (no lensing) is given in red., The diffraction pattern with $f=0$ (no lensing) is given in red.4 The diffraction pattern including lensing oscillates about the geometric-optics value of the microlensing magnification (green curve) from Eq. (7))., The diffraction pattern including lensing oscillates about the geometric-optics value of the microlensing magnification (green curve) from Eq. \ref{eq:15}) ).5 One can obtain an approximate idea of the diffraction pattern including lensing by using the lensing mapping v>v—f/v and taking the product of the geometric magnification with the unlensed diffraction pattern resulting in the blue curve., One can obtain an approximate idea of the diffraction pattern including lensing by using the lensing mapping $v \rightarrow v - f/v$ and taking the product of the geometric magnification with the unlensed diffraction pattern resulting in the blue curve.6" When the lensing effect is weak as in Fig. 4,, thisposter"," When the lensing effect is weak as in Fig. \ref{fig:1E4AU},"7"iori lensing correction works quite well, so occultation diffraction patterns can be corrected for a modest amount of lensing without calculating the full lensing diffraction pattern."," this lensing correction works quite well, so occultation diffraction patterns can be corrected for a modest amount of lensing without calculating the full lensing diffraction pattern."8" However, this mapping fails to reproduce the central fringing that occurs when both diffraction and lensing are important."," However, this mapping fails to reproduce the central fringing that occurs when both diffraction and lensing are important."9 Averaging the magnification over a finite bandwidth smooths out much of the small-scale oscillation in the light curves as shown in Fig. 3.., Averaging the magnification over a finite bandwidth smooths out much of the small-scale oscillation in the light curves as shown in Fig. \ref{fig:1E5AU_0.2}.10" However, even over a moderate bandwidth of twenty-percent the microlensed diffraction patterns are easily distinguished from the unlensed patterns."," However, even over a moderate bandwidth of twenty-percent the microlensed diffraction patterns are easily distinguished from the unlensed patterns."11 Again the lensing mapping does an reasonable job of reproducing the pattern., Again the lensing mapping does an reasonable job of reproducing the pattern.12 This important to emphasise., This important to emphasise.13" Microlensing does not simply contract the diffraction pattern so it is not covariant with varying the relative velocities of the lens, source and detector nor is it covariant with varying the impact parameter of the occultation (how close to exactly aligned the source, lens and detector become)."," Microlensing does not simply contract the diffraction pattern so it is not covariant with varying the relative velocities of the lens, source and detector nor is it covariant with varying the impact parameter of the occultation (how close to exactly aligned the source, lens and detector become)."14" The lensing both increases the amplitude of the diffractive oscillations and shifts the locations of the peaks and troughs in a non-trivial manner, following the lensing mapping if the lensing is weak."," The lensing both increases the amplitude of the diffractive oscillations and shifts the locations of the peaks and troughs in a non-trivial manner, following the lensing mapping if the lensing is weak."15" If the Eris-like asteroid were closer to Earth at 104 AU, Fig 1 indicates that the lensing would be weaker (the lower cross is well below the red lines)."," If the Eris-like asteroid were closer to Earth at $10^4$ AU, Fig \ref{fig:regimes} indicates that the lensing would be weaker (the lower cross is well below the red lines)."16 The results depicted in Fig., The results depicted in Fig.17 4 bear this out., \ref{fig:1E4AU} bear this out.18" The location of the first peak moves inward from 1.09ua to 1.04ua because the light is slightly bentabout the limb of the asteroid, decreasing the duration of the occultation by about 4.8%,, approximately the value of f/u2e 5.2%."," The location of the first peak moves inward from $u_d$ to $u_d$ because the light is slightly bentabout the limb of the asteroid, decreasing the duration of the occultation by about , approximately the value of $f/u_d^2\approx 5.2\%$ ."19 Microlensing is important for large asteroids (similar to, Microlensing is important for large asteroids (similar to20more precisely an effective temperature from Τω = 9867 to KK. a surface gravity from loge = 3.308 to 3.313 (where g Is expressed in καστ and a radius from R = 2.520 to 2.763 Κ... respectively.,"more precisely an effective temperature from $T_{\rm eff}$ = 9867 to K, a surface gravity from $\log g$ = 3.308 to 3.313 (where $g$ is expressed in $^{-2}$ ) and a radius from $R$ = 2.520 to 2.763 $_{\odot}$, respectively."21 Until know. no rapidly rotating. pole-on and observably pulsating star was known.," Until know, no rapidly rotating, pole-on and observably pulsating star was known."22 The goal of our work was therefore to search for low amplitude stellar pulsations in an extensive high-resolution quasi-continuous spectroscopic survey of Vega., The goal of our work was therefore to search for low amplitude stellar pulsations in an extensive high-resolution quasi-continuous spectroscopic survey of Vega.23 Sect., Sect.24 2 describes the observations and data reduction. Sect.," \ref{obs} describes the observations and data reduction, Sect."25 3 presents the analysis of radial velocity variations in. the spectroscopic time series of Vega. and in Sect.," \ref{searchpulsations} presents the analysis of radial velocity variations in the spectroscopic time series of Vega, and in Sect."26 4. results are discussed and a conclusion is drawn., \ref{disc} results are discussed and a conclusion is drawn.27 The analysis presented in this paper is based on three datasets obtained in 2008. 2009 and 2010.," The analysis presented in this paper is based on three datasets obtained in 2008, 2009 and 2010."28" Vega was monitored during 3 nights in 2008 (26, 27"" and 29"" of July) with the high- echelle spectropolarimeter NARVAL at the 2m Bernard Lyot Telescope (TBL. Pic du Midi. France)."," Vega was monitored during 3 nights in 2008 $^{\rm th}$, $^{\rm th}$ and $^{\rm th}$ of July) with the high-resolution echelle spectropolarimeter NARVAL at the 2m Bernard Lyot Telescope (TBL, Pic du Midi, France)."29 The first two nights observations were acquired at R = 65000 in polarimetric mode. and the last night at R = 75000 in spectroscopic mode.," The first two nights observations were acquired at R = 65000 in polarimetric mode, and the last night at R = 75000 in spectroscopic mode."30 We obtained 1213 spectra covering 19.9 hrs., We obtained 1213 spectra covering 19.9 hrs.31" In 2009 we obtained 1293 spectra covering 13.7 hrs on 3 nights (9 - 11"" of September 2009) at ESPaDOnS/CFHT (R = 68000) in polarimetric mode.", In 2009 we obtained 1293 spectra covering 13.7 hrs on 3 nights $^{\rm th}$ - $^{\rm th}$ of September 2009) at ESPaDOnS/CFHT (R = 68000) in polarimetric mode.32 Finally. in 2010. we got a huge data set of 1972 spectra covering 28.8 hrs on 5 nights (15 τοῦ of July 2010). obtained again in the polarimetric mode at NARVAL/TBL.," Finally, in 2010, we got a huge data set of 1972 spectra covering 28.8 hrs on 5 nights $^{\rm th}$ - $^{\rm th}$ of July 2010), obtained again in the polarimetric mode at NARVAL/TBL."33 Table | summarizes the log of the observations during these 43 runs., Table \ref{table:log} summarizes the log of the observations during these 3 runs.34 The general observing strategy was to obtain as many maximum S/N observations of the target during the night às possible., The general observing strategy was to obtain as many maximum S/N observations of the target during the night as possible.35 The goal was to obtain a versatile data set. enabling us to search for the presence of a magnetic field as well as stellar pulsations.," The goal was to obtain a versatile data set, enabling us to search for the presence of a magnetic field as well as stellar pulsations."36 Results of the spectropolarimetric study of the first observing run are presented in Ligniéresetal. (2009).. where the detection of a weak magnetic field 1 Vega has been announced. revealing the existence of an as-yet unexplored class of weakly magnetic stars in the intermediate mass domain.," Results of the spectropolarimetric study of the first observing run are presented in \citet{vegamag}, where the detection of a weak magnetic field in Vega has been announced, revealing the existence of an as-yet unexplored class of weakly magnetic stars in the intermediate mass domain."37 The joint analysis of the two first runs (2008 anc 2009) confirmed this first detection and indicated a rotational modulation of the polarization signature with a period of 0.732 + dd. a value which ts very close to the rotation period announced by Takedaetal.(2008) (= dd).," The joint analysis of the two first runs (2008 and 2009) confirmed this first detection and indicated a rotational modulation of the polarization signature with a period of 0.732 $\pm$ d, a value which is very close to the rotation period announced by \citet{Ta08} $\simeq$ d)."38 These results are published in Petitetal.(2010).., These results are published in \citet{vegamag2}.39. A recent analysis of the 2010 data set yielded a slightly different rotation period of 035 d (Alinaetal..2011)., A recent analysis of the 2010 data set yielded a slightly different rotation period of $^{+0.036}_{-0.029}$ d \citep{alina2011}.40 The global data set containing 4478 spectra obtained at the highest possible signal to noise should represent. as of today. the most extensive high resolution. quasi-continuous spectroscopic monitoring of Vega.," The global data set containing 4478 spectra obtained at the highest possible signal to noise should represent, as of today, the most extensive high resolution quasi-continuous spectroscopic monitoring of Vega."41 It should be noted that for such a bright star the exposure times are extremely short (4 to 13 seconds on the star) in order to avoid the saturation of the CCD. while the readout times of the CCD dominate the duty-cycle. the average time interval between two exposures being close to 0.8 min.," It should be noted that for such a bright star the exposure times are extremely short (4 to 13 seconds on the star) in order to avoid the saturation of the CCD, while the readout times of the CCD dominate the duty-cycle, the average time interval between two exposures being close to 0.8 min."42" Subexposures obtained in polarimetric mode provide as a direct result from the data reduction pipeline. in addition to the polarization information. a perfectly calibrated intensity spectrum,"," Subexposures obtained in polarimetric mode provide as a direct result from the data reduction pipeline, in addition to the polarization information, a perfectly calibrated intensity spectrum."43 The wavelength covered extends from 369 to nnm for both spectrographs., The wavelength covered extends from 369 to nm for both spectrographs.44 Standard calibration spectra were obtained at the beginning and at the end of the night: most importantly the absolute wavelength calibration relies on a Th/Ar spectrum at the beginning of the night., Standard calibration spectra were obtained at the beginning and at the end of the night; most importantly the absolute wavelength calibration relies on a Th/Ar spectrum at the beginning of the night.45 Most of the data reduction was carried out following standard reduction procedures using a dedicated spectroscopic data reduction package. based on the algorithm described in. Donatietal.(1997).," Most of the data reduction was carried out following standard reduction procedures using a dedicated spectroscopic data reduction package, based on the algorithm described in \cite{donati}."46". This package also makes use of the ""optimal extraction algorithm” (Horne.1986).."," This package also makes use of the “optimal extraction algorithm"" \citep{horne}."47 A standard heliocentric velocity correctior was performed., A standard heliocentric velocity correction was performed.48 The intrinsic wavelength calibration accuracy achieved with the 2D-polynomial fit procedure ts better than mms~! for both data sets., The intrinsic wavelength calibration accuracy achieved with the 2D-polynomial fit procedure is better than $^{-1}$ for both data sets.49 In order to be able to calibrate potential spectral shifts during the night a cross-correlation of telluric lines present in the spectra was performed by the standard reduction package., In order to be able to calibrate potential spectral shifts during the night a cross-correlation of telluric lines present in the spectra was performed by the standard reduction package.50 After all shifts have been applied to the wavelength grid. the residual telluric line velocity should reflect precisely the opposite of the heliocentric velocity correction.," After all shifts have been applied to the wavelength grid, the residual telluric line velocity should reflect precisely the opposite of the heliocentric velocity correction."51 In order to verify this. we computed least square deconvelved (LSD) profiles (Donatietal..1997) of the more than 100 telluric water vapor lines contained in each stellar spectrum. and determined their centroid by fitting a gaussian profile.," In order to verify this, we computed least square deconvolved (LSD) profiles \citep{donati} of the more than 100 telluric water vapor lines contained in each stellar spectrum, and determined their centroid by fitting a gaussian profile."52 We discovered the presence of residual radial velocity errors of the telluric lines., We discovered the presence of residual radial velocity errors of the telluric lines.53 In order to optimize the radial velocity precision we corrected then for the remaming velocity shifts., In order to optimize the radial velocity precision we corrected then for the remaining velocity shifts.54 The residual spectral stability is around mms?! (depending on the night anc on the site). taking into account all the multiplex informatior of the lines present 11 the spectra.," The residual spectral stability is around $^{-1}$ (depending on the night and on the site), taking into account all the multiplex information of the lines present in the spectra."55 At this point it should be noted that a stability analysis of Os telluric lines has been carried out by Caccin.etal. (1985)., At this point it should be noted that a stability analysis of $_2$ telluric lines has been carried out by \citet{caccin}.56.. They report that the line positions change more or less erratically with time. their displacement depending upon the horizontal wind structure above the observing site.," They report that the line positions change more or less erratically with time, their displacement depending upon the horizontal wind structure above the observing site."57 They note however. that unless the observations are made near the horizon. the component of the wind velocity along the line of sight is very seldom significant. the displacement reaching up to 10mms7! only in very severe conditions (large air mass. strong winds).," They note however, that unless the observations are made near the horizon, the component of the wind velocity along the line of sight is very seldom significant, the displacement reaching up to $^{-1}$ only in very severe conditions (large air mass, strong winds)."58 In low wind conditions and for only one to three airmasses their time instability should be probably of the order of mms., In low wind conditions and for only one to three airmasses their time instability should be probably of the order of $^{-1}$.59 This is the case for our observations of Vega. since they have been obtained in airmasses between | and 2. and only during the last night of the CFHT run airmasses up to 2.6 were reached.," This is the case for our observations of Vega, since they have been obtained in airmasses between 1 and 2, and only during the last night of the CFHT run airmasses up to 2.6 were reached."60 In a recent work. Figueiraetal.(2010) evaluated the stability of atmospheric lines with HARPS (on the mm telescope at La Silla. ESO). and concluded in a similar way to Caccinetal.(1985) that a precision of mms! can routinely be obtained in restricted. airmass conditions.," In a recent work, \citet{figueira} evaluated the stability of atmospheric lines with HARPS (on the m telescope at La Silla, ESO), and concluded in a similar way to \citet{caccin} that a precision of $^{-1}$ can routinely be obtained in restricted airmass conditions."61 What we retain from this latter work 1s the fact that increasing airmass induces asymmetry of telluric lines. this asymmetry Is therefore expected to have an impact on the measured RV.," What we retain from this latter work is the fact that increasing airmass induces asymmetry of telluric lines, this asymmetry is therefore expected to have an impact on the measured RV."62 This behaviour-depending on the airmass of the observed object repeats therefore every night for the same target (within a 3 or, This behaviour-depending on the airmass of the observed object repeats therefore every night for the same target (within a 3 or6311σ and Low Energy Transmission Grating Spectrometers (IIETGS. LETGS) on board and (the Beflection Grating Spectrometer (RGS) ofNewton.,"High and Low Energy Transmission Grating Spectrometers (HETGS, LETGS) on board and the Reflection Grating Spectrometer (RGS) of."64 Capella is a close spectroscopic binary wilh an orbital period of 104 days and a distance of 12.9 pc (Ilummeletal.1994)., Capella is a close spectroscopic binary with an orbital period of 104 days and a distance of 12.9 pc \citep{hummel94}.65.. The general features of the temperature distribution of the Capella coronal plasma were reasonably well determined. even with the previous generation X-ray and EUV observatories. equipped wilh limited spectral resolutions.," The general features of the temperature distribution of the Capella coronal plasma were reasonably well determined, even with the previous generation X-ray and EUV observatories, equipped with limited spectral resolutions."66" Observations wilh the spacecrall have shown a continuous differential emission measure (DEM) distribution over a temperature range of 10? to LO"" IX (Dupreeetal.", Observations with the spacecraft have shown a continuous differential emission measure (DEM) distribution over a temperature range of $10^5$ to $10^7$ K \citep{dupree93}.671993).. Brickhouseetal.(2000) analyzed the sinmiutaneous observations of andSCA... and concluded that the DEM is sharply peaked near LO°* NK. The abundances of Me. Si. S. and Fe were found to be consistent with solar photospheric values. and Ne was found to be underabundant by a [actor of ~3 to 4 in that analysiV.," \citet{brickhouse00} analyzed the simultaneous observations of and, and concluded that the DEM is sharply peaked near $10^{6.8}$ K. The abundances of Mg, Si, S, and Fe were found to be consistent with solar photospheric values, and Ne was found to be underabundant by a factor of $\sim 3$ to 4 in that analysis."68 since (he launch of ancNewton.. high resolution X-ray spectra have become available. aud numerous analyses of (he Capella coronal X-ray eniission have appeared using all three erating instruments.," Since the launch of and, high resolution X-ray spectra have become available, and numerous analyses of the Capella coronal X-ray emission have appeared using all three grating instruments."69 The first light observations were presented by Canizares(2000) [or ILETGS. Brinkmanetal.(2000) for LETCS. and Audardetal.(2001). [or G5. which gave an overview of the spectral data using relatively simple analvsis methocs.," The first light observations were presented by \citet{canizares00} for HETGS, \citet{brinkman00} for LETGS, and \citet{audard01} for RGS, which gave an overview of the spectral data using relatively simple analysis methods."70 Beharοἱal.(2001) investigated in detail the Fe L-shell line emission using the IIIZEGS data ancl theoretical ealeulations of the Hebrew. University. Lawrence Livermore Atomic Code (IULLAC)., \citet{behar01} investigated in detail the Fe L-shell line emission using the HETGS data and theoretical calculations of the Hebrew University Lawrence Livermore Atomic Code (HULLAC).71 Phillipsοἱal.(2001) made detailed. comparisons between the ILETGS X-ray spectra ancl extreme-ultraviolet emission tromEUVE., \citet{phillips01} made detailed comparisons between the HETGS X-ray spectra and extreme-ultraviolet emission from.72. Meweοἱal.(2001). presented temperature. densitv and abundance diagnostics using the LETGS observation and a line ratio based analysis method.," \citet{mewe01} presented temperature, density and abundance diagnostics using the LETGS observation and a line ratio based analysis method."73 Avrgiroffietal.(2003). studied the structive and variability of (he X-ray corona using multiple LETGS observations anc a Markov. Chain Monte-Carlo (AICAIC method for the DEM deconvolution developed by Kashyap&Drake(1998)., \citet{argiroffi03} studied the structure and variability of the X-ray corona using multiple LETGS observations and a Markov Chain Monte-Carlo (MCMC) method for the DEM deconvolution developed by \citet{kashyap98}.74. The X-rav elission are found (o be constant to within a lew percent on both short and long lime scales., The x-ray emission are found to be constant to within a few percent on both short and long time scales.75 Auclardetal.(2003). studied the coronal abundances and the first ionization potential (FIP) effects of several RS CVn binaries. including Capella. using the observations.," \citet{audard03} studied the coronal abundances and the first ionization potential (FIP) effects of several RS CVn binaries, including Capella, using the observations."76 All previously mentioned analyses have relied on a single grating instrument in the N-rav band., All previously mentioned analyses have relied on a single grating instrument in the X-ray band.77 Desaietal.(2005) combined multiple HETGS and LETGS observations ancl investigated. various line ratios of Fe XVIII and XIX., \citet{desai05} combined multiple HETGS and LETGS observations and investigated various line ratios of Fe XVIII and XIX.78 Large discrepancies of a factor of two were found between the observed and theoretical ratios involving 3—2 X-ray transitions and 2— EUV resonance lines., Large discrepancies of a factor of two were found between the observed and theoretical ratios involving $3\to 2$ X-ray transitions and $2\to 2$ EUV resonance lines.79 It was assumed (hat such discrepancies rellect the uncertainties ol theoretical atomic data., It was assumed that such discrepancies reflect the uncertainties of theoretical atomic data.80 However. this combined analvsis was not aimed al deriving coronal," However, this combined analysis was not aimed at deriving coronal"81equatorial plane of the convection zone is a 3D process involving the transport of angular momentum in both radius and Latitude and the Coriolis forees resulting [rom axisvimmetrie meridional circulation.,equatorial plane of the convection zone is a 3D process involving the transport of angular momentum in both radius and latitude and the Coriolis forces resulting from axisymmetric meridional circulation.82 Since our 2D geometry captures only the transport in radius. we can nol expect to achieve a realistic differential rotation profile with the 2D model.," Since our 2D geometry captures only the transport in radius, we can not expect to achieve a realistic differential rotation profile with the 2D model."83 Therefore. we impose the observed equatorial angular velocity as a function of radius in our moclel.," Therefore, we impose the observed equatorial angular velocity as a function of radius in our model."84 As mentioned above. the background. angular velocity is sel to a constant 465nlIz in the convection zone and (o a constant 435nllIz in (he radiation zone: we prescribe a smooth fit between these two values through the thin tachocline shear laver.," As mentioned above, the background angular velocity is set to a constant 465nHz in the convection zone and to a constant 435nHz in the radiation zone; we prescribe a smooth fit between these two values through the thin tachocline shear layer."85 The resulting gravity wave spectrum and angular momentum transport is then investigated., The resulting gravity wave spectrum and angular momentum transport is then investigated.86 The time series of angular velocity. ο(7./). relative to the prescribed background angular velocity. O(r). for this model is shown in Figure 1 over one simulated vear.," The time series of angular velocity, $\Omega^{'}(r,t)$, relative to the prescribed background angular velocity, $\Omega(r)$, for this model is shown in Figure 1 over one simulated year."87 As seen in {his ligure. angular velocity in the convection zone is initially prograde. relative to the prescribed O(r). in the lower part of the convection zone and retrograde motion in the upper part.," As seen in this figure, angular velocity in the convection zone is initially prograde, relative to the prescribed $\Omega(r)$, in the lower part of the convection zone and retrograde motion in the upper part."88 llowever. after (he initial period. angular velocity becomes verv (ime dependent and is dominantly retrograde in the lower part of the convection zone and prograde in the upper part.," However, after the initial period, angular velocity becomes very time dependent and is dominantly retrograde in the lower part of the convection zone and prograde in the upper part."89 This profile is expected. given the density stratification aud rotation of (he solar interior (Glatzmaier et al.," This profile is expected, given the density stratification and rotation of the solar interior (Glatzmaier et al."90 2005)., 2005).91 Intermittently progerade motion from the top of the convection zone will extend to the base of the convection zone and overshoot into the tachocline., Intermittently prograde motion from the top of the convection zone will extend to the base of the convection zone and overshoot into the tachocline.92 The angular velocity variations produced by (hese motions vary in amplitude between +/- 15nllz. slightly larger (han the amplitudes of the observed 1.3 vear oscillation (lowe et al.," The angular velocity variations produced by these motions vary in amplitude between +/- 15nHz, slightly larger than the amplitudes of the observed 1.3 year oscillation (Howe et al."93 2001)., 2001).94 Figure la clearly shows that the angular velocity of the tachocline mimics the behavior in the lower part of the convection zone: when the lower part is prograde. the (achocline is prograde ancl vice versa.," Figure 1a clearly shows that the angular velocity of the tachocline mimics the behavior in the lower part of the convection zone; when the lower part is prograde, the tachocline is prograde and vice versa."95 This indicates that the behavior of the tachocline is dictated by convection zone dvnamics. rather than by gravity. waves (see below).," This indicates that the behavior of the tachocline is dictated by convection zone dynamics, rather than by gravity waves (see below)."96 In the overshoot region {hued motions are strongly nonlinear (Rogers Glatzmaier 2005b)., In the overshoot region fluid motions are strongly nonlinear (Rogers Glatzmaier 2005b).97 Figure 2 shows the ratio of the horizontal {hid velocity to the horizontal phase speed (the Froude number) for a (vpical frequency and wavenumber (20jdIz. 1-10): this provides a measure of (he nonlinearity of waves.," Figure 2 shows the ratio of the horizontal fluid velocity to the horizontal phase speed (the Froude number) for a typical frequency and wavenumber $\mu$ Hz, l=10); this provides a measure of the nonlinearity of waves."98" For linear waves ο,<<1.", For linear waves $u_{x}/c_{x} << 1$.99 However. as is clearly seen in the figure this criterion does not hold just below the convection zone.," However, as is clearly seen in the figure this criterion does not hold just below the convection zone."100 While only one ratio is shown as a function of radius. this ean vary by an order of magnitude depending on the choice of frequency and ILowever. using reasonable values for frequency. ancl wavenumber. the smallest value of this ratio just below the convection zone is 0.1. still far [rom meeting the linearity criterion above.," While only one ratio is shown as a function of radius, this can vary by an order of magnitude depending on the choice of frequency and However, using reasonable values for frequency and wavenumber, the smallest value of this ratio just below the convection zone is 0.1, still far from meeting the linearity criterion above."101 Furthermore. it is clear in this ligure that linearization may not be justified in the solar core either. as suggested by Press," Furthermore, it is clear in this figure that linearization may not be justified in the solar core either, as suggested by Press"102We use (?) to analyse the long-slit spectra.,"We use \citep{ulyss}103 to analyse the long-slit spectra."104" This program minimizes the between the observations and a combination of SSP models, to fit the characteristics of the population and the line-of-sight velocity distribution (LOSVD) at the same time."," This program minimizes the between the observations and a combination of SSP models, to fit the characteristics of the population and the line-of-sight velocity distribution (LOSVD) at the same time."105 The program uses all the pixels of the spectrum and optimally exploits the available information., The program uses all the pixels of the spectrum and optimally exploits the available information.106 It fits the observation data as The model used in this paper may be either a single SSP or a combination of several SSPs parametrized by their age and metallicity ([Fe/H])., It fits the observation data as The model used in this paper may be either a single SSP or a combination of several SSPs parametrized by their age and metallicity $\textrm{[Fe/H]}$ ).107 W; are the weights of each of the SSPs., $W_i$ are the weights of each of the SSPs.108 The SSPs are convolved by the LOSVD which is parametrized by the systemic velocity (vsys) and the velocity dispersion (c)., The SSPs are convolved by the LOSVD which is parametrized by the systemic velocity $v_{sys}$ ) and the velocity dispersion $\sigma$ ).109" A multiplicative polynomial of order n, P,(A), renders the method insensitive to the extinction an imperfectness in the flux calibration."," A multiplicative polynomial of order $n$, $ P_{n}(\lambda)$, renders the method insensitive to the extinction an imperfectness in the flux calibration."110 For this paper we find n—20 to be the optimal order of the polynomial., For this paper we find $n=20$ to be the optimal order of the polynomial.111 More details on the analysis method can be found in ?.., More details on the analysis method can be found in \citet{ulyss}.112 The retrieved solution and errors are checked via x?--convergence map and Monte Carlo simulations., The retrieved solution and errors are checked via -convergence map and Monte Carlo simulations.113 The full spectrum fitting was extensively validated with Galactic globular clusters in ? and was used to study dE galaxies in ?.., The full spectrum fitting was extensively validated with Galactic globular clusters in \citet{koleva08a} and was used to study dE galaxies in \citet{kol2009}.114 Our SSPs spectra are computed with Pegase., Our SSPs spectra are computed with Pegase.115"HR code (?) using Padoval994 isochrones (?,andcompanion papers),, Salpeter's IMF (?) and Elodie.3.1 stellar library (?)..","HR code \citep{pegasehr}116 using Padova1994 isochrones \citep[][and companion papers]{padova94}, Salpeter's IMF \citep{salpeter55} and Elodie.3.1 stellar library \citep{elodie1, elodie31}."117" We could not perform 2D analysis and investigate the stellar population parameters along the galaxy's radius due to low S/N. However, we could reach S/N>5 binning the spectra in three different regions."," We could not perform 2D analysis and investigate the stellar population parameters along the galaxy's radius due to low S/N. However, we could reach $\textrm{S/N}\ge5$ binning the spectra in three different regions."118 The first one is the central part of aarcsec containing the globular cluster., The first one is the central part of arcsec containing the globular cluster.119 The second is, The second is120"atmospheric cutoll,",atmospheric cutoff.121 SZPYIX10 reported finding a bright UV. source in these frames within ihe M31 RV error box., SZPYK10 reported finding a bright UV source in these frames within the M31 RV error box.122 Moreover. (μον suggested that this source coincides with a relatively bright star seen in [frames taken at longer wavelengths (see below).," Moreover, they suggested that this source coincides with a relatively bright star seen in frames taken at longer wavelengths (see below)."123 I will call this star “Star S. Its J2000 coordinates are 00:43:02.43. +41:12:57.0.," I will call this star “Star S.” Its J2000 coordinates are 00:43:02.43, +41:12:57.0."124 To investigate (his claim. which is al variance with what we had reported in Paper I. ] re-examined the pair of archival images from 1995.," To investigate this claim, which is at variance with what we had reported in Paper I, I re-examined the pair of archival images from 1995."125 The two E300W exposures were taken in immniediate succession (during (he same telescope orbit) without dithering the telescope pointing. so I simply combined the images using a standard cosmic-ray (CH) rejection algorithm.," The two F300W exposures were taken in immediate succession (during the same telescope orbit) without dithering the telescope pointing, so I simply combined the images using a standard cosmic-ray (CR) rejection algorithm."126 Because there are very few stars detected in the F300W frames. I then registered the combined frame with a frame taken in 2003 at à longer wavelength in which the location of the error box could be identified unambiguously.," Because there are very few stars detected in the F300W frames, I then registered the combined frame with a frame taken in 2003 at a longer wavelength in which the location of the error box could be identified unambiguously."127 The combined F300W image indeed shows an apparent object within the M31 RV error box. but it has a very unusual appearance: il looks abnormally sharp compared to images of nearby real stars.," The combined F300W image indeed shows an apparent object within the M31 RV error box, but it has a very unusual appearance: it looks abnormally sharp compared to images of nearby real stars."128 I measure the EWIIM of the object to be only 0.7 pixels. in contrast wilh a typical 1.41.5 pixels lor real stars in the frame.," I measure the FWHM of the object to be only 0.7 pixels, in contrast with a typical 1.4–1.5 pixels for real stars in the frame."129 The FWIIAI of stellar images is set bv diffraction in the telescope optics. ancl it is physically impossible for a real point source to have a EWIIM of 0.7 pixels.," The FWHM of stellar images is set by diffraction in the telescope optics, and it is physically impossible for a real point source to have a FWHM of 0.7 pixels."130 Fieure |. illustvates (he unusual visual appearance of the SZPYIXI0 object in the two individual F300W images., Figure 1 illustrates the unusual visual appearance of the SZPYK10 object in the two individual F300W images.131 | created this mosaic by extracting 9x pixel (079x079) postage stamps around (he object (the two left-hand Games in (he mosaic) and Four real strs Irom the same (wo images. (, I created this mosaic by extracting $9\times9$ pixel $0\farcs9$$\times$$0\farcs9$ ) postage stamps around the object (the two left-hand frames in the mosaic) and four real stars from the same two images. (132The real stars were selected to be free of CR hits within the 9x boxes.),The real stars were selected to be free of CR hits within the $9\times9$ boxes.)133 lt is immediately clear that the $ZPYIN10 object lacks the broad PSF wings associated with real stars in these images., It is immediately clear that the SZPYK10 object lacks the broad PSF wings associated with real stars in these images.134" The same image stretch was used throughout Figure 1. and the real stars cover a range of magnitudes that bracket the ""magnitude"" of the M31 RV candidate."," The same image stretch was used throughout Figure 1, and the real stars cover a range of magnitudes that bracket the “magnitude” of the M31 RV candidate."135 Thus the obvious difference in appearance between (he candidate and the real stars is nol an artifact of the image presentation., Thus the obvious difference in appearance between the candidate and the real stars is not an artifact of the image presentation.136 To «quantifv (this disparitv. I measured (wo parameters in the (wo individual F300W frames for the SZPYIXIO object. and several real stars: the signal in data προς (DN) lor the brightest pixel in (he image. aud (he total background-subtracted flux (also in DN) within a 2-pixel-radius aperture centered on the object.," To quantify this disparity, I measured two parameters in the two individual F300W frames for the SZPYK10 object and several real stars: the signal in data numbers (DN) for the brightest pixel in the image, and the total background-subtracted flux (also in DN) within a 2-pixel-radius aperture centered on the object."137 Figure 2 plots the results., Figure 2 plots the results.138 Note Chat I made {hese measurements on raw [rames. which have a bias level of about 355DN.," Note that I made these measurements on raw frames, which have a bias level of about 355."139. Only stars without CR hits in their vicinity were measured: there are actually very [ew uncontaminated real stars in these lrames. and essentially all of (hem are plotted in Figure 2.," Only stars without CR hits in their vicinity were measured; there are actually very few uncontaminated real stars in these frames, and essentially all of them are plotted in Figure 2."140 There is. as expected. a linear relation between the DN value of the brightest pixel and the total stellar Εαν (with some scatter due to different centerings of the stus within the central pixel as well as Poissonian noise): a least-squares linear [it to these values is plotted in Figure 2.," There is, as expected, a linear relation between the DN value of the brightest pixel and the total stellar flux (with some scatter due to different centerings of the stars within the central pixel as well as Poissonian noise); a least-squares linear fit to these values is plotted in Figure 2."141 However. ihe SZPYIXIO object stands out strikingly from this relation in both individual images: it," However, the SZPYK10 object stands out strikingly from this relation in both individual images: it"142of the manuscript ou short notice after the prior referee's delay.,of the manuscript on short notice after the prior referee's delay.143 Extensive use was made of the SIMBAD database. operating at CDS. Strasboure. France aud the WEBDA database maittained at the University of Vienna. Austria (httpz//www.uuivie.ac.at/webda).," Extensive use was made of the SIMBAD database, operating at CDS, Strasbourg, France and the WEBDA database maintained at the University of Vienna, Austria (http://www.univie.ac.at/webda)."144 We are also grateful to the Astronomy Department at Luciana University for hospitality during our Fall 2008 stay when the core material discussed iu this paper was revised aid rewritten., We are also grateful to the Astronomy Department at Indiana University for hospitality during our Fall 2008 stay when the core material discussed in this paper was revised and rewritten.145After computing the actual rotational phases © with the new ephemeris. it is possible to gel the orientation of the star ancl its magnetosphere. (hen the direction of emission with respect to the dipole axis.,"After computing the actual rotational phases $\phi$ with the new ephemeris, it is possible to get the orientation of the star and its magnetosphere, then the direction of emission with respect to the dipole axis."146 Assuming an inclination 7=43° of the rotational axis and an obliquity o=74° of the magnetic axis (Trigilioetal.2000).. the angle & between the line of sight and (he axis of the dipole is given by: here ὦμ=0.08 is the phase delay of the magnetic curve wilh respect to the light curve (Dorra&Landstreet1980).," Assuming an inclination $i=43\degr$ of the rotational axis and an obliquity $\beta=74\degr$ of the magnetic axis \citep{tri00}, the angle $\psi$ between the line of sight and the axis of the dipole is given by: here $\phi_0=0.08$ is the phase delay of the magnetic curve with respect to the light curve \citep{bor80}."147. The maximum visibility of the North magnetichemisphere is αἱ o=0.58. while αἱ ὦ=0.38 and 0.78 the magnetic axis lies in the plane of the sky.," The maximum visibility of the North magnetichemisphere is at $\phi=0.58$, while at $\phi=0.38$ and $0.78$ the magnetic axis lies in the plane of the sky."148 By looking at the radio emission as a function of the inclination of the magnetic axis. we can see how it escapes from (he emitting region. ii. we can study its directivitv.," By looking at the radio emission as a function of the inclination of the magnetic axis, we can see how it escapes from the emitting region, i.e. we can study its directivity."149 The direction of the emission beams at 1450 and 1850 MIIz relatively to the dipole axis are shown in Fig. 4..," The direction of the emission beams at 1450 and 1850 MHz relatively to the dipole axis are shown in Fig. \ref{sphere},"150 top panel., top panel.151 Beams at hieher Irequency. are emitted al ο24°. while al lower frequency αἱ ο22O°. as the visibilitv of the peaks in Fig.," Beams at higher frequency are emitted at $\psi\approx 4\degr$, while at lower frequency at $\psi\approx 0\degr$, as the visibility of the peaks in Fig."152 1. indicates., \ref{spe} indicates.153 The emitting beams subtend an angle Xe<107 IIPDW., The emitting beams subtend an angle $\Delta \psi \la10\degr$ HPBW.154 The evelotvon maser hypothesis in hhas already. been proposed by Trigilioetal.(2000. 