ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2 Leaving the central cluster unmasked increases the fit power by 1.0 x10-?4K?.," Leaving the central cluster unmasked increases the fit power by $\sim$ 1.0 $ \times10^{-5}\, \mu {\rm K}^2$."3 We also report the results after masking the sources internally detected in the map at >30 in the second row of Table 2.., We also report the results after masking the sources internally detected in the map at $> 3 \sigma$ in the second row of Table \ref{tab:params}. .4 These results are consistent with and improved over the previous ACBAR constraints from 6«3000 of, These results are consistent with and improved over the previous ACBAR constraints from $\ell < 3000$ of5afterelows between about 2=2.5Γ aud 2=3.3Mi,afterglows between about $z=2.5$ and $z=3.3$.6 The IB excess will coutinue to be practical o quite high redshift. οι to :15 for a J color. since the ouset of neutral hydroseu absorption simply accentuates au IR excess until he absorption reaches the redder filter.," The IR excess will continue to be practical to quite high redshift, e.g. to $z\approx 15$ for a $J-K$ color, since the onset of neutral hydrogen absorption simply accentuates an IR excess until the absorption reaches the redder filter."7 Because here is considerable variance iu the πάχοςο cohunn density alone «iferent lines of sight (Macau: 1995). the redshift boundaries discussed rere are nof sharp demarcations.," Because there is considerable variance in the hydrogen column density along different lines of sight (Madau 1995), the redshift boundaries discussed here are not sharp demarcations."8 Rather. f detection efücienev declines smoothly. aud t1o characteristic redshifts elven above correspond to about 50% of peak efficiency. (," Rather, the detection efficiency declines smoothly, and the characteristic redshifts given above correspond to about $50\%$ of peak efficiency. ("9"2) Heavily obscured afterelows can drop bek""V the searcl’s detection threshold.",2) Heavily obscured afterglows can drop below the search's detection threshold.10 Extinction affe‘ts auv search metloc. though it is exacerbated for UVX aud two-color methods by the increase of extinction towards bluer optical-UV. waveleustlis ancl the necessity of observations ln oserver frame blue light.," Extinction affects any search method, though it is exacerbated for UVX and two-color methods by the increase of extinction towards bluer optical-UV wavelengths and the necessity of observations in observer frame blue light."11 Addijonallv. there will be a wuld selection agaiust finding afterglows iu galaxies with Milkv. Wav ype dust extinction at redshifts 2.2Xi83.3 using two-color optical searches.," Additionally, there will be a mild selection against finding afterglows in galaxies with Milky Way type dust extinction at redshifts $2.2 \la z12\la 3.3$ using two-color optical searches."13 ILowever. this overlaps the stronger selection dπο to interealactic IIvdrogen. absorption to such an extent as to be almost uniniportaut. (," However, this overlaps the stronger selection due to intergalactic Hydrogen absorption to such an extent as to be almost unimportant. ("143) For eamuna rav bursts occurrius near deuse molecular gas. absorption by excited molecuar hydrogen can occur for rest wavelengths as lo18o as 1650À. ((Draine 2000).,"3) For gamma ray bursts occurring near dense molecular gas, absorption by excited molecular hydrogen can occur for rest wavelengths as long as $1650$ (Draine 2000)."15 Absorption between 1650 axd L300A4 ecan reach for Πο cohununu deusities arou Lot? uD, Absorption between $1650$ and $1300$ can reach for $_2$ column densities around $10^{19}$ $^{-2}$.16 ThisYol willB act to exclude afterglowsB molecular clouds from UVNX or two-color sampCR at redshifts bevoud 1.3 (using U band) or 1.65 (using D). (, This will act to exclude afterglows in molecular clouds from UVX or two-color samples at redshifts beyond $1.3$ (using U band) or $1.65$ (using B). (17D Because afterglow spectra are broken power laws rather than pure power laws. there will be times dm the evolution of cach afterglow when its colors deviate from the models iu. section 2..,"4) Because afterglow spectra are broken power laws rather than pure power laws, there will be times in the evolution of each afterglow when its colors deviate from the models in section \ref{col_mod_results}."18 Breaks in svuchrotrou spectra are not absolutely sharp. so fjs ds unlikely to be a major sclection effect for purely optical searches. where the wavelength rauge spanned is only a factor of ~2ον," Breaks in synchrotron spectra are not absolutely sharp, so this is unlikely to be a major selection effect for purely optical searches, where the wavelength range spanned is only a factor of $\sim 2.5$."19 Searches emiplovius larger wavelength coveraexορ (UV or IB) will be more seusitive to this effect. (, Searches employing larger wavelength coverage (UV or IR) will be more sensitive to this effect. (205) Afterglows located atop brighter host ealaxies av be hard to find because the domunaut color is that of the galaxy.,5) Afterglows located atop brighter host galaxies may be hard to find because the dominant color is that of the galaxy.21 This effect will depeud ou instrumental spatial resolution as well as the intrinsic properties of the afterelow aud host ealaxv. (, This effect will depend on instrumental spatial resolution as well as the intrinsic properties of the afterglow and host galaxy. (22Variability searches Cali be simulatly conrpronised uuless nuage subtraction methyds are used.) (,Variability searches can be similarly compromised unless image subtraction methods are used.) (236) An advantage of this method is that short-ena “plateaus” in afterglow ight curves do not affec it.,6) An advantage of this method is that short-term “plateaus” in afterglow light curves do not affect it.24 It may therefore fiud some afterglows that racitiona variabilitv searches muss., It may therefore find some afterglows that traditional variability searches miss.25 Even afterglows that lic in the preicted reeion of color space may be cifhcult to ideutifv by these uethods in cases where the error box is so large hat a substantial umber of other sources occupy he same region of color space., Even afterglows that lie in the predicted region of color space may be difficult to identify by these methods in cases where the error box is so large that a substantial number of other sources occupy the same region of color space.26 The critical error ON Size Where one “confusing source is expected depends ou the maguitude limut of the search., The critical error box size where one “confusing” source is expected depends on the magnitude limit of the search.27 Ultimately. he quasar uunber-fux relation gives a lower limi to the confusion evel.," Ultimately, the quasar number-flux relation gives a lower limit to the confusion level."28 Additionally. or three fler searches. star foriumg galaxies at Doc(0.5 can add to the confusion.," Additionally, for three filter searches, star forming galaxies at $z \sim 0.5$ can add to the confusion."29" To achic""ve a unique afterglow identification. 1 IS LDecessuv o match the maeuitude Lui of hne search to he size of the error box. aud to Observe the Held while he afterglow remains xiehter than his maenituce limit."," To achieve a unique afterglow identification, it is necessary to match the magnitude limit of the search to the size of the error box, and to observe the field while the afterglow remains brighter than this magnitude limit."30 A unique ideuificaloli Wav rot always be needed. however.," A unique identification may not always be needed, however."31 In particular. a int of several viade candidates may be euouch ο obtain a sane-nieht afterglow spectrum using a imultiobject spectrograph with a sufficient field of view and rapi setup procedure.," In particular, a list of several viable candidates may be enough to obtain a same-night afterglow spectrum using a multiobject spectrograph with a sufficient field of view and rapid setup procedure."32 The correct candidate could then be identified later based O1 cither spectra or variability., The correct candidate could then be identified later based on either spectra or variability.33 The quasar numberaiuagnitude relatiou for <2.2 a magnitude 5<2 is predicted by Alalhotra Turner (1995) for roth (Q=1. A= |) and (2=0.1. A= 0.9) cosinologies. based οι οservations to D.<22 by Boyle et al (1987) and Bovle. Shauks. Peterson (1988).," The quasar number-magnitude relation for $z<2.2$ and magnitude $B<24$ is predicted by Malhotra Turner (1995) for both $\Omega=1$, $\Lambda=0$ ) and $\Omega=0.1$, $\Lambda=0.9$ ) cosmologies, based on observations to $B<22$ by Boyle et al (1987) and Boyle, Shanks, Peterson (1988)."34 The approximate ranee of redshift where sar ormiue galaxies overlap the CRB afterglow loπας in color-color space is 0.35S2X0.6 for he EYI diagram. or (115X2816 or the BV. RI diagram.," The approximate range of redshift where star forming galaxies overlap the GRB afterglow locus in color-color space is $0.35 \la z \la 0.6$ for the $U-V$, $V-I$ diagram, or $0.45 \la z \la 0.6$ for the $B-V$, $R-I$ diagram."35 I estimate a inuberauaenuitude relation for such galaxies usiug οι the local Iuninositv function from Lovemy et al (1992) and direct counts of galaxies with 45hcVI«L28 aud OL<i«V6 Toni the Canada-France Redshift Survey (Lilly," I estimate a number-magnitude relation for such galaxies using both the local luminosity function from Loveday et al (1992) and direct counts of galaxies with $0.55 < V-I < 1.28$ and $0.436< z < 0.6$ from the Canada-France Redshift Survey (Lilly"37also invertec and negative sources are extracted in the same wav as for the positive map.,also inverted and negative sources are extracted in the same way as for the positive map.38 The numbers of peaks fou above a given threshold. are listed in Table 2.. as are the numbers of peaks expected in a Gaussian field.," The numbers of peaks found above a given threshold are listed in Table \ref{tab:peaks}, as are the numbers of peaks expected in a Gaussian field."39 The tota area of the maps searched for peaks is 44.5aremin?.," The total area of the maps searched for peaks is $44.5\,\mathrm{arcmin}^2$."40 Notice that there are more negative. peaks detecte at any given noise level than are expected under. the assumption that the variance is what one caleulates from the time stream., Notice that there are more negative peaks detected at any given noise level than are expected under the assumption that the variance is what one calculates from the time stream.41 However. if the maps have Gaussian distribute noise. but with a variance 7 per cent [areer than we infer from the time series the ancl columns in Table 2. would match: the number of Gaussian peaks expected at SYN=0.93«(2.2.5.3) is (67.0. 25.0. 6.3).," However, if the maps have Gaussian distributed noise, but with a variance 7 per cent larger than we infer from the time series the and columns in Table \ref{tab:peaks} would match; the number of Gaussian peaks expected at $S/N= 0.93\times( 2, 2.5, 3) $ is (67.0, 25.0, 6.3)."42 We find this level of agreement between variance in the time series and variance in the maps encouraging. anc use the number of negative peaks to set the statistical significance of any detections of positive Hux in the maps.," We find this level of agreement between variance in the time series and variance in the maps encouraging, and use the number of negative peaks to set the statistical significance of any detections of positive flux in the maps."43The strongest limits to the production of gas in comets are placed using optical spectra ol daughter molecules (fragments of stable parent molecules produced by photocdissociation).,The strongest limits to the production of gas in comets are placed using optical spectra of daughter molecules (fragments of stable parent molecules produced by photodissociation).44 The brightest daughter emission line in the optical spectra of comets is the OL band., The brightest daughter emission line in the optical spectra of comets is the OH band.45 Unfortunately. this band lies near the ozone atmospheric absorption edge making ground- observations of OIL consequently difficult. while no suitablv sensitive space-based instruments exist.," Unfortunately, this band lies near the ozone atmospheric absorption edge making ground-based observations of OH consequently difficult, while no suitably sensitive space-based instruments exist."46 Spectroscopic detections of gas in comets are more usually made using the second-brightest line. produced by resonance fInorescence of the CN radical and located near (Schleicher 2010).," Spectroscopic detections of gas in comets are more usually made using the second-brightest line, produced by resonance fluorescence of the CN radical and located near (Schleicher 2010)."47 Whereas OIL is produced as a photoclissociation product of 1I5O. the source of CN is less certain.," Whereas OH is produced as a photodissociation product of $_2$ O, the source of CN is less certain."48 It is at least in part a photodissociation product of ΗΟΝ. but may also be released. [rom solid grains (e.g. see recent discussion in Paganini et al.," It is at least in part a photodissociation product of HCN, but may also be released from solid grains (e.g. see recent discussion in Paganini et al."49 2010)., 2010).50 Accordingly. we took spectroscopic observations targeting outgassed CN from Themis and Cybele. on UT 2010 September 11 at the Neck