2008)..," The cyclotron maser hypothesis in has already been proposed by \citet{tri00,tri08}. ."155 To be possible. the emission nist originate in a region of relatively strong magnetic field (1>> vp). aud the plasma density in region above (he magnetic pole must be relatively low.," To be possible, the emission must originate in a region of relatively strong magnetic field $\nu_{\rm{B}}>>\nu_{\rm{P}}$ ), and the plasma density in region above the magnetic pole must be relatively low."156 Following the ECME theory (Melrose&Dulk1932). the direction of emission forms an angle ο<90° (cos0&v/c. where ¢ is (he upward velocity of the emitting electrons) to (he magnetic field direction with an aperture APzz e/e). forming an hollow cone.," Following the ECME theory \citep{mel82}, the direction of emission forms an angle $\theta \la 90\degr$ $\cos\theta\approx v/c$, where $v$ is the upward velocity of the emitting electrons) to the magnetic field direction with an aperture $\Delta\theta\approx v/c$ ), forming an hollow cone."157 The frequency of the radiation is vZs p. where s is theharmonic number.," The frequency of the radiation is $\nu \ga s\;\nu_{\rm{B}}$ , where $s$ is theharmonic number."158 It is probably the second harmonic which is the most, It is probably the second harmonic which is the most159"halo and, to a lesser extent, the importance of two-body collisions.","halo and, to a lesser extent, the importance of two-body collisions."160" Biermann Shapiro (1979) and Hills (1980), under simplifying assumptions to allow an analytical treatment, found that the size evolution depends on the ejection timescale."," Biermann Shapiro (1979) and Hills (1980), under simplifying assumptions to allow an analytical treatment, found that the size evolution depends on the ejection timescale."161" If this is short compared to the dynamical time (hereafter ejection), conservation of specific kinetic energy yields for the expansion factor in terms of the ratio between the final and initial mass e=Mr/Mi; note that for e<0.5 the system becomes unbound and dissociates."," If this is short compared to the dynamical time (hereafter ), conservation of specific kinetic energy yields for the expansion factor in terms of the ratio between the final and initial mass $\epsilon\equiv162M_{\rm f}/M_{\rm i}$; note that for $\epsilon\leq 0.5$ the system becomes unbound and dissociates."163" On the other hand, if the ejection timescales is much longer than the dynamical one, conservation of adiabatic invariants yields the size evolution 'Thus, fast expulsion is more effective in increasing the size, while, if the expulsion is slow enough (adiabatic), the system remains bound independently of e."," On the other hand, if the ejection timescales is much longer than the dynamical one, conservation of adiabatic invariants yields the size evolution Thus, fast expulsion is more effective in increasing the size, while, if the expulsion is slow enough (adiabatic), the system remains bound independently of $\epsilon$."164" These relationships have been checked and substantially confirmed by several numerical simulations of star clusters dynamics, starting from the pioneristic work by Tutukov (1978)."," These relationships have been checked and substantially confirmed by several numerical simulations of star clusters dynamics, starting from the pioneristic work by Tutukov (1978)."165" However, due to a few effects not accounted for in analytical works, a portion of the system remains bound even if e is somewhat smaller than 0.5 and the mass loss is fast (see Baumgardt Kroupa 2007 and references therein)."," However, due to a few effects not accounted for in analytical works, a portion of the system remains bound even if $\epsilon$ is somewhat smaller than 0.5 and the mass loss is fast (see Baumgardt Kroupa 2007 and references therein)."166" Numerical experiments show also that, after fast mass loss ends, the system rapidly reaches a maximum transient expansion within 10—15 dynamical times, while a new equilibrium is attained over 30—40 dynamical times GGeyer Bukert, 2001; Goodwin Bastian, 2006; Baumgardt Kroupa, 2007)."," Numerical experiments show also that, after fast mass loss ends, the system rapidly reaches a maximum transient expansion within $10-15$ dynamical times, while a new equilibrium is attained over $30-40$ dynamical times Geyer Bukert, 2001; Goodwin Bastian, 2006; Baumgardt Kroupa, 2007)."167" Fan et ((2008, 2010) tentatively tested against available data a QSO driven puffing up scenario for ETGs, resting on the G04 model of joint evolution of SMBH and spheroids, and adopting the above relationships coming from star cluster dynamics."," Fan et (2008, 2010) tentatively tested against available data a QSO driven puffing up scenario for ETGs, resting on the G04 model of joint evolution of SMBH and spheroids, and adopting the above relationships coming from star cluster dynamics."168" Their findings are to some extent encouraging, but, a closer analysis reveals that the expansion time-scale seems far too short to explain the relatively old (αν1 Gyr) stellar ages claimed for high-z compact galaxies."," Their findings are to some extent encouraging, but, a closer analysis reveals that the expansion time-scale seems far too short to explain the relatively old $\gtrsim 1$ Gyr) stellar ages claimed for high-z compact galaxies."169" A similar, albeit less dramatic, problem has been pointed out by Damjanov et ((2009) when trying to explain the observed size evolution by means of mass loss due to stellar evolution."," A similar, albeit less dramatic, problem has been pointed out by Damjanov et (2009) when trying to explain the observed size evolution by means of mass loss due to stellar evolution."170" In this case the timescale of mass loss are dictated by stellar evolution, and the expected expansion is adiabatic."," In this case the timescale of mass loss are dictated by stellar evolution, and the expected expansion is adiabatic."171" However, assuming the above recipes for ETGs is only a zeroth order approximation, since in ETGs the DM halo is expected to affect the efficiency and timescale of the size evolution, and to prevent galaxy disruption even when a major fraction of baryonic mass is lost."," However, assuming the above recipes for ETGs is only a zeroth order approximation, since in ETGs the DM halo is expected to affect the efficiency and timescale of the size evolution, and to prevent galaxy disruption even when a major fraction of baryonic mass is lost."172 our purpose is to investigate these effects via simple but aimed numerical simulations., our purpose is to investigate these effects via simple but aimed numerical simulations.173 The purpose of the simulations is to investigate the evolution of collision-less particles (stars and DM) under a change of gravitational potential due to a loss of baryonic mass of the system., The purpose of the simulations is to investigate the evolution of collision-less particles (stars and DM) under a change of gravitational potential due to a loss of baryonic mass of the system.174" The escaping mass can be either the gas which has not been converted into stars during the star forming phase of the spheroid, or the mass lost from stars in form of stellar winds and SNae explosions."," The escaping mass can be either the gas which has not been converted into stars during the star forming phase of the spheroid, or the mass lost from stars in form of stellar winds and SNae explosions."175" In any case, we assume as given, and due to “external” causes (such as SNae and AGN feedbacks, or stellar evolution), the temporal dependence of this mass loss (Eq. 12)),"," In any case, we assume as given, and due to “external” causes (such as SNae and AGN feedbacks, or stellar evolution), the temporal dependence of this mass loss (Eq. \ref{eq:massloss}) ),"176" which we put by hand, and we simulate the ensuing evolution of collision-less mass distributions."," which we put by hand, and we simulate the ensuing evolution of collision-less mass distributions."177 Therefore we don't have to treat the gas dynamics., Therefore we don't have to treat the gas dynamics.178" This is the same approach followed in most simulations of puffing-up of star clusters BBoily Kroupa, 2003; Goodwin Bastian, 2006; Baumgardt Kroupa, 2007)."," This is the same approach followed in most simulations of puffing-up of star clusters Boily Kroupa, 2003; Goodwin Bastian, 2006; Baumgardt Kroupa, 2007)."179 We used the N —body code (Springel et 22005) to perform simulations with 10° and 5x109 particles., We used the $N-$ body code (Springel et 2005) to perform simulations with $10^6$ and $5\times 10^{6}$ particles.180 Half of the particles are used to sample the baryonic and dark matter components respectively., Half of the particles are used to sample the baryonic and dark matter components respectively.181" 'The density distribution of DM particles is assumed to follow the standard NFW (Navarro, Frenk White 1997) shape where Myir,om is the halo virial mass in DM (the"," The density distribution of DM particles is assumed to follow the standard NFW (Navarro, Frenk White 1997) shape where $M_{\rm vir, DM}$ is the halo virial mass in DM (the"182"Balmer break, which is located between the H and Kg bandsat redshift z=3.1—4.1.","Balmer break, which is located between the $H$ and $K_S$ bandsat redshift $z=3.1-4.1$."183" Furthermore, it is evident that the UV-brighter galaxies are also brighter in the rest optical by roughly the same scale factor as in the UV."," Furthermore, it is evident that the UV-brighter galaxies are also brighter in the rest optical by roughly the same scale factor as in the UV."184" Despite the overall similarities, however, there are some measurable differences."," Despite the overall similarities, however, there are some measurable differences."185" In the rest-frame UV portion of the SED, the UV slope 6 (= dlogF3/dlogA; measured in the observed RIJ bands) is steeper with increasing UV luminosity."," In the rest-frame UV portion of the SED, the UV slope $\beta$ $\equiv d{\rm log}F_\lambda/d{\rm log}\lambda$ ; measured in the observed $RIJ$ bands) is steeper with increasing UV luminosity."186" In the next section, we discuss the physical implications of our results using stellar population model fitting of the averaged SEDs."," In the next section, we discuss the physical implications of our results using stellar population model fitting of the averaged SEDs."187" We determine the average physical properties, specifically the stellar mass, age, and reddening, of our samples by fitting the ? stellar population synthesis models to the stacked photometry."," We determine the average physical properties, specifically the stellar mass, age, and reddening, of our samples by fitting the \citet{bc03} stellar population synthesis models to the stacked photometry."188" We assume the Chabrier (2003) initial mass function (IMF), the ? form for the effective dust extinction law, and consider only solar metallicity populations."," We assume the Chabrier (2003) initial mass function (IMF), the \citet{calzetti00} form for the effective dust extinction law, and consider only solar metallicity populations."189" We model the star formation histories (SFH) to be constant, exponentially declining ος with a wide range of 7 values (10 Myr - 5 (SFR.Gyr), or e~'/7)linearly increasing."," We model the star formation histories (SFH) to be constant, exponentially declining (SFR $\propto e^{-t/\tau}$ ) with a wide range of $\tau$ values (10 Myr - 5 Gyr), or linearly increasing."190" The stellar age is allowed to vary between 50 Myr and the age of the Universe at the redshift z where the fitting is performed (i.e., &1.66 Gyr at z 3.7)."," The stellar age is allowed to vary between 50 Myr and the age of the Universe at the redshift $z$ where the fitting is performed (i.e., $\approx1.66$ Gyr at $z\approx3.7$ )."191 The minimum age of 50 Myr is set based on dynamical timescale arguments when considering the measurements of half-light radii and velocity dispersions of galaxies at high redshift (??)..," The minimum age of 50 Myr is set based on dynamical timescale arguments when considering the measurements of half-light radii and velocity dispersions of galaxies at high redshift \citep{bouwens04c, erbetal06b}."192" While these assumptions for age ranges, IMF’, metallicity, and extinction may not be accurate descriptions of the properties of high-redshift galaxies (and may even vary with galaxy mass luminosity), our main interest lies in comparing the and/orrelative average properties of galaxies in different UV luminosity bins."," While these assumptions for age ranges, IMF, metallicity, and extinction may not be accurate descriptions of the properties of high-redshift galaxies (and may even vary with galaxy mass and/or luminosity), our main interest lies in comparing the relative average properties of galaxies in different UV luminosity bins."193" Our current study is limited by the nature of our data, which is confined to broad band photometry; more details will emerge only from deep spectroscopic observations, which is now within grasp for the bright candidates within our sample."," Our current study is limited by the nature of our data, which is confined to broad band photometry; more details will emerge only from deep spectroscopic observations, which is now within grasp for the bright candidates within our sample."194 We estimate the uncertainties on the derived physical properties that result from the finite width of the redshift distribution using a Monte Carlo approach., We estimate the uncertainties on the derived physical properties that result from the finite width of the redshift distribution using a Monte Carlo approach.195" We randomly draw a redshift from the observed N(z) distributionbottom of Figure 1)), assign it to the observed average(right SED, find the best-fit parameters at each time, and repeat this procedure 100 times."," We randomly draw a redshift from the observed $N(z)$ distribution of Figure \ref{plot_redshift}) ), assign it to the observed average SED, find the best-fit parameters at each time, and repeat this procedure 100 times."196" Although we used the observed spectroscopic redshift distribution for these analyses, we also simulated the expected redshift distribution given our adopted UV color selection criteria and a large range of theoretical galaxy SEDs."," Although we used the observed spectroscopic redshift distribution for these analyses, we also simulated the expected redshift distribution given our adopted UV color selection criteria and a large range of theoretical galaxy SEDs."197" The two distributions agree with each other reasonably well (Figure 1)), and we have verified that using one or the other does not affect our main results."," The two distributions agree with each other reasonably well (Figure \ref{plot_redshift}) ), and we have verified that using one or the other does not affect our main results."198" Given the narrow redshift distribution, the galaxies in our sample range in rest-frame UV luminosity from Mi700©—21.43 to —23.30 (see Table 1)."," Given the narrow redshift distribution, the galaxies in our sample range in rest-frame UV luminosity from $M_{1700}\approx -21.43$ to $-23.30$ (see Table 1)."199" Our sample therefore consists primarily of L=L* galaxies, and greatly increases the number of candidates for the UV brightest galaxies."," Our sample therefore consists primarily of $L\gtrsim L^*$ galaxies, and greatly increases the number of candidates for the UV brightest galaxies."200" Based on our population synthesis analyses, we find that average galaxies in our sample span roughly a decade in stellar mass, from &10— 11, and the best-fit population synthesislog(M,/Mo) ages of 200—400 Myr in the UV bins considered here."," Based on our population synthesis analyses, we find that average galaxies in our sample span roughly a decade in stellar mass, from ${\rm log}(M_*/M_\odot)\approx 10 - 11$ , and the best-fit population synthesis ages of $-$ 400 Myr in the UV bins considered here."201" We summarize our results in Figure 5. when assuming the constant SFH model, which facilitates direct comparison with other studies in the literature."," We summarize our results in Figure \ref{sedfit} when assuming the constant SFH model, which facilitates direct comparison with other studies in the literature."202" However, we note that linearly rising SFH models generally provide equally good fit to the stacked SEDs."," However, we note that linearly rising SFH models generally provide equally good fit to the stacked SEDs."203" The average stellar mass of our samples is tightly correlated with the UV luminosity, as expected from the homologous SED shapes in the different luminosity bins (Figure 3))."," The average stellar mass of our samples is tightly correlated with the UV luminosity, as expected from the homologous SED shapes in the different luminosity bins (Figure \ref{stacked_sed}) )."204" Assuming the median redshift z—3.7 to convert the /-band AB magnitude to the observed UV luminosity, we find that the correlation is well described by (top panel of Figure "," Assuming the median redshift $z=3.7$ to convert the $I$ -band AB magnitude to the observed UV luminosity, we find that the correlation is well described by (top panel of Figure \ref{sedfit}) )."205"Since the uncertainties in stellar mass fully account for 5)).both random and intrinsic scatter in the photometry within the sample, and the width of the redshift distribution, the intrinsic correlation is likely eventighter than measured here."," Since the uncertainties in stellar mass fully account for both random and intrinsic scatter in the photometry within the sample, and the width of the redshift distribution, the intrinsic correlation is likely eventighter than measured here."206 The UV luminosity range of the NDWFS sample overlaps with the luminous end of the sample (about 70 - 80 galaxies) probed by ? at Muyστ—21.2 at similar redshifts., The UV luminosity range of the NDWFS sample overlaps with the luminous end of the sample (about 70 - 80 galaxies) probed by \citet{stark09} at $M_{UV} \lesssim -21.2$ at similar redshifts.207" Our estimation of the median stellar mass at these UV bins is slightly higher than theirs as shown in Figure 5 (dashed line; we adopted the stellar mass when constant star formation is assumed), but considering the large scatter and small number of galaxies included in these bins, the two measurements are in qualitative agreement with each other."," Our estimation of the median stellar mass at these UV bins is slightly higher than theirs as shown in Figure \ref{sedfit} (dashed line; we adopted the stellar mass when constant star formation is assumed), but considering the large scatter and small number of galaxies included in these bins, the two measurements are in qualitative agreement with each other."208" We further compare our results with that of ?,, who measured thestellar mass and UV luminosity of moderately UV-luminous star-forming galaxies at z~ 2.3."," We further compare our results with that of \citet{shapleyetal05}, , who measured thestellar mass and UV luminosity of moderately UV-luminous star-forming galaxies at $z\sim2.3$ ."209 While they found nocorrelation between the UV luminosity and stellar mass in contrast, While they found nocorrelation between the UV luminosity and stellar mass in contrast210ol the University of Cambridge. Ixeele University. University of Leicester. The Opeu University. The Queenj» University Belfast. St. Andrews University and the Isaac Newton Group.,"of the University of Cambridge, Keele University, University of Leicester, The Open University, The Queen¡¯s University Belfast, St. Andrews University and the Isaac Newton Group."211 Funding for WASP comes from the consortium universities and [rom the Uls;s Science and. Technology Facilities Couucil., Funding for WASP comes from the consortium universities and from the UK¡¯s Science and Technology Facilities Council.212wo are faint and distant satellites.,two are faint and distant satellites.213 The two faint. satellites are quite close to one another. 41 kpe in projected 2 satellites found. with the following 286 kpe separalion/2.9 mag difference: 249 κρο1 separation/3.5 mag In terms of mag cdillerence. these satellites. resemble the LMC and SMC respectively. but they are the two most distant satellites in the present sample.," The two faint satellites are quite close to one another, 41 kpc in projected 2 satellites found, with the following 286 kpc separation/2.9 mag difference; 249 kpc separation/3.5 mag In terms of mag difference, these satellites resemble the LMC and SMC respectively, but they are the two most distant satellites in the present sample."214 Interestingly. they are quite close to one another. with a projected separation of 41 kpe.," Interestingly, they are quite close to one another, with a projected separation of 41 kpc."215 A-bancl ancl continuum-subtracted: Ho. images of the two satellites only (NGC 2596 is not shown) are presented. in Fie. 6.., $R$ -band and continuum-subtracted $\alpha$ images of the two satellites only (NGC 2596 is not shown) are presented in Fig. \ref{fig:n2596}.216 Both satellites have clumpy Ha emission with strong central 2 satellites found. with the following 32. kpc separation/2.32 mag dillerence: 545 kpe separation/7.4 mag The first of these is a good LAIC analogue (with barred. irregular structure ancl multiple regions. see Fig. 7)).," Both satellites have clumpy $\alpha$ emission with strong central 2 satellites found, with the following 32 kpc separation/2.3 mag difference; 54 kpc separation/7.4 mag The first of these is a good LMC analogue (with barred, irregular structure and multiple regions, see Fig. \ref{fig:n2604}) ),"217 the second is very faint. but still close to the central galaxy., the second is very faint but still close to the central galaxy.218 They do not appear to be a satellite pair. with a projected separation between the two greater than the central - satellite 5 satellites found. with the following 3 kpc separationf/54 mag cillerence: 45 Κκροὸ separation/4.5 mag difference: 98 kpc separation/3.8 mag difference: 90 kpe separation/5.9 mag dillerence: 143 kpc separation/+4.2 mae Three of the five can be considered SMC analogues in terms of mag dilference. ancl one of these also lies within the cMagellanic radius.," They do not appear to be a satellite pair, with a projected separation between the two greater than the central - satellite 5 satellites found, with the following 33 kpc separation/5.4 mag difference; 45 kpc separation/4.5 mag difference; 98 kpc separation/3.8 mag difference; 90 kpc separation/5.9 mag difference; 143 kpc separation/4.2 mag Three of the five can be considered SMC analogues in terms of mag difference, and one of these also lies within the `Magellanic radius'."219 Of the other two. both are very faint. with one being close in and the other very distant.," Of the other two, both are very faint, with one being close in and the other very distant."220 In terms of. satellite-satellite separations. it should. be. noted that the two closest-in satellites (one faint. one SMC-Hike) are also close to one another. with a projected. separation of 13 kpc.," In terms of satellite-satellite separations, it should be noted that the two closest-in satellites (one faint, one SMC-like) are also close to one another, with a projected separation of 13 kpc."221 Otherwise. the satellites are widely 2 satellites found. with the following 5T kpc separation/2.14 mag ΟΠ 17 kpc separation/5.6 mag The first of these is an excellent. LAIC analogue (see Fig. S)):," Otherwise, the satellites are widely 2 satellites found, with the following 57 kpc separation/2.4 mag difference; 77 kpc separation/5.6 mag The first of these is an excellent LMC analogue (see Fig. \ref{fig:n4666}) );"222 as with the brighter satellite of NGC 2604. it appears barred in the red continuum image. but irregular with multiple regions in the lla image.," as with the brighter satellite of NGC 2604, it appears barred in the red continuum image, but irregular with multiple regions in the $\alpha$ image."223 The other satcllite is very faint. and quite distant from both the central galaxy and the bright 2 satellites found. with the following 163. kpe separation/l.3 mag difference: I!IIakpe," The other satellite is very faint, and quite distant from both the central galaxy and the bright 2 satellites found, with the following 163 kpc separation/1.3 mag difference; 155kpc"224"1l, the iron abundance was obtained adopting both spectroscopic and photometric temperatures, several ways of normalizing for the continuum were tried, and even different people performed EW measurements in order to avoid personal bias, and in any case the result was [Fe/H] significantly higher than 0.2 dex.","\ref{datasample}, the iron abundance was obtained adopting both spectroscopic and photometric temperatures, several ways of normalizing for the continuum were tried, and even different people performed EW measurements in order to avoid personal bias, and in any case the result was [Fe/H] significantly higher than 0.2 dex."225" Our conclusions on CA evolution are still based on few stars per cluster, and they partly rely on the age scale of Salarisetal.(2004),, which uses a calibration of a photospheric age indicator made on 11 clusters."," Our conclusions on CA evolution are still based on few stars per cluster, and they partly rely on the age scale of \cite{sal}, which uses a calibration of a photospheric age indicator made on 11 clusters."226" In order to strengthen our results, or to disprove them, we need more CA measurements in solar-type stars in open clusters based on high-resolution spectra and direct age determinations of the open clusters used based on improved colour-magnitude diagrams."," In order to strengthen our results, or to disprove them, we need more CA measurements in solar–type stars in open clusters based on high–resolution spectra and direct age determinations of the open clusters used based on improved colour–magnitude diagrams."227" We should both reobserve the already analysed stars, to obtain a averaged CA level, and choose other targets."," We should both reobserve the already analysed stars, to obtain a time--averaged CA level, and choose other targets."228" The scenario suggested here contradicts the common belief that CA is well correlated with age, however our investigation does not include stars younger than the Hyades, some of which are indeed more active than the Hyades stars."," The scenario suggested here contradicts the common belief that CA is well correlated with age, however our investigation does not include stars younger than the Hyades, some of which are indeed more active than the Hyades stars."229" In addition, the fact that young stars are active and old stars are not is not questioned here, and it causes a weak correlation between CA and age."," In addition, the fact that young stars are active and old stars are not is not questioned here, and it causes a weak correlation between CA and age."230" We believe that data used in the literature to prove a deterministic relation between CA and age do not disprove our alternative view, and that more data are necessary to achieve a definitive conclusion."," We believe that data used in the literature to prove a deterministic relation between CA and age do not disprove our alternative view, and that more data are necessary to achieve a definitive conclusion."231" For instance Soderblometal.(1991) used Mount-Wilson data about several solar-type stars in visual binaries and single F dwarfs, with ages from Strómmgrengi photometry in order to prove that the relationship between CA and age is, using their words, deterministic and not statistical."," For instance \cite{sod91} used Mount--Wilson data about several solar–type stars in visual binaries and single F dwarfs, with ages from Strömmgren photometry in order to prove that the relationship between CA and age is, using their words, deterministic and not statistical."232 Figure 3 in the aforementioned paper shows that log[μι and the logarithm of age are indeed correlated.," Figure 3 in the aforementioned paper shows that $\log233R^{\prime}_{HK}$ and the logarithm of age are indeed correlated."234" However we notice, analysing data in Table 1 and 2 therein, that among stars with logP4,>—4.9, ie. more active than the Sun, the correlation between logτμ. and age is not significant, the Pearson correlation coefficient is about 0.1."," However we notice, analysing data in Table 1 and 2 therein, that among stars with $\log R^{\prime}_{HK} > -4.9$, i.e. more active than the Sun, the correlation between $\log R^{\prime}_{HK}$ and age is not significant, the Pearson correlation coefficient is about 0.1."235" As for the other stars, ie. those with logRij.«—4.9, the Pearson coefficient is 0.35, and its sign is positive, unlike what is expected according to an activity decay."," As for the other stars, i.e. those with $\log R^{\prime}_{HK} < -4.9$, the Pearson coefficient is 0.35, and its sign is positive, unlike what is expected according to an activity decay."236" In either group of stars there is, instead, a significant correlation between logR4,; and the B-V colour, and it has opposite signs."," In either group of stars there is, instead, a significant correlation between $\log237R^{\prime}_{HK}$ and the B-V colour, and it has opposite signs."238 Another calibration of CA evolution with time is that of Lachaumeetal.(1999).., Another calibration of CA evolution with time is that of \cite{lach99}.239 From Fig., From Fig.240" 4 therein, it can be seen that their result agrees with ours as far as inactive stars are concerned, i.e. CA does not evolve after it has crossed the VP gap."," 4 therein, it can be seen that their result agrees with ours as far as inactive stars are concerned, i.e. CA does not evolve after it has crossed the VP gap."241" As far as active stars older than the Hyades are concerned, there are"," As far as active stars older than the Hyades are concerned, there are"242"Firstly, to demonstrate the effectiveness of our method, we compare our method directly with the linear methods of ? and ?..","Firstly, to demonstrate the effectiveness of our method, we compare our method directly with the linear methods of \cite{sth09} and \cite{vanderplasetal11}."243" As these linear methods are only defined for Nip€Nsp, we consider the case of Nip=Nsp20, and generate a single cluster halo at a redshift of z..=0.25 following an NFW halo profile with Moo=1015Mc and c—3."," As these linear methods are only defined for $N_{\rm lp} \le N_{\rm sp}$, we consider the case of $N_{\rm lp} = N_{\rm sp} = 20$, and generate a single cluster halo at a redshift of $z_{\rm cl} = 0.25$ following an NFW halo profile with $M_{200} = 10^{15}M_\odot$ and $c=3$."244" In the SVD method of ?, we take ve=1—357.402/35""**o?= 0.01, and in the transverse and radial Wiener filtering methods of ?,, we take the tuning parameter to be a=0.05 in both cases."," In the SVD method of \cite{vanderplasetal11}, we take $v_{cut} = 1 - \sum_{i=1}^n\sigma_i^2/\sum_i^{n_{max}} \sigma_i^2 = 0.01$ , and in the transverse and radial Wiener filtering methods of \cite{sth09}, we take the tuning parameter to be $\alpha = 0.05$ in both cases."245" For our CS approach, we take the soft threshold parameter A—8, andthe data fidelity control parameter e=3."," For our CS approach, we take the soft threshold parameter $\lambda=8$, andthe data fidelity control parameter $\epsilon = 3$."246" Note that while the linear methods take d=4(0,2),R= Pa-Q, our method takes d=κ(θ,2),RQas before."," Note that while the linear methods take $\boldsymbol{d} = \boldsymbol{\gamma}(\bt, z),\ \mathbf{R} = \mathbf{P_{\gamma\kappa}Q}$ , our method takes $\boldsymbol{d} = \boldsymbol{\kappa}(\bt,z),\ \mathbf{R} = \mathbf{Q}$as before."247 The noise levels in each case are identical., The noise levels in each case are identical.248 The results are presented in figures 5 and 6.., The results are presented in figures \ref{fg:complin1} and \ref{fg:complin2}.249" Figure 5 presents the 2D projections of the reconstructions, computed by integrating the reconstruction along each line of sight, and the 1D reconstructions along the four central lines of sight."," Figure \ref{fg:complin1} presents the 2D projections of the reconstructions, computed by integrating the reconstruction along each line of sight, and the 1D reconstructions along the four central lines of sight."250" In the 3D renderings of Figure 6,, the reconstructions from our method, the SVD method and the radial Wiener filter method are thresholded at 6= (ie. the plot only shows ó;«> 3), and each is smoothed with3 a Gaussian of width σ=0.7 pix in all three directions."," In the 3D renderings of Figure \ref{fg:complin2}, the reconstructions from our method, the SVD method and the radial Wiener filter method are thresholded at $\delta = 3$ (i.e. the plot only shows $\delta_{\rm rec} \ge 3$ ), and each is smoothed with a Gaussian of width $\sigma = 0.7\,$ pix in all three directions."251" The reconstruction from the transverse Wiener filter method is heavily damped with respect to the amplitude of the density contrast; a threshold of 6=5x1079 is chosen in this case, and no smoothing is applied as the reconstruction already shows a very smooth distribution."," The reconstruction from the transverse Wiener filter method is heavily damped with respect to the amplitude of the density contrast; a threshold of $\delta = 5 \times 10^{-6}$ is chosen in this case, and no smoothing is applied as the reconstruction already shows a very smooth distribution."252" The SVD method appears, in the 1D plots, to identify the correct redshift of the cluster, with a small amount of line of sight smearing, but the plots show a prominent redshift peak along the line of sight."," The SVD method appears, in the 1D plots, to identify the correct redshift of the cluster, with a small amount of line of sight smearing, but the plots show a prominent high-redshift peak along the line of sight."253" We note that it may be possible to remove this false detection by raising veut, but at the cost of increased line of sight smearing (see ?).."," We note that it may be possible to remove this false detection by raising $v_{cut}$ , but at the cost of increased line of sight smearing \citep[see][]{vanderplasetal11}. ."254 The, The2552010).,.256". To this date, no parsec-scale binary SMBHs have been found with this method."," To this date, no parsec-scale binary SMBHs have been found with this method."257" Similarly, systematic searches for kpc-scale binary AGNs started from with two sets of narrow ,A5007 emission lines identifyingin large objectsspectroscopic surveys, such as the DEEP2 Galaxy Redshift Survey (Gerkeetal.2007;erfordetal.2009) and the Sloan Digital Sky Survey Smithetal. 2010)."," Similarly, systematic searches for kpc-scale binary AGNs started from identifying objects with two sets of narrow $\lambda$ 5007 emission lines in large spectroscopic surveys, such as the DEEP2 Galaxy Redshift Survey \citep{Gerke07,Comerford09a} and the Sloan Digital Sky Survey \citep[SDSS;][]{Xu09,Wang09,Liu10a,Smith10}."258". If double-peakedWang eemission is indicative of a binary AGN, such emission most likely represents systems with transverse separations of ~100 pc to 10 kpcs (Liuetal.2010a),, because each fiber of the SDSS spectrograph covers only oon the sky."," If double-peaked emission is indicative of a binary AGN, such emission most likely represents systems with transverse separations of $\sim$ 100 pc to $\sim$ 10 kpcs \citep{Liu10b}, because each fiber of the SDSS spectrograph covers only on the sky."259" But double-peaked emission-line profile may also arise from other mechanisms, such as peculiar narrow line regions, extended emission-line nebulae 2009)., or jet-cloud interactions (e.g.,Stocktonetal.2007;Rosarioetal. 2010)."," But double-peaked emission-line profile may also arise from other mechanisms, such as peculiar narrow line regions, extended emission-line nebulae \citep[e.g.,][]{Fu09a}, or jet-cloud interactions \citep[e.g.,][]{Stockton07,Rosario10}."260". In this we present high-resolution near-infrared imaging of paper,double-peaked AAGNS."," In this paper, we present high-resolution near-infrared imaging of double-peaked AGNs."261" This program is designed to differentiate between mergers and the contaminating scenarios involving single as an to statistical of kpc-scale galaxies,binary AGNs."," This program is designed to differentiate between mergers and the contaminating scenarios involving single galaxies, as an attempt to identify a statistical sample of kpc-scale binary AGNs."262" attemptNote that identifyspatiallya resolved samplespectroscopy is required to confirm that a merger is a binary AGN, because the double-peaked emission lines could still arise from a single galaxy in a merger or extended emission-line nebulae."," Note that spatially resolved spectroscopy is required to confirm that a merger is a binary AGN, because the double-peaked emission lines could still arise from a single galaxy in a merger or extended emission-line nebulae."263" Throughout we adopt the concordance ACDM cosmology with Q,,20.3, Q4=0.7, and Ho = 70 km s! Μρο-. Ke"," Throughout we adopt the concordance $\Lambda$ CDM cosmology with $\Omega_{\rm m}=0.3$, $\Omega_\Lambda=0.7$ , and $H_0$ = 70 km $^{-1}$ $^{-1}$."264ckIII laser guide-star adaptive-optics (LGSAO;Wiz-etal.2006) observations require a bright (R«17) star within ~60” oof the source for tip-tilt corrections., II laser guide-star adaptive-optics \citep[LGSAO;][]{Wizinowich06} observations require a bright $R < 17$ ) star within $\sim$ of the source for tip-tilt corrections.265" We selected 125 objects that are suitable for LGSAO observations from the 271 unique SDSS double-peaked AAGNSs (Wangetal.2009;Liu2010b;Smith2010,weonlyincluded""good"" objects), resulting in 31 type-1 (broad-line) AGNs and 94 type-2 (narrow-line) AGNs between 0.02«z 0.69."," We selected 125 objects that are suitable for LGSAO observations from the 271 unique SDSS double-peaked AGNs \citep[][we only included ``good"" objects]{Wang09,Liu10a,Smith10}, resulting in 31 type-1 (broad-line) AGNs and 94 type-2 (narrow-line) AGNs between $0.02 < z < 0.69$ ."266" We obtained H-band images for three sources (0400-0652, 09524-2552, and 124043534) with the OSIRIS imager (Larkinetal.2006) at 20 mas pixel! on 2010 March 6 and 7 UT, and K'-band images for another 47 sources with NIRC2 at 40 mas pixel! on 2010 June 3 and 4 UT."," We obtained $H$ -band images for three sources (0400-0652, 0952+2552, and 1240+3534) with the OSIRIS imager \citep{Larkin06} at 20 mas $^{-1}$ on 2010 March 6 and 7 UT, and $K'$ -band images for another 47 sources with NIRC2 at 40 mas $^{-1}$ on 2010 June 3 and 4 UT."267 We imaged only three sources in March because spectroscopy was the main purpose of that run., We imaged only three sources in March because spectroscopy was the main purpose of that run.268" The K’-band filter was used for most sources because (1) the AO system delivers the best image quality in K’-band, and (2) the contrast between the central AGN and the host galaxy is decreased because AGNS tend to be bluer than galaxies."," The $K'$ -band filter was used for most sources because (1) the AO system delivers the best image quality in $K'$ -band, and (2) the contrast between the central AGN and the host galaxy is decreased because AGNs tend to be bluer than galaxies."269" On the other hand, we chose H- for OSIRIS becauseof its elevated backgroundin K- (OSIRIS User's Manual)."," On the other hand, we chose $H$ -band for OSIRIS becauseof its elevated backgroundin $K$ -band (OSIRIS User's Manual)."270" Targets, which were randomly selected based on time of observation, consisted of 17 type-1s and 33 type-2s (Table 1))."," Targets, which were randomly selected based on time of observation, consisted of 17 type-1s and 33 type-2s (Table \ref{tab:sample}) )."271Currently considerable etfort is being invested in surveys of the solar neighbourhood.,Currently considerable effort is being invested in surveys of the solar neighbourhood.272 Fifteen years ago the study of nearby stars was revived by the Hipparcos mission. which pioneered space astrometry.," Fifteen years ago the study of nearby stars was revived by the Hipparcos mission, which pioneered space astrometry."273 Hipparcos put ground-based astrometry onto à more secure foundation. so now useful proper motions are available for tens of millions of stars.," Hipparcos put ground-based astrometry onto a more secure foundation, so now useful proper motions are available for tens of millions of stars."274 In the last decade the proper motions have been complemented by photometric surveys. both in the infrared and to fainter magnitudes at optical wavelengths.," In the last decade the proper motions have been complemented by photometric surveys, both in the infrared and to fainter magnitudes at optical wavelengths."275 Finally. the RAVE (Steinmetzetal.2005) and SEGUE (seeYorketal.2000:Yannyetal.2009) surveys have measured nearly a million line-of-sight velocities.," Finally, the RAVE \citep{RAVEI} and SEGUE \citep[see][]{york00,276Yanny09} surveys have measured nearly a million line-of-sight velocities."277 As a result of these major observational programmes. it is becoming possible to determine the velocity distribution within the disc of our Galaxy. not only at the location of the Sun. but also at significant distances. especially at higher Galactic latitudes.," As a result of these major observational programmes, it is becoming possible to determine the velocity distribution within the disc of our Galaxy, not only at the location of the Sun, but also at significant distances, especially at higher Galactic latitudes."278 Naturally one wants to quantify the velocity distribution observed at some location x in the Galaxy in an etficient way., Naturally one wants to quantify the velocity distribution observed at some location $\vx$ in the Galaxy in an efficient way.279 Conventionally one does this by imagining that the density of stars in velocity space forms a “velocity ellipsoid” — a triaxial ellipsoidal region of over-density in velocity space., Conventionally one does this by imagining that the density of stars in velocity space forms a “velocity ellipsoid” – a triaxial ellipsoidal region of over-density in velocity space.280 If the Galaxy were axisymmetric (which is a reasonable first approximation). we would expect that in the Galactie plane the principal axes of the the velocity ellipsoid would be aligned with the coordinate directions of cylindrical polar coordinates. (R.7.0).," If the Galaxy were axisymmetric (which is a reasonable first approximation), we would expect that in the Galactic plane the principal axes of the the velocity ellipsoid would be aligned with the coordinate directions of cylindrical polar coordinates, $(R,z,\phi)$."281 As one moves above the plane. two of the principal axes of the velocity ellipsoid are expected to tip slightly with respect to the R and 2 directions.," As one moves above the plane, two of the principal axes of the velocity ellipsoid are expected to tip slightly with respect to the $\hat\vR$ and $\hat\vz$ directions."282" Let the components of velocity parallel to these principal axes be denoted v, and v». where y,rg and v»>v; as z—0."," Let the components of velocity parallel to these principal axes be denoted $v_1$ and $v_2$, where $v_1\to v_R$ and $v_2\to v_z$ as $z\to0$."283 The third axis is expected to remain aligned with the @ direction., The third axis is expected to remain aligned with the $\hat\vphi$ direction.284" The distributions of the v, and v» components of velocity are expected to be roughly Gaussian with vanishing means and to be to good approximation aligned with the Galactie polar coordinates (minorvertexdeviationsasfoundinthesolarneighbourhoodby here)."," The distributions of the $v_1$ and $v_2$ components of velocity are expected to be roughly Gaussian with vanishing means and to be to good approximation aligned with the Galactic polar coordinates \citep[minor vertex285deviations as found in the solar neighbourhood by][will not be discussed286here]{Dehnen98}."287 Consequently. they can be characterised by their standard deviations σι and o».," Consequently, they can be characterised by their standard deviations $\sigma_1$ and $\sigma_2$."288" The distribution of the v, components peaks at a value of v, that is slightly smaller than the circular speed v...", The distribution of the $v_\phi$ components peaks at a value of $v_\phi$ that is slightly smaller than the circular speed $v_c$ .289" However. it is not at all well modelled by à Gaussian. because it is very skew. with many more stars at v,=vov than at v+y. causing the population to have non-zero asymmetric drift."," However, it is not at all well modelled by a Gaussian, because it is very skew, with many more stars at $v_\phi=v_c-v$ than at $v_c+v$, causing the population to have non-zero asymmetric drift."290" Notwithstanding this skewness that was already known to Gustav Strómmberg (Stromberg 1927)..v,distributions have traditionally been characterised by a mean"," Notwithstanding this skewness that was already known to Gustav Strömmberg \citep[][]{Stromberg27}, ,$v_\phi$distributions have traditionally been characterised by a mean"291Comet C/2007 N3 (Lulin) was observed by on 2008 October 04.3 UT (ry=1.90 AU. a Spilzer--comet distance of 1.673 AU. and a phase angle of 32.5°)) with the Infrared Spectrograph (RS:Houcketal.2004) as part of a larger Cycle 5 study assessing the water production and volatile production rates of comets (program idenüfication number [PLD] 50335: PIE: D. E. Harker).,"Comet C/2007 N3 (Lulin) was observed by on 2008 October 04.3 UT $r_{h} = 1.90$ AU, a -comet distance of 1.673 AU, and a phase angle of ) with the Infrared Spectrograph \citep[IRS;][]{houck04} as part of a larger Cycle 5 study assessing the water production and volatile production rates of comets (program identification number [PID] 50335; PI: D. E. Harker)."292 The astronomical observation request (AOR) key for the dataset is/Sa.Spitzer2581584|2581584.. and the basic calibrated data (BCD) products processed with IRS reduction pipeline $13.60.," The astronomical observation request (AOR) key for the dataset is, and the basic calibrated data (BCD) products processed with IRS reduction pipeline S18.60."293" The AOR for the short-wavelength. low-resolution SLL (7.4—14.5 j)) data discussed here executed a 7X3 spectral map (performed with no peak-up) vielding 21 spectra (6 sec x 2 eveles) with 1.37""x10.0""."" ssteps (perpendicular x parallel to the lone slit dimension)."," The AOR for the short-wavelength, low-resolution SL1 $7.4 - 29414.5$ ) data discussed here executed a $7\times 3$ spectral map (performed with no peak-up) yielding 21 spectra (6 sec $\times$ 2 cycles) with $1.87\arcsec\times10.0\arcsec$ steps (perpendicular $\times$ parallel to the long slit dimension)."295 Dackground. (shadow) observations were taken 34 hours later at the same celestial coordinates as the target spectra (AOR. kev 25988864). allowing the comet to move out of the spectral map fiekl-ol-xiew (FOV).," Background (shadow) observations were taken 34 hours later at the same celestial coordinates as the target spectra (AOR key 25988864), allowing the comet to move out of the spectral map field-of-view (FOV)."296 Further analvsis of (he SLI and LII spectra are discussed in Woodwardetal.