I 10-meter telescope atop Mauna Ixea. llawadi.," Accordingly, we took spectroscopic observations targeting outgassed CN from Themis and Cybele, on UT 2010 September 11 at the Keck I 10-meter telescope atop Mauna Kea, Hawaii."51 We used the Low Resolution huagine Spectrometer (LIIS. Oke et al.," We used the Low Resolution Imaging Spectrometer (LRIS, Oke et al."52" 1995). which is equipped with two 4096x4096 pixel charge-coupled device detectors producing an image scale 0.135"" per pixel and fed by a dichroic filter."," 1995), which is equipped with two $\times$ 4096 pixel charge-coupled device detectors producing an image scale $\arcsec$ per pixel and fed by a dichroic filter."53" We emploved the 74607 clichroic. which has transmission al4900A.. and a 1"" wide slit for all observations."," We employed the “460” dichroic, which has transmission at, and a $\arcsec$ wide slit for all observations."54 The geometrical circumstances of the observations are given in Table (1)) while the orbital properties of Cybele and Themis are listed in Table (2))., The geometrical circumstances of the observations are given in Table \ref{geometry}) ) while the orbital properties of Cybele and Themis are listed in Table \ref{orbits}) ).55 Themis and Cybele were identified using finder charts ancl confirmed by their motion relative to the fixed stars., Themis and Cybele were identified using finder charts and confirmed by their motion relative to the fixed stars.56 Integrations of 400 s ancl 330 s were secured on Themis and Cybele. respectively. together with spectra of nearby solar analogs 11D209847. and. Hyades 64.," Integrations of 400 s and 330 s were secured on Themis and Cybele, respectively, together with spectra of nearby solar analogs HD209847 and Hyades 64."57" During all observations we used an image rotator to hold the long axis of the 1.0"" wide slit perpendicular to the local horizon. thereby minimizing elfects due to atmospheric dispersion."," During all observations we used an image rotator to hold the long axis of the $\arcsec$ wide slit perpendicular to the local horizon, thereby minimizing effects due to atmospheric dispersion."58 We guided the telescope by hand using reflection from the spectrograph slit jaws to keep the Larget objects correctly positioned within the slit., We guided the telescope by hand using reflection from the spectrograph slit jaws to keep the target objects correctly positioned within the slit.59 For each new pointing of the telescope. we secured wavelength and fLIat-Deld calibration spectra using a set of lanips internal to LRIS.," For each new pointing of the telescope, we secured wavelength and flat-field calibration spectra using a set of lamps internal to LRIS."60" Data reduction was performed by flattening the waveleneth-calibrated spectra and extracting the signal [rom a region along the slit 6.75"" in length.", Data reduction was performed by flattening the wavelength-calibrated spectra and extracting the signal from a region along the slit $\arcsec$ in length.61 Reflectivity spectra were computed by dividing each object spectrum by the spectrum of a solar analogue and normalizing the result to unity at3900A., Reflectivity spectra were computed by dividing each object spectrum by the spectrum of a solar analogue and normalizing the result to unity at.62. The normalized reflectivity spectra are shown in Figure (1)). where (μον are offset vertically for clarity of presentation.," The normalized reflectivity spectra are shown in Figure \ref{spectra}) ), where they are offset vertically for clarity of presentation."63 Themis and Cybele are spectrally featureless al the wavelengths of CN., Themis and Cybele are spectrally featureless at the wavelengths of CN.64 We estimate a limit to the gas production rate using the procedure described in Jewitt, We estimate a limit to the gas production rate using the procedure described in Jewitt65stable circular orbit) ancl possibly a high energv component from Compton up-scattering in a tenuous. hot corona would be a realistic phenomenological description of the spectrum.,"stable circular orbit) and possibly a high energy component from Compton up-scattering in a tenuous, hot corona would be a realistic phenomenological description of the spectrum."66 llowever. a recent. more detailed analvsis of non-LTE accretion flows around IMDIIS αμ.IIubeny2005). has indicated that the effects of black-hole rotation aud Compton scaltering within the disk may very well lead to much higher apparent disk temperatures. up to FT~| keV. in addition to deviations from conventional AICDBB spectra at both soft and hard X-ray. energies due to metal opacity effects.," However, a recent, more detailed analysis of non-LTE accretion flows around IMBHs \citep{hui05} has indicated that the effects of black-hole rotation and Compton scattering within the disk may very well lead to much higher apparent disk temperatures, up to $kT \sim 1$ keV, in addition to deviations from conventional MCDBB spectra at both soft and hard X-ray energies due to metal opacity effects."67 The continuum specirum from the photon bubble model might be dominated by the AICDDD spectrum emanating Irom the IIDIBs., The continuum spectrum from the photon bubble model might be dominated by the MCDBB spectrum emanating from the HDRs.68 However. this spectrum might be modified during the radiation transport im the photon bubble cavities.," However, this spectrum might be modified during the radiation transport in the photon bubble cavities."69 Furthermore. the almost free-stveaming radiation of the photon bubbles could be repeatedly: Compton-reflected. off the surfaces of the IIDIBs. potentially leading to strong [orescence lines and/or radiative recombination edges. in addition to Compton reflection features from hard. X-ray. emission impineimeg upon the disk [rom radiation sources external to the disk (Dallantvne.Turner&2004:Dallantvne.Turner&Young 2005).," Furthermore, the almost free-streaming radiation of the photon bubbles could be repeatedly Compton-reflected off the surfaces of the HDRs, potentially leading to strong fluorescence lines and/or radiative recombination edges, in addition to Compton reflection features from hard X-ray emission impinging upon the disk from radiation sources external to the disk \citep{btb04,bty05}."70. Such features may be observable. assumingD it is not overwhelmed by other radiation sources. in particular the blackbody from the ILDBRs.," Such features may be observable, assuming it is not overwhelmed by other radiation sources, in particular the blackbody from the HDRs."71 Distünguishing scenarios by spectral modeling is currently. very difficult for all but the uehest quality ULX data sets. ancl spectral fitting to these ULX spectra gives contradictory results.," Distinguishing scenarios by spectral modeling is currently very difficult for all but the highest quality ULX data sets, and spectral fitting to these ULX spectra gives contradictory results."72 For example. Feng&Ixaaret(2005) recently performed a detailed spectral aud timing analvsis of archival data on 28 ULXs that had sufficient photon statistics to allow for meaningful fitting with models more complicated than a simple power-law.," For example, \citet{fk05}73 recently performed a detailed spectral and timing analysis of archival data on 28 ULXs that had sufficient photon statistics to allow for meaningful fitting with models more complicated than a simple power-law."74 They found that their continuum spectra fell into three general categories: (1) Optically thin bremsstirahlung-dominated. euasi-Lhbermal spectra with temperatures of AT0.6 0.5 keV. characteristic for A-ray emission from voung supernova remnants: (2) MCDDD spectra of temperatures AL0.1. 0.4 keV. plus occasionally a hare X-ray power-law. as possible in the case of accretion onto IAIBIIs: (2) MCDDD spectra at temperatures AZ~1 keV. plus a power-law component clominating al lower energies.," They found that their continuum spectra fell into three general categories: (1) Optically thin bremsstrahlung-dominated, quasi-thermal spectra with temperatures of $kT \sim 0.6$ – 0.8 keV, characteristic for X-ray emission from young supernova remnants; (2) MCDBB spectra of temperatures $kT \sim 750.1$ – 0.4 keV, plus occasionally a hard X-ray power-law, as possible in the case of accretion onto IMBHs; (3) MCDBB spectra at temperatures $kT \sim 1$ keV, plus a power-law component dominating at lower energies."76 Dased on these results. (2005). suggest that ULXs mas. in fact. not be a homogeneous class of objects.," Based on these results, \cite{fk05} suggest that ULXs may, in fact, not be a homogeneous class of objects."77 This is in accord with recent results of Alacdhusudhanetal.(2006) that realistic stellar evolution and population svuthesis calculations suggest (hat (he expected rate of captures of massive stars bv. IMDIIs may not be sullident to produce the total observed number of ULXs.," This is in accord with recent results of \cite{metal06}78 that realistic stellar evolution and population synthesis calculations suggest that the expected rate of captures of massive stars by IMBHs may not be sufficient to produce the total observed number of ULXs."79 Winteretal.(2006) classified ULXs into low/hard and high/solt states based on (heir ταν luminosities ancl spectra. assuming the ULXs were IMDIIs accreting in states similar to galactic X-ray binaries.," \citet{wetal06} classified ULXs into low/hard and high/soft states based on their X-ray luminosities and spectra, assuming the ULXs were IMBHs accreting in states similar to galactic X-ray binaries."80 They found that the hieh/solt ULXs were erouped around one of two blackbody temperatures: one grouped around | keV ancl one grouped around 0.1 keV. further indication that ULXs are not a homogeneous group.," They found that the high/soft ULXs were grouped around one of two blackbody temperatures: one grouped around $~1$ keV and one grouped around $~0.1$ keV, further indication that ULXs are not a homogeneous group."81 The long term monitoring of some ULXs such as NGC 5204 X-1 shows that ils X-ray spectrum hardens as its Πας, The long term monitoring of some ULXs such as NGC 5204 X-1 shows that its X-ray spectrum hardens as its flux82oovides high. resolution in both energy. (64 channels over he full 2-60 keV. PCA band) and time (16 msec)).,provides high resolution in both energy (64 channels over the full 2-60 keV PCA band) and time (16 msec).83 This is he main reason why we selected this particular observation. which also has the advantage of having been mace with all ive proportional counter units of the PCA. increasing the source count rate.," This is the main reason why we selected this particular observation, which also has the advantage of having been made with all five proportional counter units of the PCA, increasing the source count rate."84 In order to obtain sullicient statistics [or he analvsis. we rebinned the data into eight energv. bins oetween 0.14:25 keV. In this way in each energy. bin the mean count rate is above 1000 counts |.," In order to obtain sufficient statistics for the analysis, we rebinned the data into eight energy bins between 0.14–25 keV. In this way in each energy bin the mean count rate is above $\sim1000$ counts $^{-1}$."85 Notice that the contribution of background. photons to cach of these eight ins is minor compared to the source counts., Notice that the contribution of background photons to each of these eight bins is minor compared to the source counts.86 For the analysis. we used custom-nmace software written in the IDOL environment.," For the analysis, we used custom-made software written in the IDL environment."87 For cach of the eight energy bins. we extracted a Fourier Spectrum from data stretches of length 128 s. up to a INvquist frequency. of 32 Lz.," For each of the eight energy bins, we extracted a Fourier Spectrum from data stretches of length 128 s, up to a Nyquist frequency of 32 Hz."88 These Fourier spectra were averaged for constructing the PDS (normalized and the phase-lag spectra.," These Fourier spectra were averaged for constructing the PDS \citep[normalized to the squared fractional rms, see][]{BH90} and the phase-lag spectra."89 Phe Poisson contribution was subtractedby using RAPE recipes (seeZhangctal.1995)., The Poisson contribution was subtractedby using RXTE recipes \citep[see][]{Zha95}.90. Uttleyetal.