(2011)., Further analysis of the SL1 and LH spectra are discussed in \citet{woo11}.297. The spectra were reduced as follows., The spectra were reduced as follows.298 The shadow observations were subtracted fom the on-source observations. and the result was assembledinto a data cube using the CUDISM software (Simithetal.2007)... with bad. pixels masked and all extended source calibrations applied.," The shadow observations were subtracted from the on-source observations, and the result was assembledinto a data cube using the CUBISM software \citep{smith07}, with bad pixels masked and all extended source calibrations applied."299 The spectrum presented in this paper is extracted from an aperture 07225 x 97225 in size. centered on (he peak surface brightness of the comet.," The spectrum presented in this paper is extracted from an aperture 25 $\times$ 25 in size, centered on the peak surface brightness of the comet."300 The radial profile of comet C/2007 N3 (Luli) was plotted to assess the quality of the data for caleulating a dust production rate., The radial profile of comet C/2007 N3 (Lulin) was plotted to assess the quality of the data for calculating a dust production rate.301 The radial profile of C/2007 N3 (Lulin) in the V band shows a deviation from the conical L/p profile (Gehrz&Nev 1992).. suggesting," The radial profile of C/2007 N3 (Lulin) in the V band shows a deviation from the conical $1/\rho$ profile \citep{ger92}, , suggesting"302by the van der Laan (1966) mocel. where the fiux density is eiveu by FyxFEPpP? in the optically-thin regime.,"by the van der Laan (1966) model, where the flux density is given by $F_\nu\propto R^{-2p}\nu^{(1-p)/2}$ in the optically-thin regime."303 So. when J< l. ΕνxtWOx£109 for p=2.2.," So, when $\beta\ll1$ , $F_\nu\propto304t^{-4p/5}\propto t^{-1.76}$ for $p=2.2$."305 This decay is still too slow to fit the observed light curve of the N-ray jet for which the power-law fit eives a decay iudex of τοις Usaaret et al., This decay is still too slow to fit the observed light curve of the X-ray jet for which the power-law fit gives a decay index of $-3.7\pm0.7$ (Kaaret et al.306 2003)., 2003).307 HTowever. different from the continuous forward shock. the reverse shock operates ouly once. so the electrons. inchiding those with the maxima energv in the ejecta. all cool adiabatically.," However, different from the continuous forward shock, the reverse shock operates only once, so the electrons, including those with the maximum energy in the ejecta, all cool adiabatically."308" So it is likbel that. at some time. the characteristic frequency of the electrons with the maxima energy 572,08 102v fall close to the X-ray band aud the A-ray flux would decay quite rapidly since then."," So it is likely that, at some time, the characteristic frequency of the electrons with the maximum energy $\gamma_M m_e c^2$ may fall close to the X-ray band and the X-ray flux would decay quite rapidly since then."309 The maxiuun energev of the power-law distribution electrous just after the reverse shock crosses the ejecta is deternüned by the shock acceleration process. which is however not well understood.," The maximum energy of the power-law distribution electrons just after the reverse shock crosses the ejecta is determined by the shock acceleration process, which is however not well understood."310 If the olectrous iu the lieh euergv cud of the power law cool faster than the dynamical time scale. the real maxinnun ασιαον of the electrous in the ejecta is limited by the svuchrotron cooling timescale: electrons with euergv greater than this energy would have cooled down within the dvuamical timescale.," If the electrons in the high energy end of the power law cool faster than the dynamical time scale, the real maximum energy of the electrons in the ejecta is limited by the synchrotron cooling timescale; electrons with energy greater than this energy would have cooled down within the dynamical timescale."311" So, LY,2min(LapeLapeou). where Lagan and Layeooe denote the maxima energies allowed bv the shock acceleration process and the cooling process respectively, the superscript 0 iu EY, denotes the value at fy — the time when the reverse shock heats the ejecta."," So, $E_M^0=\min({E_{M,acc},E_{M,cool}})$, where $E_{M,acc}$ and $E_{M,cool}$ denote the maximum energies allowed by the shock acceleration process and the cooling process respectively, the superscript 0 in $E_M^0$ denotes the value at $t_0$ — the time when the reverse shock heats the ejecta."312 If the svuchrotrou radiation dominates the cooling of the electrous. Laycooπρο)(στ where fj=fo/D(fy) is the dynamical time in the comovingti). frame. D(ty) is the Doppler factor of the N-rav jet at the time fy. στ is the Thomson cross section.," If the synchrotron radiation dominates the cooling of the electrons, $E_{M,cool}=6\pi m_e^2 c^3/(\sigma_T B_\bot^2 t'_0)$, where $t'_0=t_0/D(t_0)$ is the dynamical time in the comoving frame, $D(t_0)$ is the Doppler factor of the X-ray jet at the time $t_0$ , $\sigma_T$ is the Thomson cross section."313" The plivsical quantities in the acdabatically expanding ejecta with radius FR relate with their initial value at ty bv ( van der Laan 1966) if the svuchrotron enüssiou cooling is uceligible. where Ry is the radius of the ejecta at time ty and salty)=EY,me,"," The physical quantities in the adiabatically expanding ejecta with radius $R$ relate with their initial value at $t_0$ by ( van der Laan 1966) if the synchrotron emission cooling is negligible, where $R_0$ is the radius of the ejecta at time $t_0$ and $\gamma_M(t_0)=E_M^0/m_e c^2$."314 These relations are derived from the asstuuption that total ummber of the electrous is conserved aud that tle magnetic field is frozen to the plasiiafluid’., These relations are derived from the assumption that total number of the electrons is conserved and that the magnetic field is frozen to the plasma.315 From the dynamic model in section 3. we ect ty)=1?1 days aud Ry=τί«107 for the castern X-ray jet from ATE J1550-561.," From the dynamic model in section 3, we get $t_0=121$ days and $R_0=0.71\times10^{18}{\rm cm}$ for the eastern X-ray jet from XTE J1550-564."316 Given the initial condition. for Wty). Batty). salty) auc raylty}. we can obtain the model light curves of the cinissious from the expanding ejecta using Eqs.(3). C1). (9) aud Rit).," Given the initial condition for $K(t_0)$, $B_\bot(t_0)$, $\gamma_m(t_0)$ and $\gamma_M(t_0)$, we can obtain the model light curves of the emissions from the expanding ejecta using Eqs.(3), (4), (9) and $R(t)$ ."317 Iu the caleulation. we have asstuned σα)= ," In the calculation, we have assumed $\gamma_M(t_0)=E_{M,cool}/m_e c^2=6\pi m_e c/(\sigma_T318B_\bot(t_0)^2 t'_0)$ ."319"We fiud that the following combination of the initial τη).values cau fit the flux data well (sec Figure 1): Baty)=O451 and Άν)=0.8cmP and +,,(to)=100."" For these values. salty)=3.55«105,"," We find that the following combination of the initial values can fit the flux data well (see Figure 4): $B_\bot(t_0)=0.5 {\rm~ m G}$ and $K(t_0)=0.8~ {\rm cm^{-3}}$ and $\gamma_m(t_0)=100$ For these values, $\gamma_M(t_0)=3.55\times10^8$."320 Noting that A=ἐν2)? and By=Varepe’. the above value for A(ty) aud By(fy) imply that the equipartition parameters for enereijes im clectrons aud magnetic field iu the reverse shock are e;=0.6 aud eg=OLLS10? respectively. if the internal energy deusity in the reverse shock is equal to that in the forward shock region at time ty.," Noting that $K=\epsilon_e(p-2)e'\gamma_m^{p-2}$ and $B_\bot=\sqrt{8\pi\epsilon_B e'}$, the above value for $K(t_0)$ and $B_\bot(t_0)$ imply that the equipartition parameters for energies in electrons and magnetic field in the reverse shock are $\epsilon_e=0.6$ and $\epsilon_B=0.44\times10^{-2}$ respectively, if the internal energy density in the reverse shock is equal to that in the forward shock region at time $t_0$."321 Surprisingly. these equipartition values are close to the typical values inferred for GRB afterglows (Cixanot et al.," Surprisingly, these equipartition values are close to the typical values inferred for GRB afterglows (Granot et al."322 1999. Wijers Calama 1999: Wang. Dai Lu 2000).," 1999, Wijers Galama 1999; Wang, Dai Lu 2000)."323 We further calculate the model spectrum for the caster jet on 1 June 2000 using the above parameter values and plot the fit of the observed data in Figure 5., We further calculate the model spectrum for the eastern jet on 1 June 2000 using the above parameter values and plot the fit of the observed data in Figure 5.324 Clearly the model fits quite well the euergv spectrum on 1 June 2000. 621 davs after the ejection of the eastern jet from NTE J1550-56LI.," Clearly the model fits quite well the energy spectrum on 1 June 2000, 621 days after the ejection of the eastern jet from XTE J1550-564."325 At this time. the characteristic frequency of the electrons with 23; is just near the N-ray baud. so tle Nav spectrum doesu't become steeper.," At this time, the characteristic frequency of the electrons with $\gamma_M$ is just near the X-ray band, so the X-ray spectrum doesn't become steeper."326 The model predicts that there should be significant steepness of N-rav spectrin at March 2002. but the relatively few counts do not give a reliable spectral iudex (Ixaaret ct al.," The model predicts that there should be significant steepness of X-ray spectrum at March 2002, but the relatively few counts do not give a reliable spectral index (Kaaret et al."327 2003)., 2003).328 We have shown that the enussiou from the shocked ejecta provides a viable mechanism for the rapidly decaving X-ray fux from the eastern jet of NTE 561., We have shown that the emission from the shocked ejecta provides a viable mechanism for the rapidly decaying X-ray flux from the eastern jet of XTE J1550-564.329 The high value for ερ in the reverse shock region relative to that in the forward shock region cau be accounted for if the ejecta has already. been magnetized before the further shockcompression”., The high value for $\epsilon_B$ in the reverse shock region relative to that in the forward shock region can be accounted for if the ejecta has already been magnetized before the further shock.330 This is reasonable as the ejecta from niücroquasus are suggested to originate from the inner accretion disks (Mirabel Rodriguez 1999)., This is reasonable as the ejecta from microquasars are suggested to originate from the inner accretion disks (Mirabel Rodriguez 1999).331" A pair-vich outflow from the microquasar probably account for the comparatively largevalue ofe, iu the reverse shock.", A pair-rich outflow from the microquasar probably account for the comparatively largevalue of $\epsilon_e$ in the reverse shock.332 Future observations of larec-scale jetsfrom mudcroquasars niav provide better understanding of the shock physics aud physical condition inrelativistic jets., Future observations of large-scale jetsfrom microquasars may provide better understanding of the shock physics and physical condition inrelativistic jets.333 It is believed. that relativistic jets exist in accreting svstenis rangius from Calactic N-rav binaries.," It is believed that relativistic jets exist in accreting systems ranging from Galactic X-ray binaries,"334Our knowledge of the properties of high-redshift galaxies (here 7:3) currently mainly comes from two very different kinds of studies. namely. the study of Lyman-Break Galaxies (LBGs) selected by the Lyman-limit break in their spectrum (e.g. Steidel et al.,"Our knowledge of the properties of high-redshift galaxies (here $\approx$ 3) currently mainly comes from two very different kinds of studies, namely, the study of Lyman-Break Galaxies (LBGs) selected by the Lyman-limit break in their spectrum (e.g. Steidel et al."335 1996. 2000: Fontana et al.," 1996, 2000; Fontana et al."336 2000: Papovich et al., 2000; Papovich et al.337 2001: Vanzella et al., 2001; Vanzella et al.338 2002). and the study of the chemical and kinematical properties of (proto)galaxies. so called Damped Ένα Absorbers (DLAs). intervening the lines of sight to QSOs (e.g. Wolfe et al.," 2002), and the study of the chemical and kinematical properties of (proto)galaxies, so called Damped $\alpha$ Absorbers (DLAs), intervening the lines of sight to QSOs (e.g. Wolfe et al."339 1986; Pettini et al., 1986; Pettini et al.340 1997; Prochaska Wolfe 2002: Ledoux et al., 1997; Prochaska Wolfe 2002; Ledoux et al.341 2002)., 2002).342 However. there is strong evidence that there is only a small overlap between the galaxies in the current LBG samples and the DLAs (Fynbo. Moller Warren 1999; Haehnelt et al.," However, there is strong evidence that there is only a small overlap between the galaxies in the current LBG samples and the DLAs (Fynbo, ller Warren 1999; Haehnelt et al."343 2000: Schaye 2001: Moller et al., 2000; Schaye 2001; ller et al.344 2002: Adelberger et al., 2002; Adelberger et al.345 2003)., 2003).346 The reason for this is that Lyman-Break galaxy samples are continuum-flux limited and that the current flux limit corresponding to R25.5 is not deep enough to reach the level of typical damped Lya absorption selected galaxies., The reason for this is that Lyman-Break galaxy samples are continuum-flux limited and that the current flux limit corresponding to $\approx$ 25.5 is not deep enough to reach the level of typical damped $\alpha$ absorption selected galaxies.347 However. due to the very steep faint-end slope of the z=3 galaxy luminosity function (Adelberger Steidel 2000; Poli et al.," However, due to the very steep faint-end slope of the z=3 galaxy luminosity function (Adelberger Steidel 2000; Poli et al."348 2001a. 2001b) ~70% of the observer rest-frame R-band flux from z=3 galaxies is emitted by galaxies fainter than R=25.5.," 2001a, 2001b) $\sim$ of the observer rest-frame R-band flux from z=3 galaxies is emitted by galaxies fainter than R=25.5."349 Therefore. besides accounting for the bulk of the damped Lyo absorption in QSO spectra. the 25.5 galaxies could dominate the integrated star-formation rate and the metal enrichment and heating of the intergalactic medium at z~3.," Therefore, besides accounting for the bulk of the damped $\alpha$ absorption in QSO spectra, the $>$ 25.5 galaxies could dominate the integrated star-formation rate and the metal enrichment and heating of the intergalactic medium at $\approx$ 3."350 In 2000. we started the programme “Building the Bridge between Damped Lya Absorbers and Lyman-break Galaxies: Lya Selection of Galaxies” at the European Southern Observatory’s Very Large Telescope (VLT).," In 2000, we started the programme “Building the Bridge between Damped $\alpha$ Absorbers and Lyman-break Galaxies: $\alpha$ Selection of Galaxies” at the European Southern Observatory's Very Large Telescope (VLT)."351 This project aims at bridging the gap between absorption- and emission-line selected galaxy populations by creating a database of zz3 galaxies that are fainter than R=25.5. and to study the properties. such as morphology. star-formation rates. clustering and continuum colours. of these faint. very numerous. and so far little studied high-redshift galaxies.," This project aims at bridging the gap between absorption- and emission-line selected galaxy populations by creating a database of $\approx$ 3 galaxies that are fainter than R=25.5, and to study the properties, such as morphology, star-formation rates, clustering and continuum colours, of these faint, very numerous, and so far little studied high-redshift galaxies."352 Our method is to obtain) deep narrow-band Ενα observations of the fields of zz3 QSO absorbers whose redshifts match existing VLT narrow-band filters., Our method is to obtain deep narrow-band $\alpha$ observations of the fields of $\approx$ 3 QSO absorbers whose redshifts match existing VLT narrow-band filters.353 We chose to observe the fields of QSO absorbers to anchor our fields to already known structures at the target redshift and. hence. minimise the risk of observing a void.," We chose to observe the fields of QSO absorbers to anchor our fields to already known structures at the target redshift and, hence, minimise the risk of observing a void."354 Lya narrow-band imaging can. with comparatively short integration times. lead to the detection of a significant sample of zz:3 galaxies havingσι much fainter continuum fluxes than LBGs. as demonstrated by. e.g.. Cowie et al. (," $\alpha$ narrow-band imaging can, with comparatively short integration times, lead to the detection of a significant sample of $\approx$ 3 galaxies having much fainter continuum fluxes than LBGs, as demonstrated by, e.g., Cowie et al. ("3551998). Kudritzki et al. (,"1998), Kudritzki et al. ("3562000). and Fynbo et al. (,"2000), and Fynbo et al. ("3572000. 2001. 2002).,"2000, 2001, 2002)."358 In the following. we shall use the acronym LEGO for Lya-Emitting Galaxy-buildingσι Objects (Moller Fynbo 2001) to refer to the Lye emitters.," In the following, we shall use the acronym LEGO for $\alpha$ -Emitting Galaxy-building Objects ller Fynbo 2001) to refer to the $\alpha$ emitters."359 In this first paper. we describe the results of deep narrow and broad-band imaging and subsequent follow-up multi-object spectroscopy of the fields of the QSOs 0322 and 4427.," In this first paper, we describe the results of deep narrow and broad-band imaging and subsequent follow-up multi-object spectroscopy of the fields of the QSOs $-$ 0322 and $-$ 4427."360 These QSOs have intervening high neutral hydrogen column density Ένα absorbers at redshifts z=3.15 (logCN(IE1)).~ 19.9) and z=2.85 (οσα= 20.9) respectively (Francis Hewett 1993; Storrie-Lombardi et al., These QSOs have intervening high neutral hydrogen column density $\alpha$ absorbers at redshifts z=3.15 $\log(N(\ion{H}{i}))\sim19.9$ ) and z=2.85 $\log(N(\ion{H}{i}))=20.9$ ) respectively (Francis Hewett 1993; Storrie-Lombardi et al.361 1996)., 1996).362 The paper is organized in the following way., The paper is organized in the following way.363 First. in Sect.," First, in Sect."364 2 we describe the imaging and the selection of LEGO candidates., 2 we describe the imaging and the selection of LEGO candidates.365 Then. in Sect.," Then, in Sect."366 3 we describe the observations and results from the first spectroscopic run., 3 we describe the observations and results from the first spectroscopic run.367 Finally. in Sect.," Finally, in Sect."368 4., 4.369 we discuss our findings., we discuss our findings.370" Throughout this paper we assume a cosmology with 77,265 km + !. Q,,=0.3 and O 420.7."," Throughout this paper we assume a cosmology with $H_0$ =65 km $^{-1}$ $^{-1}$, $\Omega_m$ =0.3 and $\Omega_\Lambda$ =0.7."371" In this model. a redshift of 3.15(2.85) corresponds to a luminosity distance d;,,, = 29.05(25.76) Gpe and ea distance modulus of 47.31(47.05)."," In this model, a redshift of 3.15(2.85) corresponds to a luminosity distance $d_{lum}$ = 29.05(25.76) Gpc and a distance modulus of 47.31(47.05)."372 One aresecond on the sky corresponds to 8.18(8.42) proper kpe and the look-back time is 12.3(12.1) Gyr (roughly of the time since the event commonly referred to as the Big Bang)., One arcsecond on the sky corresponds to 8.18(8.42) proper kpc and the look-back time is 12.3(12.1) Gyr (roughly of the time since the event commonly referred to as the Big Bang).37322003). like some UC TTT regions (see I&oo 11996: Caray 11993: and Nautz 11999) are surrounded by extended low-density ionized halos.,"2003), like some UC HII regions (see Koo 1996; Garay 1993; and Kurtz 1999) are surrounded by extended low-density ionized halos."374 The most likely explanation for the halos is that IIC and UC WIT regions are highly clumped. thereby. producing porous nebulae to UV photous.," The most likely explanation for the halos is that HC and UC HII regions are highly clumped, thereby producing porous nebulae to UV photons."375 Au example of a HIC. ΠΠ region with a power-law SED is 1IT2O. whose spectrum from 6 cin to Tonua is shown in Figure 1..," An example of a HC HII region with a power-law SED is $_2$ O, whose spectrum from 6 cm to 7 mm is shown in Figure \ref{fig1}."376 WC IIII regious are found iu the vicinity of massive star formation and are often coincideut with strong II2O masers., HC HII regions are found in the vicinity of massive star formation and are often coincident with strong $_2$ O masers.377 Some TC IIIE regious appear to be driving bipolar molecular outflows (Ποιος 11996: Shepherd 11998)., Some HC HII regions appear to be driving bipolar molecular outflows (Hofner 1996; Shepherd 1998).378 Sewilo ((2003) have suggested that Πο ΠΠ regious may represeut an evolutionary stage between hot molecular cores and UC WIT reeious., Sewilo (2003) have suggested that HC HII regions may represent an evolutionary stage between hot molecular cores and UC HII regions.379 During this period. rapid accretion outo the central protostar sluts down. aud a circumstellae HIT regiou first becomes laree cuough to be detected.," During this period, rapid accretion onto the central protostar shuts down, and a circumstellar HII region first becomes large enough to be detected."380 A property of at least some IC WIT regions that concerns this paper is their power-law SEDs at radio wavelengths., A property of at least some HC HII regions that concerns this paper is their power-law SEDs at radio wavelengths.381" The SEDs of WC WT reeions ave spectral iudices à between |0.3 to |1.6 65,x77) with typical values of az|1 from short cii to nuu wavelengths.", The SEDs of HC HII regions have spectral indices $\alpha$ between $+0.3$ to $+1.6$ $S_{\nu}\propto\nu^{\alpha}$ ) with typical values of $\alpha\approx +1$ from short cm to mm wavelengths.382 All Πο ΠΠ regions secu to have rising power spectra iu the range z3.6 ci to x23 uum. but he slopes may differ frou source to source.," All HC HII regions seem to have rising power spectra in the range $\approx 3.6$ cm to $\leq 3$ mm, but the slopes may differ from source to source."383 These spectral iudices are expecially interesting because they cannot casily be explained by thermal or ronthermal radio contimmiun emission for coustaut density nebulae., These spectral indices are especially interesting because they cannot easily be explained by thermal or nonthermal radio continuum emission for constant density nebulae.384 They are too shallow for optically thick hermal emission. too steep for optically thin thermal eiissiou. aud the waveleneth interval is too broad. to represcut the transition from optically thick to thin thermal eiissiou.," They are too shallow for optically thick thermal emission, too steep for optically thin thermal emission, and the wavelength interval is too broad to represent the transition from optically thick to thin thermal emission."385 The spectral iudices are iconsistcut with optically thin svuchrotrou emission: also. radio recombination lines require that IC ITIT reeious are hermal.," The spectral indices are inconsistent with optically thin synchrotron emission; also, radio recombination lines require that HC HII regions are thermal."386 In this paper. we explore the possibility that the power-law SEDs of IC ΠΠ reeious wieght possibly )o the result of hicrarchial clumping.," In this paper, we explore the possibility that the power-law SEDs of HC HII regions might possibly be the result of hierarchial clumping."387 It has been known for some time that power-lay density eradicuts with distance from the ionizing star of TMI regious produce radio power-law SEDs (Oluou 1975: Panagia Felli 1975: Wright Barlow 1975)., It has been known for some time that power-law density gradients with distance from the ionizing star of HII regions produce radio power-law SEDs (Olnon 1975; Panagia Felli 1975; Wright Barlow 1975).388 Olnon (1975) showed that the relationship between tle slope of the SED (6) and the slope of the power-law density eradieut (ω where p.xr Sy) isa=(δωBALfe0.5) for ο1.5., Olnon (1975) showed that the relationship between the slope of the SED $\alpha$ ) and the slope of the power-law density gradient $\omega$ where $n_{e}\propto r^{-\omega}$ ) is $\alpha=(2\omega-3.1)/(\omega-0.5)$ for $\omega>1.5$.389 Thus. for a=0.6. 2=2.0: oy a= [low=2.6: aud fora=11.5. w=LT.," Thus, for $\alpha=0.6$, $\omega=2.0$; for $\alpha=+1$, $\omega=2.6$; and for $\alpha=+1.5$, $\omega=4.7$."390 The a=0.6. 2=2.0 parameters correspond to the classical values for a constant velocity wind (Wright Barlow 1975: Panagia Felli 1975).," The $\alpha=0.6$, $\omega=2.0$ parameters correspond to the classical values for a constant velocity wind (Wright Barlow 1975; Panagia Felli 1975)."391 Oluou (1975) »oiuts out that when the density eracieut has a power-law depeudeuce on radius. the slope of the SED will o determined by the value of w at the radius where the optical depth is about unity.," Olnon (1975) points out that when the density gradient has a power-law dependence on radius, the slope of the SED will be determined by the value of $\omega$ at the radius where the optical depth is about unity."392 That is. the size of he effective radiating surface depends on both the deusity eracicnt aud frequency.," That is, the size of the effective radiating surface depends on both the density gradient and frequency."393" Wartinann Cassinelli (1977) showed that a radial outflow whose velocity is a power-law with radius of iudex 2 has a deusity vower-law dependence on radius of 2. resulting iu à SED power-law (5,xντο for a constant velocity wind)."," Hartmann Cassinelli (1977) showed that a radial outflow whose velocity is a power-law with radius of index $\beta$ has a density power-law dependence on radius of $\beta-2$, resulting in a SED power-law $S_{\nu}\propto\nu^{2/3}$ for a constant velocity wind)."394 The density power-law iudex w increases so rapidly with a that wis improbably huge for a=|1 (wc 2.6)., The density power-law index $\omega$ increases so rapidly with $\alpha$ that $\omega$ is improbably large for $\alpha\geq +1$ $\omega\geq 2.6$ ).395 In light of the observed density structure of TWD regions discussed above. it seenis unlikely. that real HIT regions have such steep aud wel-bchaved density structures with radius; especially in the very carly stages of evolution expected for WC ΠΠ regions.," In light of the observed density structure of HII regions discussed above, it seems unlikely that real HII regions have such steep and well-behaved density structures with radius, especially in the very early stages of evolution expected for HC HII regions."396 We therefore investigate an alternate possible explanation for the observed radio power-law SEDs of UC III regions. namely hierarchal clumping of nebular gas.," We therefore investigate an alternate possible explanation for the observed radio power-law SEDs of HC HII regions, namely hierarchal clumping of nebular gas."397 As used heres “hierarchial chunupine” refers to a reeion filled with chumps of ionized eas having a rauge of sizes. temperatures. aud optical depths defined by power-law distributions.," As used here, “hierarchial clumping” refers to a region filled with clumps of ionized gas having a range of sizes, temperatures, and optical depths defined by power-law distributions."398 There need not be a medium iu which all the chuups are embedded although such a structure could be accommodated in our analysis., There need not be a medium in which all the clumps are embedded although such a structure could be accommodated in our analysis.399 A luerarclial chup distribution is not the same as a fractal distribution which posits chumps within chuups within chuups., A hierarchial clump distribution is not the same as a fractal distribution which posits clumps within clumps within clumps.400In a fractal structure the cmereent SED is complicated by the fact that every clump is enibedded in clumps of larger size. whereas in a lierarchically clamped structure the main complication arises,"	In a fractal structure the emergent SED is complicated by the fact that every clump is embedded in clumps of larger size, whereas in a hierarchically clumped structure the main complication arises"401 (Riessetal.1998;Perlmutter1999) (Hui&Greene2006:Coorayetal.2006:Sarkar2008b).. (Hamuy2006:Strovink2007).," \citep{Riess:98, Perl:99} \citep{Huterer:05,sullivan:07,sarkar:08a}. \citep{huigreene:06,cooraycaldwell:06,cooray:06,sarkar:08b}. \citep{hamuy:95, livio:00, scannapieco:05,mannucci:06, sullivan:06,402strovink:07}."403. Howelletal.(2007) between the two components. based on a difference of (8.1+2.7)% in the width of lightcurves.," \citet{howell:07} between the two components, based on a difference of $(8.1 \pm 2.7)\%$ in the width of lightcurves."404 Since the SN lightcurves are used to calibrate the intrinsic. luminosity (Phillips1993;Riessetal.1996;Perlmutter1997;Tonry 2007).. a systematic difference in intrinsic lumimosity could conceivably be calibrated out. if the SN ltghteurve calibration relation is the same for both populations.," Since the SN lightcurves are used to calibrate the intrinsic luminosity \citep{phillips:93, riess:96, perlmutter:97,405tonry:03, prieto:06, guy:07, jha:07}, a systematic difference in intrinsic luminosity could conceivably be calibrated out, if the SN lightcurve calibration relation is the same for both populations."406 However. it is unclear whether the full intrinsic difference in luminosity between the two populations is captured by a calibratable difference in the Hghtcurves.," However, it is unclear whether the full intrinsic difference in luminosity between the two populations is captured by a calibratable difference in the lightcurves."407 A residual in the calibrated Juminosity could potentially remain. leading to a redshift-dependent shift in the Hubble diagram. and systematic errors in the best-fit cosmological parameters.," A residual in the calibrated luminosity could potentially remain, leading to a redshift-dependent shift in the Hubble diagram, and systematic errors in the best-fit cosmological parameters."408 For example. itis likely that the intrinsic colors of Type la SNe are not uniquely determined by light-curve shape (Conleyetal. 2008).," For example, it is likely that the intrinsic colors of Type Ia SNe are not uniquely determined by light-curve shape \citep{conley08}."409 Even if this is not the case. differences in intrinsic. color between the populations might introduce systematic differences in post-calibration luminosity (e.g.. through differences in the extinction corrections).," Even if this is not the case, differences in intrinsic color between the populations might introduce systematic differences in post-calibration luminosity (e.g., through differences in the extinction corrections)."410 We model the two-population systematic. constraining the magnitude of the effect with current data.," We model the two-population systematic, constraining the magnitude of the effect with current data."411 With large SN samples 1t may be possible to estimate the magnitude of the systematic directly from the data (e.g.. by correlating observed SN brightnesses with properties of the host galaxies (Hamuyetal.1996b:lagheretal. 2008))).," With large SN samples it may be possible to estimate the magnitude of the systematic directly from the data (e.g., by correlating observed SN brightnesses with properties of the host galaxies \citep{hamuy:96b,Riess:99,sullivan:06,jha:07,412gallagher:08}) )."413 We quantify the level of calibration required to avoid significantly degrading the determination of the dark energy EOS., We quantify the level of calibration required to avoid significantly degrading the determination of the dark energy EOS.414 The paper is organized as follows: in 52 we discuss a model for incorporating a two-population systematic residual lummosity into the Hubble diagram., The paper is organized as follows: in $\S$ 2 we discuss a model for incorporating a two-population systematic residual luminosity into the Hubble diagram.415 In 53 we investigate the possibility of detecting this systematic from both current and future SN data. and the impact on dark energyparameter estimation.," In $\S$ 3 we investigate the possibility of detecting this systematic from both current and future SN data, and the impact on dark energyparameter estimation."416 The use of SNe as standardizable candles to constrain the, The use of SNe as standardizable candles to constrain the417(2011).,.418. The pressure-temperature profiles adopted for our models are shown in Figure 1.., The pressure-temperature profiles adopted for our models are shown in Figure \ref{figure:profiles}.419 The profile lor Gliese 229D is taken from Model D of Saumonοἱal.(2000)., The profile for Gliese 229B is taken from Model B of \citet{saumon2000}.420. The profiles for ILD L89733b are [rom Mosesetal.(2011) ancl represent davside-average ancl terminator-average thermal structures based upon the 3-D GCSM simulations of Showmanetal.(2009)., The profiles for HD 189733b are from \citet{moses2011} and represent dayside-average and terminator-average thermal structures based upon the 3-D GCM simulations of \citet{showman2009}.421. These profiles are chosen for (heir relevance to almospheric conditions al secondary eclipse and primary (ransil. respectively. and include extensions to low pressures using the (hermospheric models of GarcíaMunoz(2007) aud extensions to high pressures using the 1D models of Fortnevetal.(200Ga)..," These profiles are chosen for their relevance to atmospheric conditions at secondary eclipse and primary transit, respectively, and include extensions to low pressures using the thermospheric models of \citet{garciamunoz2007} and extensions to high pressures using the 1D models of \citet{fortney2006dyn}."422 We adopt protosolar elemental abundances from Locdders (2009).. with an assumed 0.5x protosolar composition ([Fe/Il]=—0.3) for Gliese 229D based upon Model Bin Sammonetal.(2000)... ancl an assumed 1x protosolar composition ([Fe/Il]= 0) for ILD 189733b.," We adopt protosolar elemental abundances from \citet{lodders2009}, with an assumed $\times$ protosolar composition $[\textrm{Fe/H}]=-0.3$ ) for Gliese 229B based upon Model B in \citet{saumon2000}, and an assumed $\times$ protosolar composition $[\textrm{Fe/H}]=0$ ) for HD 189733b."423 For both objects. we assume uniform metallicity for all elements(e.g.. solar C'/O ratio) and consider the removal of of oxvgen bv. reaction wilh rock-formineg elements in the deep atmosphere (e.g..notesilicatecondensationcurvesinFig. 1:2005).," For both objects, we assume uniform metallicity for all elements, solar C/O ratio) and consider the removal of of oxygen by reaction with rock-forming elements in the deep atmosphere \citep[e.g., note silicate condensation curves in Fig.~\ref{figure:profiles}; ."424 Thermochemical equilibrium ealeulations are used to determine (he initial atinosphlieric composition in (he absence of transport. as is described in Visscherοἱal.(2010) ancl Mosesetal. (2010)..," Thermochemical equilibrium calculations are used to determine the initial atmospheric composition in the absence of transport, as is described in \citet{visscher2010icarus} and \citet{moses2010}. ."425 The reaction list in our thermochemical kinetics aud transport model is similar to that described in Visseheretal.(2010) and. Mosesetal.(2010.2011).," The reaction list in our thermochemical kinetics and transport model is similar to that described in \citet{visscher2010icarus} and \citet{moses2010,moses2011}."426.. All of the chemical reactions in the model are reversed using the principle of microscopic reversibility., All of the chemical reactions in the model are reversed using the principle of microscopic reversibility.427 As an aid to other investigators. we discuss this approach in detail to show how reverse rate coefficients are correctly caleulated. particularly for reactions wilh an unequal number of reactants ancl products.," As an aid to other investigators, we discuss this approach in detail to show how reverse rate coefficients are correctly calculated, particularly for reactions with an unequal number of reactants and products."428" For example. if we consider a balanced. elementary. gas-phase chemical reaction. {here are @ molecules of species A. b molecules of species D. and so on. aud the expression for the equilibrium constant A,eg of thereaction can be written as"," For example, if we consider a balanced, elementary, gas-phase chemical reaction, there are $a$ molecules of species A, $b$ molecules of species B, and so on, and the expression for the equilibrium constant $K_{eq}$ of thereaction can be written as"429"the total compression ratio is found to be fi,~9 for both values of the Mach number. while the prediction of standard non-linear theory. would be Πως~112 for M,=500 and Hj~LT for M,=50.","the total compression ratio is found to be $\Rt\sim 9$ for both values of the Mach number, while the prediction of standard non-linear theory would be $\Rt\sim 112$ for $M_0=500$ and $\Rt\sim 17$ for $M_0=50$."430 Clearly. the shallower precursor comes from the decrease of the fraction of bulk energy that is converted into cosmic ravs. which however remains considerable: €; is reduced from more than to around 6054... for both values of M (Fig. 1..," Clearly, the shallower precursor comes from the decrease of the fraction of bulk energy that is converted into cosmic rays, which however remains considerable: $\xi_1$ is reduced from more than to around , for both values of $M_0$ (Fig. \ref{fig:Ucsispettro},"431 left bottom panel)., left bottom panel).432 The remaining Iraction of bulk energy ends up being converted into heating ancl energy ol the turbulent magnetic field., The remaining fraction of bulk energy ends up being converted into heating and energy of the turbulent magnetic field.433 We define the thermal emissivity as and we report. in the last column of Tab. 2..," We define the thermal emissivity as and we report, in the last column of Tab. \ref{tab:err},"434" the ratio between its downstream value computed within modified shock theorv (25) and the prediction lor the same shock in test. particle theory (7,5).", the ratio between its downstream value computed within modified shock theory $\varepsilon_2$ ) and the prediction for the same shock in test particle theory $\varepsilon_{tp}$ ).435 The temperature (next to last column in Tab. 2)), The temperature (next to last column in Tab. \ref{tab:err}) )436 and thermal emissivitv downstream: are always much smaller than in (he test-particle approximation. since a considerable fraction of the shock ram pressure is now going into particle acceleration and magnetic field amplification.," and thermal emissivity downstream are always much smaller than in the test-particle approximation, since a considerable fraction of the shock ram pressure is now going into particle acceleration and magnetic field amplification."437" Nevertheless. it is clear (hat the effect of the magnetized jump conditions is to enhance both quantities (e.g. 75 is enhanced by a [factor >100 [or Ti,=10! IX). as a net result of the increased temperature jump 75/Tj (Eqs. 11..10))"," Nevertheless, it is clear that the effect of the magnetized jump conditions is to enhance both quantities (e.g. $T_2$ is enhanced by a factor $>100$ for $T_0=10^4\degK$ ), as a net result of the increased temperature jump $T_2/T_1$ (Eqs. \ref{T2T1}, \ref{p2p1}) )"438" and the reduced compressibility of the upstream plasma (lower /2),/).", and the reduced compressibility of the upstream plasma (lower $\Rt$ ).439 We should recall that (he compression ratios actually felt by cosmic ravs depend on the relative velocity between them and the scattering centers. i.e.the Allvénn waves. according," We should recall that the compression ratios actually felt by cosmic rays depend on the relative velocity between them and the scattering centers, i.e.the Alfvénn waves, according"440spherical havmonic transform. or Ofax,"spherical harmonic transform, or ${\cal O}(\ell_{\textrm{max}}^{3})$."441 Future work will attempt to push the ecneralized Cübbs || ALICAIC suupliug scheme presented lere to smaller angular scales. ultimately limited by the degree to which we can conrpute harmonic trausformis.," Future work will attempt to push the generalized Gibbs + MCMC sampling scheme presented here to smaller angular scales, ultimately limited by the degree to which we can compute harmonic transforms."442 Tere we review the derivation of the accept probability in Markov Chain Monte Carlo when using deteriiuistic proposals (or proposals where some of the degrees of freedom are specified as deterministic functions of the past state and/or proposed variations in some other degrees of freedom)., Here we review the derivation of the accept probability in Markov Chain Monte Carlo when using deterministic proposals (or proposals where some of the degrees of freedom are specified as deterministic functions of the past state and/or proposed variations in some other degrees of freedom).443 We first briefly review the \Letropolis-Hastings Markov Chain Monte Carlo algorithm and the proof ofits convergence. aud then turn to the special case involving deteriiuistic proposals.," We first briefly review the Metropolis-Hastings Markov Chain Monte Carlo algorithm and the proof of its convergence, and then turn to the special case involving deterministic proposals."444 Much of the review of the AICAIC aleorithin here follows (Sokal1989)., Much of the review of the MCMC algorithm here follows \citep{Sokal:1989}.445. We also note that simular techuical considerations including deterministic elemieuts iu proposals are presented in (ποσα.1995) iu the context of AICAIC algorithius in which the dimension of the state space itself is included as a random variable to be sampled over., We also note that similar technical considerations including deterministic elements in proposals are presented in \citep{Green:1995} in the context of MCMC algorithms in which the dimension of the state space itself is included as a random variable to be sampled over.446" The goal is the coustruction of a transition mane TiCSsv8d) such that after initializing the Markov Chain with a sample fom anv probability deusity py(C.fucj. we generate samples from a sequence of probability densities which eventually couverge to an aC}) We remind the reader of the sufficient conditions to establish couvergeunce of an MCMC(C algorithiua:stutionarity. which means that the ΙΟΝΤΟ transition matrix satisfies and@reducability, which meaus that for any two states. there is a finite number of iterations which eive a probability to trausition frou one state to the other."," The goal is the construction of a transition matrix $T(C_{l}, \Bs | C_{l}', \Bs', \Bd)$ such that after initializing the Markov Chain with a sample from any probability density $p_{0}(C_{l}, \Bs | \Bd)$, we generate samples from a sequence of probability densities which eventually converge to an $\pi(C_{l}, \Bs | \Bd)$ We remind the reader of the sufficient conditions to establish convergence of an MCMC algorithm:, which means that the MCMC transition matrix satisfies and, which means that for any two states, there is a finite number of iterations which give a non-vanishing probability to transition from one state to the other."447 It is well known that these two properties are sufficicut to establish convergence. as can be seeu simply from the triangle inequality The Moetropolis-Hastiugs Markov Chain Moute Carlo algorithin is one method of coustructing such a transition matrix.," It is well known that these two properties are sufficient to establish convergence, as can be seen simply from the triangle inequality The Metropolis-Hastings Markov Chain Monte Carlo algorithm is one method of constructing such a transition matrix."448" We chooseay proposal matrix (C.s[CT.s'.d) aud then accept the proposed move with a probability while rejecting the proposed move with probability 1A leads to a ""null transition” where the next state in the Markov Chain remains the same."," We choose proposal matrix $w(C_{l}, \Bs | C_{l}', \Bs', \Bd)$ and then accept the proposed move with a probability while rejecting the proposed move with probability $1 - A$ leads to a “null transition” where the next state in the Markov Chain remains the same."449 Application of this aleorithm then leads to the sequence of probability deusities which satisfv where the first term is the coustribution to the probability deusity μι if we reject auy proposed move. while the second teri is the contribution from accepting the proposed move from any possible previous state.," Application of this algorithm then leads to the sequence of probability densities which satisfy where the first term is the constribution to the probability density $p_{n+1}$ if we reject any proposed move, while the second term is the contribution from accepting the proposed move from any possible previous state."450 If we demand that. for a chosen proposal matrix. the accept probability satisfies," If we demand that, for a chosen proposal matrix, the accept probability satisfies"451Thin disces are an important model for accretion Lows in a number of dillerent. astrophysical objects. including active ealactic nuclei. interacting binary systems. and voung stars.,"Thin discs are an important model for accretion flows in a number of different astrophysical objects, including active galactic nuclei, interacting binary systems, and young stars."452 Most clise mocels areffe. icc. the clise is planar. for simplicity and because there has been little theoretical or observational motivation to Consider non-coplanar. orwarped disces although observations of the accreting neutron star svstenir Ler X-1 have long been interpreted as requiring a precessing disc that. lies out of. the plane of the binary system (Tananbaum οἱ al.," Most disc models are, i.e. the disc is planar, for simplicity and because there has been little theoretical or observational motivation to consider non-coplanar, or discs – although observations of the accreting neutron star system Her X-1 have long been interpreted as requiring a precessing disc that lies out of the plane of the binary system (Tananbaum et al."453 1972: Ixatz 1973: Roberts 1974)., 1972; Katz 1973; Roberts 1974).454 A pair of developments in the [ast lew vears now strongly motivates theoretical interest in warped cdises., A pair of developments in the last few years now strongly motivates theoretical interest in warped discs.455 First. Pringle (1996) found an instability of a thin disc moclel that tends to. produce large scale warps.," First, Pringle (1996) found an instability of a thin disc model that tends to produce large scale warps."456 The instability is driven by radiation torques exerted on the disc as it is differentially illuminated by the central source and then re-radiates., The instability is driven by radiation torques exerted on the disc as it is differentially illuminated by the central source and then re-radiates.457 Second. the megamaser in the nucleus ofNGC 4258 has been resolved by the VLBA and can be understood as an almost precisely Weplerian. but warped. thin disc.," Second, the megamaser in the nucleus of NGC 4258 has been resolved by the VLBA and can be understood as an almost precisely Keplerian, but warped, thin disc."458 Phe maser spots trace out the position of the disc anc allow accurate measurements of its distance. the mass of the central object. and the parameters of the warp (Alivoshi et al.," The maser spots trace out the position of the disc and allow accurate measurements of its distance, the mass of the central object, and the parameters of the warp (Miyoshi et al."459 1995)., 1995).460" Of Course. warps niv also be excited by direct forcing. e.g. by idal interaction of a T Lauri disc with a binary companion (Papaloizou ""Terquem 1995)."," Of course, warps may also be excited by direct forcing, e.g. by tidal interaction of a T Tauri disc with a binary companion (Papaloizou Terquem 1995)."461 Warps in unmagnetized. non-self-eravitating. inviscid Ixeplerian discs are rather special. as we shall review in 83 low.," Warps in unmagnetized, non-self-gravitating, inviscid Keplerian discs are rather special, as we shall review in 3 below."462 This is because à warp (with azimuthal wavenumber m= 1) that is quasistatic in an inertial frame sets up vertically-varving horizontal pressure gradients in the disc hat oscillate at the rotation [requeney © as viewed in a ocally corotating frame., This is because a warp (with azimuthal wavenumber $m=1$ ) that is quasi-static in an inertial frame sets up vertically-varying horizontal pressure gradients in the disc that oscillate at the rotation frequency $\Omega$ as viewed in a locally corotating frame.463 In Ixeplerian dises this is resonant with the epicvelie frequency. ancl so modest warps can excite large amplitude motions we shall call them — in the disc.," In Keplerian discs this is resonant with the epicyclic frequency, and so modest warps can excite large amplitude motions – we shall call them – in the disc."464 As a result. warps and. bending waves propagate approximately non-cispersively. at nearly the sound: speed. in a Weplerian disc.," As a result, warps and bending waves propagate approximately non-dispersively, at nearly the sound speed, in a Keplerian disc."465 In a non-Ixeplerian disc. the in-plane oscillations are much weaker and bending waves are dispersive (Papaloizou Lin 1995: Ogilvie 1999).," In a non-Keplerian disc, the in-plane oscillations are much weaker and bending waves are dispersive (Papaloizou Lin 1995; Ogilvie 1999)."466 The special nature of warps in Weplerian dises raises a number of interesting astrophysical issues., The special nature of warps in Keplerian discs raises a number of interesting astrophysical issues.467 Are the in-plane oscillations stable?, Are the in-plane oscillations stable?468 We shall show via two cillerent lines of analysis that they are not in £3 and §4., We shall show via two different lines of analysis that they are not in 3 and 4.469 For small warp amplitudes. the warp is unstable to a parametric instability. a possibility presciently hinted at by Papaloizou “Perquem (1995).," For small warp amplitudes, the warp is unstable to a parametric instability, a possibility presciently hinted at by Papaloizou Terquem (1995)."470 Next. what is the non-linear outcome of the instability?," Next, what is the non-linear outcome of the instability?"471 This we explore numerically in 85. which," This we explore numerically in 5, which"472"detector light curve. cleaned from the source contribution, and ready for further analvsis.","detector light curve, cleaned from the source contribution, and ready for further analysis."473 Using the background model (Appendix Appendix À:)) we obtained for cach the predieted detector count rate. as shown in Fig. 5..," Using the background model (Appendix \ref{section:model}) ) we obtained for each the predicted detector count rate, as shown in Fig. \ref{fig:datafit}."474 The detailed view of the observed and predicted detector Πο curves aud their residuals diving a spacecraft orbit 961 is shown in Fig. G.., The detailed view of the observed and predicted detector light curves and their residuals during a spacecraft orbit 964 is shown in Fig. \ref{fig:fit}.475 We deuoted regions of background measurement (|) É—20() in blue. and actual GRNE observations (]|b|« 20°) in red.," We denoted regions of background measurement $|b|>=20^{\circ}$ ) in blue, and actual GRXE observations $|b|<20^{\circ}$ ) in red."476 Fie., Fig.477 6 shows that the background behavior iu an individual orbit cau be captured ouly with fast scanning observations such as GLSss. The backerouud model. with low intrinsic scatter. exactly follows the observed detector rate. and the scatter of residuals (lower panel of Fig. 6)) A," \ref{fig:fit}478 shows that the background behavior in an individual orbit can be captured only with fast scanning observations such as s. The background model, with low intrinsic scatter, exactly follows the observed detector rate, and the scatter of residuals (lower panel of Fig. \ref{fig:fit}) )"479Wis AC‘dHaparableeA to “the &ta|intitle πο... t the IMTIROS procedure (Appendix AppendixC)., is comparable to the statistical uncertainty of the IROS procedure (Appendix \ref{section:accuracy}) ).480 Using the entire data set at |=155°. we avidraecd gGsiduals over Cedéetic latitugleSas shown iu B@G," Using the entire data set at $l=155^{\circ}$, we averaged residuals over Galactic latitude, as shown in Fig."481 7 by red poiuts., \ref{fig:ridge} by red points.482"⋅↴↴ The latitude∙⋅ profile∙⋅ does- not, showase anyLLL sienificantdeu excess in the (ήθος plane region at bES4)5", The latitude profile does not show any significant excess in the Galactic plane region at $b=0^\circ$.4830As expected. TJBic CRANE associated with the old stellar 1s not detected iu the GA.," As expected, the GRXE associated with the old stellar population is not detected in the GA."484 The Lo upper limit oupopulation the CRNE fux in the [5|<5° latitude range. which roughly corresponds to the IBIS fully coded FOV. is ~2.8 mCrab. or —G. mCrab taking systematic uncertainties iuto account.," The $1\sigma$ upper limit on the GRXE flux in the $|b|<5^\circ$ latitude range, which roughly corresponds to the IBIS fully coded FOV, is $\sim 2.8$ mCrab, or $\sim 6.4$ mCrab taking systematic uncertainties into account."485 We later refer to à 20 upper limit of ~12.5 Crab., We later refer to a $2\sigma$ upper limit of $\sim 12.8$ mCrab.486 One can convert the achieved upper luit to more convenieut units using the effective solid angle of the IBIS telescope ~2a6 dee? aud taking into account that the GRXE is much less extended in the Galactic latitude than the average cross-section of IBIS FOV., One can convert the achieved upper limit to more convenient units using the effective solid angle of the IBIS telescope $\sim286$ $^2$ and taking into account that the GRXE is much less extended in the Galactic latitude than the average cross-section of IBIS FOV.487" For iustauce. the 26 upper Hut ou the CRXE fux at /=155"" per uut Galactic longitude is 0.7 11€rab "," For instance, the $2\sigma$ upper limit on the GRXE flux at $l=155^{\circ}$ per unit Galactic longitude is $0.7$ mCrab $^{-1}$."488One can test the GRXE non-detection in the CA for consistenev with stellar aud truly diffuse GRXE origins., One can test the GRXE non-detection in the GA for consistency with stellar and truly diffuse GRXE origins.489 To this end. we compared the observed drop of the hard A-rav fux frou the GC to the GA region (per IBIS FOV) with the correspouding change of the intensity of a eiven tracer.," To this end, we compared the observed drop of the hard X-ray flux from the GC to the GA region (per IBIS FOV) with the corresponding change of the intensity of a given tracer."490 We used the COBE/DIRBE L.9snn as oa tracer of stellar mass. and the ECRET eamunua-rav backgroundmap above LOO MeV as a tracer of the cosmic-ray induced eiauuuia-ray backerouud.," We used the COBE/DIRBE $4.9\mu$ m as a tracer of stellar mass, and the EGRET gamma-ray backgroundmap above $100$ MeV as a tracer of the cosmic-ray induced gamma-ray background."491 The ECRET backeround iuteusitv drops from the GC to the GA by a factor of ~3., The EGRET background intensity drops from the GC to the GA by a factor of $\sim3$.492" Therefore. using the couscrvative estimate of the GRAE fux in the GC from IK07 of 15023:15 τιςτα we expect the correspouding flux from the GÀ to be ~50 ταςτα,"," Therefore, using the conservative estimate of the GRXE flux in the GC from K07 of $150\pm15$ mCrab, we expect the corresponding flux from the GA to be $\sim50$ mCrab."493In This contrast.is definitely uot observed according to Fie. 7.., This is definitely not observed according to Fig. \ref{fig:ridge}. .494 thereis a factor of 270 dropin the NIR {μι intensity from 2.7&10j ," In contrast, there is a factor of $270$ drop in the NIR $4.9\mu$ m intensity from $2.7 \times 10^{-5}$ "495quantitatively the observed. and. the theoretical frequency spectra of excited. multiperiocic oscillations.,quantitatively the observed and the theoretical frequency spectra of excited multiperiodic oscillations.496 As a first step. we tried to fit the observed. and theoretical Frequency ranges of the unstable modes.," As a first step, we tried to fit the observed and theoretical frequency ranges of the unstable modes."497 The main uncertainty of such a study is the unsatisfactory description of convection in the stellar envelope and. its interaction with pulsations., The main uncertainty of such a study is the unsatisfactory description of convection in the stellar envelope and its interaction with pulsations.498 Phe fact that convection may influence the instability of stars not only near the lec Edge but almost in the whole classical instability strip was discussed. by Stcllinewerl (1984) in connection with the problem of the determination of helium abundance in globular clusters from the temperature at the Blue Edge of the RRO Lwrae instability domain., The fact that convection may influence the instability of stars not only near the Red Edge but almost in the whole classical instability strip was discussed by Stellingwerf (1984) in connection with the problem of the determination of helium abundance in globular clusters from the temperature at the Blue Edge of the RR Lyrae instability domain.499 0 Scuti stars are generally hotter than RR Lyrae stars. but even in this par of the instability strip convection influences the onset of he instability. for low overtones of radial and nonraclia oscillations.," $\delta$ Scuti stars are generally hotter than RR Lyrae stars, but even in this part of the instability strip convection influences the onset of the instability for low overtones of radial and nonradial oscillations."500 Fig., Fig.501 9 of Pamvatnykh (2000) demonstrates tha convection significantly displaces the racial fundamenta Bluc Edge to hotter temperatures due to increased. driving in the hyelrogen ionization zone which is more extende han in the radiative models., 9 of Pamyatnykh (2000) demonstrates that convection significantly displaces the radial fundamental Blue Edge to hotter temperatures due to increased driving in the hydrogen ionization zone which is more extended than in the radiative models.502 A part of this contribution o the driving may also be caused by the generallv-usec assumption that the convective flux does not. vary during an oscillation cvcle., A part of this contribution to the driving may also be caused by the generally-used assumption that the convective flux does not vary during an oscillation cycle.503 μις simple assumption is probably incorrect in the hyelrogen convection zone., This simple assumption is probably incorrect in the hydrogen convection zone.504 Therefore. the reality. of the additional convective destabilization in the outer hydrogen zone must be examined by using a nonlocal imce-dependent treatment of convection.," Therefore, the reality of the additional convective destabilization in the outer hydrogen zone must be examined by using a nonlocal time-dependent treatment of convection."505 First. promising results in this direction (see Michel et al., First promising results in this direction (see Michel et al.506 1999. Houcdek 2000) exist.," 1999, Houdek 2000) exist."507 Note that the total driving in à od Scuti star (with main contribution due to the & mechanism operating in the second. helium ionization zone) only slightly exceeds he total damping., Note that the total driving in a $\delta$ Scuti star (with main contribution due to the $\kappa$ mechanism operating in the second helium ionization zone) only slightly exceeds the total damping.508 Pherefore even small contributions to the driving are important., Therefore even small contributions to the driving are important.509 Due to these uncertainties we consider our results as oeliminarv and our models as test. models., Due to these uncertainties we consider our results as preliminary and our models as test models.510 Nevertheless. even with such a simple description of the convection we may have a possibility to constrain the stellar parameters rom instability stuclies.," Nevertheless, even with such a simple description of the convection we may have a possibility to constrain the stellar parameters from instability studies."511 In Fig., In Fig.512 5 we show evolutionary tracks for selected. mocels. computed by taking overshooting from the stellar convective core into account.," 5 we show evolutionary tracks for selected models, computed by taking overshooting from the stellar convective core into account."513 The models with ellective temperature dip=SOOO. 7900 and 7800IxIx. in which we study. the oscillations. are marked. by filled: circles.," The models with effective temperature $T_{\rm{eff}}=8000$, 7900 and K, in which we study the oscillations, are marked by filled circles."514 The luminosities of the higher and the lower-mass models. approximately correspond to the luminosity of the primary and secondary stellar components. respectively.," The luminosities of the higher and the lower-mass models approximately correspond to the luminosity of the primary and secondary stellar components, respectively."515 For the primary component. we have chosen models at 16 beeinning of the post-main-sequence. (hereafter. called post-MS) expansion stage. which burn hydrogen in a thick gawell just after full hydrogen exhaustion in the stellar core.," For the primary component, we have chosen models at the beginning of the post-main-sequence (hereafter called post-MS) expansion stage, which burn hydrogen in a thick shell just after full hydrogen exhaustion in the stellar core."516 This evolutionary stage of the primary was proposed earlier bv Ixróllikowska (1992) for a significantly hotter model of about S200 Ix. without overshooting., This evolutionary stage of the primary was proposed earlier by Króllikowska (1992) for a significantly hotter model of about 8200 K without overshooting.517 Moreover. we studied slightly more massive models of similar effective temperature and Luminosity in the ALS stage as well as post-M$S models without overshooting.," Moreover, we studied slightly more massive models of similar effective temperature and luminosity in the MS stage as well as post-MS models without overshooting."518 The secondary. component. which is fainter by approximately 1.1 mag (whieh corresponds to the dillerence by 0.44 in logL between the components) is à main-sequence star with hydrogen burning in the convective core.," The secondary component, which is fainter by approximately 1.1 mag (which corresponds to the difference by 0.44 in $\log L$ between the components) is a main-sequence star with hydrogen burning in the convective core."519 In Fig., In Fig.520 5 we also plot the Blue Ecges of the instability strip taken from Pamwatnvkh (2000). which were computed for nonrotating models without overshooting for .X=0.70. )— 028. Z=0.02 and with an assumed. mixine-leneth parameter a=1.0.," 5 we also plot the Blue Edges of the instability strip taken from Pamyatnykh (2000), which were computed for nonrotating models without overshooting for $X=0.70$, $Y=0.28$ , $Z=0.02$ and with an assumed mixing-length parameter $\alpha = 1.0$."521 The general Blue Eclge is defined as the hotter envelope of unstable overtones. from radial niocle ps (seventh overtone) near the ZAXMS to modepz (fourth," The general Blue Edge is defined as the hotter envelope of unstable overtones, from radial mode $p_8$ (seventh overtone) near the ZAMS to mode$p_5$ (fourth"522jpc3.5. but La. varies from zc1079Lp. for the Pei (1995) model (solid. curve) to 210Lp... for the model of Madan et (01999).,"$\beta_h \approx 3.5$, but $L_\ast$ varies from $\approx 10^{10}~L_{B,\odot}$ for the Pei (1995) model (solid curve) to $\approx 10^{12}~L_{B,\odot}$ for the model of Madau et (1999)."523 The curves iu the bottom panel all have £.%10117Eg... but have different values of 3).," The curves in the bottom panel all have $L_\ast\approx 10^{11.5}~L_{B,\odot}$, but have different values of $\beta_h$."524 The parameters of the LES are suumiaized in Table 1.., The parameters of the LFs are summarized in Table \ref{tab:LF}. .525 The values are given at redshift +=6: we allow for slightly different values for the characteristic Iuuinositv over the range 5.8τς6.28 bv inchiding the redshift dependence of L. as parameterized in cach case by Pei (1995). Madau et ((1999). and Werithe Loeb (2002).," The values are given at redshift $z=6$; we allow for slightly different values for the characteristic luminosity over the range $5.8<z<6.28$ by including the redshift dependence of $L_\ast$ as parameterized in each case by Pei (1995), Madau et (1999), and Wyithe Loeb (2002)."526 The lensing probability depends on the intrinsic LE. which is not directly observable.," The lensing probability depends on the intrinsic LF, which is not directly observable."527 In usine the Fan et ((2001b) data point as a constraint on the intrinsic LF. we thus implicitly assimued that Ieusine does not have a laree overall effect ou the LF.," In using the Fan et (2001b) data point as a constraint on the intrinsic LF, we thus implicitly assumed that lensing does not have a large overall effect on the LF."528 Tf maguification bias is significant. then this assumption breaks down for the bright-cud of the LF.," If magnification bias is significant, then this assumption breaks down for the bright-end of the LF."529 Thus. to match the observations. the normalizations of the iutrinsic LFs should in fact be lowered bv a factor equal to the magnification bias for the observed quasars.," Thus, to match the observations, the normalizations of the intrinsic LFs should in fact be lowered by a factor equal to the magnification bias for the observed quasars."530 However. for the purpose of computing the a posteriori lensing probability this is irrelevant. since the magnification bias is iudependeut of the normalization of the intrinsic LF.," However, for the purpose of computing the a posteriori lensing probability this is irrelevant, since the magnification bias is independent of the normalization of the intrinsic LF."531 The SDSS observations provide au upper luit on the slope of the bright-cud of the observed LE: yi.«1.3 at 99 percent confidence (Fan et 22001a.b).," The SDSS observations provide an upper limit on the slope of the bright-end of the observed LF: $\beta_{h,obs} < 4.3$ at 99 percent confidence (Fan et 2001a,b)."532 If magnification bias is muportaut. then this constraiut will always be satisfied since lensing by an isothermal sphere will result in a bright-eud slope of οςS (the intrinsic differential lensing probability dp/djxye? for feo2).," If magnification bias is important, then this constraint will always be satisfied since lensing by an isothermal sphere will result in a bright-end slope of $\beta_{h,obs} = 3.0$ (the intrinsic differential lensing probability $dp/d\mu \propto \mu^{-3}$ for $\mu > 2$ )."533 This is illustrated in Fig. ἐν," This is illustrated in Fig. \ref{fig:lfobs},"534" which shows the intrinsic and observed LEs for our most extreme model. which has 3),=15 (dashed curve in the lower paucl of Fig. 3))."," which shows the intrinsic and observed LFs for our most extreme model, which has $\beta_h = 4.5$ (dashed curve in the lower panel of Fig. \ref{fig:lf}) )."535 Since the maenification bias increases with jj. observations cannot directly constrain the stecpuess of the intrinsic. bright-cud slope of the LF.," Since the magnification bias increases with $\beta_h$, observations cannot directly constrain the steepness of the intrinsic, bright-end slope of the LF."536 Wowever. we will see below that the slope can be coustrained indirectly. by measuring the fraction of umltiply inuaged quasars.," However, we will see below that the slope can be constrained indirectly, by measuring the fraction of multiply imaged quasars."537 Fig., Fig.538 5 shows the a posteriori probabilities for the 25.99 SDSS quasar to be magnified by at least a factor µ. subject to the coustraimt that ouly one image is detectable by SDSS.," \ref{fig:lensprob} shows the a posteriori probabilities for the $z=5.99$ SDSS quasar to be magnified by at least a factor $\mu$ , subject to the constraint that only one image is detectable by SDSS."539 The siuall discoutinuity iu the probabilities at pe=6.112 occurs because for po<6.172 the fainter image is too faint to be detectable. and we do not impose any constraint on the splitting anele.," The small discontinuity in the probabilities at $\mu=6.172$ occurs because for $\mu<6.172$ the fainter image is too faint to be detectable, and we do not impose any constraint on the splitting angle."540 On the other hand. for HOD6.172 both nuages would be brighter than SDS! threshold. aud sve therefore impose the coudition A0«1f ou the splitting anele.," On the other hand, for $\mu>6.172$ both images would be brighter than SDSS's threshold, and we therefore impose the condition $\Delta\theta<1^{\prime\prime}$ on the splitting angle."541 The seven curves shown in Fie., The seven curves shown in Fig.542" correspond to the seven iutriusic LFs in Fig. δν,", \ref{fig:lensprob} correspond to the seven intrinsic LFs in Fig. \ref{fig:lf}.543 From the figure it is clear that a wide range of probabilities is possible for a given nüiuiunmu magnification., From the figure it is clear that a wide range of probabilities is possible for a given minimum magnification.544 Iu. particular. because of the lack of coustraimts ou the iutrisic LE. they can be significantly hieher than the maxinuun value of ~30% found bx Writlie Loeb (2002). who considered a more restricted ranec of LFs (theshort dashed curve in the upper pancl iu Fig.," In particular, because of the lack of constraints on the intrinsic LF, they can be significantly higher than the maximum value of $\sim 30\%$ found by Wyithe Loeb (2002), who considered a more restricted range of LFs (theshort dashed curve in the upper panel in Fig."545 3represents their most extreme model that results in their maxinuun lensing probabilities)., \ref{fig:lf} represents their most extreme model that results in their maximum lensing probabilities).546 For exiuuploe. if," For example, if"547subdomains aud expaud to low order iu cach subdomain. whereas spectral methods use conrparativelv few subdomains with Ligh expansion orders.,"subdomains and expand to low order in each subdomain, whereas spectral methods use comparatively few subdomains with high expansion orders."548 Finite elements are particularly well suited to imegular ecometrics appearing iu many engineernug applications., Finite elements are particularly well suited to irregular geometries appearing in many engineering applications.549 For sufficicutly regular domains. however. spectral methods are generally faster and/or more accurate.," For sufficiently regular domains, however, spectral methods are generally faster and/or more accurate."550 Multidoimaiu spectral methods date back at least to the work of Orszag]?|.., Multidomain spectral methods date back at least to the work of \cite{Orszag:1980}.551 Iu a nultidomain spectral method. oue has to match the solution across different sDdomains.," In a multidomain spectral method, one has to match the solution across different subdomains."552 Often this is accomplished by a combination of solves on individual sbdomains together with a elobal scheme to find the function values at the ternal sbdomain boundaries., Often this is accomplished by a combination of solves on individual subdomains together with a global scheme to find the function values at the internal subdomain boundaries.553 Exaniples of such global schemes are relaxational itcration|?|.. an influence matrix|?.?].. or the spectral projection decomposition iethod|?]..," Examples of such global schemes are relaxational \cite{Funaro-Quarteroni-Zanolli:1988}, an influence \cite{Macaraeg-Streett:1986,Boyd:2001}, or the spectral projection decomposition \cite{Gervasio-Ovtchinnikov-Quarteroni:1997}."554 For siuple PDEs like the Uehuholtz equation. fast solvers for the subdoimain solves are available.," For simple PDEs like the Helmholtz equation, fast solvers for the subdomain solves are available."555 For more complicated PDEs. or for coupled PDEs. the subdomain solves will typically use an iterative solver.," For more complicated PDEs, or for coupled PDEs, the subdomain solves will typically use an iterative solver."556 Oue drawback of these schemes is that information from the iterative subdomain solves is not used in the elobal matching procedure until the subdomain solves have completely couverecd., One drawback of these schemes is that information from the iterative subdomain solves is not used in the global matching procedure until the subdomain solves have completely converged.557 The question arises whether efficiency. cau be improved by avoiding this delay iu comnimnmunication with the matching procedure., The question arises whether efficiency can be improved by avoiding this delay in communication with the matching procedure.558 Iu this paper we present a new spectral inethod. for coupled noulinear PDEs based on pseudospoectral collocation with domain decomposition., In this paper we present a new spectral method for coupled nonlinear PDEs based on pseudospectral collocation with domain decomposition.559 This method does not split subdomain solves aud matching into two distinct clemeuts., This method does not split subdomain solves and matching into two distinct elements.560 Iustead it colmbines satisfying the PDE ou cach subdomain. matching between subdomains. and satisfying the boundary conditions iuto oue set of equations.," Instead it combines satisfying the PDE on each subdomain, matching between subdomains, and satisfying the boundary conditions into one set of equations."561 This svstei of equations is then solved with au iterative solver. typically GMBRES[?]..," This system of equations is then solved with an iterative solver, typically \cite{Templates}."562 At cach iteration. this solver thus has up-to-date information about residuals on the individual subdomains and about matching and thus can make optimal use of all information.," At each iteration, this solver thus has up-to-date information about residuals on the individual subdomains and about matching and thus can make optimal use of all information."563 The individual subdomains implemented are rectangular blocksend spherical shells., The individual subdomains implemented are rectangular blocks spherical shells.564 Whereas either rectangular blocks (see e.g. |?.7. 23) or spherical shells(?| jive been emploved before. we are not aware of work using both.," Whereas either rectangular blocks (see e.g. \cite{Demaret-Deville:1991, Ku:1995, Pinelli-Vacca-Quarteroni:1997}) ) or spherical \cite{Grandclement-Bonazzola-et-al:2001} have been employed before, we are not aware of work using both."565 The code supports an arbitrary number of blocks and shells that cau touch each other and/or overlap., The code supports an arbitrary number of blocks and shells that can touch each other and/or overlap.566 Moreover. the operator & at the core of the method (see section 3.3)) turus out o be modular. ie. the code fragments used. to evaluate the PDE. the boundary conditions. aud the matching coucitionus are independent of cach other.," Moreover, the operator $\cal S$ at the core of the method (see section \ref{sec:OperatorS}) ) turns out to be modular, i.e. the code fragments used to evaluate the PDE, the boundary conditions, and the matching conditions are independent of each other."567 Thus the structure of the resulting code allows for exeat flexibility. which is further eubliauced wa novel point of view of the mappings that are used to map collocation coordinates o the physical coordinates.," Thus the structure of the resulting code allows for great flexibility, which is further enhanced by a novel point of view of the mappings that are used to map collocation coordinates to the physical coordinates."568 This flexibility is highhehted iu the following aspects:, This flexibility is highlighted in the following aspects:569à M... 2007).,"$\delta$ $M_{\odot}$ \citep{fea07,mac07}."570. 2) The lack of successful asteroseisiule analyses las encouraged authors to reconsider their approach., 2) The lack of successful asteroseismic analyses has encouraged authors to reconsider their approach.571 Ou the oue haud. much progress has been made in observational mode identification. while on the other. authors are beeinning to study these stars iu systems where the uunuber of free paraiaetersis reduced," On the one hand, much progress has been made in observational mode identification, while on the other, authors are beginning to study these stars in systems where 	the number of free parametersis reduced"572best-fit model become significant al the 36 level.,best-fit model become significant at the $3 \sigma$ level.573 Based on this we quote an inclination i=οἱ1., Based on this we quote an inclination $i = 89\degr^{+1}_{-2}$.574 In Figs., In Figs.575 2 sand 3.. we compare our data with best fit models of two cifferent inclinations.," \ref{vprime} and \ref{iprime}, we compare our data with best fit models of two different inclinations."576 The model fits al lower inclination first begin to become unsatisfactory ad the contact points (ὁ2£0.015 and 40.01).," The model fits at lower inclination first begin to become unsatisfactory at the contact points $\phi \approx577\pm 0.015$ and $\pm 0.01$ )."578 Using this constraint. the ratio of the stellar radii is5 Rafas=0.268⋅⋅∣∣∡∣∣⊽⊁rab. where the uncertainties∙ include− the uncertainty⋅ in.⋅ ιτ).," Using this constraint, the ratio of the stellar radii is $R_{Ab} / R_{Aa} = 0.268^{+0.015}_{-0.004}$, where the uncertainties include the uncertainty in $f_{Aa} (V)$."579"∙ry The measured {νε and {ix contribution fom component D (providing the third light) are consistent with it being a normal main sequence star. based on comparison wilh Yiel and Girardiοἱal.(2000) isochrones using a distance modulus (53—M),=9.72 (Sandquist 2003)."," The measured $T_{eff}$ and flux contribution from component B (providing the third light) are consistent with it being a normal main sequence star, based on comparison with \citet{yy} and \citet{gir00}580 isochrones using a distance modulus $(m - M)_V = 9.72$ (Sandquist 2003)."581" In the following analvsis. we will assume that component D is a normal main sequence star and a cluster member,"," In the following analysis, we will assume that component B is a normal main sequence star and a cluster member."582 Based on (hat. we can constrain the photonmetric properties of the primary star in the eclipsing binary (component Aa) without resorting to models.," Based on that, we can constrain the photometric properties of the primary star in the eclipsing binary (component Aa) without resorting to models."583" Our calibration of the ensemble photometry (Sandequist 2003) leads to a value for ihe sum of the three stars of Vj,=12.729 and (V—/)),,=0.643.", Our calibration of the ensemble photometry (Sandquist 2003) leads to a value for the sum of the three stars of $V_{tot} = 12.729$ and $(V-I)_{tot} = 0.643$.584 Fig., Fig.585 6 shows the V7 CAD for our deconvolution of component D Irom the total light of the eclipsing binary., \ref{cmd} shows the $VI$ CMD for our deconvolution of component B from the total light of the eclipsing binary.586 The three linked points delineate the range of {ιτ) allowed by our spectra., The three linked points delineate the range of $f_{Aa} (V)$ allowed by our spectra.587" Our derived values are Vy,=12.86€0.02 and (V—£),,=0.61940.002."," Our derived values are $V_{bin} = 12.86 \pm5880.02$ and $(V-I)_{bin} = 0.619 \pm 0.002$."589 Assuming again that the secondary component of the eclipsing binary Ab is a normal main sequence member of the cluster. we can deconvolve the (small) contribution of its light and get an estimate of the photometry of the primary alone.," Assuming again that the secondary component of the eclipsing binary Ab is a normal main sequence member of the cluster, we can deconvolve the (small) contribution of its light and get an estimate of the photometry of the primary alone."590" From the measured secondary eclipse depth ancl estimates of the relative flux contributions of components Aa and D. we find: Ly,—=4.85. or Ly,=10.10.—0.09qus."," From the measured secondary eclipse depth and estimates of the relative flux contributions of components Aa and B, we find $I_{Ab} - I_{Aa} = 4.85$, or $I_{Ab} =59117.10^{+0.09}_{-0.08}$."592" Component-. Ab. essentially: does not contribute+]. in: V (only about 0.004 mag). so that the corrected primary star values are Wy,=12.860.03 and (V—2)4,=0.611z0.003."," Component Ab essentially does not contribute in $V$ (only about 0.004 mag), so that the corrected primary star values are $V_{Aa} = 12.86 \pm 0.02$ and $(V-I)_{Aa} = 0.611 \pm 0.003$."593 The deconvolved photometry values for the primary place il sienilicantlv to the blue of the most densely populated portions of the turnolf., The deconvolved photometry values for the primary place it significantly to the blue of the most densely populated portions of the turnoff.594. We have 2152 observations of S986 in V and 816 in J and comparable nunbers of observations of many other (urnoll stars. so that error in the photometry relative to (urnoll stars can be ruled out.," We have 2152 observations of S986 in $V$ and 816 in $I$ and comparable numbers of observations of many other turnoff stars, so that error in the photometry relative to turnoff stars can be ruled out."595 If we are wrong in our assumption that component D is a normal main sequence star and il is actually an unresolved binary itsell this would make D redder and would require component Aa to be bluer still.," If we are wrong in our assumption that component B is a normal main sequence star and it is actually an unresolved binary itself, this would make B redder and would require component Aa to be bluer still."596 The effective temperature measured [rom our spectra indicates that it is hotter (han other stars that are clearly on the single-star sequence in the color-magnitude diagram., The effective temperature measured from our spectra indicates that it is hotter than other stars that are clearly on the single-star sequence in the color-magnitude diagram.597Figure 6 shows the time evolution of the torque per unit mass exerted on a protoplanet of equivalent. parameters to that in run Gl but embedded in a laminar disc.,Figure \ref{fig7} shows the time evolution of the torque per unit mass exerted on a protoplanet of equivalent parameters to that in run G1 but embedded in a laminar disc.598 The upper line shows the (positive) torque due to the disc ling interior to the protoplanet orbital radius. the lowest line shows the torque due to the outer disc. and the middle line shows the total (negative) torque.," The upper line shows the (positive) torque due to the disc lying interior to the protoplanet orbital radius, the lowest line shows the torque due to the outer disc, and the middle line shows the total (negative) torque."599 It is clear that a well defined. ne torque acting on the protoplanet may be defined. along with a corresponding inward migration rate.," It is clear that a well defined net torque acting on the protoplanet may be defined, along with a corresponding inward migration rate."600 Figure 7. shows a similar plot but for the turbulen disc mocdel €i., Figure \ref{fig8} shows a similar plot but for the turbulent disc model G1.601 Lt is clear that the forcing experienced. by he protoplanet in this case dilfers dramatically from tha obtained in the laminar disc., It is clear that the forcing experienced by the protoplanet in this case differs dramatically from that obtained in the laminar disc.602 Phe torques from the inner anc outer disc suller very large [luctuations as a result of the ootoplanet interacting eravitationally with the turbulen wakes apparent in figures 3. and 4 as they shear past. the xotoplanet. and this causes the net torque experienced. by he protoplanet to oscillate between negative ancl positive values.," The torques from the inner and outer disc suffer very large fluctuations as a result of the protoplanet interacting gravitationally with the turbulent wakes apparent in figures \ref{fig4} and \ref{fig5} as they shear past the protoplanet, and this causes the net torque experienced by the protoplanet to oscillate between negative and positive values."603 The orbital migration of the protoplanet is thus ikelv to occur as a random walk rather than as a monotonic inward. drift normally associated. with tvpe L migration., The orbital migration of the protoplanet is thus likely to occur as a random walk rather than as a monotonic inward drift normally associated with type I migration.604 In his run. for which the spiral wakes generated by the planet are completely dominated by the turbulent walkes. the usual separation between inner and outer dise torques is barely discernible due to the high amplitude turbulent Ductuations.," In this run, for which the spiral wakes generated by the planet are completely dominated by the turbulent wakes, the usual separation between inner and outer disc torques is barely discernible due to the high amplitude turbulent fluctuations."605 The time evolution of the running time average of the torque per unit mass in model GI is shown in figure S.., The time evolution of the running time average of the torque per unit mass in model G1 is shown in figure \ref{fig9}.606 The upper line shows the running time average of the torque due to the inner disc. the lowest line shows the time averaged torque due to the outer disc. and the middle line shows the running time average of the total torque.," The upper line shows the running time average of the torque due to the inner disc, the lowest line shows the time averaged torque due to the outer disc, and the middle line shows the running time average of the total torque."607 The straight line shows the time average of the total torque per unit mass experienced. in an equivalent laminar disc model., The straight line shows the time average of the total torque per unit mass experienced in an equivalent laminar disc model.608 Phe firsthing to note [rom figure S. is that the running time averaged orque in run GI does not converge to a well defined value or the time over which the simulation was run (just over 20 planet orbits)., The firstthing to note from figure \ref{fig9} is that the running time averaged torque in run G1 does not converge to a well defined value for the time over which the simulation was run (just over 20 planet orbits).609 Near the beginning of the simulation the ime average is close to that obtained from a similar laminar disc run. but as the calculation evolves the running time average changes continuously.," Near the beginning of the simulation the time average is close to that obtained from a similar laminar disc run, but as the calculation evolves the running time average changes continuously."610 By the end of the simulation. he torque experienced by the protoplanet will be positive on average. Corresponding to outward migration on a time scale of ~2.8 Myr.," By the end of the simulation, the torque experienced by the protoplanet will be positive on average, corresponding to outward migration on a time scale of $\simeq 2.8$ Myr."611 1 we assume that there exists a well defined long terni mean for the torque experienced. by the protoplanet. then we can express the torque as the sum of this mean torque and a Iluctuating component: where71) is the torque experienced at time /. 