(2005). showed that the rms-ux relation. the non-linear behavior and the lognormal lux clistribution observed in the hard state of BIB represent three clillerent aspects of the same underlving process.," \citet{Utt05} showed that the rms-flux relation, the non-linear behavior and the lognormal flux distribution observed in the hard state of BHB represent three different aspects of the same underlying process."91 This non-linearity can be reproduced as an exponential of a linear light curve., This non-linearity can be reproduced as an exponential of a linear light curve.92 As the plan is to simulate the source light curve in cillerent energy bands. we must first check that this non-linearity holds also for separate energy band.," As the plan is to simulate the source light curve in different energy bands, we must first check that this non-linearity holds also for separate energy band."93 We then produced the rmis-ux relation and the Gus (count rate) distribution for each of our eight energy bins (see Fig., We then produced the rms-flux relation and the flux (count rate) distribution for each of our eight energy bins (see Fig.94 1. and Fig. 2))., \ref{fig_rmsflux} and Fig. \ref{fig_fluxhis}) ).95 ‘The rms in Fig., The rms in Fig.96 1 was measured by integrating the PDS of the eight bins over the 132 Hz frequency interval for 1s segments., \ref{fig_rmsflux} was measured by integrating the PDS of the eight bins over the 1–32 Hz frequency interval for 1 s segments.97 Its relation with the count rate. also in 1-5 bins. is consistent with linearity for all bins.," Its relation with the count rate, also in 1-s bins, is consistent with linearity for all bins."98 This linear relation holds also when the length of the light curve segments and the frequeney range for the integration are changed., This linear relation holds also when the length of the light curve segments and the frequency range for the integration are changed.99 At the same time. the Dux distribution Gwith a time bin of 0.25 s in Fig. 2))," At the same time, the flux distribution (with a time bin of 0.25 s in Fig. \ref{fig_fluxhis}) )"100 fits a lognormal model., fits a lognormal model.101 Further subdividing the enerev range into narrower bins we did not find significant deviations., Further subdividing the energy range into narrower bins we did not find significant deviations.102 As shown by Uttleyetal.(2005)... for typical observed light curves with the PDS dominated by broad components and a fractional rms of 2040 per cent. the clistorting elfect of the exponential transformation on the shape of the PDS is relatively small.," As shown by \citet{Utt05}, for typical observed light curves with the PDS dominated by broad components and a fractional rms of 20–40 per cent, the distorting effect of the exponential transformation on the shape of the PDS is relatively small."103 A quantitative analysis (not. presented here) suggests that for Lorentzian-shaped PDS components with fractional rms smaller than 50 per cent. the distortion is not serious if the quality [actor Q2.," A quantitative analysis (not presented here) suggests that for Lorentzian-shaped PDS components with fractional rms smaller than 50 per cent, the distortion is not serious if the quality factor $Q\la 2$."104 We tested the distortion on the PDS caused by exponential transformation of data in the time domain: we calculated the PDS from the logarithm of the real data and compared it with the original one (Pig. 3))., We tested the distortion on the PDS caused by exponential transformation of data in the time domain: we calculated the PDS from the logarithm of the real data and compared it with the original one (Fig. \ref{fig_pdslog}) ).105 The PDS shapes are almost unchanged between the raw data and the logarithmically translormiccl data., The PDS shapes are almost unchanged between the raw data and the logarithmically transformed data.106 Therefore in our simulation below. it is justified. to use the observed PDS as the PDS of the input linear light curve without the need to correct the distortion elfect of the exponential transformation.," Therefore in our simulation below, it is justified to use the observed PDS as the PDS of the input linear light curve without the need to correct the distortion effect of the exponential transformation."107 However. it is still important to apply the appropriate correction to the normalization of the input PDS in order to return the desired: variance in the output light curve. because the exponential transformation will cause the increase of the light curve variance.," However, it is still important to apply the appropriate correction to the normalization of the input PDS in order to return the desired variance in the output light curve, because the exponential transformation will cause the increase of the light curve variance."108 Also the mean count rate of light curve would change after the exponential transformation. and a correction factor needs to be multiplied to the non-linear light curve.," Also the mean count rate of light curve would change after the exponential transformation, and a correction factor needs to be multiplied to the non-linear light curve."109 We extracted an average PDS from each of the eight energv bins. covering the [requenev range 0.00532) 12 (Fig. 4)).," We extracted an average PDS from each of the eight energy bins, covering the frequency range 0.008–32 Hz (Fig. \ref{fig_pdsfrq}) )."110 No narrow QPOs are seen., No narrow QPOs are seen.111 Ao simple mocel consisting of two broad Lorentzians was used for the fit., A simple model consisting of two broad Lorentzians was used for the fit.112 Phe goodness of the fit is reasonably good. with all reduced. \ smaller than 2.2 (obtaining a formal reduced us of the order of unity is cifficult for these high-signal PDS).," The goodness of the fit is reasonably good, with all reduced $\chi^2$ smaller than 2.2 (obtaining a formal reduced $\chi^2$ of the order of unity is difficult for these high-signal PDS)."113 Adopting a more complex model (c.g.Bellonietal.L997) the goodness of fit would be improved but the fit parameters would be »x»orlv constrained., Adopting a more complex model \citep[e.g. ][]{Bel97} the goodness of fit would be improved but the fit parameters would be poorly constrained.114 Phere are three free parameters for cach Lorentzian: the normalization (the square of the integrated ractional rms). the centroicl frequency ancl FWIIM.," There are three free parameters for each Lorentzian: the normalization (the square of the integrated fractional rms), the centroid frequency and FWHM."115 The evolution of the PDS shape with energv can be well described. by the energy. dependence of the best-fitting xvwameters. which is shown in Fig. 5..," The evolution of the PDS shape with energy can be well described by the energy dependence of the best-fitting parameters, which is shown in Fig. \ref{fig_pdsen}."116 Concerning the second Lorentzian. lor the last three energy bins the best-fitting centroid frequency decreases to zero. the lower bound of this ree parameter.," Concerning the second Lorentzian, for the last three energy bins the best-fitting centroid frequency decreases to zero, the lower bound of this free parameter."117 For those three bins. uncertainties were not xotted.," For those three bins, uncertainties were not plotted."118 The time lag of the light curve in cach energv bin relative to that of the lowest energv bin (0.14.3.4 keV) was calculated. from the cross-spectra between 0.06 anc 30 Lz., The time lag of the light curve in each energy bin relative to that of the lowest energy bin (0.14–3.4 keV) was calculated from the cross-spectra between 0.06 and 30 Hz.119 Positive lags here correspond to the hard time series lagging he soft., Positive lags here correspond to the hard time series lagging the soft.120 Phe lags were logarithniically rebinned in frequency in order to reduce noise., The lags were logarithmically rebinned in frequency in order to reduce noise.121 Since their calculations involve the splitting of the data into two energy. bands. compared with he PDS the measurement of time lags is more sensitive to counting noise.," Since their calculations involve the splitting of the data into two energy bands, compared with the PDS the measurement of time lags is more sensitive to counting noise."122 Nowaketal.(1999). estimated the expected noise level for the time [ag measurements ancl concluded hat for frequencies below: ~0.1 Lz and above ~30 Lz ags cannot be measured because of noise limitations., \citet{Now99} estimated the expected noise level for the time lag measurements and concluded that for frequencies below $\sim0.1$ Hz and above $\sim30$ Hz lags cannot be measured because of noise limitations.123 As the pequency approaches ~0.1 Hz or ~30 Lz. the lags tend to zero due to the ellect of noise.," As the frequency approaches $\sim0.1$ Hz or $\sim30$ Hz, the lags tend to zero due to the effect of noise."124 When sampling Iuctuations come Comparable to the intrinsic lags. they scatter around zero and exhibit negative values.," When sampling fluctuations become comparable to the intrinsic lags, they scatter around zero and exhibit negative values."125 We adopted the same strategy as. for. the PDS o quantitatively ceseribe the energy. dependence. of lag spectrum in a uniform way., We adopted the same strategy as for the PDS to quantitatively describe the energy dependence of lag spectrum in a uniform way.126 Nowaketal.(1999) showed that he time lags approximately show a power law dependence upon frequency⋅ (xf.⊽∩⊽≓ 7).," \citet{Now99} showed that the time lags approximately show a power law dependence upon frequency $\propto127f^{-0.7}$ )."128 We ⇁⋅found significant.⋠⋠⋅ deviationss rom a simple power law model., We found significant deviations from a simple power law model.129 Phe time lag spectra show a two-humped shape similar to that published. in previous studies (e...Mivamotoetal.1992:Cui1997:Nowak 1909)..," The time lag spectra show a two-humped shape similar to that published in previous studies \citep[e.g., ][]{Miya92,Cui97,Now99}. ."130 We used a two-Lorentzian model to fit the time, We used a two-Lorentzian model to fit the time131 n(ki) (he)11] Next we can do the angulare integrations.> usinge κιk»=Ay AS).," n(k_1)[ n(k_2)+1] Next we can do the angular integrations, using $\bk_1\cd\bk_2=\frac{1}{2} (k^2-k_1^2-k_2^2)$ ."132" ἰκ convenient to introduce the two dimensionless integration variables Yo=(A,|fe)fA and Yoth,ο).", It is convenient to introduce the two dimensionless integration variables $X=(k_1+k_2)/k$ and $Y=(k_1-k_2)/k$.133 Εις we find Pk) = Jpeax 4Y1- Jo perform the integrals. we may expand. the denominators. obtaining PUK) (16)).)," Thus we find (k) = dX dY. To perform the integrals, we may expand the denominators, obtaining (k) )^8 ).)"134 The integrals can now be performed., The integrals can now be performed.135" To write the result in a reasonably concise form. we introduce the abbreviation . ""E Then we find P() ∝∖⋖≸∆↙∣⋝⋝∑∑↴ We are most interested in the limiting forms of 7 for small and large &/7."," To write the result in a reasonably concise form, we introduce the abbreviation f_r = Then we find (k) )^8 +3) - +3)] We are most interested in the limiting forms of $\cP$ for small and large $k/T$."136 Expanding in powers of &/T we find that all terms in. (4/27κατι cancel. and the leacing. term is. valid. for &0 and in agreement with the classical expression [or this limit.," Expanding in powers of $k/T$ we find that all terms in $(k/T)^2$ cancel, and the leading term is = valid for $k \to 0$ and in agreement with the classical expression for this limit."137 To further elaborate. upon this agreement. (36)) is smallerthan the power spectrum. of thermal photons in the small & limit hy a factor of two. which is exactly what one expects because photons have two internal degrees of freedom (ο)2 and wv are both larger. hence (80/003)? smaller. by two times relative to the massless particles).," To further elaborate upon this agreement, \ref{PSmallk}) ) is smallerthan the power spectrum of thermal photons in the small $k$ limit by a factor of two, which is exactly what one expects because photons have two internal degrees of freedom $(\de u)^2$ and $\bar u$ are both larger, hence $(\de u/\<u\>)^2$ smaller, by two times relative to the massless particles)."138 So [ar as the Iarge-& behavior is concerned. we can drop all terms involving decreasing exponential factors.," So far as the $k$ behavior is concerned, we can drop all terms involving decreasing exponential factors."139 The only surviving terms are those with s=0 and where the two exponentials cancel., The only surviving terms are those with $s=0$ and where the two exponentials cancel.140 Weeping only these. we have TS) MES ))," Keeping only these, we have (k) )^8 )."141 The leading term is the one in L/ft. which gives infty).," The leading term is the one in $1/f_r^4$, which gives )."142 The point at which the two asymptotic forms (36)) aux (44)) agree is where &/T=6., The point at which the two asymptotic forms \ref{PSmallk}) ) and \ref{PLargek}) ) agree is where $k/T=6$.143 Lt would also appear that. from the nature of this calculation. P(&) becomes laree a large & for many other states besides exactly thermal ones.," It would also appear that, from the nature of this calculation, $P(k)$ becomes large at large $k$ for many other states besides exactly thermal ones."144 3elore leaving this section we revisit. our procedure of divergence removal to show that. d0 is robust. ane consistent., Before leaving this section we revisit our procedure of divergence removal to show that it is robust and consistent.145 When calculating (7 we subtracted the infinite vacuum contribution. or equivalently normally ordered. the factors in vw.," When calculating $\<u\>$ we subtracted the infinite vacuum contribution, or equivalently normally ordered the factors in $u$ ."146 In the case of éu(r)n(O) we again subtractec the divergent vacuum contribution. but in that case the," In the case of $\<u(\br) u({\bf 0})\>$ we again subtracted the divergent vacuum contribution, but in that case the"147We have identified 9 objects in our sample (~40% of the total) which show broad permitted: emission lines in their spectra and should therefore be classified asBLRG?.,We have identified 9 objects in our sample $\sim$ of the total) which show broad permitted emission lines in their spectra and should therefore be classified as.148. With the exception of PI&S0035-2 (3C17). and possibly also PINSS1547-79. none of the BLRG in our sample is highly polarized. in the UV. despie the presence of large UV excesses.," With the exception of PKS0035-02 (3C17), and possibly also PKS1547-79, none of the BLRG in our sample is highly polarized in the UV, despite the presence of large UV excesses."149 Therefore. it ds likedy that we are observing the nuclei cirecthy in these sources. and that the UV. excess is due to direct. AGN light. wih only a minor contribution. if anv. from. scattered AGN light.," Therefore, it is likely that we are observing the nuclei directly in these sources, and that the UV excess is due to direct AGN light, with only a minor contribution, if any, from scattered AGN light."150 This is in line with polarimetrie observations of low redshift DLIU and quasars which show low levels of polarization in most objects (Stockman. Angel Miley 1979. Antonucei 1984).," This is in line with polarimetric observations of low redshift BLRG and quasars which show low levels of polarization in most objects (Stockman, Angel Miley 1979, Antonucci 1984)."151 Clearly. objects such as 3€234 ClEran. Cohen Goodrich 1995) and 3C109 (Goodrich Cohen 1992). in which the broad. lines are reaclily detected in optical spectra. and which also show a high degree of linear polarization. are the exception rather than the rule.," Clearly, objects such as 3C234 (Tran, Cohen Goodrich 1995) and 3C109 (Goodrich Cohen 1992), in which the broad lines are readily detected in optical spectra, and which also show a high degree of linear polarization, are the exception rather than the rule."152 lt is interesting to consider how these BLRG Lit into the orientation-based unified schemes for powerful. racio galaxies. in which it is proposed that radio galaxies ancl quasars are the same thing viewed from different directions. with the quasar nucleus blocked from direct view in the radio ealaxies by a central obscuring torus (Barthel 1989).," It is interesting to consider how these BLRG fit into the orientation-based unified schemes for powerful radio galaxies, in which it is proposed that radio galaxies and quasars are the same thing viewed from different directions, with the quasar nucleus blocked from direct view in the radio galaxies by a central obscuring torus (Barthel 1989)."153 There are two main possibilities:, There are two main possibilities:154tvpically show more power at half (he true period than the true period itself. we use twice the peak period as the matching value.,"typically show more power at half the true period than the true period itself, we use twice the peak period as the matching value."155 Thus. we define {δη=22%.," Thus, we define $P_m = 2P_k$."156 We find (hat successful period recoverability is strongest for short period EBs ancl declines relatively evenly in logP., We find that successful period recoverability is strongest for short period EBs and declines relatively evenly in $\log P$.157 This is expected since phase coverage lor short period EBs is more complete than for long period EBs (cL., This is expected since phase coverage for short period EBs is more complete than for long period EBs (cf.158 Fie. 3))., Fig. \ref{fig:lightcurves}) ).159 The results from the AoV analvsis for different EB types are shown in Figure 4., The results from the AoV analysis for different EB types are shown in Figure \ref{fig:aov1}.160" In this plot. we split up the input lighteurve sample according to the physical parameters of the EBs. based on the parameter combination (p,+pa).oE which is roughly the sum of the radii of the components. 2(/*4+Ha)."," In this plot, we split up the input lightcurve sample according to the physical parameters of the EBs, based on the parameter combination $\rho_1 + \rho_2) P^{2/3}$, which is roughly the sum of the radii of the components, $\approx (R_1 + R_2)$."161 We separate (he sample into Dwarls (£24+de<52.) and Giants (Ry+Ro 5R.)., We separate the sample into Dwarfs $R_1 + R_2 \leq 5 R_{\odot}$ ) and Giants $R_1 + R_2 > 5 R_{\odot}$ ).162 The dashed lines show the distribution of input svstems ancl the solid lines show the recoverability. as a function of period.," The dashed lines show the distribution of input systems and the solid lines show the recoverability, as a function of period."163 Anv attempt at period recovery lor eround-based data tvpically encounters aliasing effects at integral fractions and multiples of 1 day., Any attempt at period recovery for ground-based data typically encounters aliasing effects at integral fractions and multiples of 1 day.164 For svstems where the true period is very close to those periods. recovery tends (o decrease strongly.," For systems where the true period is very close to those periods, recovery tends to decrease strongly."165 In Fig 4.. the resolution in period space is too large to see sienilicant aliasing effects.," In Fig \ref{fig:aov1}, the resolution in period space is too large to see significant aliasing effects."166 While such effects are inherently present in LSST data. thev are actually marginal due to the LAST cadence.," While such effects are inherently present in LSST data, they are actually marginal due to the LSST cadence."167 Because of the combination of inlreequent sampling (1-3 visits/night every 20 nights) and the very. long time baseline (10 vears). aliasing effects at the diurnal evele are fairly small compared to hieher-cadence and/or single-season campaigns.," Because of the combination of infrequent sampling (1-3 visits/night every $\sim$ 20 nights) and the very long time baseline (10 years), aliasing effects at the diurnal cycle are fairly small compared to higher-cadence and/or single-season campaigns."168 It may seem surprising that we are able to accurately recover EB periods as long as  1000 d. We find that in many of these cases. particularly where one of the stellar components is a giant. it is the ellipsoidal variations (hal provide the strong observational handle on the svstemrs period.," It may seem surprising that we are able to accurately recover EB periods as long as $\sim$ 1000 d. We find that in many of these cases, particularly where one of the stellar components is a giant, it is the ellipsoidal variations that provide the strong observational handle on the system's period."169 In an ED where one component is a giant star. the giant can fill a large fraction of the semi-major axis even though the orbital period max be quite long.," In an EB where one component is a giant star, the giant can fill a large fraction of the semi-major axis even though the orbital period may be quite long."170 The proximity of the companion star can then raise tidal bulges on the giant star (hat lead, The proximity of the companion star can then raise tidal bulges on the giant star that lead17111997: Gerhard 2002. 2006).,"1997; Gerhard 2002, 2006)."172 [Cis also possible to invert the procedure and derive a plausible detailed surface deusitv distribution [rom the observed terminal velocity curve., It is also possible to invert the procedure and derive a plausible detailed surface density distribution from the observed terminal velocity curve.173 The major conclusions of this work are as follows., The major conclusions of this work are as follows.174 ]t is hard to imagine (hat all this could follow [rom a Formula devoid of physical meaning., It is hard to imagine that all this could follow from a formula devoid of physical meaning.175We investigated: all the ARP and UVOT data that were obtained within two hours after the BAT trigger.,We investigated all the XRT and UVOT data that were obtained within two hours after the BAT trigger.176 The ART spectra could. be successfully modelled by. blackbocy radiation and revealed cooling during the decay. which confirms that this was a thermonuclear event.," The XRT spectra could be successfully modelled by blackbody radiation and revealed cooling during the decay, which confirms that this was a thermonuclear event."177 This testifies that ccontains an accreting neutron star and classifies the svstem. in all likelihood. as an LAINB.," This testifies that contains an accreting neutron star and classifies the system, in all likelihood, as an LMXB."178 The UVOT V Z-band images revealed an optical source that was fading simultaneously with the observed. decrease in X-ray lux., The UVOT $WH$ -band images revealed an optical source that was fading simultaneously with the observed decrease in X-ray flux.179 Such behavior is tvpical of tvpe-E X-ray bursts and is thought to result from reprocessing of N-ravs1995)., Such behavior is typical of type-I X-ray bursts and is thought to result from reprocessing of X-rays.180. This provides strong evidence that the fading UVOT source is the counterpart of1735., This provides strong evidence that the fading UVOT source is the counterpart of.181.. X similar. fading was detected in. Zi band images obtained with the (telescope., A similar fading was detected in $R$ -band images obtained with the telescope.182 Using theNTT.. aandVET. we detect an optical/near-H1t source within the UVOT positional uncertainty ofJ1735.," Using the, and, we detect an optical/near-IR source within the UVOT positional uncertainty of."183. Phe oobservations reveal a spectrum with a single-peaked comission line., The observations reveal a spectrum with a single-peaked emission line.184 Such emission is tvpical for X-ray binaries. accreting white dwarls and Be stars.," Such emission is typical for X-ray binaries, accreting white dwarfs and Be stars."185 Phe broadband colours of the counterpart after correcting for the recdcening are not consistent with a Be star. which has a bluer spectral energy clistribution (SED) than observed (efSection??2000).," The broadband colours of the counterpart after correcting for the reddening are not consistent with a Be star, which has a bluer spectral energy distribution (SED) than observed \citep[cf. Section~\ref{subsec:photometry} ."186 This ellectively rules out the possibility that we detect a Be star interloper within the UVOT error circle., This effectively rules out the possibility that we detect a Be star interloper within the UVOT error circle.187 Thus. we conclude that we have detected the optical/near-LR counterpart ofJ1735.," Thus, we conclude that we have detected the optical/near-IR counterpart of."188. The aand emission line broadening observed in the sspectra is stronely allected: by the instrumental profile. which makes it difficult to assess whether or not the lines are double-peaked.," The and emission line broadening observed in the spectra is strongly affected by the instrumental profile, which makes it difficult to assess whether or not the lines are double-peaked."189 We subtract in quadrature the instrumental width to find a EWLIIM of 19249 and 22512kms+ for the aand Ca lines respectively (see Section ?22))., We subtract in quadrature the instrumental width to find a FWHM of $192 \pm 9$ and $225 \pm 12~\kms$ for the and Ca lines respectively (see Section \ref{subsec:specres}) ).190 The ratio of these EWHIIAMIs are consistent with the ratio of the rest wavelengths ancl thereby with Doppler broadening of the line., The ratio of these FWHMs are consistent with the ratio of the rest wavelengths and thereby with Doppler broadening of the line.191 The observed. EW and intrinsic ENIM of the lines match two possible scenarios for the origin of the line emission., The observed EW and intrinsic FWHM of the lines match two possible scenarios for the origin of the line emission.192 The first is that the emission. arises fron the accretion disc. in which case the line profile would be unless if the svstem is viewed face-on (e.g. 1972).," The first is that the emission arises from the accretion disc, in which case the line profile would be double-peaked unless if the system is viewed face-on \citep[e.g.,][]{huang72}."193. In the second. scenario. the emission is due to N-ray reprocessing in the hemisphere of the secondary. [acing the neutron star. which would. produce a single-peakecl profile (e...Bassaetal.2009).," In the second scenario, the emission is due to X-ray reprocessing in the hemisphere of the secondary facing the neutron star, which would produce a single-peaked profile \citep[e.g.,][]{bassa09}."194. Further spectroscopic observations at higher spectral resolution max. test these hypothesis., Further spectroscopic observations at higher spectral resolution may test these hypothesis.195 The parameters of the X-ray. burst. from1735... as inferred [rom spectral analysis of the BAT and. NIE. data. are summarized in Table 5..," The parameters of the X-ray burst from, as inferred from spectral analysis of the BAT and XRT data, are summarized in Table \ref{tab:burstpar}."196 These show that it was no ordinary tvpe-L N-aray burst. which are triggered by unstable burning of LL/Lle and tvpically last 10.