7 is the mean torque. anc Z(/) is the [üctuating component.," If we assume that there exists a well defined long term mean for the torque experienced by the protoplanet, then we can express the torque as the sum of this mean torque and a fluctuating component: where$T(t)$ is the torque experienced at time $t$, ${\overline T}$ is the mean torque, and $T_f(t)$ is the fluctuating component."612 The running time average of the torque is given by then we can write Assuming that the amplitude of the torque Iuctuations TyjG) about the mean Fo follow a Gaussian. distribution with standard: cleviation op and recur on a characteristic timescale £g. we can estimate from equation 5 that the lluctuations in the running mean satisfy which may be used to estimate how long we need to run a simulation before we can expect the running time average of the torque to converge to a well defined. value (i.c. when theDuctuation estimate from equation 6 becomes significantly less than [7]).," The running time average of the torque is given by then we can write Assuming that the amplitude of the torque fluctuations $T_f(t)$ about the mean $\overline T$ follow a Gaussian distribution with standard deviation $\sigma_T$ and recur on a characteristic timescale $t_f,$ we can estimate from equation \ref{T_av2} that the fluctuations in the running mean satisfy which may be used to estimate how long we need to run a simulation before we can expect the running time average of the torque to converge to a well defined value (i.e. when the fluctuation estimate from equation \ref{T_av3} becomes significantly less than $|{\overline T}|$ )."613" Inspection of ligure 7 suggests hat the /; is is twpically about one half of a planetary orbit. D,/2."," Inspection of figure \ref{fig8} suggests that the $t_f$ is is typically about one half of a planetary orbit, $P_p/2$."614 Euation ο tells us that the larger the relative amplitude of [uctuations. the longer we have to integrate or the running mean to converge.," Equation \ref{T_av3} tells us that the larger the relative amplitude of fluctuations, the longer we have to integrate for the running mean to converge."615 lt is clear that the level of Éuctuations associated. with he torques is very much lareer than the running mean in igure 7.., It is clear that the level of fluctuations associated with the torques is very much larger than the running mean in figure \ref{fig8}.616 Lowe take the mean value of the torque to be Tz9.10' from the straight line in fig 7.. then the tvpical magnitude of the fluctuations can be estimated to be apc 10-7. but with extreme IHuctuations being a [actor of," If we take the mean value of the torque to be ${\overline T} \simeq 9 \times 10^{-7}$ from the straight line in fig \ref{fig8}, , then the typical magnitude of the fluctuations can be estimated to be $\sigma_T \simeq 2 \times 10^{-5}$ , but with extreme fluctuations being a factor of"617ol an infinite number of measurements (7—2c) uniformly distributed in stellar rotation phase.,of an infinite number of measurements $n \to \infty$ ) uniformly distributed in stellar rotation phase.618 Using Eq. (, Using Eq. (6191) and replacing the summation with integration over (he phases ©. we will obtain irighl]],"1) and replacing the summation with integration over the phases $\phi$, we will obtain ]."620(7) Similarly. we ean also find that By j|](," Similarly, we can also find that B_p ]."621"8) and u/3)max BB/D,. B,/D, and ουκ, are plotted against the inclination of the rotation axis / forangles 5 equal to 307. 45° and 607."," and B/B_p, ${\cal B}_{\mbox{\sz m}}/B_p$ and ${\cal B}_{\mbox{\sz extr}}/B_p$ are plotted against the inclination of the rotation axis $i$ forangles $\beta$ equal to $30^{\circ}$, $45^{\circ}$ and $60^{\circ}$."622 We see that these dimensionless ratios vary within the range 0.12. 0.30 with mean values close to 0.20., We see that these dimensionless ratios vary within the range 0.12 – 0.30 with mean values close to 0.20.623 In real observations. the number of magnetic field measurements is usually small.," In real observations, the number of magnetic field measurements is usually small."624 To understand how the values of the quantities we consider depend in this case on (he number of field measurements for various angles 7 and ο. let us model the field measurement process in the following wav.," To understand how the values of the quantities we consider depend in this case on the number of field measurements for various angles $i$ and $\beta$, let us model the field measurement process in the following way."625 Supposethat the field measurements for each of (he possible angles 7 and ο) were performed μι (mes. where the number μι can be equal to one.," Supposethat the field measurements for each of the possible angles $i$ and $\beta$ were performed $N_{\mbox{\sz mf}}$ times, where the number $N_{\mbox{\sz mf}}$ can be equal to one."626 We will assume that the stellar rotation phase ó al which the field was measured is a random variable uniformly distributed in the interval [0.1].," We will assume that the stellar rotation phase $\phi$ at which the field was measured is a random variable uniformly distributed in the interval $[0,1]$."627 Suppose also that 7 is a random variable determined by the random orientations of the stellar rotation axis., Suppose also that $i$ is a random variable determined by the random orientations of the stellar rotation axis.628 At the same time. the angle ;2 probably varies over a narrower range (+~15 ) wilh a mean value close to 45° (see. ee. Ixholtveinetal.(2007): Auriereetal. (2007))).," At the same time, the angle $\beta$ probably varies over a narrower range $\pm \sim 15^{\circ}$ ) with a mean value close to $45^{\circ}$ (see, e.g., \cite{2007AN....328.1170K}; \cite{2007A&A...475.1053A}) )."629" For this reason. we performed our caleulations for two ranges of 2:30—GO"" and 0—907."," For this reason, we performed our calculations for two ranges of $\beta$:$30-60^{\circ}$ and $0-90^{\circ}$."630 The calculations were performed as follows: we chose z5000 random values of the angles Hand S (hat varied within the above ranges., The calculations were performed as follows: we chose $\approx 5000$ random values of the angles $i$ and $\beta$ that varied within the above ranges.631 The number μμ of random rotation phases ᾧ was determined for each pair of / and ο., The number $N_{\mbox{\sz mf}}$ of random rotation phases $\phi$ was determined for each pair of $i$ and $\beta$.632 D; was determined for each of these phases © from Eq. (, $B_l$ was determined for each of these phases $\phi$ from Eq. (6331).,1).634" The values of B; obtained were used to calculate the ratios ορ. 5,/D, and Bosiy/B, from Eqs. ("," The values of $B_l$ obtained were used to calculate the ratios ${\cal B}/B_p$, ${\cal B}_{m}/B_p$ and ${\cal B}_{\mbox{\sz extr}}/B_p$ from Eqs. ("6352) (4).,2) – (4).636" Since these ratios do not depend on D,. the latter was taken to beequal to one."," Since these ratios do not depend on $B_p$, the latter was taken to beequal to one."637" For 5/ D,. 5,/D, and Boa/ D,. we determined the mean values of these quantities and the corresponding standard deviations e. σᾳ, and Toy, in a standard way."," For ${\cal B}/B_p$ , ${\cal B}_{m}/B_p$ and ${\cal B}_{\mbox{\sz extr}}/B_p$ , we determined the mean values of these quantities and the corresponding standard deviations $\sigma$ , $\sigma_m$ and $\sigma_{\mbox{\sz extr}}$ in a standard way."638 The results of our numerical experiment are presented in Fig., The results of our numerical experiment are presented in Fig.639 2., 2.640an effect of diffusion and consider ouly effects of gvration and eraclient-curvature Generally. an interplanetary magnetic [hix rope expands as it propagates through interplanetary space.,"an effect of diffusion and consider only effects of gyration and gradient-curvature Generally, an interplanetary magnetic flux rope expands as it propagates through interplanetary space."641 Llowever. we ignore flux rope expansion because ils rate is many orders of magnitude less (han the speed of a cosmic ray particle.," However, we ignore flux rope expansion because its rate is many orders of magnitude less than the speed of a cosmic ray particle."642 We consider a non-expanding cvlindrical magnetic [Iux rope model with radius Ay (e.g.. Marubashi 1997).," We consider a non-expanding cylindrical magnetic flux rope model with radius $R_0$ (e.g., Marubashi 1997)."643" The model is defined in cvlindrical coordinates (7.2.2) as where By is (he magnetic [ield intensity alone the fIux rope axis. ancl Jy and 4 are and first-order Bessel functions of the first kind. respectively; s=1 and s=—1 also correspond (to parallel aud antiparallel types of flux rope. respectively,"," The model is defined in cylindrical coordinates $r$ $\varphi$ $z$ ) as where $B_0$ is the magnetic field intensity along the flux rope axis, and $J_0$ and $J_1$ are zeroth-order and first-order Bessel functions of the first kind, respectively; $s=1$ and $s=-1$ also correspond to parallel and antiparallel types of flux rope, respectively."644 Parallel/antiparallelf [Iux ropes are (hose with electric current flowing parallel/antiparallel to the maenetic field in (he flix rope., Parallel/antiparallel flux ropes are those with electric current flowing parallel/antiparallel to the magnetic field in the flux rope.645 The constant à222.40483 is the smallest positive number of the zero point ol the zeroth-orcler Bessel function of the first kind: that is. μία)=0. The Newton-Lorentz equation for a cosmic ray particle inside a flux rope is written as where m. q. v. . and e are (he mass. electric charge. velocity. Lorentz factor of a cosmic rav particle. and the speed of light. respectively.," The constant $a\approx 2.40483$ is the smallest positive number of the zero point of the zeroth-order Bessel function of the first kind; that is, $J_0(a)=0$ The Newton-Lorentz equation for a cosmic ray particle inside a flux rope is written as where $m$, $q$, $\vec v$, $\gamma$, and $c$ are the mass, electric charge, velocity, Lorentz factor of a cosmic ray particle, and the speed of light, respectively."646 A solution of Equation (5)) is generally described by one parameter /., A solution of Equation \ref{eom}) ) is generally described by one parameter $t$.647 ILowever. as the solution mathematically defines a curved line on the spherical surface in (he velocity space. il is possible to choose another parameter as long as one-to-one correspondence between (he parameter and the (ime / is confirmed.," However, as the solution mathematically defines a curved line on the spherical surface in the velocity space, it is possible to choose another parameter as long as one-to-one correspondence between the parameter and the time $t$ is confirmed."648 Since a distance r [rom the flux rope axis to the particle position is described as, Since a distance $r$ from the flux rope axis to the particle position is described as649satisfied.,satisfied.650 In the 4 galaxies. no SSS-3¢ provided enough enough photons to allow a spectral fit.," In the 4 galaxies, no $3\sigma$ provided enough enough photons to allow a spectral fit."651 To carry out a fit we therefore considered a composite of 7 SSS-36 sources., To carry out a fit we therefore considered a composite of 7 $3\sigma$ sources.652 Although this composite spectrum appears to be significantly harder than the SSS-HRs. both the formal and systematic uncertainties (the latter largely associated with ereating the composite spectrum) are large.," Although this composite spectrum appears to be significantly harder than the SSS-HRs, both the formal and systematic uncertainties (the latter largely associated with creating the composite spectrum) are large."653 We therefore note that our results on SSSs are dominated by the bright SSS-HRs in our sample., We therefore note that our results on SSSs are dominated by the bright SSS-HRs in our sample.654 We were able to derive fits for 10 QSSs and 3 QSScomposites identified by using other conditions., We were able to derive fits for $10$ QSSs and $3$ QSScomposites identified by using other conditions.655 As is to be expected. the photon statistics were generally not quite as good for sources identified via the other conditions. and the uncertainties in the spectral parameters are The fits of two of these spectra (M101-53. and the SNOH composite in MIOI) seem compatible with what we might expect for SNRs.," As is to be expected, the photon statistics were generally not quite as good for sources identified via the other conditions, and the uncertainties in the spectral parameters are The fits of two of these spectra (M101-53, and the SNOH composite in M101) seem compatible with what we might expect for SNRs."656 For the other spectra. the best-fit temperatures are generally higher than for sources in the HR category.," For the other spectra, the best-fit temperatures are generally higher than for sources in the HR category."657 Nevertheless. with just one exception. AT«175 eV. The QSS spectra are generally harder and the values of Ny appear to be systematically higher.," Nevertheless, with just one exception, $k\, T < 175$ eV. The QSS spectra are generally harder and the values of $N_H$ appear to be systematically higher."658" In fact 7 of the fits yield. values of Nj, larger than the largest value derived for HR-identified sources.", In fact $7$ of the fits yield values of $N_H$ larger than the largest value derived for HR-identified sources.659 In at least 3 cases. internal absorption would have to be very significant. or the gas would have to be associated with à high-gas-density region. in order for the derived values of Nj; to be physical.," In at least $3$ cases, internal absorption would have to be very significant, or the gas would have to be associated with a high-gas-density region, in order for the derived values of $N_H$ to be physical."660 This could be a genuine selection effect. since some of these categories were especially designed to allow us to identify SSSs located behind large gas columns. which could be associated with the system or which could be spread out along the line of sight.," This could be a genuine selection effect, since some of these categories were especially designed to allow us to identify SSSs located behind large gas columns, which could be associated with the system or which could be spread out along the line of sight."661 When spectral fits are possible for only a small fraction of sources in an external galaxy. the luminosity function is usually computed by assuming that a single factor can convert the count rate of each source into an estimated source luminosity.," When spectral fits are possible for only a small fraction of sources in an external galaxy, the luminosity function is usually computed by assuming that a single factor can convert the count rate of each source into an estimated source luminosity."662 The uncertainties can be estimated by using a set of spectral models (perhaps drawn from those that fit the high count-rate sources) to compute independent conversion factors. and using them to derive a range of physically plausible LFs.," The uncertainties can be estimated by using a set of spectral models (perhaps drawn from those that fit the high count-rate sources) to compute independent conversion factors, and using them to derive a range of physically plausible LFs."663 For VSSs. however. the conversion from count rate to luminosity depends critically on both the source temperature and the value of Nj. To gain insight into the distribution of luminosities we can therefore rely only on the sources for which we have spectral fits.," For VSSs, however, the conversion from count rate to luminosity depends critically on both the source temperature and the value of $N_H.$ To gain insight into the distribution of luminosities we can therefore rely only on the sources for which we have spectral fits."664 In table 6 we list the computed luminosities for each source and composite for which we derived spectral fits., In table $6$ we list the computed luminosities for each source and composite for which we derived spectral fits.665 For each source we list both a low value of the luminosity (assuming that the galaxy’s distance from us is the minimum listed in Table 1) and a high value (assuming that the galaxy's distance from us is the maximum listed in Table 1)., For each source we list both a low value of the luminosity (assuming that the galaxy's distance from us is the minimum listed in Table 1) and a high value (assuming that the galaxy's distance from us is the maximum listed in Table 1).666 We have used these values to compute | LF for the associated VSSs using the lower distance estimate., We have used these values to compute $1$ LF for the associated VSSs using the lower distance estimate.667 For those sources that are composites. we have assumed that the spectra of the sources contributing to the composite are similar.," For those sources that are composites, we have assumed that the spectra of the sources contributing to the composite are similar."668 We have therefore assigned to each source a fraction of the total luminosity that is equal to the fraction of the total counts contributed by that source., We have therefore assigned to each source a fraction of the total luminosity that is equal to the fraction of the total counts contributed by that source.669 In total. 40 sources contribute to our LF: 14 single sources and 26 sources Whose luminosities were determined by studying the spectrum of a composite to which they contributed.," In total, $40$ sources contribute to our LF: $14$ single sources and $26$ sources whose luminosities were determined by studying the spectrum of a composite to which they contributed."670 The results are shown in Figure 2., The results are shown in Figure 2.671 While the function shown in Figure 2 displays some interesting-looking features. it is not possible to compare it directly to the LFs of galactic populations of harder sources.," While the function shown in Figure 2 displays some interesting-looking features, it is not possible to compare it directly to the LFs of galactic populations of harder sources."672 Perhaps the largest uncertainty is that we do not know how well our assumed distribution of luminosities for sources comprising composites reflects reality., Perhaps the largest uncertainty is that we do not know how well our assumed distribution of luminosities for sources comprising composites reflects reality.673 In addition. for some of the composites. the temperatures and luminosities are not very well constrained.," In addition, for some of the composites, the temperatures and luminosities are not very well constrained."674 Finally. we do not know how well this distribution reflects the characteristics of the dimmer sources in our sample.," Finally, we do not know how well this distribution reflects the characteristics of the dimmer sources in our sample."675 Nevertheless there are a few noteworthy features., Nevertheless there are a few noteworthy features.676" Among the sources in this sample. about 18% have L«10°"" ergs s! and of the sources have L>10? ergs s!"," Among the sources in this sample, about $18\%$ have $L < 10^{37}$ ergs $^{-1}$ and of the sources have $L > 10^{38}$ ergs $^{-1}$."677 Referring to Table 6. we find that the low-Iuminosity sources (Qc10°? eres sv!) tend to have high temperatures. between 80 and 170 eV. The high temperature of the low-luminosity sources Is a selection effect-we simply would not have detected these sources had their temperatures been well under 100 eV. It is. however. interesting that there are low-luminosity sources with such high temperatures.," Referring to Table 6, we find that the low-luminosity sources $L < 10^{37}$ ergs $^{-1}$ ) tend to have high temperatures, between $80$ and $170$ eV. The high temperature of the low-luminosity sources is a selection effect–we simply would not have detected these sources had their temperatures been well under $100$ eV. It is, however, interesting that there are low-luminosity sources with such high temperatures."678 One of the predictions of nuclear-burning WD models is that the luminosities and temperatures are larger for WDs of higher mass., One of the predictions of nuclear-burning WD models is that the luminosities and temperatures are larger for WDs of higher mass.679 Low-L/high-T sources do not seem to fit this pattern., Low-L/high-T sources do not seem to fit this pattern.680 Given the uncertainties in the spectral parameters. and the assumptions made about the composite spectra. it may be too early to conclude that the apparent low-L/high-T sources are not nuclear-burning white dwarfs (NBWDs).," Given the uncertainties in the spectral parameters, and the assumptions made about the composite spectra, it may be too early to conclude that the apparent low-L/high-T sources are not nuclear-burning white dwarfs (NBWDs)."681 But the data do suggest that these systems may be described by a different physical model., But the data do suggest that these systems may be described by a different physical model.682 Figure 3 shows. for each galaxy. the distribution of count rates for VSSs (red) and for all other sources (black).," Figure 3 shows, for each galaxy, the distribution of count rates for VSSs (red) and for all other sources (black)."683 There are no obvious breaks in the distributions as we approach lower count rates., There are no obvious breaks in the distributions as we approach lower count rates.684 This indicates that. if we had longer and/or more sensitive observations. we would detect both VSSs and other sources that are even dimmer than the sources discovered so far.," This indicates that, if we had longer and/or more sensitive observations, we would detect both VSSs and other sources that are even dimmer than the sources discovered so far."685 In general. there are fewer VSSs than non-VSSs in each galaxy.," In general, there are fewer VSSs than non-VSSs in each galaxy."686 This is especially true for NGC 4697 and MSI., This is especially true for NGC 4697 and M51.687 There is nevertheless some preliminary evidence that count-rate distribution for VSSs in each galaxy is more sparsely populated at high-count-rates., There is nevertheless some preliminary evidence that count-rate distribution for VSSs in each galaxy is more sparsely populated at high-count-rates.688 This makes the few high-count-rates SSSs particularly interesting., This makes the few high-count-rates SSSs particularly interesting.689 One of the VSSs is clearly an ultraluminous X-ray source (ULX)., One of the VSSs is clearly an ultraluminous X-ray source (ULX).690 With a luminosity that appears to be larger than 4.107 eres τὶς MIOI-102 (a HR source) is clearly Eddington for a neutron star.," With a luminosity that appears to be larger than $4 \times 10^{39}$ ergs $^{-1}$, M101-102 (a HR source) is clearly super-Eddington for a neutron star."691 It cannot be explained by a NBWD model., It cannot be explained by a NBWD model.692 Three of the sources in NGC 4697 are also particularly luminous., Three of the sources in NGC 4697 are also particularly luminous.693 The 3 sources comprising the HR composite in NGC 4697 are roughly equally bright., The $3$ sources comprising the HR composite in NGC 4697 are roughly equally bright.694 The luminosities of the individual sources would therefore be ~10? ergs s! if the distance to NGC 4697 is 11.7 Mpe. but they could be as high as —4sc10% eres s7! if the distance to NGC 4697 is 23.3 Mpc.," The luminosities of the individual sources would therefore be $\sim 10^{38}$ ergs $^{-1}$ if the distance to NGC 4697 is $11.7$ Mpc, but they could be as high as $\sim 4 \times \sim 10^{38}$ ergs $^{-1}$ if the distance to NGC 4697 is $23.3$ Mpc."695 If the true luminosities are sub-Eddington for a 1.4M.. object. then these systems could include NBWDs that are both hot and," If the true luminosities are sub-Eddington for a $1.4 M_\odot$ object, then these systems could include NBWDs that are both hot and"696"jet-cloud interactions cannot explain the gas kincimatics iu SATALIN2399-0136,",jet-cloud interactions cannot explain the gas kinematics in SMM02399-0136.697 We discuss here several possible mechanisus that could explain the extreme kinematics in some UZRC., We discuss here several possible mechanisms that could explain the extreme kinematics in some HZRG.698We solve this equation numerically on a fixed mesh that is uniform r2. with 200 ericl points (likeMartinetal.2007).,We solve this equation numerically on a fixed mesh that is uniform $r^\frac{1}{2}$ with 200 grid points \citep[like][]{martin07}.699. We choose zero torque boundary conditions at theinner boundary 7=10rg and the outer boundary rou=0.9rg.," We choose zero torque boundary conditions at theinner boundary $r_{\rm in}=10^{-3}\,r_{\rm H}$ and the outer boundary $r_{\rm out}=0.9\,r_{\rm H}$."700 The inner boundary allows the material there to be acereted by the planet., The inner boundary allows the material there to be accreted by the planet.701 Hs position has been chosen so that it is about equal to the radius of a Jupiter planet at a distance of 5AU from a central solar mass star.," Its position has been chosen so that it is about equal to the radius of a Jupiter planet at a distance of $5\,\rm AU$ from a central solar mass star."702 With the tidal torque acting. the outer boundary is far enough out that it does not alfect the evolution because the tidal torque prevents the mass from reaching the outer regions.," With the tidal torque acting, the outer boundary is far enough out that it does not affect the evolution because the tidal torque prevents the mass from reaching the outer regions."703 However. if there is no tidal torque. the disc extends as far as it can and the outer boundary. will alfect the mass in the cise because mass is removed there.," However, if there is no tidal torque, the disc extends as far as it can and the outer boundary will affect the mass in the disc because mass is removed there."704 The viscous torque is given in equation (53)) and we take X—0 at the boundaries to have zero torques there., The viscous torque is given in equation \ref{visct}) ) and we take $\Sigma=0$ at the boundaries to have zero torques there.705 We initially take the surface density to be a constant but very small value ancl allow it to build up by mass accretion at a raclius ri., We initially take the surface density to be a constant but very small value and allow it to build up by mass accretion at a radius $r_{\rm inj}$.706" We set the accretion rate on to the dise to be A=1.78107AL,O,."," We set the accretion rate on to the disc to be $\dot M=1.78 \times70710^{-8}\, M_{\rm s}\, \Omega_{\rm p}$."708 For a Jupiter mass planet orbiting a solar mass star at a radius of 5AU this corresponds an aceretion rate of AZ=107M.veον ," For a Jupiter mass planet orbiting a solar mass star at a radius of $5\,\rm AU$ this corresponds an accretion rate of $\dot M=10^{-8}\,\rm M_\odot\,yr^{-1} $."709We start with a disc of nearly zero mass., We start with a disc of nearly zero mass.710 We note that changing the accretion rate does not change the results in bie. 3..," We note that changing the accretion rate does not change the results in Fig. \ref{evolution},"711 only the amount of mass in the disc., only the amount of mass in the disc.712 We parametrise the viscosity with the a-preseription in equation (5))., We parametrise the viscosity with the $\alpha$ -prescription in equation \ref{alphavisc}) ).713 For a Ixeplerian disc with a=10. and a constant disc aspect ratio Z//r=0.3. we have gas kinematic turbulent. viscosity Disc mass builds up as mass is injected.," For a Keplerian disc with $\alpha=10^{-3}$ and a constant disc aspect ratio $H/r=0.3$, we have gas kinematic turbulent viscosity Disc mass builds up as mass is injected."714 We ran the numerical code until it reached a steady state., We ran the numerical code until it reached a steady state.715 In Fig., In Fig.716 3. we plot the surface density evolution of the disc for dillerent injection radii., \ref{evolution} we plot the surface density evolution of the disc for different injection radii.717 Phe surface density in each of the plots increases as time goes on., The surface density in each of the plots increases as time goes on.718 The top left plot shows the evolution without the tidal torque and an injection radius rj;=0.2ry.," The top left plot shows the evolution without the tidal torque and an injection radius $r_{\rm inj}=0.2\,r_{\rm H}$."719 We see that the disc spreads out as far as it can out to the outer boundary. where mass is removed.," We see that the disc spreads out as far as it can out to the outer boundary, where mass is removed."720 All the other three plots in Fig., All the other three plots in Fig.721 3 include the tidal torque and we vary the position that mass is added [rom ring=0.1rg (top right). 0.2rg (bottom left) anc 0.3rg (bottom right).," \ref{evolution} include the tidal torque and we vary the position that mass is added from $r_{\rm inj}=0.1\,r_{\rm H}$ (top right), $0.2\,r_{\rm H}$ (bottom left) and $0.3\,r_{\rm H}$ (bottom right)."722 With the tidal torque acting. the disc cannot expand out to the outer boundary. it becomes truncated: well inside that boundary.," With the tidal torque acting, the disc cannot expand out to the outer boundary, it becomes truncated well inside that boundary."723 The position of the injection of the mass does not alfect the outer boundary of the disc. it only mildly mocifies the surface density profile of the steady state clisc.," The position of the injection of the mass does not affect the outer boundary of the disc, it only mildly modifies the surface density profile of the steady state disc."724 In this section we find steady-state analytical solutions for the surface density of a cireumplanetary. aceretion disc., In this section we find steady-state analytical solutions for the surface density of a circumplanetary accretion disc.725 Our approach is similar to that of Canup&Ward(2002) anc Ward&Canup (2010).. but we include the strong tidal torques near the orbit crossing radius.," Our approach is similar to that of \cite{canup02} and \cite{ward10}, , but we include the strong tidal torques near the orbit crossing radius."726 Phere are three regions in the disc. as shown in Fig. 4..," There are three regions in the disc, as shown in Fig. \ref{sketch}."727 Inside of the raclius where mass is added. ring. the disc acts as a normal accretion clisc.," Inside of the radius where mass is added, $r_{\rm inj}$ , the disc acts as a normal accretion disc."728 Outside of this radius. the disc acts as a decretion disc in termsof the density," Outside of this radius, the disc acts as a decretion disc in termsof the density"729"are of the order of 7;=10°, 104, 10°, and 106 for the four disk masses respectively, orders of magnitude higher than for the Pascucci et al.","are of the order of $\tau_I=10^3$ , $10^4$, $10^5$, and $10^6$ for the four disk masses respectively, orders of magnitude higher than for the Pascucci et al."730 benchmark., benchmark.731" The corresponding maximum optical depths perpendicular to the disk are of the order of τι--100, 10°, 104, and 10° respectively."," The corresponding maximum optical depths perpendicular to the disk are of the order of $\tau_I=100$, $10^3$, $10^4$, and $10^5$ respectively."732" The benchmark test compares SEDs, images and polarization maps at 10 viewing angles corresponding to cost=0.05 to 0.95 in steps of 0.10, corresponding to viewing angles from 18.2 (almost pole-on) to 87.1° (almost edge-on)."," The benchmark test compares SEDs, images and polarization maps at 10 viewing angles corresponding to $\cos{i}=0.05$ to $0.95$ in steps of $0.10$, corresponding to viewing angles from $18.2$ (almost pole-on) to $87.1^\circ$ (almost edge-on)."733" The images and polarization maps are computed at 1m, and span 251x pixels, and a physical size of 900x AAU."," The images and polarization maps are computed at $\mu$ m, and span $251\times251$ pixels, and a physical size of $900\times900$ AU."734" Due to the single grain size, the scattering phase function oscillates strongly around jum and at shorter wavelengths."," Due to the single grain size, the scattering phase function oscillates strongly around $\mu$ m and at shorter wavelengths."735" Thus, these oscillations have a direct impact on scattered-light images computed at these wavelengths."," Thus, these oscillations have a direct impact on scattered-light images computed at these wavelengths."736" While a single grain size, and therefore these oscillations, would not be seen in a real disk, this allows codes to test whether they correctly compute the scattering of photon packets."," While a single grain size, and therefore these oscillations, would not be seen in a real disk, this allows codes to test whether they correctly compute the scattering of photon packets."737" 'The benchmark models were computed using a cylindrical polar grid with dimensions (n-,nz,n¢)=(499,399,1) extending out to the outer disk radius."," The benchmark models were computed using a cylindrical polar grid with dimensions $(n_r, n_z, n_\phi)=(499, 399, 1)$ extending out to the outer disk radius."738 The SEDs were computed at exact wavelengths using the monochromatic radiative transfer described in refsec:seds.., The SEDs were computed at exact wavelengths using the monochromatic radiative transfer described in \\ref{sec:seds}.739" As before, the MieX code was used to compute the optical properties of the dust."," As before, the MieX code was used to compute the optical properties of the dust."740" The convergence algorithm discussed in refsec:convergence was used, with p=99%,, Qthres=2, and Athres=1.02."," The convergence algorithm discussed in \\ref{sec:convergence} was used, with $p=99$, $Q_{\rm thres}=2$, and $\Delta_{\rm thres}=1.02$."741 The MRW (with y= 2) and PDA approximations were used due to the high optical depths., The MRW (with $\gamma=2$ ) and PDA approximations were used due to the high optical depths.742" The models were run with enough photon packets to provide very high signal-to-noise in the temperatures, SEDs, andimages, and were run using the parallel version of the code on 32 cores, requiring a wall clock time of 12 to 17 hours to compute the temperature and SEDs for the 7;=10? to 106 models, and an additional 11 hours for the images and polarization maps."," The models were run with enough photon packets to provide very high signal-to-noise in the temperatures, SEDs, and, and were run using the parallel version of the code on 32 cores, requiring a wall clock time of 12 to 17 hours to compute the temperature and SEDs for the $\tau_I=10^3$ to $10^6$ models, and an additional 11 hours for the images and polarization maps."743" The temperaturesconverged after 7, 9, 9, and 10 iterations for the τι=10°, 104, 10°, and 106 models respectively."," The temperaturesconverged after 7, 9, 9, and 10 iterations for the $\tau_I=10^3$, $10^4$ , $10^5$ , and $10^6$ models respectively."744" Figure 4 compares the mid-plane temperature profile in two of the models (7;=10? and τι= 109), as well as two vertical cuts in the most optically thick model (7;— 10°)."," Figure \ref{fig:pinte_temp} compares the mid-plane temperature profile in two of the models $\tau_I=10^3$ and $\tau_I=10^6$ ), as well as two vertical cuts in the most optically thick model $\tau_I=10^6$ )."745" Figure 5. compares the SEDs for the four models at four of the viewing angles (18.2, 75.5, 81.4, 87.1?)."," Figure \ref{fig:pinte_seds} compares the SEDs for the four models at four of the viewing angles (18.2, 75.5, 81.4, $^\circ$ )."746" Finally, Figures 6 and 7 compare the total intensity and polarization fraction maps for the most optically thick model (τ= 10°)."," Finally, Figures \ref{fig:pinte_I} and \ref{fig:pinte_pol} compare the total intensity and polarization fraction maps for the most optically thick model $\tau_I=10^6$ )."747" In all cases, the results produced by are within the dispersion of results obtained from the other codes."," In all cases, the results produced by are within the dispersion of results obtained from the other codes."748" To demonstrate the capabilities of the code, a radiative transfer calculation on a simulation of a low-mass star forming cloud was carried out in order to produce synthetic observations from near-infrared to sub-milimeter wavelengths."," To demonstrate the capabilities of the code, a radiative transfer calculation on a simulation of a low-mass star forming cloud was carried out in order to produce synthetic observations from near-infrared to sub-milimeter wavelengths."749" The demonstration uses a simulation of low-mass star formation computed with the ORION AMR three-dimensional gravito-radiation-hydrodyamics code (?,andreferences therein)..", The demonstration uses a simulation of low-mass star formation computed with the ORION AMR three-dimensional gravito-radiation-hydrodyamics code \citep[][and references therein]{offner:09:131}.750" The simulation contains MMo of gas and dust in a box of side ppc, and resolves size-scales down to AAU, with an effective resolution of 4096°."," The simulation contains $_\odot$ of gas and dust in a box of side pc, and resolves size-scales down to AU, with an effective resolution of $4096^3$."751" ? studied the effects of heating from protostars on the formation of stars, and therefore ran a simulation including radiative heating, and a control case with no radiation heating."," \citeauthor{offner:09:131} studied the effects of heating from protostars on the formation of stars, and therefore ran a simulation including radiative heating, and a control case with no radiation heating."752" The simulation used here is a snapshot of the one includingradiative heating, for t~tg, where tg is the free-fall time."," The simulation used here is a snapshot of the one includingradiative heating, for $t\sim t_{\rm ff}$, where $t_{\rm ff}$ is the free-fall time."753 The radiative transfer through the star-forming region was simulated by taking into account both the luminosity fromthe forming stars (c.f., The radiative transfer through the star-forming region was simulated by taking into account both the luminosity fromthe forming stars (c.f.754" Appendix B of ?)), represented by sink particles in the simulation, and the interstellar radiation field at the solar neighborhood from ?,, which includes contributions from the stellar emission, PAHemission, and far-infrared thermal emission?.."," Appendix B of \citealt{offner:09:131}) ), represented by sink particles in the simulation, and the interstellar radiation field at the solar neighborhood from \citet{Porter:05:77}, , which includes contributions from the stellar emission, PAHemission, and far-infrared thermal ."755 The simulation was embedded atthe center of a cube of side, The simulation was embedded atthe center of a cube of side756simulation and model light curves are similar.,simulation and model light curves are similar.757" However, the further off-axis the observer, the later the observer time at which the simulation full "," However, the further off-axis the observer, the later the observer time at which the simulation provides full coverage."758"In the we have truncated the light providescurves at the coverage.observer time figure,before which radiation from the blast wave with y>20 would have been required."," In the figure, we have truncated the light curves at the observer time before which radiation from the blast wave with $\gamma > 20$ would have been required."759" For two blast wave jets viewed sideways (0,5,= 90°), for example, full starts beyond 100 "," For two blast wave jets viewed sideways $\theta_{obs} = 90^\circ$ ), for example, full coverage starts beyond 100 days."760"This means that, even though the coverageinitial slopes agree days.between simulation and model, the early time shape of off-axis light curves in reality will be largely dictated by the initial shape of the blast wave, which does not need to be anything like the BM solution."," This means that, even though the initial slopes agree between simulation and model, the early time shape of off-axis light curves in reality will be largely dictated by the initial shape of the blast wave, which does not need to be anything like the BM solution."761" Collapsar jet simulations indicate the existence of a cocoon around the emerging jet (see e.g., 222?))