—100 s releasing a total energy of ~LOBo͵Lu erg.," These show that it was no ordinary type-I X-ray burst, which are triggered by unstable burning of H/He and typically last $\sim10-100$ s releasing a total energy of $\sim 10^{39-40}$ erg."197 YetJ it tis not as energetic. as the so-called superbursts. which endure for many hours and are thought to be fuelled by carbon rather then 11Πο. resulting in a total energy release of ~107. ore (eg.Strohmayer&Dildsten 2006).," Yet it is not as energetic as the so-called superbursts, which endure for many hours and are thought to be fuelled by carbon rather then H/He, resulting in a total energy release of $\sim 10^{42-43}$ erg \citep[e.g.,][]{strohmayer06}."198. Instead. the duration (~2 h) and total energy output (LinusS15104 erg) suggest that the rav burst [rom bbelongs to the rare class of intermediately lone X-ray bursts.," Instead, the duration $\sim 2$ h) and total energy output $E_{\mathrm{burst}} \lesssim 1.5 \times10^{41}$ erg) suggest that the X-ray burst from belongs to the rare class of intermediately long X-ray bursts."199 The driving mechanism behind these events is thought to be the ignition of a thick laver of He ancl their host svstems probe unusual acerction regimes (in|Zand 2006).," The driving mechanism behind these events is thought to be the ignition of a thick layer of He and their host systems probe unusual accretion regimes \citep{zand05,zand07,cumming06}."200.Several intermediately lone X-ray bursts have. been detected: from. (candidate) ultra-compact X-ray binaries, .Several intermediately long X-ray bursts have been detected from (candidate) ultra-compact X-ray binaries201clear how to define these.,clear how to define these.202" Nevertheless, the global structure of the disk remains consistent with the initial conditions and vertical hydrostatic equilibrium through the simulation."," Nevertheless, the global structure of the disk remains consistent with the initial conditions and vertical hydrostatic equilibrium through the simulation."203 In the left panel of the we show density distribution of the magnetised case., In the left panel of the we show density distribution of the magnetised case.204" In contrast to non-magnetised simulation, the laminar motion breaks into turbulence at t2100."," In contrast to non-magnetised simulation, the laminar motion breaks into turbulence at $t \approx 100$."205" For earlier times, the laminar flow permits the magnetic field to grow to (81)=0.1 as shown in the top panel of the20."," For earlier times, the laminar flow permits the magnetic field to grow to $\langle \beta^{-1} \rangle \approx 0.1$ as shown in the top panel of the."206". Of the particular interest here, is the value of the magnetic stresses, am=—B,Bg/Pzas, which determines the accretion rate in the disk."," Of the particular interest here, is the value of the magnetic stresses, $\alpha_{\rm M} = -B_r B_\theta/P_{\rm gas}$, which determines the accretion rate in the disk."207 Time dependence of the volume average magnetic stress is shown in the bottom panel of the20., Time dependence of the volume average magnetic stress is shown in the bottom panel of the.208". The growth continues until tz100, after which the flow become turbulent and the volume averaged magnetic stress remain roughly constant at (am)70.01."," The growth continues until $t \approx209100$, after which the flow become turbulent and the volume averaged magnetic stress remain roughly constant at $\langle \alpha_{\rm M} \rangle \approx 0.01$."210" In contrast to 2D axisymmetric shearing sheet simulation, neither magnetic energy nor magnetic stressed decay with time, implying the dynamo activity in the disk."," In contrast to 2D axisymmetric shearing sheet simulation, neither magnetic energy nor magnetic stressed decay with time, implying the dynamo activity in the disk."211 The density distribution in the mid plane of the disk is shown in21., The density distribution in the mid plane of the disk is shown in.212". The left and right panels of the figure display non-magnetised and magnetised cases respectively, and the top and bottom panel show the profile at t=100 and t=150."," The left and right panels of the figure display non-magnetised and magnetised cases respectively, and the top and bottom panel show the profile at $t =213100$ and $t = 150$."214" The turbulent structure of the magnetised disk for t>100 is apparent through the existence of small scale structures in density,"," The turbulent structure of the magnetised disk for $t > 100$ is apparent through the existence of small scale structures in density,"215he XN-rav cussion relative to the svuchrotron (radio/optical) is explained by lypothesizine a onlk velocity of the jet fluid which is relativistic even on large (kpe) scales.,the X-ray emission relative to the synchrotron (radio/optical) is explained by hypothesizing a bulk velocity of the jet fluid which is relativistic even on large (kpc) scales.216 If this were the case. iu he frame of the jet the effective photon energy density of the cosmüc mucrowave backeromud (CAIB) would be augmented by the square of the jet’s Lorentz factor. D. and it was demonstrated hat quite reasonable combinations of DP aud the vcamine factor. à could be invoked to explain the observed intensities.," If this were the case, in the frame of the jet the effective photon energy density of the cosmic microwave background (CMB) would be augmented by the square of the jet's Lorentz factor, $\Gamma$, and it was demonstrated that quite reasonable combinations of $\Gamma$ and the beaming factor, $\delta$ could be invoked to explain the observed intensities."217 Iu this paper we review the common enüssiou o0rocesses (section 77)): present a curent dist of jet sources and suggest a classification scheme (section 7?) deseribe ai formulation of the vcamming model which relies ou an evaluation of he magnetic feld streneth from the equipartitiou field aud includes the anisotropic nature of the IC scattering (section 77]): aud exandue he conflicting evidence anc ranudfieatious for the svuchrotron aud dnverse-Coniptou (IC) models (section ??))., In this paper we review the common emission processes (section \ref{sec:emission}) ); present a current list of jet sources and suggest a classification scheme (section \ref{sec:classify}) ); describe a formulation of the beaming model which relies on an evaluation of the magnetic field strength from the equipartition field and includes the anisotropic nature of the IC scattering (section \ref{sec:beam}) ); and examine the conflicting evidence and ramifications for the synchrotron and inverse-Compton (IC) models (section \ref{sec:conflict}) ).218 The appendix coutains the details of our beaming formulation., The appendix contains the details of our beaming formulation.219 For numuerical results we use ces units unless stated otherwise aud assiumne H4250 nis. 1 1l. and qy=0., For numerical results we use cgs units unless stated otherwise and assume $_0$ =50 km $^{-1}$ $^{-1}$; and $_0$ =0.220" We follow the couveutiou that the spectral index of a power ανν is defined bv fiux density. S,=ky""."," We follow the convention that the spectral index of a power law is defined by flux density, $_{\nu}~=~k~\nu^{-\alpha}$."221 For mauy sources wlüch displav couvincine evidence that the N-ray απ radio. enissiou originate iu the same volume. (e.g. hotspot D of 3€C390.3. Tarris Leighly Lealhyw 1998) it has been argued that thermal broiisstralilung does not provide a satisfactory iiodel for the N-rav ciission. because the required amount of hot eas is large (~ LOMAS). over-pressired. far frou the parent ealaxv. aud the predicted Faraday rotation and depolauizatiou are uot observed.," For many sources which display convincing evidence that the X-ray and radio emission originate in the same volume, (e.g. hotspot B of 3C390.3, Harris Leighly Leahy 1998) it has been argued that thermal bremsstrahlung does not provide a satisfactory model for the X-ray emission because the required amount of hot gas is large $\approx~10^{10}M_{\odot}$ ), over-pressured, far from the parent galaxy, and the predicted Faraday rotation and depolarization are not observed."222 Recent Chaudra results (c.g. 3€ 273. \avshall et al.," Recent Chandra results (e.g. 3C 273, Marshall et al."223 2001a) confini that the N-rav. cussion from jet features has no line enission and is best characterized by a power law., 2001a) confirm that the X-ray emission from jet features has no line emission and is best characterized by a power law.224" Svuchrotron enusson has Όσοι. considered the ""process of choice’ for X-rays from knots iu radio jets mainly because the optical polarization observed im sources such as AIST is) conviucig evidence that the optical enussion as well as the radio euussion comes from the svuchnrotron process.", Synchrotron emission has been considered the `process of choice' for X-rays from knots in radio jets mainly because the optical polarization observed in sources such as M87 is convincing evidence that the optical emission as well as the radio emission comes from the synchrotron process.225 Demonstrations that the N-vayv iuteusity was consistent either with a single power law extrapolation from radio aud optical bands (e.g. hotspot D of 3€ 2390.3. Tlarvis. Leigh. Leal 1998) or with a broken power law (e.g. knot A iu AINT. Diretta. Steru. Harris 1991) were takeu as circuuustautial evidence that the N-ravs were also generated by svuchrotrou emission.," Demonstrations that the X-ray intensity was consistent either with a single power law extrapolation from radio and optical bands (e.g. hotspot B of 3C 390.3, Harris, Leighly, Leahy 1998) or with a broken power law (e.g. knot A in M87, Biretta, Stern, Harris 1991) were taken as circumstantial evidence that the X-rays were also generated by synchrotron emission."226 Required for this model is the presence of electrons with Lorentz factor 5>10 (ef., Required for this model is the presence of electrons with Lorentz factor $\gamma > 10^7$ (cf.227 values of 10° for optical cluission)., values of $^5$ for optical emission).228" Iu the typical equipartitiou. fields of B z10 !G. the radiation half lives 7, of the N-rav ocuittine clectrous would be of order 10 vears (however. see Alarouian (2001) for problems associated with very fast cooliug times)."," In the typical equipartition fields of B $\approx 10^{-4}$ G, the radiation half lives $\tau_o$ of the X-ray emitting electrons would be of order 10 years (however, see Aharonian (2001) for problems associated with very fast cooling times)."229 There are. however. a number of sources for which the optical fux deusities or limits preclude a simple construction of a broken power law.," There are, however, a number of sources for which the optical flux densities or limits preclude a simple construction of a broken power law."230" Iu general. assuning the usual shock acceleration processes and dominance of losses to the relativistic clectrous that eo with the energv squared. we expect that both the electron distribution aud the resulting svuchrotron ciissiou spectrum will be concave dowmward when displaved ou the usual log S, vs. log v plot."," In general, assuming the usual shock acceleration processes and dominance of losses to the relativistic electrons that go with the energy squared, we expect that both the electron distribution and the resulting synchrotron emission spectrum will be concave downward when displayed on the usual log $_{\nu}$ vs. log $\nu$ plot."231 For this reason. N-rav iutensitfies that lie well above the extrapolatiou of the radio/optical svuchrotrou spectrun are taken to be strong evidence against the “simple svuchrotrou model.," For this reason, X-ray intensities that lie well above the extrapolation of the radio/optical synchrotron spectrum are taken to be strong evidence against the 'simple' synchrotron model."232 The cussion of most of these sources however can still be explained with inhomogeneous svuchrotron models., The emission of most of these sources however can still be explained with inhomogeneous synchrotron models.233 Spatially separated emission coniponeuts which cannot be resolved with the current N-rav detectors would be the consequence of diffusive shock acceleration with a time depeudent high enerev cut-off of accelerated particles., Spatially separated emission components which cannot be resolved with the current X-ray detectors would be the consequence of diffusive shock acceleration with a time dependent high energy cut-off of accelerated particles.234 While the low enerev radio aud optical enission is dominated by radiatively aged particle populations further downstream. the X-ray cussion is oulv euuütted by recently accelerated. particles.," While the low energy radio and optical emission is dominated by radiatively aged particle populations further downstream, the X-ray emission is only emitted by recently accelerated particles."235 In this scenario the projected extension of the X-ray ciission, In this scenario the projected extension of the X-ray emission236falls in the region occupied by T Tauri and HAeBe stars.,falls in the region occupied by T Tauri and HAeBe stars.237" Stars that lie outside the region of reddened main-sequence objects (i.e. redward of the reddening line drawn from the base of the main-sequence dwarf branch, that is, redward of the middle of the three vectors) are YSOs with intrinsic colour excesses."," Stars that lie outside the region of reddened main-sequence objects (i.e. redward of the reddening line drawn from the base of the main-sequence dwarf branch, that is, redward of the middle of the three vectors) are YSOs with intrinsic colour excesses."238" We shall refer to these as “probable cluster members"".", We shall refer to these as “probable cluster members”.239" By de-reddening the stars on the CC diagram that fall within the first two reddening vectors (encompassing the main-sequence and giant stars) to the dwarf locus, a visual extinction (Av) for each star was calculated."," By de-reddening the stars on the CC diagram that fall within the first two reddening vectors (encompassing the main-sequence and giant stars) to the dwarf locus, a visual extinction $A{\rm_V}$ ) for each star was calculated."240" The individual extinction values range from 0 to 20 mag, resulting in an average extinction of Ay — 7.6 mag."," The individual extinction values range from 0 to 20 mag, resulting in an average extinction of $A{\rm_V}$ = 7.6 mag."241 