."," Collapsar jet simulations indicate the existence of a cocoon around the emerging jet (see e.g., \citealt{Zhang_WM_2003_ApJ, Zhang_WH_2004_ApJ, 2007ApJ...665..569M,762 Mizuta2009}) )."763 We can understand why the off-axis light curves from the simulation are initially brighter than those from the simplified model by looking at one of the angles in more details., We can understand why the off-axis light curves from the simulation are initially brighter than those from the simplified model by looking at one of the angles in more details.764 In Fig., In Fig.765" 7 we have again plotted the simulation and model light curves for an observer at 0,5,=90? (1.57 rad), together with a number of variations."," \ref{beaming_figure} we have again plotted the simulation and model light curves for an observer at $\theta_{obs} = 90^\circ$ (1.57 rad), together with a number of variations."766" We have now also included light curve where we continue using the BM solution to determinea the local fluid conditions, instead of the dynamical simulation results, but otherwise as if we were reading the fluid quantities from disc proceed(because of this, the curve also serves as a consistency check on the radiation calculation itself)."," We have now also included a light curve where we continue using the BM solution to determine the local fluid conditions, instead of the dynamical simulation results, but otherwise proceed as if we were reading the fluid quantities from disc (because of this, the curve also serves as a consistency check on the radiation calculation itself)."767 The same approach has been used to generate the light curve in Fig. 5.., The same approach has been used to generate the light curve in Fig. \ref{exactlightcurve_figure}.768 The curve initially lies significantly below the simulation light curve., The curve initially lies significantly below the simulation light curve.769 It also lies above the simplified model curve., It also lies above the simplified model curve.770 The flux level of this BM curve is determined in part by the numerical resolution that we assume., The flux level of this BM curve is determined in part by the numerical resolution that we assume.771" In the plot we have used a resolution similar to that for the simulation curve, which initially resolves the radial profile with approximately 17 cells."," In the plot we have used a resolution similar to that for the simulation curve, which initially resolves the radial profile with approximately 17 cells."772" Increasing the resolution moves the BM curve closer to the slab curve, and not to the simulation curve."," Increasing the resolution moves the BM curve closer to the simplified slab curve, and not to the simulation curve."773 The difference simplifiedbetween the BM curve and the simulation curve is real and we have added to the plot two hybrid simulation / model curves to make clear the cause of this difference., The difference between the BM curve and the simulation curve is real and we have added to the plot two hybrid simulation / model curves to make clear the cause of this difference.774" First, when we completely ignore the velocity vg in the angular direction for the purpose of calculating the emission but otherwise still use the simulation dynamics, we find that the resulting light curve, labeled in the figure, initially lies somewhat below the simulation curve before the two eventually merge."," First, when we completely ignore the velocity $v_\theta$ in the angular direction for the purpose of calculating the emission but otherwise still use the simulation dynamics, we find that the resulting light curve, labeled in the figure, initially lies somewhat below the simulation curve before the two eventually merge."775" This tells us that part of the observed flux level is caused by beaming towards the observer of material spreading sideways, but that this is not the main cause of the difference between simulation and the hard edge jet models."," This tells us that part of the observed flux level is caused by beaming towards the observer of material spreading sideways, but that this is not the main cause of the difference between simulation and the hard edge jet models."776 At late times beaming no longer plays any role and the two curves are indeed no longer expected to be different., At late times beaming no longer plays any role and the two curves are indeed no longer expected to be different.777 The main reason for the difference is shown by the second additional curve., The main reason for the difference is shown by the second additional curve.778 When calculating the light curve labeled in the figure we have omitted the contribution to the radiation of any material that has spread sideways outside the original jet opening angle., When calculating the light curve labeled in the figure we have omitted the contribution to the radiation of any material that has spread sideways outside the original jet opening angle.779" The resulting curve lies very close to the BM light curve at first, before becoming orders of magnitude lower than all other curves."," The resulting curve lies very close to the BM light curve at first, before becoming orders of magnitude lower than all other curves."780" The late time behavior is as expected, for then only a small fraction of the energy and particle density is still contained within the original opening angle; the actual simulation flow has become roughly spherical."," The late time behavior is as expected, for then only a small fraction of the energy and particle density is still contained within the original opening angle; the actual simulation flow has become roughly spherical."781 The early time behavior and the similarity between the truncated cone and BM light curves is more relevant., The early time behavior and the similarity between the truncated cone and BM light curves is more relevant.782 It demonstrates that the light curve for an off-axis observer is dominated by the emission from material that has spread sideways out of the original jet opening angle even though the energy of the material is very little and the sideways spreading is not yet dynamically important., It demonstrates that the light curve for an off-axis observer is dominated by the emission from material that has spread sideways out of the original jet opening angle even though the energy of the material is very little and the sideways spreading is not yet dynamically important.783" In hindsight, the fact that the material on the side of the jet dominates the observed radio flux can easily be understood."," In hindsight, the fact that the material on the side of the jet dominates the observed radio flux can easily be understood."784" It is not so much due to the fact that it moves a little faster towards the observer, for the vg component to the beaming is not that strong (as we have shown above)."," It is not so much due to the fact that it moves a little faster towards the observer, for the $v_\theta$ component to the beaming is not that strong (as we have shown above)."785" It is instead due to the fact that the radial velocity component v, drops quickly outside of the original jet opening angle and as a result the material outside the original jet opening angle is not beamed away from the observer as much as the material in the original jet cone.", It is instead due to the fact that the radial velocity component $v_r$ drops quickly outside of the original jet opening angle and as a result the material outside the original jet opening angle is not beamed away from the observer as much as the material in the original jet cone.786" By contrast, for an on-axis observer the opposite is true and for a long time the received flux is dominated by emission from material inside the original jet opening angle."," By contrast, for an on-axis observer the opposite is true and for a long time the received flux is dominated by emission from material inside the original jet opening angle."787 This has been demonstrated explicitly by ?.., This has been demonstrated explicitly by \citet{vanEerten2010b}.788 In the above sections we did not discuss the effects of synchrotron self-absorption., In the above sections we did not discuss the effects of synchrotron self-absorption.789" We will postpone addressing synchrotron self-absorption, which is not included in the simulation, until section 5.."," We will postpone addressing synchrotron self-absorption, which is not included in the simulation, until section \ref{orphan_afterglows_section}."790 A large number of X-ray afterglow light curves have been obtained by the satellite since it was launched in 2004 (?).., A large number of X-ray afterglow light curves have been obtained by the satellite since it was launched in 2004 \citep{Gehrels2004}.791" In a surprisingly large number of cases, these light curves fail to show clearly discernable jet break (??).."," In a surprisingly large number of cases, these light curves fail to show a clearly discernable jet break \citep{Racusin2009, Evans2009}."792" Using our simulation resultsa as a basis to generate synthetic data sets for observers positioned at different angles from the jet axis, we show that the effect of observer position on the temporal evolution inferred from the data can be profound and sometimes render the jet break difficult to detect."," Using our simulation results as a basis to generate synthetic data sets for observers positioned at different angles from the jet axis, we show that the effect of observer position on the temporal evolution inferred from the data can be profound and sometimes render the jet break difficult to detect."793 The data sets that we produce should be comparable to syntheticthose produced by the on-line repository (?).., The synthetic data sets that we produce should be comparable to those produced by the on-line repository \citep{Evans2007}.794" Also they should have data points at a sufficiently late time that, if this were actual data, the jet break would be"," Also they should have data points at a sufficiently late time that, if this were actual data, the jet break would be"795at the benchlunark point00.52.. 33)) (right-hand. panel).,"at the benchmark point, ) (right-hand panel)."796 Iu the latter case. there is no siugle. nou-leptonic channel in which evidence for the Higgs bosou cau be obtained at the 5o level.," In the latter case, there is no single, non-leptonic channel in which evidence for the Higgs boson can be obtained at the $5\sigma$ level."797 To further illustrate the point. in Fig. ll..," To further illustrate the point, in Fig. \ref{fig:SigsComb},"798 we display the combined statistical signilicauces for the leptonie chanuels discussed iu Secion 5.. as well as the combined siguilicauces for all other relevant channels for Higgs discovery. both tn the SM aud in the L2HDM at the benchmark poiut. (sina=0.55. tau= 3).," we display the combined statistical significances for the leptonic channels discussed in Section \ref{sec:LHCSignatures}, as well as the combined significances for all other relevant channels for Higgs discovery, both in the SM and in the L2HDM at the benchmark point $\sin\alpha = 0.55$, $\tan\beta=3$ )."799 ludeed. lor this particular parameter choice. all relevant nou-leptonic eliauuels are suppressed relative to their Standard-Mocdel to sueh an extentthat. for most of the 120GeVSayz110 mass window displayed in the plot. their combiued signuilicauce does uot even provide 3e. evideuce for — much less a So discovery of— a light Higgs boson.," Indeed, for this particular parameter choice, all relevant non-leptonic channels are suppressed relative to their Standard-Model to such an extentthat, for most of the $120\mbox{~GeV}\lesssim m_h \lesssim 140\mbox{~GeV}$ mass window displayed in the plot, their combined significance does not even provide $3\sigma$ evidence for — much less a $5\sigma$ discovery of — a light Higgs boson."800 On the other laud. statistical siguilicauce for leptonic Hi:ees decay elianuels are enlhanced. therefore becoming the dominant discovery. elianuels for the light CUP-even Higgs in the L2HDM inodel.," On the other hand, statistical significance for leptonic Higgs decay channels are enhanced, therefore becoming the dominant discovery channels for the light $CP$ -even Higgs in the L2HDM model."801 This clearly illustrates the crucial role leptonic clhiaunels can play in the LHC phenomenology of models with extended (aud particularly leptophilic) Higgsao seclols., This clearly illustrates the crucial role leptonic channels can play in the LHC phenomenology of models with extended (and particularly leptophilic) Higgs sectors.802 We emphasize that these plots represent the results fora single benchmark point. aud oue iu which the j-factors are not particularly extreme.," We emphasize that these plots represent the results fora single benchmark point, and one in which the $\eta$ -factors are not particularly extreme."803 There exist other points in the parameter space of the model allowed by all coustraints for which the deviatious of the effective couplings of / to the other fields in the theory areeven more severe., There exist other points in the parameter space of the model allowed by all constraints for which the deviations of the effective couplings of $h$ to the other fields in the theory areeven more severe.804" As anexample. couskler the case in which sina=0.65 and tan;= 2.2. for which yj,= OSL jy= —1.57. and quz= 0.30."," As anexample, consider the case in which $\sin\alpha=0.65$ and $\tan\beta=2.2$ , for which $\eta_q=0.84$ , $\eta_\ell = -1.57$ , and $\eta_{W,Z}=0.30$ ."805 For this choice, For this choice806poloidal projection of a field line.,poloidal projection of a field line.807 The equation for W is commonly referred to as the Grad-Shafranov equation (Lovelace et al., The equation for $\Psi$ is commonly referred to as the Grad-Shafranov equation (Lovelace et al.808 1986)., 1986).809" For axisvuuuetric conditions the flow field can be written as v—v,|e;e, where v, is the poloidal (r.+) conmponuent. ο=wre>0 ds the toroidal component. and e,, is the unit toroidal vector."," For axisymmetric conditions the flow field can be written as ${\bf v}={\bf v}_p810+ v_\phi {\bf e}_\phi$ where ${\bf v}_p$ is the poloidal $(r,z)$ component, $v_\phi =811\omega r >0$ is the toroidal component, and ${\bf e}_\phi$ is the unit toroidal vector."812" Similarly. the magnetic field cau be written as B—B,|D,e,."," Similarly, the magnetic field can be written as ${\bf B} =813{\bf B}_p + B_\phi {\bf e}_\phi$."814 The ideal MIID equations then inply that certain quantities are constants on any eiven flux surface W(r.:) —const or equivalently they are coustauts along any given streai line or a given magnetic field liue.," The ideal MHD equations then imply that certain quantities are constants on any given flux surface $\Psi(r,z)=$ const or equivalently they are constants along any given stream line or a given magnetic field line."815 These integrals are functions of V (see for example Lovelace ct al., These integrals are functions of $\Psi$ (see for example Lovelace et al.816 1986). Tere. 9 is the entropy. a is the enthalpy. and d is the gravitational potential.," 1986), Here, $S$ is the entropy, $w$ is the enthalpy, and $\Phi$ is the gravitational potential."817 The quantity A corresponds to the conservation of mass alonea streamline. A to the conservation of angular momentum. O to the conservation of helicity. S to the conservation of entropy. aud £ (Dernoullis constant) to the conservation of enerev.," The quantity $K$ corresponds to the conservation of mass alonga streamline, $\Lambda$ to the conservation of angular momentum, $\Omega$ to the conservation of helicity, $S$ to the conservation of entropy, and $E$ (Bernoulli's constant) to the conservation of energy."818 The remaining MIID equation (which cannot be written in the iutegral form) is the Euler force equation across the poloidal maguetic field line (Bogovalov. 1997). which is equivaleut to the Curad-Shafrauov equation.," The remaining MHD equation (which cannot be written in the integral form) is the Euler force equation across the poloidal magnetic field line (Bogovalov 1997), which is equivalent to the Grad-Shafranov equation."819" Tere. 0/00 is the derivative in the direction perpendicular o imaenetic field lines aud directed. outward from the axis. 0 is the angle of inclination of the poloidal maguetic field line away from the :- axis. s is the distance from he disk along a maguetic feld line. ea,=|B,|/Ip and ci,=ονIp are the poloidal aud azimuthal Alfvénn velocities."," Here, ${\partial}/{\partial n}$ is the derivative in the direction perpendicular to magnetic field lines and directed outward from the axis, $\theta$ is the angle of inclination of the poloidal magnetic field line away from the $z-$ axis, $s$ is the distance from the disk along a magnetic field line, $v_{Ap}\equiv820|{\bf B}_p|/\sqrt{4\pi\rho}$ and $v_{A\phi}\equiv |B_\phi|/\sqrt{4\pi \rho}$ are the poloidal and azimuthal Alfvénn velocities."821 The quantity 00/05 is the curvature of naenetic field line., The quantity ${\partial\theta}/{\partial s}$ is the curvature of magnetic field line.822 The first two terms in equation (6) are determined by the non-diagoual (tension) part of the stress eusor. pe;cy|(pο.le.," The first two terms in equation (6) are determined by the non-diagonal (tension) part of the stress tensor, $\rho v_i v_k +823\left( p + {{\bf B}^2}/{8 \pi} \right) \delta_{ik}824- {B_i B_k}/{4 \pi}$."825 The third terii is determined by the total (1iatter plus magnetic) pressure p|B?/sz aud the eravity force 00/0., The third term is determined by the total (matter plus magnetic) pressure $p + {{\bf B}^2}/{8 \pi}$ and the gravity force $\partial \Phi/\partial n$.826" To clarity the plivsical scuse of the integrals of iiotion. it is useful to derive the fluxes of mass. augular 1iomienutuui (about the : axis). and cnerev,"," To clarify the physical sense of the integrals of motion, it is useful to derive the fluxes of mass, angular momentum (about the $z-$ axis), and energy."827" The correspouding conservation laws for stationary conuditious are Because v,|B,. the vector fux deusities are directed along the field lincs."," The corresponding conservation laws for stationary conditions are Because ${\bf v}_p \parallel {\bf B}_p$, the vector flux densities are directed along the field lines."828 Consider the fluxes through an annular region with surface area clement dS., Consider the fluxes through an annular region with surface area element $d{\bf S}$.829 The matter fux through the axisviunietrie surface 8 exteuding out from the 2 axis is where we took iuto account the integral (1)., The matter flux through the axisymmetric surface $\bf S$ extending out from the $z-$ axis is where we took into account the integral (1).830" dS-B, is the magnetic dux through the aunulur region bounded by fux surfaces V and W|dW.", $d{\bf S}\cdot{\bf B}_p$ is the magnetic flux through the annular region bounded by flux surfaces $\Psi$ and $\Psi + d\Psi$ .831 Thus we can chanec froin space iuteeration to inteeration over W., Thus we can change from space integration to integration over $\Psi$ .832 Because B=(líry)W/O: aud B.=(l/rowor. we have where W=0 corresponds to the 2 axis.," Because $B_r=-(1/r){\partial\Psi/\partial z}$ and $B_z=(1/r){\partial \Psi/\partial r}$, we have where $\Psi=0$ corresponds to the $z-$ axis."833 Similarly. Thus. AWN/2 is the matter flux between the flux surfaces separated by dW. ΑΙ i the aneular momentiin fux. aud (2|AO)AVV/2 is the energy flux.," Similarly, Thus, $Kd\Psi/2 $ is the matter flux between the flux surfaces separated by $d\Psi$, $\Lambda Kd\Psi/2 $ is the angular momentum flux, and $(E + \Lambda \Omega) Kd\Psi/2$ is the energy flux."834" Note that AQY) is specific angular momentum carried along the maguctic field lino W= const. E(V)|AQCW) is the specific energy. and Ω(Ψ} is the angular velocity of the disk at the poiut where the magnetic ficld line or fiux surface VW=const intersectsthe disk(for |v,|»0 at the disk)."," Note that $\Lambda(\Psi)$ is specific angular momentum carried along the magnetic field line $\Psi={\rm const}$ , $E(\Psi) + \Lambda \Omega (\Psi)$ is the specific energy, and $\Omega(\Psi)$ is the angular velocity of the disk at the point where the magnetic field line or flux surface $\Psi ={\rm const}$ intersectsthe disk(for $|{\bf v}_p| \rightarrow 0$ at the disk)."835"For au optically thin. homogenous cloud. the 21 cii optical depth τοι is related to the coluun density Nyy aud the spin temperature Ly bv the expression (Rolilfs1986)) where T, is 2.in Nh.- Nyy- in. D7 and dVT in kins +.","For an optically thin, homogenous cloud, the 21 cm optical depth $\tau_{21}$ is related to the column density $N_{\rm H~{\sc i}}$ and the spin temperature $T_s$ by the expression \cite{rohlfs86}) ) where $T_s$ is in K, $N_{\rm H~{\sc i}}$ in $^{-2}$ and dV in km $^{-1}$."836 The: covering factor f can usually be estimated frou VLBI observations: nufortunatelv. uo such observations exist iu the literature for133.," The covering factor $f$ can usually be estimated from VLBI observations; unfortunately, no such observations exist in the literature for."837.. The source. however. has an exceediuglv fiat spectralu. with flux values of 330 mJv at 1.29 αν (our observations). 320 iuJw at 2.7 GIIz and 300 uty at 5 CIIz (Quiuieutoetal. 1988)). and is thus likely to be very conroet.," The source, however, has an exceedingly flat spectrum, with flux values of 330 mJy at 1.29 GHz (our observations), 320 mJy at 2.7 GHz and 300 mJy at 5 GHz \cite{quiniento}) ), and is thus likely to be very compact."838 We hence assume a COVCLi18o actor of unity: this shotΠε]. of course. be verified by VLBI observations.," We hence assume a covering factor of unity; this should, of course, be verified by VLBI observations."839 Next. t10 20.101 absorber towareIs PIS LPdo) Is à caxdidate daniped svseni. with STLOιο MeII. ALII. FeIT. Si and € absorption lines SCCIL intιο HST spectiuu (Petitjoanetal. 1996)).," Next, the $z = 0.101$ absorber towards PKS $-$ 433 is a candidate damped system, with strong Mg, Al, Fe, Si and C absorption lines seen in the HST spectrum \cite{petitjean96}) )."840 The equivalent width ratios of these low-ionization lines iudicae hat he svsteni is probably damped (see also Rao Tirushds 20003). with Vpic1OÓ7 ? falthegh ε1ο Lyuiura ine has itself no so far been observe for this iorber).," The equivalent width ratios of these low-ionization lines indicate that the system is probably damped (see also Rao Turnshek 2000), with $N_{\rm H~{\sc i}}841\sim 10^{20}$ $^{-2}$ (although the $\alpha$ line has itself not so far been observed for this absorber)."842 This cstimate of Αι agrees well with ie N-ray spectrum of which showpA absorption corresIOIine to Ν΄Γι233US1030 per cii> (Wilkes-.eta. 1992)). with a Calactic contribution O 1:)d0.]SLOP? axDu cn? (Lockman&Savage 1995).," This estimate of $N_{\rm H~{\sc i}}$ agrees well with the X-ray spectrum of which shows absorption corresponding to $N_{\rm H~{\sc i}} = 2.3 \pm 0.8 \times 10^{20}$ per $^2$ \cite{wilkes92}) ), with a Galactic contribution of $1.3 \pm 0.1 \times 10^{20}$ per $^2$ \cite{lockman95}) )."843" The system ds tla sqlite likely to be a moderate column density damped aSOLver,", The system is thus quite likely to be a moderate column density damped absorber.844" Our Dans | resolution ATCA spectruni las a peal optical depth 7,4410076: equation (1 hen vicds a column deusitv of Nj;=τιςtot”T, οι3.", Our 9 km $^{-1}$ resolution ATCA spectrum has a peak optical depth $\tau_{max} \sim 0.0076$; equation \ref{eqn:Tspin}) ) then yields a column density of $N_{\rm H~{\sc i}} = 1.4 \times 10^{17} \ T_s$ $^{-2}$.845 Coubinius this with the column csity of Petitjoan ο (, Combining this with the column density of Petitjean et al. (8461006) eives a spin temperature Ix. Note that this is alower liwit to the spin temperature. since the uypc rdiuit to the «»ptical depth is —¢).tτο,"1996) gives a spin temperature of $\sim 730$ K. Note that this is a limit to the spin temperature, since the upper limit to the optical depth is $\sim 0.0076$."847 Tf the 3.30 featre of figure 1 isnof real. it wouk inply that the svsten has an even üeher spin temperature.," If the $3.3 \sigma$ feature of figure \ref{fig:fig2} is real, it would imply that the system has an even higher spin temperature."848 As cliscussecl ii Cheugalur Iauckar (2000). spira ealaxies tend to have ow spin temperatures (TiX300 I&): it is thus unlikely that the absorber is a large spiral galaxy.," As discussed in Chengalur Kanekar (2000), spiral galaxies tend to have low spin temperatures $T_s \la 300$ K); it is thus unlikely that the absorber is a large spiral galaxy."849 The LOL-¢etection of emission cau be used to place limits ou the II mass of the 2—0.1VL absorber., The non-detection of emission can be used to place limits on the H mass of the $z \sim 0.101$ absorber.850 Of course. the peal liue Hux is a function of the velocity distribution iu theeuittiie eas: for a eiven II mass. a cloud with a larecr velocMy ¢ispersion will result in a lower peak flux.," Of course, the peak line flux is a function of the velocity distribution in the emitting gas; for a given H mass, a cloud with a larger velocity dispersion will result in a lower peak flux."851 We will. Or siuplicity. asssuie a uniform velocity distribution with avith AV.," We will, for simplicity, asssume a uniform velocity distribution with a width $\Delta V$."852" Tn this case. he ID rinass of the csuitting clouc is related to AV. aud the ine flux ο bv the exο 2.35 1U*SAV DF where AV is in kins J|2 9 is in Jy aud AZg; is in sok masses,"," In this case, the H mass of the emitting cloud is related to $\dV$ and the line flux $S$ by the expression = 2.35 10^5 S D_L^2, where $\dV$ is in km $^{-1}$, $S$ is in Jy and $M_{\rm H~{\sc i}}$ is in solar masses."853 Dy is the Iuwinosity distance of the cloud in MXC (Dp=113.72 Alpe. Or a system at 2=QU1Ul).," $D_L$ is the luminosity distance of the cloud in Mpc $D_L = 413.72$ Mpc, for a system at $z = 0.101$ )."854 Velocity widths in dwarf galaxies are of the oxer of a few tens of klos 1, Velocity widths in dwarf galaxies are of the order of a few tens of km $^{-1}$.855 On the «ther hand. iu the case of spirals. the kinematics are dominated by rotation. and the velocity spreads of ID ΠΕ profies depend Cnclallv ou the incination of the system to he liue «of sigit.," On the other hand, in the case of spirals, the kinematics are dominated by rotation, and the velocity spreads of H emission profiles depend crucially on the inclination of the system to the line of sight."856 Face-on spirals tend to have velocity widlis siniar to those of dwiufs. AV2030 TES 1l. however. cisss WIh laveeo immclinations cai have cuiission spread over a few hundred km 1," Face-on spirals tend to have velocity widths similar to those of dwarfs, $\dV \sim 20 - 30$ km $^{-1}$; however, disks with large inclinations can have emission spread over a few hundred km $^{-1}$."857 Even in the lafor cases. however. velocity crowding in the tangen poiuts results iu ac raracteristic “douwble-lhormed’ xofile. where each horn js 30IO ni | wide. with a wide plateau in between.," Even in the latter cases, however, velocity crowding in the tangent points results in a characteristic `double-horned' profile, where each horn is $\sim 30 - 40$ km $^{-1}$ wide, with a wide plateau in between."858 m he iuermediate case. of iucination angles of the order of DU. νί‘locity widths of ~70WO kus ! aC COLL.," In the intermediate case, of inclination angles of the order of $45^\circ$, velocity widths of $\sim 70 - 100$ km $^{-1}$ are common."859 We will hence use two velocity widths. AV=XVhs | alu AV=70lans !. to obtai- nuts οithe IT 1 amass of the absorber.," We will hence use two velocity widths, $\dV = 30$ km $^{-1}$ and $\dV = 70$ km $^{-1}$, to obtain limits on the H mass of the absorber."860" The 30 ku 1 resolution spect111u. with aneular TORlution ~10"". Ge. withou automa 6). vields a 30 upper huit of 1.11 uJv ou the line fix."," The 30 km $^{-1}$ resolution spectrum, with angular resolution $\sim 40 ''$ (i.e. without antenna 6), yields a $3\sigma$ upper limit of 1.44 mJy on the line flux."861" [If we assiune the ο1 profile has AV~30 ku |. equaion (2]) IVCSs AdyifJo)<1.6.10?AZ,."," If we assume the emission profile has $\dV \sim 30$ km $^{-1}$, equation \ref{eqn:flux}) ) gives $M_{\rm H~{\sc i}}(3\sigma) < 1.6 \times 10^9 862M_{\odot}$."863 The 7πμ... resolutiou spectrum las a 320 uper limit of 0.87 Jy on the emission: for AV-T Haus 1 . this gives Ay(3c)<225 109A...," The 70 km $^{-1}$ resolution spectrum has a $3\sigma$ upper limit of 0.87 mJy on the emission; for $\dV = 70$ km $^{-1}$ , this gives $M_{\rm H~{\sc i}}(3\sigma) < 2.25 \times 10^9 M_{\odot}$ ."864 Doth the aove estimates are siialler εvan the IT mass of the Miloy Wav. or which aSHoxlo?A...," Both the above estimates are smaller than the H mass of the Milky Way, for which $\approx 5 \times 10^9$."865 Fiπα]. the 200 kau | resolution spsctrmm also rules out the possibiitv that the emission is sead over a wide velcity range: this spectra vields aji upper limit of Aly(30)c33«10AL... AAI siialer than the ILi mass of the Mikv Way.," Finally, the 200 km $^{-1}$ resolution spectrum also rules out the possibility that the emission is spread over a wide velocity range; this spectrum yields an upper limit of $M_{\rm H~{\sc i}} 866(3\sigma) < 3.3 \times 10^9$, again smaller than the ${\rm H~{\sc i}}$ mass of the Milky Way."867 Petitjean et al. (, Petitjean et al. (8681996) identified tle absorberas an lL~5L* spiral galaxy Guipact parait που T kpc). from its COMUES Hi eroiud based images: they~ also estimated an inclination ange o£ 'assundne a disk wnorpholoey.,"1996) identified the absorber as an $L \sim 0.45 869L^\star$ spiral galaxy (impact parameter $\sim$ 7 kpc), from its colours in ground based images; they also estimated an inclination angle of $^\circ$, assuming a disk morphology."870 The oitial resolution of the imaging was. however. not high rough to confirm the morphology.," The spatial resolution of the imaging was, however, not high enough to confirm the morphology."871 Oir observations. ο- ic other hand. show that the ITi coueut of the absorber is lcss than that of normal spirals like tjc Milky: War. anea SCCu to rule out the possibility that i is à large. gas-rich spi‘al galaxy.," Our observations, on the other hand, show that the ${\rm H~{\sc i}}$ content of the absorber is less than that of normal spirals like the Milky Way, and seem to rule out the possibility that it is a large, gas-rich spiral galaxy."872 It is. of course. possible that the svstem is a- eary-type. gas-poor spiral.," It is, of course, possible that the system is an early-type, gas-poor spiral."873 High resoution UST imagine ofthe absorber is necessary to resolve lis issue., High resolution HST imaging of the absorber is necessary to resolve this issue.874 The :0.101 absorber towS Is he second low-redshift cdlauuec Lyman Svsteniwlich has been searched for 21 c ewission. the ot101) bei18o the :=0.0912) absorber tcvvarcds the quasar OI363 (Laneetal. 200053).," The $z \sim 0.101$ absorber towards is the second low-redshift damped $\alpha$ systemwhich has been searched for 21 cm emission, the other being the $z = 0.0912$ absorber towards the quasar OI363 \cite{em2000}) )."875 Both svsclus have high spintemperatures (Ti~775 K for the +=0.0912svsteu. Cheugalur Ikauckar 1999. Lane et al.," Both systems have high spintemperatures $T_s \sim 775$ K for the $z = 0.0912$system, Chengalur Kanekar 1999, Lane et al."876 2000a). far hig101) than those of local spirals or of damped svstemswhich," 2000a), far higher than those of local spirals or of damped systemswhich"877indicate a central velocity consistent with the literature at ~ 9.7s.,indicate a central velocity consistent with the literature at $\sim$ 9.7.878" Au additional shoulder coupoucut arising from dense eas in the outflow was also detected in both trausitious at ~ 8.3τν, and an absorption component was observed in theJ=3 profile at ~ 16.2st."," An additional shoulder component arising from dense gas in the outflow was also detected in both transitions at $\sim$ 8.3, and an absorption component was observed in the$J=3$ profile at $\sim$ 16.2."879 The 16 feature has been previously observed ia emission for the CS = 10 line by Takanoetal.(198D) and IWitammractal.(1992)., The 16 feature has been previously observed in emission for the CS = 1–0 line by \citet{Tak84} and \citet{Kit02}.880. Previous iueasureiuents of several transitions from 211365 Giz by Mauguu&Wootten(1993) estimate = s0 EK aud e(153) =e, Previous measurements of several transitions from 211–365 GHz by \citet{MW93} estimate = 80 K and ) =.881nv? Tauberal.(1988) used the (211 Gz) and (225 GIIz) transitions of to estimate the density in the region aud found (Πο) —cm., \citet{Tau88} used the (211 GHz) and (225 GHz) transitions of to estimate the density in the region and found ) $\sim$.882 A uderoturbuleut model of CS aud C?!SS cunission from Zhouetal.(1990) vieldled a best fif to the deusity at with the deusitv of the outflow emission being >enr., A microturbulent model of CS and S emission from \citet{Zh91} yielded a best fit to the density at with the density of the outflow emission being $>$.883 Our LVG analysis vielded a significantly higher density for the outflow component than for the central enission peak., Our LVG analysis yielded a significantly higher density for the outflow component than for the central emission peak.884 It is possible that our two-component Caussiau fit to the spectra is improperly separating the components., It is possible that our two-component Gaussian fit to the spectra is improperly separating the components.885 An aualvsis of the total integrated cmission over the FWZI of the eutire line profile vields (Πο) =c, An analysis of the total integrated emission over the FWZI of the entire line profile yields ) =.886nr?.. Massive star-forming region also known as 8255 FIR lor G192.60-AIATL that les at one end of an extended molecular ridee opposite S255IR (everetal. 1989).., 		 Massive star-forming region also known as S255 FIR 1 or G192.60-MM1 that lies at one end of an extended molecular ridge opposite S255IR \citep{Hey89}. .887 Three compact cores; SALAL3. were resolved in the 1.3 nuu coutinuun maps of Cyveanowskietal.(2007).. who also combined an analysis of transition ratios295...Boy. and 259: 218219 GIIZ) aud a spectral energy. distribution (SED) model to estimate a teiiperature range of LO100 I& and densitics betweenem.," Three compact cores, SMA1–3, were resolved in the 1.3 mm continuum maps of \citet{Cyg07}, who also combined an analysis of transition ratios, and ; 218–219 GHz) and a spectral energy distribution (SED) model to estimate a temperature range of 40–100 K and densities between."888.. The observations presented in Cyeanowskietal.(2007) are centered on either side of SAIAL (NE and SW) aud indicate velocity components at ~ 6.9 and 12.11. while our spectra. centered between the two. show a single couipoueut at ~ δ.0s," The observations presented in \citet{Cyg07} are centered on either side of SMA1 (NE and SW) and indicate velocity components at $\sim$ 6.9 and 12.1, while our spectra, centered between the two, show a single component at $\sim$ 8.9."889"t, Ultra compact (UC) III region with au associated hot core that has become a prototypical example of cometary morphology (Wood&Churchwell1989:vanBurenetal. 1990)."," Ultra compact (UC) HII region with an associated hot core that has become a prototypical example of cometary morphology \citep{WC89,vB90}."890". The hot molecular eas (80.175 IX) is sugeested to be the outer laver of a massive. cool core that is being externally heated by the UC ΠΠ region. from which it is offset bv ~ 2"" (Ileatonetal.1989:Watt&Muudy 1999)."," The hot molecular gas (80–175 K) is suggested to be the outer layer of a massive, cool core that is being externally heated by the UC HII region, from which it is offset by $\sim$ $\arcsec$ \citep{Heat89,WM99}."891". Single dish CN observations conducted by Churchwelletal.(1992). suggest eas temperatures of 166 Ik and densities >ασ, while Mookerjeaotal.(2007) also found a temperature of 160 Ix using the brightuess temperatures of several optically thick ues."," Single dish CN observations conducted by \citet{Chu92} suggest gas temperatures of 166 K and densities $>$, while \citet{Mook07} also found a temperature of 160 K using the brightness temperatures of several optically thick lines."892" Deeply embedded. source within the Serpeus molecular cloud coutaining ai protostar with an associated outflow (Wolf-Chaseetal.1998).. suggested by MeMullin.et.al.(2000) to be an example of a ""cool core. with properties intermediate to coldeui condensations."," 	 Deeply embedded source within the Serpens molecular cloud containing a protostar with an associated outflow \citep{Wolf98}, suggested by \citet{Mc00} to be an example of a “cool core,” with properties intermediate to cold/warm condensations."893 MeMwullinetal.(2000).— used. relative iuteusities of four transitions (73 Cz). (116 Cz). (215 (αν). aud (218 GITZ)| to derive a kinetic temperature range of 35TO WS but report fiat-topped line profiles suggesting au overestimation due to optical depth effects and adopt an estimate of 35 [KK for thei measurements.," \citet{Mc00} used relative intensities of four transitions (73 GHz), (146 GHz), (218 GHz), and (218 GHz)] to derive a kinetic temperature range of 35--70 K but report flat-topped line profiles suggesting an overestimation due to optical depth effects and adopt an estimate of 35 K for their measurements."894 ιτotal.(1996) also examined four transitions (218 6111). (218 κ). (863 Cz). (365 ΠΠ] to determine a higher temperature of around 75 Is. Both studies also report spatial deusity estimates with MeMwulliunetal.(2000) finding »(1I5)) = usingCCO!.. SiO. aud DCN. while IIurtetal.(1996) found usiιοCO.," \cite{Hurt96} also examined four transitions (218 GHz), (218 GHz), (363 GHz), (365 GHz)] to determine a higher temperature of around 75 K. Both studies also report spatial density estimates with \citet{Mc00} finding ) = using, SiO, and DCN, while \citet{Hurt96} found using."895.. Dominant region of tle massive star-forming site W51. which Martin(1972) revealed to consist of eight distinct coniponeuts at ceutimoeter waveleneths.," Dominant region of the massive star-forming site W51, which \citet{Mar72} revealed to consist of eight distinct components at centimeter wavelengths."896 Our observatious are centered on W5le. itself divided iuto four UC ΠΠ reeions eld (Cameetal.1993).. whose association witli dense molecular cores and maser activity is kuown as W51-Maiu (Zhaug&Πο1997).," Our observations are centered on W51e, itself divided into four UC HII regions e1–4 \citep{Gau93}, whose association with dense molecular cores and maser activity is known as W51-Main \citep{ZH97}."897". Remijanetal.(2001) used. CIT;CCN. to fud. temperatures of 123 and 153 toward el and οὗ, respectively, aud a deusity of for both sources;"," \citet{Rem04} used CN to find temperatures of 123 and 153 toward e1 and e2, respectively, and a density of for both sources."898 Zliaιο&Πο(1997). derive higher densities of for the region usingNIL., \citet{ZH97} derive higher densities of for the region using.899.. Starforming region m an carly phase of its evolution which has wet to see substantial ionization of the molecular material surrounding newlv-forimed. massive D stars.," Star-forming region in an early phase of its evolution which has yet to see substantial ionization of the molecular material surrounding newly-formed, massive B stars."900" Manguiaetal.(1992). detected. four principal condensations labelled M. N. W. aud S. Our observations are centered on DBR21(00ID-M.. which i$. subdivided into two components separated bv ~ s"", AMIATL and AIM2."," \citet{Man92} detected four principal condensations labelled M, N, W, and S. Our observations are centered on DR21(OH)-M, which is subdivided into two components separated by $\sim$ $\arcsec$, MM1 and MM2."901 Despite their proximity. MMI and MM. differ substantialhe," Despite their proximity, MM1 and MM2 differ substantially."902 MALL is hot (— 160 EK). dense (— eur?)). aud moderately Iuninous (~ lsolar)). while MAI2 is cooler (~ 30 I. denser (~ em?}). and less luminous (~ ]solar)) (Manguiaetal.1991.1992:Manguii&Woot- 1993).," MM1 is hot $\sim$ 160 K), dense $\sim$ ), and moderately luminous $\sim$ ), while MM2 is cooler $\sim$ 30 K), denser $\sim$ ), and less luminous $\sim$ ) \citep{Man91,Man92,MW93}."903". Our J=3 spectrum indicates distinct peaks at -L5 and -1.3sl. attributed to MM and MAElo respectively,"," Our $J=3$ spectrum indicates distinct peaks at -4.5 and -1.3, attributed to MM1 and MM2, respectively."904 The J=14 spectrum is severely bleuded and demands a surprisinglyhigh contribution from the -L3 (MM2) component., The $J=4$ spectrum is severely blended and demands a surprisinglyhigh contribution from the -1.3 (MM2) component.905 Since this regiou las not been mapped at these frequencies aud the spectra were so highly bleuded. due caution should be exercised when assessing our results.," Since this region has not been mapped at these frequencies and the spectra were so highly blended, due caution should be exercised when assessing our results."906" Massive star forming region known to consist of 16 compact (~ 1"") components clustered within a 25” radius and aligned iu an inverted Y-shaped structure (Carayetal. 1996)...", Massive star forming region known to consist of 16 compact $\sim$ $\arcsec$ ) components clustered within a $\arcsec$ radius and aligned in an inverted Y-shaped structure \citep{Gar96}. .907" Our observations are centered on the continuum source ΠΑΝΟ, — 3"" south of the dominant source ITW2."," Our observations are centered on the continuum source HW3, $\sim$ $\arcsec$ south of the dominant source HW2."908. TW? is well within our beam and ds associated witha promising candidate for the detection of a massive disk (Torrellesetal.1996:Patel 2005).. though other studies suggest that this elongated molecular structure is explained by the superposition of at least three hot cores," HW2 is well within our beam and is associated witha promising candidate for the detection of a massive disk \citep{Tor96,Pat05}, , though other studies suggest that this elongated molecular structure is explained by the superposition of at least three hot cores"909means that. if not corrected. the pulse signal will drift by ~I70s(as/AU)sin/. where 7 is (he inclination.,"means that, if not corrected, the pulse signal will drift by $\sim 170\,{\rm s} (a_2/\au)\sin i$, where $i$ is the inclination."910 This is many times lareer (han (he pulse width. especially considering that for a3<6AU. the svstem will complete at least half an orbit in 5 vears.," This is many times larger than the pulse width, especially considering that for $a_2<6\,\au$, the system will complete at least half an orbit in 5 years."911 Hence. if the orbit around (he third body is not included. the pulses will not alien. even approximately. and the signal cannot be recovered.," Hence, if the orbit around the third body is not included, the pulses will not align, even approximately, and the signal cannot be recovered."912 llence. for each sky position (and ils corresponding barycentric correction). and each combination of (Q.P./544). where /i4; is the time of pericenter of the inner binary. one nisl conduct at least a 3-parameter search. corresponding to the period. phase. and amplitude of a sinusoidal orbit about M4.," Hence, for each sky position (and its corresponding barycentric correction), and each combination of $(\Omega,P,t_\peri)$, where $t_\peri$ is the time of pericenter of the inner binary, one must conduct at least a 3-parameter search, corresponding to the period, phase, and amplitude of a sinusoidal orbit about $M_3$."913" Then the number of such trials would be ~[(02,,,,/3)0]*101. where (oma,~6ÀU."," Then the number of such trials would be $\sim [(a_{2,\rm max}/3)\Omega]^3\sim 10^4$, where $a_{2,\rm max}\sim 6\,\au$."914" For do>(2,4444. a simpler one parameter unilorm-acceleration moclel would be acequate."," For $a_2>a_{2,\rm max}$, a simpler one parameter uniform-acceleration model would be adequate."915" Thus. the full search would be over 4xCAU()τς>2x10""3 skv posiGions.↽−− Psion10!"" inner binary periods and phases. [(02,44,,/3)0]*~101 outer binary trials. and perhaps 10 different pulse widths."," Thus, the full search would be over $4\pi\,(\au\,\Omega)^2=2\times91610^3$ sky positions, $P_{\rm max} T_{\rm mission}\Omega^2\sim 3\times91710^{10}$ inner binary periods and phases, $[(a_{2,\rm918max}/3)\Omega]^3\sim 10^4$ outer binary trials, and perhaps 10 different pulse widths."919 This is 10 independent (rials. which requires a detection threshold ol SNR. >9.," This is $10^{19}$ independent trials, which requires a detection threshold of SNR $>9$."920 The sheer volume of computations is forbidding., The sheer volume of computations is forbidding.921" As already mentioned. there are efficient algorithms for doing the 3x10!"" period search caleulations."," As already mentioned, there are efficient algorithms for doing the $3\times 10^{10}$ period search calculations."922 The problem is (hat these must each be done for 2x10 different configurations., The problem is that these must each be done for $2\times 10^8$ different configurations.923 Here I will simply assume that Moore's Law will handle (his problem. although there is probably room for algorithnic improvements as well," Here I will simply assume that Moore's Law will handle this problem, although there is probably room for algorithmic improvements as well."924 In particular. the shorter-period binaries (hat dominate (he “noise” will be detectable from subintervals 7«Tig; which will permit elimination of the (rials. and even allow standard Fourier techniques in many cases.," In particular, the shorter-period binaries that dominate the “noise” will be detectable from subintervals $T\ll T_{\rm mission}$, which will permit elimination of the outer-binary trials, and even allow standard Fourier techniques in many cases."925 Removal of this dominant “noise will be essential to finding the more numerous high-eccentricity binaries., Removal of this dominant “noise” will be essential to finding the more numerous high-eccentricity binaries.926 What parameters can be extracted from such observations. and how can the remaining degeneracies be resolved?," What parameters can be extracted from such observations, and how can the remaining degeneracies be resolved?"927 I will arene that full resolution requires identification of optical counterparts., I will argue that full resolution requires identification of optical counterparts.928 The counterparts thal are easiest to identify are 2-WD systems. and (hese are also (he most likely to vield kev spectroscopic data leading to complete resolution.," The counterparts that are easiest to identify are 3-WD systems, and these are also the most likely to yield key spectroscopic data leading to complete resolution."929 I therefore focus first on these svstems., I therefore focus first on these systems.930 There will of course be a huge munber of svstems without. counterparts. which could be subjected (o statistical analysis. bul the analvsis of that problem is beyond the scope of this Letter.," There will of course be a huge number of systems without counterparts, which could be subjected to statistical analysis, but the analysis of that problem is beyond the scope of this Letter."931 First. E review the observables.," First, I review the observables."932 The best-fit barvcentric correction gives the direction on (he sky. and the waveform gives the three Euler angles of the binary (up to discrete degeneracies due to (he quadrupole nature of GWs).," The best-fit barycentric correction gives the direction on the sky, and the waveform gives the three Euler angles of the binary (up to discrete degeneracies due to the quadrupole nature of GWs)."933 These will be of use further below but, These will be of use further below but934importantly. the same ratios by number.,"importantly, the same ratios by number."935 This positive test further strengthens our observational result., This positive test further strengthens our observational result.936 Since we do not have a knowledge of the total mass involved. the most insightful measurement we obtain from X-ray best fit data is the ratio by number of the abundances of C. N and O. We derive C/N=0.9!neL2 and O/N=0.3.05Mi Cor logarithmicH abundances relativeH to the solar value (C/N|=0.5!E[ and [O/N|=1. L3).," Since we do not have a knowledge of the total mass involved, the most insightful measurement we obtain from X–ray best fit data is the ratio by number of the abundances of C, N and O. We derive ${\rm937C/N}=0.9^{+3.2}_{-0.7}$ and ${\rm O/N}=0.3^{+0.6}_{-0.2}$ (or logarithmic abundances relative to the solar value $[{\rm C/N}]=-0.5^{+0.7}_{-1.5}$ and $[{\rm O/N}]=-1.4^{+0.5}_{-0.2}$ )."938 This extremely low ratio O/N is very difficult to account for in terms of standard interstellar medium and of stellar evolution models of isolated stars., This extremely low ratio O/N is very difficult to account for in terms of standard interstellar medium and of stellar evolution models of isolated stars.939 In particular. solar metallicity models are unable to reproduce these abundance ratios (Hirschi et al.," In particular, solar metallicity models are unable to reproduce these abundance ratios (Hirschi et al."940 2005: Portinar et al., 2005; Portinari et al.941 1998)., 1998).942 Possibly. binary evolutionary models can account for this constraints more easily. having more degrees of freedom. but recent models seem to indicate that conditions similar to single star progenitors are needed (Detmers et al.," Possibly, binary evolutionary models can account for this constraints more easily, having more degrees of freedom, but recent models seem to indicate that conditions similar to single star progenitors are needed (Detmers et al."943 2008)., 2008).944 A key ingredient in the evolution of single massive stars is missing: rotation-induced mixing in the stellar interior., A key ingredient in the evolution of single massive stars is missing: rotation-induced mixing in the stellar interior.945 If the ejected mass reflects the C/N and O/N ratios that would be expected at the end of the main sequence phase as observed in several nebulae around bright stars. we would need a large rotation-induced mixing fraction with only ~10% of the initial mass unprocessed (based on calculations in Lamers et al.," If the ejected mass reflects the C/N and O/N ratios that would be expected at the end of the main sequence phase as observed in several nebulae around bright stars, we would need a large rotation-induced mixing fraction with only $\sim94610\%$ of the initial mass unprocessed (based on calculations in Lamers et al."947 2001)., 2001).948 This mixing can occur only in the case of a very fast stellar rotation (close to break-up)., This mixing can occur only in the case of a very fast stellar rotation (close to break-up).949 A viable alternative could be also provided by a close binary system. either in terms of tidal locking or evolution through a common envelope phase during which an enriched shell might be ejected.," A viable alternative could be also provided by a close binary system, either in terms of tidal locking or evolution through a common envelope phase during which an enriched shell might be ejected."950 The collapsar scenario requires massive helium stars with rapidly rotating cores to produce a GRB (Woosley 1993)., The collapsar scenario requires massive helium stars with rapidly rotating cores to produce a GRB (Woosley 1993).951 However. stellar models with magnetic torques fail to retain such high core angular momentum.," However, stellar models with magnetic torques fail to retain such high core angular momentum."952 In the last few years there has been mounting theoretical support the idea that only massive stars that are initially very rapidly rotating and have sufficiently low metallicities can satisfy the conditions for GRB formation (Yoon Langer 2005; Woosley Heger 2006)., In the last few years there has been mounting theoretical support the idea that only massive stars that are initially very rapidly rotating and have sufficiently low metallicities can satisfy the conditions for GRB formation (Yoon Langer 2005; Woosley Heger 2006).953 In fact. below a suitable metallicity threshold. a rotationally-induced mixing process produces a quasi chemically homogeneous stellar evolution avoiding the spin-down of the stellar core.," In fact, below a suitable metallicity threshold, a rotationally-induced mixing process produces a quasi chemically homogeneous stellar evolution avoiding the spin-down of the stellar core."954 As a test-bed we consider massive star evolution models at sub-solar initial metallicities (Yoon et al., As a test-bed we consider massive star evolution models at sub-solar initial metallicities (Yoon et al.955 2006)., 2006).956 We also limit the mass range of the progenitor tol5205AL... according to the detailed modelling of the supernova ejecta (Mazzali et al.," We also limit the mass range of the progenitor to $15-25\msole$, according to the detailed modelling of the supernova ejecta (Mazzali et al."957 2006)., 2006).958 We find that a number of models are able to satisfy our constraints (see Fig., We find that a number of models are able to satisfy our constraints (see Fig.959 2)., 2).960 All these models are characterized by a fast semi-convective mixing of the core., All these models are characterized by a fast semi-convective mixing of the core.961 Within the initial mass range of the progenitor we are able to constrain the initial fraction of the Keplerian velocity Coi) of the equatorial rotational velocity to 0.15ZcgiegLX0.8 and the initial metallicity to Z<0.1Z ...," Within the initial mass range of the progenitor we are able to constrain the initial fraction of the Keplerian velocity $v_{\rm K}$ ) of the equatorial rotational velocity to $0.45\lsim v_{\rm ini}/v_{\rm K}\lsim 0.8$ and the initial metallicity to $Z<0.1\,Z_\odot$ ."962 With these parameters the progenitor star fits nicely within the allowed region for the GRB production (Yoon et al., With these parameters the progenitor star fits nicely within the allowed region for the GRB production (Yoon et al.963 2006)., 2006).964 It thus appears that the observations of GRBO60218 provide the first observational evidence that only a progenitor star characterized by a fast stellar rotation and sub-solar initial metallicity can lead to such an explosive event., It thus appears that the observations of GRB060218 provide the first observational evidence that only a progenitor star characterized by a fast stellar rotation and sub-solar initial metallicity can lead to such an explosive event.965Whatever mass is not used to form heavy nuclei remains as Helium. i.e. Xp—l1—Xy.,"Whatever mass is not used to form heavy nuclei remains as Helium, i.e. $X_{\rm He} \simeq 1 - X_{\rm h}$."966 Although heavy nuclei may form deep in the wind. they could in principle be destroyed at larger radii in the jet.," Although heavy nuclei may form deep in the wind, they could in principle be destroyed at larger radii in the jet."967 In particular. spallation can oceur if heavy nuclei collide with a particle of relative energy exceeding the nuclear binding energy =8 MeV nucleon'," In particular, spallation can occur if heavy nuclei collide with a particle of relative energy exceeding the nuclear binding energy $\approx 8$ MeV $^{-1}$."968 For heavy nuclei. the cross section for inelastic nuclear collisions is ~| barn. similar to the Thomson (photon) cross section.," For heavy nuclei, the cross section for inelastic nuclear collisions is $\sim 1$ barn, similar to the Thomson (photon) cross section."969" Because the flow contains ~Z electrons per nucleon, this implies that inelastic scattering is only important at radii well inside the Thomson photosphere at ry,~10! em (e.g. Koers 2007)."," Because the flow contains $\sim Z$ electrons per nucleon, this implies that inelastic scattering is only important at radii well inside the Thomson photosphere at $r_{\rm ph} \sim 10^{11}$ cm (e.g. \citealt{Koers&Giannios07}) )."970 If strong shocks were to take place at these small radii. the resultant heating could in principle destroy the nuclei.," If strong shocks were to take place at these small radii, the resultant heating could in principle destroy the nuclei."971 However. for the strongly magnetized under consideration. the magnetization is probably still high at jetsthese radii. such that strong shocks are highly suppressed (e.g. Kennel&Coroniti 19843).," However, for the strongly magnetized jets under consideration, the magnetization is probably still high at these radii, such that strong shocks are highly suppressed (e.g. \citealt{Kennel&Coroniti84}) )."972 In particular. the radial profile of acceleration to a Lorentz factor Poxr’ occurs more in MHD jets (8s1/3—1/2: Drenkhahn»Spruit2002:: gradually‘howVlahakis&Kónigl 2003a.b:: Komissarovetal.200ο Tehekhovetal. 20092: Granotetal. 20109) than in accelerated fireballs (8= 1).," In particular, the radial profile of acceleration to a Lorentz factor $\Gamma \propto r^{\beta}$ occurs more gradually in MHD jets $\beta \approx 1/3-1/2$; \citealt{Drenkhahn&Spruit02}; \citealt{Vlahakis&Konigl03a,Vlahakis&Konigl03b}; ; \citealt{Komissarov+09}; \citealt{Tchekhovskoy+09}; \citealt{Granot+10}) ) than in thermally-accelerated fireballs $\beta = 1$ )."973" This implies that full acceleration to Fl~o,100—1000 is generally only possible at large distances (typically >10'* em). well into the region where the plasma is collisionless with respect to direct nuclear collisions."," This implies that full acceleration to $\Gamma \sim \sigma_{0} \sim 100-1000$ is generally only possible at large distances (typically $\gtrsim 10^{12}$ cm), well into the region where the plasma is collisionless with respect to direct nuclear collisions."974 We thus conclude it is unlikely that nuclei are destroyed during the collimation and acceleration phase of the jet (although inby$3.3 we discuss the conditions under which nuclei are destroyed GRB photons during the subsequent UHECR acceleration phase)., We thus conclude it is unlikely that nuclei are destroyed during the collimation and acceleration phase of the jet (although in $\S\ref{sec:photo}$ we discuss the conditions under which nuclei are destroyed by GRB photons during the subsequent UHECR acceleration phase).975 Heavy nuclei may also be produced in GRB outflows powered by black hole accretion. provided that the jet is magnetically-driven.," Heavy nuclei may also be produced in GRB outflows powered by black hole accretion, provided that the jet is magnetically-driven."976 If the jet threads the black hole event horizon (as occurs if its power derives from the spin of the black hole: Blandford&Zna-jek 1977)). then the outflow composition is eftectively baryon-free near the ergosphere.," If the jet threads the black hole event horizon (as occurs if its power derives from the spin of the black hole; \citealt{Blandford&Znajek77}) ), then the outflow composition is effectively baryon-free near the ergosphere."977 To what degree baryons are entrained in the jet at larger radii depends on uncertain diffusive processes from the jet walls. thereby making c dificult to predict with contidence (e.g. Levinson&Eichler20031:McKinney 2005)).," To what degree baryons are entrained in the jet at larger radii depends on uncertain diffusive processes from the jet walls, thereby making $\sigma_{0}$ difficult to predict with confidence (e.g. \citealt{Levinson&Eichler03}; \citealt{McKinney05}) )."978 The entropy in this case depends on the amount of heating (due to e.g. v—x annihilation or magnetic reconnection) and this uncertain baryon loading., The entropy in this case depends on the amount of heating (due to e.g. $\nu-\bar{\nu}$ annihilation or magnetic reconnection) and this uncertain baryon loading.979 If. on the other hand. the jet directly threads the surface of the accretion disk (e.g. Blandford&Payne1982) its mass-loading may (as in proto-magnetar winds) be M by neutrino heating in the disk atmosphere (e.g. Levinson2006::-Surman 06: Metzger.Thompson&Quataert.2008:: Quataert.2008)).," If, on the other hand, the jet directly threads the surface of the accretion disk (e.g. \citealt{Blandford&Payne82}) ), its mass-loading may (as in proto-magnetar winds) be controlled by neutrino heating in the disk atmosphere (e.g. \citealt{Levinson06}; \citealt{Surman+06}; \citealt*{Metzger+08b}; \citealt*{Metzger+08c}) )."980" In this case. the outflow is likely to be proton- (Metzger.Thompson&Quataert2008)... with an entropy and expansion timescale similar to those in proto-magnetar winds. but depending on the accretion rate. black hole mass. open magnetic field geometry. i wind launching radius (see e.g. Metzger.Piro&Quataert2008::""their eqs. ["," In this case, the outflow is likely to be proton-rich \citep*{Metzger+08b}, with an entropy and expansion timescale similar to those in proto-magnetar winds, but depending on the accretion rate, black hole mass, open magnetic field geometry, and wind launching radius (see e.g. \citealt*{Metzger+08c}; their eqs. ["98124] and [26].,24] and [26]).982" Although the outflow properties are certain than in proto-magnetar winds. ethcient nucleosynthesis may well lead to a heavy fraction Xj,~| in aecretion-powered outflows as well."," Although the outflow properties are less certain than in proto-magnetar winds, efficient nucleosynthesis may well lead to a heavy fraction $X_{\rm h}\sim 1$ in accretion-powered outflows as well."983 Near the light cylinder radius Αι~ km the power in the magnetar wind is concentrated in the rotational equator (e.g. Bucciantinietal. 200600)., Near the light cylinder radius $R_{\rm L} \sim 100$ km the power in the magnetar wind is concentrated in the rotational equator (e.g. \citealt{Bucciantini+06}) ).984 On larger scales the wind is collimated into a bipolar jet by its interaction with the Prosser star (e.g. Uzdensky&MacFadyen2007:: Bucciantinietal.‘breaks2007.2008. 2009).," On larger scales the wind is collimated into a bipolar jet by its interaction with the progenitor star (e.g. \citealt{Uzdensky&MacFadyen07}; \citealt{Bucciantini+07, Bucciantini+08, Bucciantini+09}) )."985 After the jet propagates through the star and out” of the surface on a timescale /[O0 s (e.g. Aloyetal.2000)) the magnetar wind escapes through a relatively clear channel.," After the jet propagates through the star and `breaks out' of the surface on a timescale $t\sim 10$ s (e.g. \citealt{Aloy+00}) ), the magnetar wind escapes through a relatively clear channel."986" High energy emission (the ""GRB') occurs when the jet dissipates its energy via shocks or magnetic reconnection at larger radii ~10!10' em (see below).", High energy emission (the `GRB') occurs when the jet dissipates its energy via shocks or magnetic reconnection at larger radii $\sim 10^{13}-10^{16}$ cm (see below).987 Although there are many potential sources of short timescale variability in the outflow (e.g. interaction of the jet with the confining stellar envelope). numerical simulations show that the time- and angle-averaged values of Et) and o6) (Fig. 13) ," Although there are many potential sources of short timescale variability in the outflow (e.g. interaction of the jet with the confining stellar envelope), numerical simulations show that the time- and angle-averaged values of $\dot{E}(t)$ and $\sigma_{0}(t)$ (Fig. \ref{fig:wind}) )"988match those set by the magnetar wind at much smaller radii (e.g. Morsonyetal. 20103)., match those set by the magnetar wind at much smaller radii (e.g. \citealt{Morsony+10}) ).989" We assume that the opening angle of the jet at the stellar surface is 6j~4° (e.g. Bucciantini 2009). such that the isotropic jet luminosity is related to the wind power by EEjfi. where fi,=eL2xl0?isthe beaming fraction."," We assume that the opening angle of the jet at the stellar surface is $\theta_{\rm j} \sim 4^{\circ}$ (e.g. \citealt{Bucciantini+09}) ), such that the isotropic jet luminosity is related to the wind power by $\dot{E}_{\rm iso} = \dot{E}/f_{\rm b}$, where $f_{\rm b} = \theta_{\rm j}^{2}/2 \simeq 2\times 10^{-3}$ is the beaming fraction."990 If UHECRs originate from GRBs. they are probably accelerated by the same dissipative mechanisms responsible for accelerating electrons and powering the GRB emission.," If UHECRs originate from GRBs, they are probably accelerated by the same dissipative mechanisms responsible for accelerating electrons and powering the GRB emission."991 For magnetically-dominated outflows. most of the jet's. energy resides in Poynting flux near the central engine: a sizable fraction of this magnetic energy must be converted into bulk energy in order to explain the high Lorentz factors (T> 107) kineticinferred from GRB observations (e.g. Lithwick&Sari 20011).," For magnetically-dominated outflows, most of the jet's energy resides in Poynting flux near the central engine; a sizable fraction of this magnetic energy must be converted into bulk kinetic energy in order to explain the high Lorentz factors $\Gamma \gtrsim 10^{2}$ ) inferred from GRB observations (e.g. \citealt{Lithwick&Sari01}) )."992" Depending on the means and efficacy of acceleration in the jet ganimia- emission (and UHECR acceleration) may be poweredeither by the dissipation of the jets Poynting flux directly (magnetic reconnection’) near or above the photosphere ($3.13: and/or via ""internal shocks’ within the jet at larger radii ($3.2)."," Depending on the means and efficacy of acceleration in the jet, gamma-ray emission (and UHECR acceleration) may be poweredeither by the dissipation of the jet's Poynting flux directly (`magnetic reconnection') near or above the photosphere $\S\ref{sec:reconnection}$ ); and/or via `internal shocks' within the jet at larger radii $\S\ref{sec:shocks}$ )."993 Below we discuss the conditions for UHECR acceleration in magnetar jets., Below we discuss the conditions for UHECR acceleration in magnetar jets.994 Our treatment closely follows past work that relies on direct constraints from GRB observations (e.g. Waxman 1995)., Our treatment closely follows past work that relies on direct constraints from GRB observations (e.g. \citealt{Waxman95}) ).995wo wave.,two ways.996 First. the peak fluxes of such bursts from cach individual source should be the same.," First, the peak fluxes of such bursts from each individual source should be the same."997 Second. the peak Tuninosities inferred for sources with iudepeudenut distauce neasurclents. such as those iu globular clusters. should correspond to the Eddiuston limit for a neutron star.," Second, the peak luminosities inferred for sources with independent distance measurements, such as those in globular clusters, should correspond to the Eddington limit for a neutron star."998 Since the original discovery of Eddineton-limited bursts. a Πο of authors have addressed these questions.," Since the original discovery of Eddington-limited bursts, a number of authors have addressed these questions."999 Iu carly observations. a significant nunber of radius expausion musts had been detected from three sources and their oak fluxes were found to be similar to within ~20% (IU. 230: Vaccaetal.1986:Damen 1990: IU 536: Damenetal.1990: LU 31: DBasiuskaetal 1981)).," In early observations, a significant number of radius expansion bursts had been detected from three sources and their peak fluxes were found to be similar to within $\simeq 20$ (4U $-$ 30: \citealt{vlvp86,damen90}; ; 4U $-$ 536: \citealt{damen90}; 4U $-$ 34: \citealt{bas84}) )."1000 Iun particular. the peak dlunimosities of radius-expausion bursts observed from LU 30. which resides iu the gobular cluster NGC 6621 were found to © Colmparable to the Eddingtou limit for a neutron star.," In particular, the peak luminosities of radius-expansion bursts observed from 4U $-$ 30, which resides in the gobular cluster NGC 6624 were found to be comparable to the Eddington limit for a neutron star."1001 Although successful iu providing support to the mocel of LEddiustou-Imuited bursts. these carly studies were Ipnuuited o a small πο” of sources and suffered from the statistical uncertaiuties inherent to fitting spectral models o low signal-to-noise data.," Although successful in providing support to the model of Eddington-limited bursts, these early studies were limited to a small number of sources and suffered from the statistical uncertainties inherent to fitting spectral models to low signal-to-noise data."1002 In recent wears. observations with and the (RATE)) have revealed a large umuber of Eddiuston- bursts from several sources. which have beeu studied iu great detail.," In recent years, observations with and the ) have revealed a large number of Eddington-limited bursts from several sources, which have been studied in great detail."1003 Usine aud data. I&kuulkersetal.(20024)— recently studied the Eddineton-limited bursts of 12 elobular cluster sources with well known distances aud showed that. with one exception. their peak fluxes were constant to within ~15% and were comparable to the Eddiugton lint for neutron stars with II-poor atinosphlieres.," Using and data, \cite{kuul02} recently studied the Eddington-limited bursts of 12 globular cluster sources with well known distances and showed that, with one exception, their peak fluxes were constant to within $\simeq 15$ and were comparable to the Eddington limit for neutron stars with H-poor atmospheres."1004 Iu this series of articles. we use all the publicly available data obtained with to date in order to observationallv test the lypothesis that Eddinegton-liuited bursts cau be used as distance indicators for neutron-star LAINBs.," In this series of articles, we use all the publicly available data obtained with to date in order to observationally test the hypothesis that Eddington-limited bursts can be used as distance indicators for neutron-star LMXBs."1005" In the preseut study we quantify. and examine the causes of. svstematic variations iu the peak burst flux from the source with the ereatest nuniber of bursts detected byΠΑΤΕ,31."," In the present study we quantify, and examine the causes of, systematic variations in the peak burst flux from the source with the greatest number of bursts detected by,."1006 The N-rav source (GN 35110: 72= 3503.6= (0215) was first resolved by scaus of the Galactic center region (Forman 1976).," The X-ray source (GX 354+0; $l=354\fdg3$, $b=-0\fdg15$ ) was first resolved by scans of the Galactic center region \cite[]{ftj76}."1007. Theruouuclear N-rav bursts from wwere discovered during observations (Lewinctal.1976:IIofinanetal. 1976).," Thermonuclear X-ray bursts from were discovered during observations \cite[]{lcd76,hoff76}."1008. The bursting behavior was subsequently studied in detail using exteusive observations o»$45-3. which accumulated 96 bursts in total.," The bursting behavior was subsequently studied in detail using extensive observations by, which accumulated 96 bursts in total."1009 Frou hese data Basinskaetal.(1981) showed evideuce or a narrow distribution of peal burst fluxes. as well as a correlation between the peak flux aud the burst duence.," From these data \cite{bas84} showed evidence for a narrow distribution of peak burst fluxes, as well as a correlation between the peak flux and the burst fluence."1010 The distance to the source has previously beeu estimated from measurements of the peak burst fluxes as οσοι [26.1 kpe (wanParadijs1978:Basiuskactal.1981:Wamuukeretal. 1989).," The distance to the source has previously been estimated from measurements of the peak burst fluxes as between 4.2–6.4 kpc \cite[]{vp78,bas84,kam89}."1011. The estimated extinction o the source is Ay —Lk only a precise position ollowing from the detection. of a radio counterpart allowed ideutification with a A=15 iufrared source (Martictal.1998)., The estimated extinction to the source is $A_V\approx14$; only a precise position following from the detection of a radio counterpart allowed identification with a $K=15$ infrared source \cite[]{marti98}.1012 No independeut distance nuieasurement is available., No independent distance measurement is available.1013" Long-term, lucasurements, as well as the first two vens of monitoring bv the All-Sky Monitor (ASAD) on boardRATE. sugeest the preseuce of a lone-teru quasi-periodicity of 63 or 72 d. respectively (Nongctal.1998)."," Long-term measurements, as well as the first two years of monitoring by the All-Sky Monitor (ASM) on board, suggest the presence of a long-term quasi-periodicity of 63 or 72 d, respectively \cite[]{kong98}."1014. RNTE//PCA observations of the source in 1996 led to the discovery of nearly coherent millisecond oscillations caving the X-ray bursts (Strolunaveretal.1996)., /PCA observations of the source in 1996 led to the discovery of nearly coherent millisecond oscillations during the X-ray bursts \cite[]{stroh96}.1015. Similar oscillations were subsequently observed in 9 other sources (vanderαν2000:Wijnandsetal.2001:Gallowayct2001:Ἱναατοίetal. 2002).," Similar oscillations were subsequently observed in 9 other sources \cite[]{vdk00,wij01,1916burst,kaaret02}."1016. A substantial archive (1110 ks) of public /PCA data frou hhas accumulated throughout these observatious. dating frou shortly after the lunch of the satellite ou 1995 December 30.," A substantial archive (1140 ks) of public /PCA data from has accumulated throughout these observations, dating from shortly after the launch of the satellite on 1995 December 30."1017 Subsets of the bursts observed. during the PCA observations have been studied by vanStraatenetal.(2001) and Franco(2001).. with particular attention to the relationship between the appearance of burst oscillations and the mass acerction rate.," Subsets of the bursts observed during the PCA observations have been studied by \cite{vs01} and \cite{franco01}, with particular attention to the relationship between the appearance of burst oscillations and the mass accretion rate."1018 A significant fraction of the bursts observed by show evidence for photospheric radius expausion. exlibiting the characteristic temporary iucrease iu the apparent blackbody radius. coincident with a decrease in the color temperature in the carly stages of the burst.," A significant fraction of the bursts observed by show evidence for photospheric radius expansion, exhibiting the characteristic temporary increase in the apparent blackbody radius, coincident with a decrease in the color temperature in the early stages of the burst."1019 Ἁπιιοetal.(2001) used this dataset to find a correlation between the frequency of the burst oscillations aud the prefercutial appearance m radius expansion or non-radius expansion bursts im niue sources., \cite{muno01} used this dataset to find a correlation between the frequency of the burst oscillations and the preferential appearance in radius expansion or non-radius expansion bursts in nine sources.1020 We have obtained all the available public ddata to date from the Wieh-Enerey Astroplivsics Science Archive Research οσα (HIIEASARC: /heasarc.estc.uasa.egov)., We have obtained all the available public data to date from the High-Energy Astrophysics Science Archive Research Center (HEASARC; ).1021 This study is part of a larger effort involving more than 70 kuown bursters: the burst detection and analysis procedures. aswell as the resulting burst database are deseribed iu more detail iu wlloway et al. (," This study is part of a larger effort involving more than 70 known bursters; the burst detection and analysis procedures, aswell as the resulting burst database are described in more detail in Galloway et al. ("10222003b. in preparation).,"2003b, in preparation)."1023 Several of the bursts frou, Several of the bursts from1024"of these differences we decided to reinvestigate the validity of their method, exploring if the result is similar for larger mass ratios like ours (1:10) and for other satellite and primary galaxy morphologies.","of these differences we decided to reinvestigate the validity of their method, exploring if the result is similar for larger mass ratios like ours (1:10) and for other satellite and primary galaxy morphologies."1025 Our results for the specific AM of stars originally in the primary disk and in the satellite galaxy are shown in Figs., Our results for the specific AM of stars originally in the primary disk and in the satellite galaxy are shown in Figs.1026 14 and 15.., \ref{AMsat1} and \ref{AMsat2}.1027" We divided the stars into two regions, one at |z |<1 kpc and another at |z |21 kpc."," We divided the stars into two regions, one at $\mid z\mid\le$ 1 kpc and another at $\mid1028z\mid\ge$ 1 kpc."1029 The general result confirms that the difference between the specific AM of satellite stars and primary disk stars is significant in the outer disk regions: typically the difference is 20% at radii of 1.5-2Ry., The general result confirms that the difference between the specific AM of satellite stars and primary disk stars is significant in the outer disk regions: typically the difference is $\%$ at radii of $R_d$.1030 But at these radii the fraction of satellite stars with |z [<1 kpc is only a few percent of the total number of stars., But at these radii the fraction of satellite stars with $\mid z\mid\le$ 1 kpc is only a few percent of the total number of stars.1031 This means that it can be extremely difficult to detect these stars in an observational sample., This means that it can be extremely difficult to detect these stars in an observational sample.1032" We find, however, that the fraction of satellite stars is five to ten times larger at greater heights: at |z |=1 kpc, outside a radius of 1.5-2R; the specific AM content of accreted stars can be significantly different from that of primary stars, and their fraction sufficiently higher (around 10%) to make the observational detection of this signature more likely."," We find, however, that the fraction of satellite stars is five to ten times larger at greater heights: at $\mid z\mid\ge$ 1 kpc, outside a radius of $R_d$ the specific AM content of accreted stars can be significantly different from that of primary stars, and their fraction sufficiently higher (around $\%$ ) to make the observational detection of this signature more likely."1033 Note however that generally the satellite stars with the lowest AM content are found very far from the galaxy midplane (|z |=>5 kpc)., Note however that generally the satellite stars with the lowest AM content are found very far from the galaxy midplane $\mid z\mid\ge$ 5 kpc).1034" We want to point out that there are also cases in which there is no discernible difference in the specific AM of satellite and primary disk stars at any radius, even at the largest radii plotted in Figs."," We want to point out that there are also cases in which there is no discernible difference in the specific AM of satellite and primary disk stars at any radius, even at the largest radii plotted in Figs."1035 14 and 15))., \ref{AMsat1} and \ref{AMsat2}) ).1036" This is in agreement with what was found in Fig. 12,,"," This is in agreement with what was found in Fig. \ref{transvel},"1037 where primary and satellite stars show remarkably similar tangential velocities., where primary and satellite stars show remarkably similar tangential velocities.1038" Obviously, the specific AM becomes a better discriminant if satellite orbits counter-rotate with respect to the primary disk — a clear sign of an external origin of stars."," Obviously, the specific AM becomes a better discriminant if satellite orbits counter-rotate with respect to the primary disk – a clear sign of an external origin of stars."1039 We find counter-rotation in all merger remnants which formed from satellites on retrograde orbits (some examples are shown in Fig. 15))., We find counter-rotation in all merger remnants which formed from satellites on retrograde orbits (some examples are shown in Fig. \ref{AMsat2}) ).1040 We will discuss the main properties of counter-rotating stars further in the next section., We will discuss the main properties of counter-rotating stars further in the next section.1041 Counter-rotating stellar disks are observed in external galaxies (see?) and counter-rotation is also found in the Milky Way halo (see?).., Counter-rotating stellar disks are observed in external galaxies \citep[see ][]{yoachimD205} and counter-rotation is also found in the Milky Way halo \citep[see ][]{carollo207}.1042" The presence of stars (in the thick disk or in the halo) rotating in a direction which is reverse of the galaxy main spin cannot be explained with secular evolution processes, and is a strong evidence for an external origin."," The presence of stars (in the thick disk or in the halo) rotating in a direction which is reverse of the galaxy main spin cannot be explained with secular evolution processes, and is a strong evidence for an external origin."1043" It is thus of great interest to investigate the characteristics of counter-rotating stars in our merger remnants — specifically, their fraction and vertical distribution with radius."," It is thus of great interest to investigate the characteristics of counter-rotating stars in our merger remnants – specifically, their fraction and vertical distribution with radius."1044 Examples are shown in Figs., Examples are shown in Figs.1045 16 and 17 for a number of dissipationless and dissipative retrograde mergers., \ref{counter_nogas} and \ref{counter_gas} for a number of dissipationless and dissipative retrograde mergers.1046" In these plots four different regions are selected: (1) at |z|€1 kpc, (2) at 1<|z|x3 kpc, (3) at 3<|z|<5 kpc and (4) at 5<|z[x10 kpc."," In these plots four different regions are selected: (1) at $\mid z\mid\le$ 1 kpc, (2) at $\le\mid z\mid\le$ 3 kpc, (3) at $\le\mid z\mid\le$ 5 kpc and (4) at $\le\mid z\mid\le$ 10 kpc."1047" It is clear that counter-rotating stars are found at all values of z, from the galaxy midplane to 10 kpc above it, and that the probability to find counter-rotating stars increases with height: the fraction Na/N;s, of counter-rotating stars to the total number of stars in the region is <5% up to |z|<3 kpc, typically around 10% in the 3 kpc<|z|x5 kpc and it can reach 30% in the region highest above the disk."," It is clear that counter-rotating stars are found at all values of z, from the galaxy midplane to 10 kpc above it, and that the probability to find counter-rotating stars increases with height: the fraction $N_{ct}/N_{tot}$ of counter-rotating stars to the total number of stars in the region is $\le$ $\%$ up to $\mid z\mid\le$ 3 kpc, typically around $\%$ in the 3 $\le\mid z\mid\le$ 5 kpc and it can reach $\%$ in the region highest above the disk."1048" This trend is also due to the fact that the fraction of satellite stars N, to the total number of stars increases with z. In other words, it is the overall increase in the fraction of satellite stars with z which determines this trend, not simply a decrease in the number of disk stars as a function of height above the disk."," This trend is also due to the fact that the fraction of satellite stars $N_s$ to the total number of stars increases with z. In other words, it is the overall increase in the fraction of satellite stars with z which determines this trend, not simply a decrease in the number of disk stars as a function of height above the disk."1049" Furthermore the fraction of counter- stars depends also on the initial orbital inclination of the satellite: for a satellite on an orbit inclined by 60 degrees with respect to the primary disk, this fraction is lower at all z (?).."," Furthermore the fraction of counter-rotating stars depends also on the initial orbital inclination of the satellite: for a satellite on an orbit inclined by 60 degrees with respect to the primary disk, this fraction is lower at all z \citep{villalobosH208}."1050" If counter-rotating stars are a natural outcome of low orbital inclination in single minor mergers with satellites on retrograde orbits, would a second retrograde merger then increase the fraction of counter-rotating stars even further at all heights?"," If counter-rotating stars are a natural outcome of low orbital inclination in single minor mergers with satellites on retrograde orbits, would a second retrograde merger then increase the fraction of counter-rotating stars even further at all heights?"1051 In our models (Fig. 18)), In our models (Fig. \ref{multi_counter}) )1052" the effect of a second retrograde merger with the same mass ratio is to increase the fraction of rotating stars by a factor of about two, at all heights."," the effect of a second retrograde merger with the same mass ratio is to increase the fraction of counter-rotating stars by a factor of about two, at all heights."1053 We can conclude from this that repeated retrograde minor mergers have a cumulative effect on the number of counter-rotating stars in the thick disk and inner halo., We can conclude from this that repeated retrograde minor mergers have a cumulative effect on the number of counter-rotating stars in the thick disk and inner halo.1054" The AM evolution of the baryonic component during merging processes discussed in the ?? is naturally reflected in an evolution of the line-of-sight velocity γιος and the vij,/o, ratio.", The AM evolution of the baryonic component during merging processes discussed in the \ref{angm} is naturally reflected in an evolution of the line-of-sight velocity $v_{los}$ and the $v_{los}/\sigma_v$ ratio.1055" Minor mergers always produce a decrease in γιος and an increase in the velocity dispersion c, of the stellar component at all radii (Fig. 19)).", Minor mergers always produce a decrease in $v_{los}$ and an increase in the velocity dispersion $\sigma_v$ of the stellar component at all radii (Fig. \ref{multi-v}) ).1056" The remnant stellar disks usually have a smaller vi5,/c', ratio than the initial values before interaction.", The remnant stellar disks usually have a smaller $v_{los}/\sigma_v$ ratio than the initial values before interaction.1057" Consecutive satellite accretions have cumulative effects on decreasing the γιος and increasing the c, and thus deceasing the vij,/c*, ratio."," Consecutive satellite accretions have cumulative effects on decreasing the $v_{los}$ and increasing