Fig.55 shows the UKIDSS GPS K/H—K CM diagram for the cluster and the control region., 5 shows the UKIDSS GPS $K/H-K$ CM diagram for the cluster and the control region.242" From the control region plot panel) it is possible to clearly identify the dwarf and giant branches of the stellar population, i.e. sources with an H—K colour of less than 1.0."," From the control region plot ) it is possible to clearly identify the dwarf and giant branches of the stellar population, i.e. sources with an $H-K$ colour of less than 1.0."243" In contrast, the cluster region panel) displays the dwarf branch (the group of stars"," In contrast, the cluster region ) displays the dwarf branch (the group of stars"244isotropic or anisotropic). it is vital that full. multiple-deflection Monte Carlo simulations be used.,"isotropic or anisotropic), it is vital that full, multiple-deflection Monte Carlo simulations be used."245 Especially important is accounting for the fact that the images of the bright. foreground. centres are likely to have been weakly Iensed.," Especially important is accounting for the fact that the images of the bright, foreground centres are likely to have been weakly lensed."246 LE the effects of multiple dellections are not. taken into account when interpreting an observed galaxy-ealaxy lensing signal. there is a high. probability. that incorrect conclusions will be crawn about the nature of the haloes surrounding the lens galaxies.," If the effects of multiple deflections are not taken into account when interpreting an observed galaxy-galaxy lensing signal, there is a high probability that incorrect conclusions will be drawn about the nature of the haloes surrounding the lens galaxies."247 lt is a pleasure. to thank the BPC40 survey team. particularly Emilio Falco. Chris IxXochanek. Malcolm Smith and Richard Green. for allowing us to use their data.," It is a pleasure to thank the BTC40 survey team, particularly Emilio Falco, Chris Kochanek, Malcolm Smith and Richard Green, for allowing us to use their data."248 Support from the National Science Foundation under NSE contracts AST-O0406844 and AST-0T08468 is) gratefully acknowledged., Support from the National Science Foundation under NSF contracts AST-0406844 and AST-0708468 is gratefully acknowledged.249"specifically in the case of CC clusters when Naay and/or lensing formation is σσπιο,",specifically in the case of CC clusters when X-ray and/or lensing information is missing.250 Tt is well known that. rather than the central Comptonization paraiueter yy. affected by the choice of cluster profile modeling. au iutegrated quantity. like the parameter Y. appears to be a amore robust mass proxy.," It is well known that, rather than the central Comptonization parameter $y_0$, affected by the choice of cluster profile modeling, an integrated quantity, like the parameter $Y$, appears to be a more robust mass proxy."251" Nevertheless. we have shown that CC clusters can generate observedVania0(0 g μιαςnη in1 whichduc theH ICAL1 morphology.ντ couldB stillbe sub«tantiall hidden, even for the current most sensitive experiments operating from the largest available imuu/subnmuu telescopes."," Nevertheless, we have shown that CC clusters can generate observed $y$ maps in which the ICM morphology could still be substantially hidden, even for the current most sensitive experiments operating from the largest available mm/submm telescopes."252" WhileTOi a general asstuuption: ofJ cluster morphology is. efficient""M at detecting. them iu. blind. SZ. maps. the possible- mismatchDl withP the actual clusterass profilesusp. resultssous in. a nass bias."," While a general assumption of cluster morphology is efficient at detecting them in blind SZ maps, the possible mismatch with the actual cluster profile results in a mass bias."253". Iu fact. simple. ICAL, models. like. the isothermal. befa-1inodel. applied to SZ observations ca wrougly estiuate cluster total ass in the presence of peculiar. TOAD dynamics as in CC clusters. which are studied in the current analysis. aud mergers."," In fact simple ICM models, like the isothermal -model, applied to SZ observations can wrongly estimate cluster total mass in the presence of peculiar ICM dynamics as in CC clusters, which are studied in the current analysis, and mergers."254 We analyzed the mass bias as derived iu a limited MM of cight CC clusters observed by Chandra. both . Underthe ∐↸∡∐⋖∩↓∶∣∙⋅↱⊐⋟⋜⊔≼↧↖↖⇁↕↑∐↕∏∶↴∙⊾∐⋯⋜↧↴," We analyzed the mass bias as derived in a limited sample of eight CC clusters observed by Chandra, both nearby $0.1<z<0.5$ ) and with high mass $M>10^{14}$ $M_{\odot}$ )."255∖∷∖↴∐∫ at AL. asstuuption of an isothermal bete-—amodel. the cluster total mass was derived applying three citteren ⋜∪↻↥⋅∪⋜↧↸⊳↕∐∖↴∖↴∶↑↕∐∖∐⋅↖↽≼⊔⋅∪↴∖↴↑⋜↧⊓↸⊳↸∖≺∏∐∐↴⋝↥⋅⋯⋯↸∖≺∣∏⋜↧⊓∪∐∙⋜↧∏⊼↸∖≼ (tap ⋅ ⋅ eas fraction. aud a sel£siuibw Mj;Y relation.," Under the assumption of an isothermal -model, the cluster total mass was derived applying three different approaches: the hydrostatic equilibrium equation, a fixed gas fraction, and a self-similar $M_{tot}-Y$ relation."256" Asstuning we had no information from N-rav observations. we reported the bias on the derived total lass as dependent ou electron eas temperature,"," Assuming we had no information from X-ray observations, we reported the bias on the derived total mass as dependent on electron gas temperature."257 Ouly in the case of hydrostatic equilibrimm does this bias appear almost constant for the considered clusters in the rauge ∪⋡⋅↱≻∩≓≺∖, Only in the case of hydrostatic equilibrium does this bias appear almost constant for the considered clusters in the range of 50-80.258∖∩↸⊲↕∐↸⊳↕≼∐∖∐↑⋜↧∐↖↽⋅∖↖↽↸∖∐∪↑↕↸⊳↸∖↑∐⋜↧↑⋜⋯↸∖↕↸∖↸⊳⊓⋅∪∐↼∖ vaIne exists. for; which. the ' aud SL. ss biases femperatiurevanish.," Incidentally, we notice that an electron temperature value exists for which the FGF and SL mass biases vanish."259 This could be the ouly case in POEwhich a simple isothermal beta--model accurately reproduces the mass of CC clusters., This could be the only case in which a simple isothermal -model accurately reproduces the mass of CC clusters.260 The large biases on total cluster mass recovery in CC clusters represcut another reason to definitely discux the isothermal bete-model for this purpose aud to fimlyv support more sophisticated models. with universa |oxessure profiles (0.5. iclArnaud|etal. 20103).," The large biases on total cluster mass recovery in CC clusters represent another reason to definitely discard the isothermal -model for this purpose and to firmly support more sophisticated models, with universal pressure profiles (e.g. \cite{Arnaud10}) )."261 This is already| enmrplovedpes1 ffor modeling° clusterlust ‘atmospherest]1 in ‘aliuos14 all the present blud-survey data reduction (SPT aac Plauck). aud it is planned in the next future for ACT observations.," This is already employed for modeling cluster atmospheres in almost all the present blind-survey data reduction (SPT and Planck), and it is planned in the next future for ACT observations."262fim=A|Dexp(C.(m18)). while the RMS magnitude deviation of variable sources is expected to be noticeably larger.,"$f(m)~=~A~+~B~\,~\exp~(C~\,~(m~-~18))$, while the RMS magnitude deviation of variable sources is expected to be noticeably larger."263 We consider two lightcurve samples. that of PSF-like objects (MEANOBJECT.TYPE= 6) and non-PSF-like objects (MEANOBJECTTYPE= 3).," We consider two lightcurve samples, that of PSF-like objects ${\tt MEAN\_OBJECT\_TYPE} = 6$ ) and non-PSF-like objects ${\tt MEAN\_OBJECT\_TYPE} = 3$ )."264 For each lighteurve sample and wave band. we iteratively fitted f(r) to the corresponding RMS diagrams using a 3c-elip algorithm. employing PSF magnitudes for the star lighteurve sample and exponential magnitudes for the galaxy lightcurve sample.," For each lightcurve sample and wave band, we iteratively fitted $f(m)$ to the corresponding RMS diagrams using a $\sigma$ -clip algorithm, employing PSF magnitudes for the star lightcurve sample and exponential magnitudes for the galaxy lightcurve sample."265 In each case we also constructed a function g(1) describing the standard deviation of the scatter around f(5) via a four-degree polynomial fit to the standard deviation of the RMS magnitude deviations measured in 0.25 magnitude bins., In each case we also constructed a function $g(m)$ describing the standard deviation of the scatter around $f(m)$ via a four-degree polynomial fit to the standard deviation of the RMS magnitude deviations measured in 0.25 magnitude bins.266 Then. for any light curve. the Vidrih index V. was calculated as its RMS magnitude deviation minus (11). normalized by g(nmi). with negative values set to zero. and it is stored in the quantities with tag names starting (Table 43).," Then, for any light curve, the Vidrih index $V$ was calculated as its RMS magnitude deviation minus $f(m)$, normalized by $g(m)$, with negative values set to zero, and it is stored in the quantities with tag names starting (Table \ref{tab:hlc1}) )."267 Note that due to the way the Vidrih indices are, Note that due to the way the Vidrih indices are268ACD and must have exceeded their πιααπ radius on he FOB. which iniplies a larger imitial orbital separation.,"AGB and must have exceeded their maximum radius on the FGB, which implies a larger initial orbital separation."269 Secoud. the binding euergv paramcter A is ercater for stars on the ACD (atleastforlow-arcintermeciate-Massprimaries.see ?).. which aplies less binding euergv of the envelope.," Second, the binding energy parameter $\lambda$ is greater for stars on the AGB \citep[at least for low- and intermediate-mass primaries, see][]{dewi+tauris00-1}, which implies less binding energy of the envelope."270 This effect would be even stronger if a raction of the internal energy. like recombination. helps o expel the euvelope.," This effect would be even stronger if a fraction of the internal energy, like recombination, helps to expel the envelope."271 This energy becomes comparable to he lower gravitational enerey in more extended envelopes. and therefore its relative contribution iu reducing the iudiug enerev of the cuvelope (increasing A) is greater.," This energy becomes comparable to the lower gravitational energy in more extended envelopes, and therefore its relative contribution in reducing the binding energy of the envelope (increasing $\lambda$ ) is greater."272 Recently. 7? have reconstructed the CE evolution of a xuuple of PCEDs aud predicted a dependency of the CE efficiency age on the mass ratio. leading to a larger final separation for those PCEBs coutaining lower mass secondary stars.," Recently, \citet{demarcoetal11-1} have reconstructed the CE evolution of a sample of PCEBs and predicted a dependency of the CE efficiency $\alpha_\mathrm{CE}$ on the mass ratio, leading to a larger final separation for those PCEBs containing lower mass secondary stars."273 The PCEBs in our sample show exactly the opposite., The PCEBs in our sample show exactly the opposite.274 As our sample is not significantly biased. neither against low-inass secondaries nor long orbital periods. we can exclude the existence of a large currently unidentified population of PCEBs with low-mass (M6-AI9) secondaries and long orbital periods (large binary separatious. sec? for details on the orbital period distribution of SDSS PCEBs).," As our sample is not significantly biased, neither against low-mass secondaries nor long orbital periods, we can exclude the existence of a large currently unidentified population of PCEBs with low-mass (M6-M9) secondaries and long orbital periods (large binary separations, see \citealt{nebot-gomez-moranetal11-1} for details on the orbital period distribution of SDSS PCEBs)."275 This is in clear contrast to the relation proposed by ?.., This is in clear contrast to the relation proposed by \citet{demarcoetal11-1}.276 A possible explanation for the observed relation between the final orbital period (binary separation) aud the companion lass rofüe:M2)) ds that systems with massive secondaries have iore initial orbital euergv available. aud therefore a smaller fraction of this euerev is enough to uubind the envelope.," A possible explanation for the observed relation between the final orbital period (binary separation) and the companion mass \\ref{fig:M2}) ) is that systems with massive secondaries have more initial orbital energy available, and therefore a smaller fraction of this energy is enough to unbind the envelope."277 However. this interpretation is far too «Πίο because the average initial conditious may also depeud on the secondary mass.," However, this interpretation is far too simple because the average initial conditions may also depend on the secondary mass."278" In addition. the relation itself. certainly present in the available data. should be regarded with some suspicion because the currently available sample of PCEDs onlv covers a relatively narrow range of secondary star masses,"," In addition, the relation itself, certainly present in the available data, should be regarded with some suspicion because the currently available sample of PCEBs only covers a relatively narrow range of secondary star masses."279 More PCEBs with hieh-niass secondaries are needed to conf the trend., More PCEBs with high-mass secondaries are needed to confirm the trend.280 The PCEBs in our sample are consistent with a coustaut value of the CT cfiiciency. but each system cau be reconstructed using a relatively broad rauge of values for acq (8). which miplies a wide range of possible initial