the $\sigma_v$ , and thus deceasing the $v_{los}/\sigma_v$ ratio."1058" Nevertheless, smaller variations in both vj, and σν can be found in minor mergers with gas, compared to gas-free merger cases, due to the fact that dissipative gascan help preserve disk rotation by forming new rotating disk stars during mergers."," Nevertheless, smaller variations in both $v_{los}$ and $\sigma_v$ can be found in minor mergers with gas, compared to gas-free merger cases, due to the fact that dissipative gascan help preserve disk rotation by forming new rotating disk stars during mergers."1059" The decreases in γιος and the vj5,/c', ratio", The decreases in $v_{los}$ and the $v_{los}/\sigma_v$ ratio1060at y-ray and optical energies correlate with those of the radio emission at VLBI scales. which imply a common emission region.,"at $\gamma$ -ray and optical energies correlate with those of the radio emission at VLBI scales, which imply a common emission region."1061 This emission region is related to the inner jet. extending over a distance of up to ppe from the VLBI core. which i5 at a distance of >> ppe from the central engine. well beyond the BLR.," This emission region is related to the inner jet, extending over a distance of up to pc from the VLBI core, which is at a distance of $\gg$ pc from the central engine, well beyond the BLR."1062 The mechanism for the emission at radio and optical wavelengths is therefore dominated by the synchrotron emission from the relativistic jet itself., The mechanism for the emission at radio and optical wavelengths is therefore dominated by the synchrotron emission from the relativistic jet itself.1063 The simultaneity of y-ray emission implies inverse Compton upscattering of synchrotror photons produced in the jet., The simultaneity of $\gamma$ -ray emission implies inverse Compton upscattering of synchrotron photons produced in the jet.1064 The relative increase of optical and radio emission compared to y-ray emission Is a factor of 2 higher in the radio and even a factor of 4 higher in the optical emission. which is consistent with the mechanism of synchrotror self-Compton.," The relative increase of optical and radio emission compared to $\gamma$ -ray emission is a factor of 2 higher in the radio and even a factor of 4 higher in the optical emission, which is consistent with the mechanism of synchrotron self-Compton."1065" An external contribution of ""seed photons. as proposed by external Compton scenarios (e.g. is not required to produce the amount of the observed y-ray emission."," An external contribution of “seed” photons, as proposed by external Compton scenarios \citep[e.g.][]{2010MNRAS.405L..94T} is not required to produce the amount of the observed $\gamma$ -ray emission."1066 Additionally. we have found that the properties of the emission Il this region are consistent with the Compton-loss stage of a shock (Section 3.1.3)).," Additionally, we have found that the properties of the emission in this region are consistent with the Compton-loss stage of a shock (Section \ref{sec:flux}) )."1067 Altogether. this contradicts the common theoretical high energy production scenario described in the previous paragraph.," Altogether, this contradicts the common theoretical high energy production scenario described in the previous paragraph."1068 Recent observations of TeV emission from FSRQs (e.g.?) should not have been possible 1f the high energy emission site were within the BLR. which ts expected to be opaque to y-rays at TeV energies due to yy interactions.," Recent observations of TeV emission from FSRQs \citep[e.g.][]{2011ApJ...730L...8A} should not have been possible if the high energy emission site were within the BLR, which is expected to be opaque to $\gamma$ -rays at TeV energies due to $\gamma\gamma$ interactions."1069 The observed kinematics of the jet is now combined with the rise times of the radio. optical. and y-ray emission.," The observed kinematics of the jet is now combined with the rise times of the radio, optical, and $\gamma$ -ray emission."1070 The component Q9 is the first new component identified in 2008 and is most likely the emission region responsible for the initial flux increase., The component Q9 is the first new component identified in 2008 and is most likely the emission region responsible for the initial flux increase.1071 Using the long-term trends extracted. the distance at which Q9 was located during the onset of the flaring period in 2008 is «0.05 mmas from the VLBI core.," Using the long-term trends extracted, the distance at which Q9 was located during the onset of the flaring period in 2008 is $\sim$ mas from the VLBI core."1072 This marks the region between the stationary feature and the core at GGHz., This marks the region between the stationary feature and the core at GHz.1073 Instead of using the combined flux trend that is related to the sum of the radio emission regions. we calculate the time between the peak brightness of Q9 (2009.40) and the first y- flare observed (2008.73).," Instead of using the combined flux trend that is related to the sum of the radio emission regions, we calculate the time between the peak brightness of Q9 (2009.40) and the first $\gamma$ -ray flare observed (2008.73)."1074 If we use the average component speed and assume no acceleration. then the closest Q9 could have been during the time of the first observed y-ray flare is consistent with the position of the radio core at 43 GHz.," If we use the average component speed and assume no acceleration, then the closest Q9 could have been during the time of the first observed $\gamma$ -ray flare is consistent with the position of the radio core at 43 GHz."1075 This finding strongly supports the interpretation of the parsec-scale jet being responsible for driving the observed high energy emission., This finding strongly supports the interpretation of the parsec-scale jet being responsible for driving the observed high energy emission.1076 ? have reported on the location of a y-ray flare in 2287. which was placed at a distance of more than I4ppe from the central engine.," \citet{2011ApJ...726L..13A} have reported on the location of a $\gamma$ -ray flare in 287, which was placed at a distance of more than pc from the central engine."1077 They proposed a model for the multi-wavelength emission where the high energy emission could be explained by the synchrotron self-Compton process or inverse Compton scattering of infrared radiation from a hot dusty torus. although it was concluded that the hot dusty torus scenario is less likely.," They proposed a model for the multi-wavelength emission where the high energy emission could be explained by the synchrotron self-Compton process or inverse Compton scattering of infrared radiation from a hot dusty torus, although it was concluded that the hot dusty torus scenario is less likely."1078 In the case of 3345 it seems to be clear that multiple compact emission features are responsible for the observed variability and what seems to be a reasonable model for the case of 2287. could apply for 3345 às well.," In the case of 345 it seems to be clear that multiple compact emission features are responsible for the observed variability and what seems to be a reasonable model for the case of 287, could apply for 345 as well."1079 A new plasma disturbance passes through a first conical shock in the core and produces a fast rise in high energy emission: às it continues to propagate down the jet it continues to produce high energy emission., A new plasma disturbance passes through a first conical shock in the core and produces a fast rise in high energy emission; as it continues to propagate down the jet it continues to produce high energy emission.1080 Based on 32 VLBA observations of 3345 at GGHz. we have investigated the structure and evolution of the radio emission and related this to variations of the y-ray and optical emission observed 2008-2010 by Fermi--LAT and a number of optical observatories.," 	Based on 32 VLBA observations of 345 at GHz, we have investigated the structure and evolution of the radio emission and related this to variations of the $\gamma$ -ray and optical emission observed 2008–2010 by -LAT and a number of optical observatories."1081 We have identified and analyzed four new moving emission features (jet components) i the radio jet of 3345., 	We have identified and analyzed four new moving emission features (jet components) in the radio jet of 345.1082 These regions are found to move at apparent speeds of ce. with the corresponding Doppler and. Lorentz factors derived to be in the ranges of 12-243 and 12-15. respectively.," These regions are found to move at apparent speeds of c, with the corresponding Doppler and Lorentz factors derived to be in the ranges of 12–23 and 12–15, respectively."1083 The kinematic data strongly favor a viewing angle of bbetween the jet axis and the line of sight., The kinematic data strongly favor a viewing angle of between the jet axis and the line of sight.1084 We have presented evidence for the y-ray emission to be produced not in a compact region near the central engine of the AGN. but in the Compton-loss dominated zone of the parsec-scale jet extending up to r=0.3 mmas. corresponding to a deprojected linear extent of = ppe (accounting for the source distance and jet orientation).," 	We have presented evidence for the $\gamma$ -ray emission to be produced not in a compact region near the central engine of the AGN, but in the Compton-loss dominated zone of the parsec-scale jet extending up to $r\approx 0.3$ mas, corresponding to a deprojected linear extent of $\approx$ pc (accounting for the source distance and jet orientation)."1085" This zone is further marked by a break in the evolution of the brightness temperature. 7). of the radio emission. with Tyc;70952999? at <0.3mmas and T,xpodeos at larger separations."," This zone is further marked by a break in the evolution of the brightness temperature, $T_\mathrm{b}$, of the radio emission, with $T_\mathrm{b}1086\propto r^{-(0.95\,\pm\,0.69)}$ at $r\le 0.3$ mas and $T_\mathrm{b} \propto r^{-(4.11\,\pm\,0.85)}$ at larger separations."1087 Ejections of new superluminally moving and apparently accelerating features in the jet are linked to the flaring component of the y-ray and optical emission., Ejections of new superluminally moving and apparently accelerating features in the jet are linked to the flaring component of the $\gamma$ -ray and optical emission.1088 These findings favor the synchrotron self-Compton mechanism of the high-energy emission production. while questioning the entire class of models that place the high energy emission site within ppe. from the central engine of AGN. with external seed photons for inverse Compton scattering from the accretion disk or broad-line-region.," These findings favor the synchrotron self-Compton mechanism of the high-energy emission production, while questioning the entire class of models that place the high energy emission site within pc from the central engine of AGN, with external seed photons for inverse Compton scattering from the accretion disk or broad-line-region."1089 They also imply that a significant part of the y-ray emission Is generated by highly-relativistic electrons propagating at a large bulk speed in the jet., They also imply that a significant part of the $\gamma$ -ray emission is generated by highly-relativistic electrons propagating at a large bulk speed in the jet.1090 In the context of newly emerging results. stimulated by Fermi data. more detailed analytical and numerical descriptions of such a scenario are clearly needed in order to explain the observed connection between radio and y-ray variability.," In the context of newly emerging results, stimulated by Fermi data, more detailed analytical and numerical descriptions of such a scenario are clearly needed in order to explain the observed connection between radio and $\gamma$ -ray variability."1091 At the same time. continued monitoringσι and more densely sampled VLBI observations of well studied. bright blazar radio jets represent an essential requirement for improving the degree of detail and statistical. accuracy of the correlation reported and further improving the spatial localization of individual flares in relativistic jets.," At the same time, continued monitoring and more densely sampled VLBI observations of well studied, bright blazar radio jets represent an essential requirement for improving the degree of detail and statistical accuracy of the correlation reported and further improving the spatial localization of individual flares in relativistic jets."1092among the EPIC cameras (see. for instance. the discussion in Molencdi οἱ al.,"among the EPIC cameras (see, for instance, the discussion in Molendi et al."1093 2003). at least in their highest energy band.," 2003), at least in their highest energy band."1094 Data were retrieved. from the NMM-Newton. Targe of Opportunity public WEB page as Observation Data Files (ODE). and. reprocessecl with SAS v5.4.1. using a calibration index file corresponding to the most. upclatec calibration files available at February 21. 2003.," Data were retrieved from the XMM-Newton Target of Opportunity public WEB page as Observation Data Files (ODF), and reprocessed with SAS v.5.4.1, using a calibration index file corresponding to the most updated calibration files available at February 21, 2003."1095" Spectra were extracted from a circular region around the source centroic (ου=16""31"" 487.6. 2000=48°49/00"": Schartel e al."," Spectra were extracted from a circular region around the source centroid $\alpha_{2000} = 16^h31^m48^s.6$ , $\delta_{2000} = -48^o49 \arcmin 00 \arcsec$; Schartel et al."1096" −⋅2003) with. a ""T radius.", 2003) with a $\arcsec$ radius.1097. As the extraction. region. encompassed two CCDs. background spectra were extract from a nearby source-[ree. region. having the same area ratio between the two chips as the source extraction region.," As the extraction region encompassed two CCDs, background spectra were extracted from a nearby source-free region, having the same area ratio between the two chips as the source extraction region."1098 We verified that the results are not substantially dilferent. if the source ancl background pn spectra are extracted from a smaller region (11 radius). fully comprised in the same CCD.," We verified that the results are not substantially different, if the source and background pn spectra are extracted from a smaller region $\arcsec$ radius), fully comprised in the same CCD."1099 The spectra were accumulated: using single- and ouble-events., The spectra were accumulated using single- and double-events.1100 Pile-up is negligible. as well as the contribution. of the background. lower than in the 515 keV energy band.," Pile-up is negligible, as well as the contribution of the background, lower than in the 5–15 keV energy band."1101 Nevertheless. a short interval of about 1.25 ks duration. where the background. count rate (calculated on the single-event light curve extracted above 10 keV) exceeded Los was removed from the scientific product. accumulation.," Nevertheless, a short interval of about 1.25 ks duration, where the background count rate (calculated on the single-event light curve extracted above 10 keV) exceeded 1 $s^{-1}$, was removed from the scientific product accumulation."1102 The background is otherwise quite stable., The background is otherwise quite stable.1103 Phe fits described in this Letter were performed with ASPEC v.11.1., The fits described in this Letter were performed with XSPEC v.11.1.1104 As already noted by de Plaa ct al. (, As already noted by de Plaa et al. (11052003). the NMAM-rewton spectra are characterized by a heavily absorbed continuum and 3 emission lines.,"2003), the XMM-Newton spectra are characterized by a heavily absorbed continuum and 3 emission lines."1106 Phe lines are most naturally interpreted. as the Fe Ίνα and. and. the Ni Ίνα., The lines are most naturally interpreted as the Fe $\alpha$ and $\beta$ and the Ni $\alpha$.1107 We herefore fitted the spectrum (in the 5-13 keV. energy band. as below 5 keV a small excess emüssion is present. see low) with the simplest possible model: an absorbed power aw plus three (unabsorbecl) narrow intrinsic width. e. ixed to 1 eV) Gaussian lines.," We therefore fitted the spectrum (in the 5-13 keV energy band, as below 5 keV a small excess emission is present, see below) with the simplest possible model: an absorbed power law plus three (unabsorbed) narrow intrinsic width, $\sigma$, fixed to 1 eV) Gaussian lines."1108 The photoelectric absorption model has been used with element abundances fron Anders CGrevesse (1989) and. photoclectric cross sections rom Balucinska-Church MeCanmmon (1992)., The photoelectric absorption model has been used with element abundances from Anders Grevesse (1989) and photoelectric cross sections from Balucinska-Church McCammon (1992).1109 We left the iron abundance [ree to vary independently of the other elements., We left the iron abundance free to vary independently of the other elements.1110 As the absorbing matter results to be Comptonhick (see below). we included: also Thompson absorption (model CABS).," As the absorbing matter results to be Compton--thick (see below), we included also Thompson absorption (model )."1111 Lt is worth noting that this model. ignoring he scatteringD of photons. is. strictly speaking.5 valid. only or absorbing matter along the line of sight with a negligible covering factor (see belowfor à discussion). The fit is reasonably good (47—99.1/64. cof).," It is worth noting that this model, ignoring the scattering of photons, is, strictly speaking, valid only for absorbing matter along the line of sight with a negligible covering factor (see belowfor a discussion), The fit is reasonably good $\chi^2$ =99.1/64 d.o.f.),"1112 but residuals around the iron Wa [ine are visible. most. likely due to the Compton Shoulder (CS). as already observed in the reflection spectrum of the Circinus Galaxy. (Bianchi et al.," but residuals around the iron $\alpha$ line are visible, most likely due to the Compton Shoulder (CS), as already observed in the reflection spectrum of the Circinus Galaxy (Bianchi et al."1113 2002: Molencdi ct al., 2002; Molendi et al.1114 2003). ancl expected on theoretical eround (see. Matt 2002 ancl references therein).," 2003), and expected on theoretical ground (see Matt 2002 and references therein)."1115 Moceling for simplicity the Compton Shoulder. with a Gaussian with centroid energy fixed to 6.3 keV. and σ [fixed to 50 eV. a significant improvement is found. (A7 —80.9/63 d.o.É.," Modeling for simplicity the Compton Shoulder with a Gaussian with centroid energy fixed to 6.3 keV, and $\sigma$ fixed to 50 eV, a significant improvement is found $\chi^2$ =80.9/63 d.o.f.,"1116 corresponding to confidence level)., corresponding to confidence level).1117 In. the following we will refer to the complete model: (absorbed power-law plus 4 Gaussian emission lines) as themodel., In the following we will refer to the complete model (absorbed power-law plus 4 Gaussian emission lines) as the.1118 Phe best fit results are summarized in Table 1.., The best fit results are summarized in Table \ref{bestfit}.1119 Phe observed 2-10 keV lux is 6.7. 07 erg ts +., The observed 2-10 keV flux is $\times$ $^{-12}$ erg $^{-1}$ $^{-1}$.1120" Phe lux corrected. for absorption is instead. 9 Ore 1 i corresponding to a luminosity of LOdt, erg . where dio is the distance to the source in units of LO kpe."," The flux corrected for absorption is instead $\times$ $^{-9}$ erg $^{-1}$ $^{-1}$, corresponding to a luminosity of $\times10^{37} d^2_{10}$ erg $^{-1}$, where $d_{10}$ is the distance to the source in units of 10 kpc."1121 Given the large column density of the lineofsigh absorber. if the covering factor of the absorbing matter is large. a significant contribution from photons scatterec towards the line of sight is expected. as discussed in. Mat et al. (," Given the large column density of the line–of–sight absorber, if the covering factor of the absorbing matter is large, a significant contribution from photons scattered towards the line of sight is expected, as discussed in Matt et al. ("11221999).,1999).1123 We therefore fitted. the spectrum with the Monte-Carlo model. described. in that paper., We therefore fitted the spectrum with the Monte-Carlo model described in that paper.1124 The [fit is completely. unacceptable., The fit is completely unacceptable.1125 This may be due to the fact tha 1e model has been calculated adopting the Morrison AleCammon (1983) cross sections. which made use of the Anders Ebthara (1982) clement abundances.," This may be due to the fact that the model has been calculated adopting the Morrison McCammon (1983) cross sections, which made use of the Anders Ebihara (1982) element abundances."1126 In this se 1¢ iron abundance is about 0.7 times that given by Anders Grevesse (1983). while from Table. 1. it seems tha 10 actual iron. abundance (mainly derived in the fit. [rom 1e depth of the iron edge) in the absorbing material is oser to the one given by the latter authors.," In this set the iron abundance is about 0.7 times that given by Anders Grevesse (1983), while from Table \ref{bestfit} it seems that the actual iron abundance (mainly derived in the fit from the depth of the iron edge) in the absorbing material is closer to the one given by the latter authors."1127 Moreover. rw Matt ct al. (," Moreover, the Matt et al. ("11281999) mocel assumed. spherical geometry uxi homogeneous matter. while the covering factor may x: significantly smaller than one and the average column ensity smaller than that on the lineofsight (see below).,"1999) model assumed spherical geometry and homogeneous matter, while the covering factor may be significantly smaller than one and the average column density smaller than that on the line–of–sight (see below)."1129 Coming back to the results summarized in Table 1.. we must first of all remark that the rather small errors on E and Ng are somewhat misleading.," Coming back to the results summarized in Table \ref{bestfit}, we must first of all remark that the rather small errors on $\Gamma$ and $_{\rm H}$ are somewhat misleading."1130 In fact. as it is clear from the contour plot (Fig. 19).," In fact, as it is clear from the contour plot (Fig. \ref{gamma_nh}) ),"1131 the 472 distribution is shallow and not very smooth., the $\chi^2$ distribution is shallow and not very smooth.1132 Phe calculated errors correspond to the Ay? in the vieinity of the best fit. bat other regions with Ay? less than 2.71 do exist.," The calculated errors correspond to the $\Delta\chi^2$ in the vicinity of the best fit, but other regions with $\Delta\chi^2$ less than 2.71 do exist."1133 We have verified that Ng and Ag. are only slightly correlated each other., We have verified that $_{\rm H}$ and $_{\rm Fe}$ are only slightly correlated each other.1134 To avoid problems in the estimate of the errors for the line parameters. we fixed Land Ny to their best fit values.," To avoid problems in the estimate of the errors for the line parameters, we fixed $\Gamma$ and $_{\rm H}$ to their best fit values."1135 This does not allect very much the errors on the Fe and Ni Ke lines. but. stabilizes the values for the Fe Wat. which otherwise would be very difficult to find. due to its proximity to the iron edge," This does not affect very much the errors on the Fe and Ni $\alpha$ lines, but stabilizes the values for the Fe $\beta$, which otherwise would be very difficult to find, due to its proximity to the iron edge."1136 The energies of the Fe and Ni Ίνα lines correspond to neutral or low ionized atoms (Llouse 1969)., The energies of the Fe and Ni $\alpha$ lines correspond to neutral or low ionized atoms (House 1969).1137 On the contrary. the ke centroid energy is significantly larger than expected.," On the contrary, the Fe $\beta$ centroid energy is significantly larger than expected."1138 This cannot be due to high ionization. not only because it does not agree with the Ka energy. but also because for significantly ionized matter the Wee linebecomes much fainter. to disappear completely for Fe or more. when no M electrons remain.," This cannot be due to high ionization, not only because it does not agree with the $\alpha$ energy, but also because for significantly ionized matter the $\beta$ linebecomes much fainter, to disappear completely for Fe or more, when no M electrons remain."1139 Instead. the observed IN2/Ixo. ratio (0.202455) is slightly larger than expected for. neutral iron (see the discussion. in Alolendi ct al., Instead the observed $\beta$ $\alpha$ ratio $ 0.20 \pm^{0.02}_{0.03}$ ) is slightly larger than expected for neutral iron (see the discussion in Molendi et al.1140 2003. where however the matter was seen in rellection. not transmission:," 2003, where however the matter was seen in reflection, not transmission;"1141which an estimate seoes to imfudtv as 0 erows.,which an estimate goes to infinity as $x$ grows.1142 The breakdown poiut of conveutional mean aud variance is 0., The breakdown point of conventional mean and variance is 0.1143 The breakdown point of median is L5. Le. up to of data iav be outliers aud hey do not alter the correct value of the median.," The breakdown point of median is 0.5, i.e., up to of data may be outliers and they do not alter the correct value of the median."1144 Taking into consideration our practical goal O0 use estimates of variance in observations. two neasures of stability will be exploited for the ollowiusg statistical procedures.," Taking into consideration our practical goal to use estimates of variance in observations, two measures of stability will be exploited for the following statistical procedures."1145 1l., 1.1146 The relative ορΊσα influence function with he following modification: for a sample leneth N the number of additional outliers with an amplitude Nery will be M=ΙεΝΙ. where ή) ueaus the ereatest iuteecr part of q.," The relative empirical influence function with the following modification: for a sample length $N$ the number of additional outliers with an amplitude $X_{RFI}$ will be $M=[\epsilon N]$, where $[q]$ means the greatest integer part of $q$."1147 Tle estimate calculated for a contaminated sample is compared with the estinate correspoudius to a “clean” siuuple: The relative empirical influence function will be calculated during computer sinmlation for the estimates clescribed below., The estimate calculated for a contaminated sample is compared with the estimate correspondimg to a “clean” sample: The relative empirical influence function will be calculated during computer simulation for the estimates described below.1148 2., 2.1149 Stability against outlicrs is achieved at the expense of the effectiveness of au estimate., Stability against outliers is achieved at the expense of the effectiveness of an estimate.1150 In the absence of outliers the standard deviation of a robustly estimated variance ix. as a rule. larecr than that of a simple estimate (1).," In the absence of outliers the standard deviation of a robustly estimated variance is, as a rule, larger than that of a simple estimate (1)."1151 To characterize this loss the pazameter LOSS will be used: For a small increase of Ac<<c6 two sigual- ratios SNR are compared: SNR. of a eiven estimate of variance Dy(7) and SNRO of the estimate (1) with the best potential effectiveness., To characterize this loss the parameter $LOSS$ will be used: For a small increase of $\Delta \sigma << \sigma$ two signal-to-noise ratios $SNR$ are compared: $SNR_{T_{N}}$ of a given estimate of variance $\widehat{T_{N}(\sigma )}$ and $SNR0$ of the estimate (1) with the best potential effectiveness.1152 The relative. enpirical influence functiou aud loss are calculated via computer simulations (0Lon= 10°) for the estimates presented below.," The relative empirical influence function and loss are calculated via computer simulations $\sigma=1, n=10^{5}$ ) for the estimates presented below."1153" Let yer, be a random sample and let HeyySoMa,Xo.Sty be the observatious sorted in ascending order."," Let $x_{1},...., x_{n}$ be a random sample and let $x_{(1)} \leq1154x_{(2)}\leq...\leq x_{(n)}$ be the observations sorted in ascending order."1155 The /fh largest value sus ds called the (th , The $ith$ largest value $x_{(i)}$ is called the $ith$ .1156statistic. Let 5 denote the chosen amount of trinnüug. 0sxO05 and k=[so].," Let $\gamma $ denote the chosen amount of trimming, $0 \leq \gamma \leq 0.5$ and $k=[\gamma n]$."1157 The sample trimmed variance is computed by removing the & largest aud & snallest data and using the values that remain: where pes; Is the sample mean of the πιο. data., The sample trimmed variance is computed by removing the $k$ largest and $k$ smallest data and using the values that remain: where $\mu_{trim}$ is the sample mean of the trimmed data.1158" Trimming Iesscus the variance of data and the coefficient /;,;,, makes T4 the consisteut estimator for data with normal distribution.", Trimming lessens the variance of data and the coefficient $K_{trim}$ makes $T_{1}$ the consistent estimator for data with normal distribution.1159" Table l gives the values of /A,,;,, for different 5.", Table 1 gives the values of $K_{trim}$ for different $\gamma$.1160 The third row in this table eives the values of LOSS for different . Fie., The third row in this table gives the values of $LOSS$ for different $\gamma$ Fig.1161 l shows the relative οπήΊσα. influence functions for untrinnned data (Fig., 1 shows the relative empirical influence functions for untrimmed data (Fig.1162 la) aud for the variances computed for trimuned data with ~=0.05 (Fie., 1a) and for the variances computed for trimmed data with $\gamma=0.05$ (Fig.1163 Ub)., 1b).1164 The paraneter € (7eps) indicates the percentage of outhers in the total volume of data., The parameter $\epsilon$ (“eps”) indicates the percentage of outliers in the total volume of data.1165 A sample a.c17 IS sorted in ascendingo order.," A sample $x_{1},...., x_{n}$ is sorted in ascending order."1166" For the chosen 0<5zx0.5 and k=[ση] winsorization of thesorted data consists of setting The wiusorized sanuple mican is jn,=+M{Wi and the wiusorized sample variance is"," For the chosen $0 \leq \gamma \leq 0.5$ and $k=[\gamma n]$ winsorization of thesorted data consists of setting The winsorized sample mean is $\widehat{1167\mu_{w}}=\frac{1}{n}\sum_{i=1}^{n}W_{i}$ and the winsorized sample variance is"1168originates in the pulsarmagnetosphere!*.. whereas the thermal component is emitted from hot polar caps on the NS surface.,"originates in the pulsar, whereas the thermal component is emitted from hot polar caps on the NS surface."1169 Depending on assumption about the polar cap temperature distribution. one gets different relative contributions from these two components.," Depending on assumption about the polar cap temperature distribution, one gets different relative contributions from these two components."1170 In the model with uniformly heated polar caps. the nonthermal component described as a PL of photon index ~=2.72.9. provides about in the X-ray flux and dominates at— energies below 0.6 keV and above 2.7 keV. However. this model encounters the same problems in the EUV and optical bands as the broken PL (the steeper slope of this PL component predicts even higher fluxes in theB and V bands).," In the model with uniformly heated polar caps, the nonthermal component described as a PL of photon index $\gamma=2.7-2.9$ provides about in the X-ray flux and dominates at energies below 0.6 keV and above 2.7 keV. However, this model encounters the same problems in the EUV and optical bands as the broken PL (the steeper slope of this PL component predicts even higher fluxes in the$B$ and $V$ bands)."1171 If we assume a more plausible polar cap model with temperature decreasing outwards from the cap center. then the thermal component becomes dominant between 0.06 keV and 2.5 keV. providing some of the X-ray flux. while the PL component of 5=1.6—2.5 dominates outside this band.," If we assume a more plausible polar cap model with temperature decreasing outwards from the cap center, then the thermal component becomes dominant between 0.06 keV and 2.5 keV, providing some of the X-ray flux, while the PL component of $\gamma=1.6-2.5$ dominates outside this band."1172 In addition to a more realistic temperature distribution. the latter model is well consistent with the data and yields estimates on the hydrogen column density in agreement with the indirect. measurements.," In addition to a more realistic temperature distribution, the latter model is well consistent with the data and yields estimates on the hydrogen column density in agreement with the indirect measurements."1173 As this PL component is fainter than in the two other models. its extension to the optical falls below the observed radiation of the white dwarf companion for photon indices +<1.9.," As this PL component is fainter than in the two other models, its extension to the optical falls below the observed radiation of the white dwarf companion for photon indices $\gamma < 1.9$."1174 This allows us to predict that the PL component should be observable in the UV (particularly. far-UV) range where it is brighter than the Wien tul of the white dwarf spectrum. assuming there is no turnover of the nonthermal spectrum between the UV and soft-X-ray energies.," This allows us to predict that the PL component should be observable in the UV (particularly, far-UV) range where it is brighter than the Wien tail of the white dwarf spectrum, assuming there is no turnover of the nonthermal spectrum between the UV and soft-X-ray energies."1175 On the other side of the X-ray band. extrapolation of the PL component to the gamma-ray energies above 100 MeV predicts a photon flux f<2«107 s! em? (5> 1.6). below the upper limit. f<1.5«107 s! em™. obtained from the EGRET observations (Fierro et al.," On the other side of the X-ray band, extrapolation of the PL component to the gamma-ray energies above 100 MeV predicts a photon flux $f<2\times 10^{-8}$ $^{-1}$ $^{-2}$ $\gamma>1.6$ ), below the upper limit, $f < 1.5\times 10^{-7}$ $^{-1}$ $^{-2}$, obtained from the EGRET observations (Fierro et al."1176 1995)., 1995).1177 We emphasize that these models require the thermal radiation be emitted from hydrogen (or helium) NS. atmosphere., We emphasize that these models require the thermal radiation to be emitted from hydrogen (or helium) NS atmosphere.1178 The high spectral resolution of the ACIS data rules out an atmosphere comprised of heavier chemical elements., The high spectral resolution of the ACIS data rules out an atmosphere comprised of heavier chemical elements.1179 The HRC-S observation of hhas demonstrated the timing capability at a millisecond level., The HRC-S observation of has demonstrated the timing capability at a millisecond level.1180 The HRC-S pulse profile looks narrower. and the pulsed fraction ts somewhat higher. than those obtained in the earlier and observations at lower energies. which could be explained by the properties of the thermal radiation from polar caps covered with a hydrogen or helium atmosphere.," The HRC-S pulse profile looks narrower, and the pulsed fraction is somewhat higher, than those obtained in the earlier and observations at lower energies, which could be explained by the properties of the thermal radiation from polar caps covered with a hydrogen or helium atmosphere."1181 On the other hand. the shape of the profile is clearly asymmetric. with a longer rise and faster decay. which cannot be explained by a simple axisymmetric temperature distribution.," On the other hand, the shape of the profile is clearly asymmetric, with a longer rise and faster decay, which cannot be explained by a simple axisymmetric temperature distribution."1182 Relativistic effects (particularly. the Doppler boost) should lead to a different asymmetry — a faster rise and longer trail (Braje Romani 2000: Ford 2000).," Relativistic effects (particularly, the Doppler boost) should lead to a different asymmetry — a faster rise and longer trail (Braje Romani 2000; Ford 2000)."1183 The analysis of HRC-S data demonstrates. for the first time. that the phase of the X-ray pulse virtually coincides with that of the radio pulse.," The analysis of HRC-S data demonstrates, for the first time, that the phase of the X-ray pulse virtually coincides with that of the radio pulse."1184 If. as we suggest. the main contribution to the HRC-S band is due to the thermal polar cap radiation. and if the pulsar radio beam is directed along the magnetic axis. then the radio emission must be generated close to the NS surface — e.g.. the time difference of <0.1 ms between the X-ray and radio phases corresponds to a distance of<30 km. much smaller than the light cylinder radius. Aj;=275 km.," If, as we suggest, the main contribution to the HRC-S band is due to the thermal polar cap radiation, and if the pulsar radio beam is directed along the magnetic axis, then the radio emission must be generated close to the NS surface — e.g., the time difference of $<0.1$ ms between the X-ray and radio phases corresponds to a distance of $<30$ km, much smaller than the light cylinder radius, $R_{\rm lc}=275$ km."1185 Alternatively. if the radio emission is generated at a higher altitude. the combination of field-line sweepback and aberration must contrive to cancel the radial travel-time difference.," Alternatively, if the radio emission is generated at a higher altitude, the combination of field-line sweepback and aberration must contrive to cancel the radial travel-time difference."1186" The observations show no sign of an X-ray PWN that could accompany the bow-shock revealed by the H,, observations.", The observations show no sign of an X-ray PWN that could accompany the bow-shock revealed by the $_\alpha$ observations.1187 Three-sigma upper limits on the PWN brightness (in counts arcsec) can be estimated as 3(5/A)7. where b is the background surface brightness (5=0.51. and 0.28 counts aresec for the ACIS-S and HRC-I images. respectively). and A is the PWN area (we will scale it as A= aresec. assuming that a typical transverse size of the PWN£4 somewhat exceeds the stand-off distance. 10”. of the bow shock).," Three-sigma upper limits on the PWN brightness (in counts $^{-2}$ ) can be estimated as $3(b/A)^{1/2}$ where $b$ is the background surface brightness $b=0.51$ and 0.28 counts $^{-2}$ for the ACIS-S and HRC-I images, respectively), and $A$ is the PWN area (we will scale it as $A=1000 f_A$ $^2$, assuming that a typical transverse size of the PWN somewhat exceeds the stand-off distance, $10''$, of the bow shock)."1188" For a power-law PWN spectrum with a photon index ~=|.5-2 (similar to those observed from other PWNe). these upper limits correspond to the PWN intensities 7,nmax(l.3- 18)«107UfL7 and Fla<B.645.7) <1f,7 erg em7 s! aresee. for the ACIS-S and HRC-L respectively. in the 0.1—10 keV range."," For a power-law PWN spectrum with a photon index $\gamma=1.5$ –2 (similar to those observed from other PWNe), these upper limits correspond to the PWN intensities $I_{x,{\rm pwn}}<(1.3$ $1.8)\times 10^{-17} f_A^{-1/2}$ and $I_{x,{\rm pwn}}<(3.6$ $5.7)\times 10^{-17} f_A^{-1/2}$ erg $^{-2}$ $^{-1}$ $^{-2}$ , for the ACIS-S and HRC-I, respectively, in the 0.1–10 keV range."1189" The corresponding upper limits on the PWN X-ray luminosity. LipστAzdAL,pon are much smaller than the rotational energy loss rate. £=3.8«10? erg s! — eg. Lepan<(3.0-4.2) «10fi. eng Vo for the more sensitive ACIS-S limit."," The corresponding upper limits on the PWN X-ray luminosity, $L_{x,{\rm pwn}}\approx 4\pi d^2 A I_{x,{\rm pwn}}$ are much smaller than the rotational energy loss rate, $\dot{E}=3.8\times 10^{33}$ erg $^{-1}$ — e.g., $L_{x,{\rm pwn}} < (3.0$ $4.2)\times 10^{28} f_A^{1/2}$ erg $^{-1}$ for the more sensitive ACIS-S limit."1190 The low upper limits on the PWN luminosity in X-rays can be simply explained by a low magnetic field in the PWN region. expected for a particle-dominated pulsar wind.," The low upper limits on the PWN luminosity in X-rays can be simply explained by a low magnetic field in the PWN region, expected for a particle-dominated pulsar wind."1191" The shock in the relativistic pulsar wind should be located just interior to the observed H,, bow shock (Arons Tavani 1993).", The shock in the relativistic pulsar wind should be located just interior to the observed $_\alpha$ bow shock (Arons Tavani 1993).1192" When the wind electrons pass through the shock. their directions of motion become ""randomized"". and their synchrotron radiation may result in an. X-ray nebula. provided the electron energies and the magnetic field are high enough in the post-shock region."," When the wind electrons pass through the shock, their directions of motion become “randomized”, and their synchrotron radiation may result in an X-ray nebula, provided the electron energies and the magnetic field are high enough in the post-shock region."1193" The pre-shock magnetic field can be estimated as By=(E/(fortey|!σαee?=ISΙσo]? µα. wn r,2«10"" em is the stand-off distance corresponding » factor10"" at d=140 pe. foAO/(E)x1 is the collimation of the wind. and the= * parameter"" σ is the ratio of the Poynting flux smenetizationto the kinetic energy flux."," The pre-shock magnetic field can be estimated as $B_1=[\dot{E}/(f_\Omega r_s^2c)]^{1/2}1194[\sigma/(1+\sigma)]^{1/2}=18\,f_\Omega^{-1/2} [\sigma/(1+\sigma)]^{1/2}~\mu$ G, where $r_s\approx 2\times 10^{16}$ cm is the stand-off distance corresponding to $10''$ at $d=140$ pc, $f_\Omega=\Delta\Omega/(4\pi)\leq 1$ is the collimation factor of the wind, and the “magnetization parameter” $\sigma$ is the ratio of the Poynting flux to the kinetic energy flux."1195" The maximum value of the post-shock magnetic field. B~B,—18fo)2 HG. is obtained for σ2»1."," The maximum value of the post-shock magnetic field, $B\simeq B_1\simeq 18\, f_\Omega^{-1/2}~\mu$ G, is obtained for $\sigma\gg 1$."1196 However. according to Kennel Coronity (1984: KC84 hereafter). à. significant fraction of the total energy flux upstream can be converted into. (observable) synchrotron luminosity downstream only if 020.1 (e.g.. these authors estimate σ~0.003 for the Crab pulsar).," However, according to Kennel Coronity (1984; KC84 hereafter), a significant fraction of the total energy flux upstream can be converted into (observable) synchrotron luminosity downstream only if $\sigma \lapr 0.1$ (e.g., these authors estimate $\sigma\approx 0.003$ for the Crab pulsar)."1197" For o&I. the post-shock magnetic field is Bx3(1-40)B,~53fo”στ]--4,5σ)) μα (e.g.. fromDuas. ofradiatingelectronsand. consequently, themaximum frequen of the synchrotron radiation."," For $\sigma\ll 1$, the post-shock magnetic field is $B\simeq 3(1-4\sigma)1198B_1\simeq 53\,f_\Omega^{-1/2}1199\sigma^{1/2}(1-4.5\sigma)~\mu$ G (e.g., from, of radiating electrons and, consequently, the maximum frequency $\nu_{\rm max}$ of the synchrotron radiation."1200" Since the Larmor radius of most energetic electrons. rj=1.7«10""LBς,cm. cannot exceed the shock radius +, we obtain Dia,<105f,B s. hascGieBíAzxm.eLsubstantially.DUM0.6£2Bὁ keV. where ὃς=B/Q0 4G). f,—rifri VÉ."," Since the Larmor radius of most energetic electrons, $r_{L}=1.7\times 10^8\, \Gamma_{\rm max} B_{-5}^{~~-1}~{\rm cm}$, cannot exceed the shock radius $r_s$ substantially, we obtain $\Gamma_{\rm max} < 10^8\, f_s B_{-5}$ , $h\nu_{\rm max} \sim (heB/4\pi m_e c)\Gamma_{\rm max}^2 

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