confieuratious for cach system.," The PCEBs in our sample are consistent with a constant value of the CE efficiency, but each system can be reconstructed using a relatively broad range of values for $\alpha_\mathrm{CE}$ \citep{zorotovicetal10-1}, which implies a wide range of possible initial configurations for each system."281 We therefore sugecst that an even larger and more homogeucous sample is required to evaluate possible depeucencies of agg ou the binary piriuneters using reconstruction aleoritlinus., We therefore suggest that an even larger and more homogeneous sample is required to evaluate possible dependencies of $\alpha_\mathrm{CE}$ on the binary parameters using reconstruction algorithms.282" The orbital period distribution of PCEBs containing ITc-core primaries peaks at a significautlv shorter orbital period (4,~ 0.28dd) than the oue for svstenis containing C/O-core WDs (Poi~0.57 dd). which is not the result of a continuous increase in orbital period with WD amass."," The orbital period distribution of PCEBs containing He-core primaries peaks at a significantly shorter orbital period $\Porb \sim 0.28$ d) than the one for systems containing C/O-core WDs $\Porb \sim 0.57$ d), which is not the result of a continuous increase in orbital period with WD mass."283 Iu coutrast o recent predictions. we find that the post-CE binary separation increases with the mass of the secondary. star.," In contrast to recent predictions, we find that the post-CE binary separation increases with the mass of the secondary star."284 Even though the PCEB sample is still heavily affected by selection effects against detecting PCEBs coutaimiug ligh-ass secondaries. the relations ideutified here may able to coustrain the energy budect of CE evolution if combined with biuarv-population-svuthesis models that corporate observational selection effects that are as detailed as possible aud that ake the different possible combinations of mütial conditions and CE efficiencies mto account.," Even though the PCEB sample is still heavily affected by selection effects against detecting PCEBs containing high-mass secondaries, the relations identified here may be able to constrain the energy budget of CE evolution if combined with binary-population-synthesis models that incorporate observational selection effects that are as detailed as possible and that take the different possible combinations of initial conditions and CE efficiencies into account."285 On the observational side. we highly eucourage to search for PCEBs coutaimiug high-mass secondaries. which is needed to evaluate possible dependencies of veg ou the binary parameters based ou reconstruction algorithius.," On the observational side, we highly encourage to search for PCEBs containing high-mass secondaries, which is needed to evaluate possible dependencies of $\alpha_\mathrm{CE}$ on the binary parameters based on reconstruction algorithms."286Provicing feedback to the Galaxy Zoo Supernovac community is a vital part of the overall website experience to encourage volunteers to return. to the website.,Providing feedback to the Galaxy Zoo Supernovae community is a vital part of the overall website experience to encourage volunteers to return to the website.287 This is partly clone using forums and blogs where scientists can comment on individual events classified by the zoo., This is partly done using forums and blogs where scientists can comment on individual events classified by the zoo.288" In addition. cach volunteer can view a history of the candidates that they have classified on their ""My Supernovae! page."," In addition, each volunteer can view a history of the candidates that they have classified on their `My Supernovae' page."289 The My Supernovae’ (AINSN) page displavs the candidate triplets., The `My Supernovae' (MySN) page displays the candidate triplets.290 Those which have been observed are overlaid. with a small svmbol identifving the candidate as à SN. variable star. or asteroid.," Those which have been observed are overlaid with a small symbol identifying the candidate as a SN, variable star, or asteroid."291 Clicking on one of the candidates. also allows the volunteer to see the average rating across all classifications. the number of classifiers and whether the candidate was selected for followup by the PLE team.," Clicking on one of the candidates also allows the volunteer to see the average rating across all classifications, the number of classifiers and whether the candidate was selected for followup by the PTF team."292 PTL observers are encouraged to leave comments on the science dashboard that the classificrs can also see on their MySN page., PTF observers are encouraged to leave comments on the science dashboard that the classifiers can also see on their MySN page.293 Galaxy Zoo Supernovac was first. triallecl on two specific occasions supporting PPE spectroscopic follow-up observations— at the 4.2m William Herschel Telescope (WITT). in August 2009 and October 2009.," Galaxy Zoo Supernovae was first trialled on two specific occasions supporting PTF spectroscopic follow-up observations at the 4.2m William Herschel Telescope (WHT), in August 2009 and October 2009."294 Phe selection of the candidates observed by WHIP was guided. by. the Zoo results. with a particular emphasis on comparing the classifications produced. by Galaxy Zoo Supernova with those produced. by PPE human scanners working on the same data.," The selection of the candidates observed by WHT was guided by the Zoo results, with a particular emphasis on comparing the classifications produced by Galaxy Zoo Supernova with those produced by PTF human scanners working on the same data."295 Lhe top 20 scored. candidates from this initial trial run of Galaxy Zoo Supernovae are shown in Lig. 4., The top 20 scored candidates from this initial trial run of Galaxy Zoo Supernovae are shown in Fig. \ref{fig:montage}.296 Sixteen of these candidates: were observed by WIIT: 15 were confirmed as SNe. with 1 cataclysmic variable.," Sixteen of these candidates were observed by WHT; 15 were confirmed as SNe, with 1 cataclysmic variable."297 Since April 2010. Galaxy Zoo Supernovae has been running Full-time on PPE candidates. ancl by July. 15th. 2010 had classified. =18.900 SN. candidates at the rate of several hundred: candidates per observing night.," Since April 2010, Galaxy Zoo Supernovae has been running full-time on PTF candidates, and by July 15th 2010 had classified $\simeq13,900$ SN candidates at the rate of several hundred candidates per observing night."298 In. all but. the earliest weeks of the project. all submitted. candidates were classified by the zoo.," In all but the earliest weeks of the project, all submitted candidates were classified by the zoo."299 This classified sample forms the basis of our analysis in this section., This classified sample forms the basis of our analysis in this section.300 A distribution of the scores (54) For all of these candidates can be found in Fig. 5.., A distribution of the scores $S_{\mathrm{ave}}$ ) for all of these candidates can be found in Fig. \ref{fig:scoredist}.301 Phe σης of the candidates uploaded are classified as likely not astrophysically real events. ancl correspond. to subtraction artefacts or other reduction problems.," The bulk of the candidates uploaded are classified as likely not astrophysically real events, and correspond to subtraction artefacts or other reduction problems."302 This is indicative of he conservative cuts that are made in the PLE pipeline to avoid losing real SN events for follow-up. and highlights the currently. essential requirement for visual inspection of the Pipeline candidates.," This is indicative of the conservative cuts that are made in the PTF pipeline to avoid losing real SN events for follow-up, and highlights the currently essential requirement for visual inspection of the pipeline candidates."303 The performance of the public at classifving candidates can be gauged by comparing with the classifications the PTE team assigned to the same objects., The performance of the public at classifying candidates can be gauged by comparing with the classifications the PTF team assigned to the same objects.304 The PPE team broadly Classify objects into 4 visual categories: not interesting (not assigned a tvpe). asteroids. variable stars. ancl transients (such as SNe).," The PTF team broadly classify objects into 4 visual categories: not interesting (not assigned a type), asteroids, variable stars, and transients (such as SNe)."305 Asteroids are not screened. for by Galaxy Zoo BSupernovae — onlv one image is uploaded. for each PTE candidate. which clearly cannot be used to distinguish moving objects.," Asteroids are not screened for by Galaxy Zoo Supernovae – only one image is uploaded for each PTF candidate, which clearly cannot be used to distinguish moving objects."306 Asteroids are typically removed from the candidate list prior to upload by insisting on two separate detections of a candidate within oof each other. though this process is not perfect. particularly with slow moving asteroids where the apparent motion can be only a [ew areseconcls a clay.," Asteroids are typically removed from the candidate list prior to upload by insisting on two separate detections of a candidate within of each other, though this process is not perfect, particularly with slow moving asteroids where the apparent motion can be only a few arcseconds a day."307 ‘To illustrate the performance of Galaxy Zoo Supernovac. we split the candidates by their PTE assigned categories ancl calculate the fraction in each category as a function Of Save.," To illustrate the performance of Galaxy Zoo Supernovae, we split the candidates by their PTF assigned categories and calculate the fraction in each category as a function of $S_{\mathrm{ave}}$."308 Fig., Fig.309 G6 is a stacked box plot of the results., \ref{fig:breakdown} is a stacked box plot of the results.310 At low scores practically all candidates are those which the PTE team decide ave not interesting: these will include poor subtractions. artefacts/cosmic ravs. ete; As Sq increases we see a steady rise in the number of both variable star candidates and transients.," At low scores practically all candidates are those which the PTF team decide are not interesting: these will include poor subtractions, artefacts/cosmic rays, etc.. As $S_{\mathrm{ave}}$ increases we see a steady rise in the number of both variable star candidates and transients."311 By a score of around 1.4. variable stars are no longer selected. and instead the majority of the candidates are SN-like transients.," By a score of around $1.4$, variable stars are no longer selected, and instead the majority of the candidates are SN-like transients."312 A number of caveats should. be borne in mind when examining this plot., A number of caveats should be borne in mind when examining this plot.313 “Phe first is that not all variable stars identified by Galaxy. Zoo Supernovae will be assigned. that tvpe by the PEE. scanners., The first is that not all variable stars identified by Galaxy Zoo Supernovae will be assigned that type by the PTF scanners.314 As the primary goal of PTE is the study of explosive transients. variable stars are frequently not. recorded. in the P'TE catalogue (i.e... they will be assigned. “No type” in Fig. 6)).," As the primary goal of PTF is the study of explosive transients, variable stars are frequently not recorded in the PTF catalogue (i.e., they will be assigned “No type” in Fig. \ref{fig:breakdown}) )."315 The second caveat is that each PEE. candidate is potentially observed: many times over a period of several weeks over many epochs. vet should only be uploaded to Galaxy Zoo Supernovac once.," The second caveat is that each PTF candidate is potentially observed many times over a period of several weeks over many epochs, yet should only be uploaded to Galaxy Zoo Supernovae once."316 If there is some problem with the particular epoch that is uploaded to the zoo (a poor image subtraction. or poor seeing conditions). then a real astrophysical event may be x»orlw scored by the zoo on that epoch.," If there is some problem with the particular epoch that is uploaded to the zoo (a poor image subtraction, or poor seeing conditions), then a real astrophysical event may be poorly scored by the zoo on that epoch."317 However. that candidate may potentially be saved. by a human scanner owed. On an image from a different epoch.," However, that candidate may potentially be saved by a human scanner based on an image from a different epoch."318 Thus. real ransient events can occasionally be poorly scored. hy the zoo if the uploaded image is of poor quality: this is the case or some of the real transients that scored Sige«0., Thus real transient events can occasionally be poorly scored by the zoo if the uploaded image is of poor quality; this is the case for some of the real transients that scored $S_{\mathrm{ave}}<0$.319 Finally. it is important to note that the true nature of many of the candidates remains unknown. and the comparison clrawn rere is between the zoo selection and that of a subjective (though experienced) expert opinion.," Finally, it is important to note that the true nature of many of the candidates remains unknown, and the comparison drawn here is between the zoo selection and that of a subjective (though experienced) expert opinion."320 Figure 6 demonstrates that Galaxy Zoo Supernovac is capable of prioritising good candidates. and that the highest ranked candidates are likely to be SNe rather than variable stars.," Figure \ref{fig:breakdown} demonstrates that Galaxy Zoo Supernovae is capable of prioritising good candidates, and that the highest ranked candidates are likely to be SNe rather than variable stars."321 The candidates which were classified: as asteroids in the Galaxy Zoo Supernovae sample are given a relatively high score bv the zoo volunteers they typically mimic high-quality “hostless” transient events., The candidates which were classified as asteroids in the Galaxy Zoo Supernovae sample are given a relatively high score by the zoo volunteers – they typically mimic high-quality `hostless' transient events.322 Some of the Galaxy. Zoo Supernovae classified: candidates were observed. spectroscopically by the PPE collaboration. as well as candidates. identified by other techniques.," Some of the Galaxy Zoo Supernovae classified candidates were observed spectroscopically by the PTF collaboration, as well as candidates identified by other techniques."323 We examine the Si... distribution for these ~—140 spectroscopically confirmed. SNe (Fig. 7)).," We examine the $S_{\mathrm{ave}}$ distribution for these $\sim140$ spectroscopically confirmed SNe (Fig. \ref{fig:snscores}) ),"324 equivalent to, equivalent to325problem.,problem.326 Nevertheless in (his work we do not pursue on quantization., Nevertheless in this work we do not pursue on quantization.327 Below we show these fluctuations are described by a non-linear equation., Below we show these fluctuations are described by a non-linear equation.328 Ii section 2 we present (he linear case and in section 3 (he non-linear case which is solved by IHirota's method S].., In section 2 we present the linear case and in section 3 the non-linear case which is solved by Hirota's method \cite{fl:a2}.329 In section 4 we present some conclusions and perspectives for future work., In section 4 we present some conclusions and perspectives for future work.330 We consider the Lagrangian density £ of a scalar field o :ox. where A is a coupling constant and qi—c./.," We consider the Lagrangian density ${\cal L}$ of a scalar field $\phi$ :, where $\lambda$ is a coupling constant and $\mu=x,t$."331 From (1)) we derive the following equation of motion. —Q.," From \ref{ft1}) ) we derive the following equation of motion, =0."332 With the signature (+———). we can write the equation (2) in dimension (1+1) as: The problem now is to solve (he equation (3) for ó decomposed in a sum of a static solution ΠΕ and a small fInetuation Cre./).," With the signature $(+---)$, we can write the equation $\ref{ft2}$ ) in dimension $(1+1)$ as: The problem now is to solve the equation $(\ref{ft2.1})$ for $\phi$ decomposed in a sum of a static solution $\phi_{0}(x)$ and a small fluctuation $\eta(x,t)$."333 In fact. in order to compare our results in linear case wilh the non-linear one. which will be presented in section 3 we can. without loss of generality. write Using (4) in (3) and taking the equations for @y and + we find: and Solutions for the equation (5) are. in general. given by Abelian Theta Functions using the First Integral formalism [9].," In fact, in order to compare our results in linear case with the non-linear one, which will be presented in section $3$ we can, without loss of generality, write Using $(\ref{ft2.3})$ in $(\ref{ft2.1})$ and taking the equations for $\phi_{0}$ and $\eta$ we find: and Solutions for the equation $(\ref{ft2.4})$ are, in general, given by Abelian Theta Functions using the First Integral formalism ${\cite{baker}}$ ."334 Now we want to solve the equation (6). and. for this we divide the analvsis in two cases: ssince 7 is a perturbation in the equation (6). we assume that (ον)=e£(v.f) wheree is a small constant and then. the last term. which is of order ©(j£) can beneglected.," Now we want to solve the equation $(\ref{ft2.5})$, and, for this we divide the analysis in two cases: Since $\eta$ is a perturbation in the equation $(\ref{ft2.5})$, we assume that $\eta(x,t)=\epsilon \xi(x,t)$ where$\epsilon$ is a small constant and then, the last term, which is of order $\left.\cal{O}\right.\left(\eta^{2}\right)$ can beneglected."335 So the equation reduces to:, So the equation reduces to:336COSMOS names. coordinates. redshifts and tvpe (πας for tvpe 2 AGN. 7q2e7 for hybrid and a question mark next to the type denotes a questionable classification) taken from ‘Trumpetal.(2007)... Table 2. and the Spitzer Ηχος (from Sandersctal. 2007). respectively. for the first 20 objects of the sample.,"COSMOS names, coordinates, redshifts and type (“q2” for type 2 AGN, “q2e” for hybrid and a question mark next to the type denotes a questionable classification) taken from \cite{trump07}, Table 2, and the Spitzer fluxes (from \citealt{sanders07}) ), respectively, for the first 20 objects of the sample."337 The full tables are available online., The full tables are available online.338 We also use a list of type 2 AGN taken from the mid-LH1 selected spectroscopic sample of galaxies and GN from the ELALS-SWILRIE survey. presented in Ciruppionictal. (2008).," We also use a list of type 2 AGN taken from the mid-IR selected spectroscopic sample of galaxies and AGN from the ELAIS-SWIRE survey, presented in \cite{gruppioni08}."339. From the 203 spectroscopically identified objects in the sample (hereafter. ELALS sample). we selected a total of 23 tvpe 2 AGN that had sullicient. photometric coverage.," From the 203 spectroscopically identified objects in the sample (hereafter ELAIS sample), we selected a total of 23 type 2 AGN that had sufficient photometric coverage."340 The ELALS names and Spitzer (SWIIIZ) κος for these objects can be found in Gruppionietal.(2008)... Table 1.," The ELAIS names and Spitzer (SWIRE) fluxes for these objects can be found in \cite{gruppioni08}, Table 1."341 Fie., Fig.342 2 shows the position of the galaxies on the LRAC colour diagram Saof/Ss versus S5s/555., \ref{fig:colours} shows the position of the galaxies on the IRAC colour-colour diagram $_{8.0}$ $_{4.5}$ versus $_{5.8}$ $_{3.6}$.343 In the left panel. he samples in black. red. blue. ancl green. are the [ow-z. COSMOS. ELALS and the quasar samples. respectively.," In the left panel, the samples in black, red, blue, and green are the $z$, COSMOS, ELAIS and the quasar samples, respectively."344 The ?oints inside open circles denote detections at., The points inside open circles denote detections at.345μα... The different: loci formed. by the four different samples rellect he distinct selection techniques ancl hence. properties. of he objects., The different loci formed by the four different samples reflect the distinct selection techniques and hence properties of the objects.346 As suggested. by Sajinaetal.(2005). from a study based. on empirical templates. and as will be demonstrated. shortly. the objects at the lower left of the xot are dominated by stellar emission: the objects rising in Sso/5S45 while maintaining à low κο (Le. the bulk of the low-z sample with about a third. of the COSMOS sample bving in the same region) are those dominated. by PALL emission. while the objects with both colours rising. towards the upper right corner of the plot. are continuum dominated objects.," As suggested by \cite{sajina05} from a study based on empirical templates, and as will be demonstrated shortly, the objects at the lower left of the plot are dominated by stellar emission; the objects rising in $_{8.0}$ $_{4.5}$ while maintaining a low $_{5.8}$ $_{3.6}$ (i.e., the bulk of the $z$ sample with about a third of the COSMOS sample lying in the same region) are those dominated by PAH emission while the objects with both colours rising, towards the upper right corner of the plot, are continuum dominated objects."347 The quasar locus occupies a very well confined. region of the colour space. as shown already. (c.g. Lacyetal.20042): in their majority and up to a redshift of —2. they lie on a straight line of slope of one. simply indicating the rise of the torus emission as a power law.," The quasar locus occupies a very well confined region of the colour space, as shown already (e.g. \citealt{lacy04}) ); in their majority and up to a redshift of $\sim$ 2, they lie on a straight line of slope of one, simply indicating the rise of the torus emission as a power law."348 We should note that the position of X-ray selected ACN has already been shown by Cardamonectal.(2008).. that sample however contained a much smaller fraction of objects with star formation. and was plagued by a large fraction of objects with unknown redshifts.," We should note that the position of X-ray selected AGN has already been shown by \cite{cardamone08}, that sample however contained a much smaller fraction of objects with star formation, and was plagued by a large fraction of objects with unknown redshifts."349 Interestingly. their colors tend to populate the lower right part of the colour space. which is strikinely empty in our larger sample.," Interestingly, their colors tend to populate the lower right part of the colour space, which is strikingly empty in our larger sample."350 One should keep in mind that the various samples have not only different observed properties but also very. clillerent average redshifts. asseen in the right. panel of Fig. 2..," One should keep in mind that the various samples have not only different observed properties but also very different average redshifts, asseen in the right panel of Fig. \ref{fig:colours}. ."351 A histogram of the redshift distributions is shown in the upper panel of Fig. 3.., A histogram of the redshift distributions is shown in the upper panel of Fig. \ref{fig:zhisto2}.352 Ehe middle and lower panels of Fi, The middle and lower panels of Fig.353s 3 show the distributions of the 3.6 and 24 luminosities of the various saniples.," \ref{fig:zhisto2}354 show the distributions of the 3.6 and 24 luminosities of the various samples."355 The observed UV. to FIR SED of à galaxy can. be decomposed in three distinct. components: stars with the bulk of their power emitted. in the optical ancl near-Lh. hot cust mainly heated by UVoptical emission from gas accreting onto the central supermassive black hole and whose cnussion peaks somewhere between a few and a few tens of microns. and. cold. dust. principally heated. by star formation.," The observed UV to FIR SED of a galaxy can be decomposed in three distinct components: stars with the bulk of their power emitted in the optical and near-IR, hot dust mainly heated by UV/optical emission from gas accreting onto the central supermassive black hole and whose emission peaks somewhere between a few and a few tens of microns, and cold dust principally heated by star formation."356 In the present work we consider all three components. which we model as follows.," In the present work we consider all three components, which we model as follows."357 The stellar component is the sum of Simple Stellar Population (SSP) models of dillerent age. all having a common (solar) metallicity.," The stellar component is the sum of Simple Stellar Population (SSP) models of different age, all having a common (solar) metallicity."358 Phe set of SSPs is built using the Padova evolutionary tracks (Bertellietal.L9904).. a Salpeter IME with masses in the range 0.15 120 M. and the Jacoby(1984). library of observed stellar spectra in the optical domain.," The set of SSPs is built using the Padova evolutionary tracks \citep{bertelli94}, a Salpeter IMF with masses in the range 0.15 – 120 $_\odot$ and the \cite{jacoby84} library of observed stellar spectra in the optical domain."359 Phe extension to the UV and Hi range is derived from the Ixurucz theoretical libraries., The extension to the UV and IR range is derived from the Kurucz theoretical libraries.360 Dust. emission [rom circumstellar. envelopes. of ACGD stars has been added: by Dressanetal.(1998)., Dust emission from circumstellar envelopes of AGB stars has been added by \cite{bressan98}.361". Ehe weight in the final spectrum of cach SSPs. as a function of age. is computed according to à Schmidt law for the star formation rate: where Je, is the age of the galaxy. (Le. of the oldest SSP). which is assumed to be as old as the age of the universe at the ealaxy’s redshift. and τος is the duration of the burst in units of 7c."," The weight in the final spectrum of each SSPs, as a function of age, is computed according to a Schmidt law for the star formation rate: where $T_G$ is the age of the galaxy (i.e. of the oldest SSP), which is assumed to be as old as the age of the universe at the galaxy's redshift, and $\tau_{sf}$ is the duration of the burst in units of $T_G$."362 Extinction is applied to the final SED bv assuming a uniform foreground dust screen with a standard Galactic extinction law (C'ardellietal. 1989)., Extinction is applied to the final SED by assuming a uniform foreground dust screen with a standard Galactic extinction law \citep{cardelli89}. .363. Thefree parameters are. therefore. the duration of the initial burst and the amount of extinction.," Thefree parameters are, therefore, the duration of the initial burst and the amount of extinction."364stars defined a new value for Vu. and the process was iterated until convergence.,"stars defined a new value for $V_{{\rm HB}}$, and the process was iterated until convergence."365 We estimated the (random) errors in these values again using the proscription of Sarajedini (1994)., We estimated the (random) errors in these values again using the proscription of Sarajedini \shortcite{s94}.366".. The accuracy with which we could measure Vui was generally 20.05. mag. while that for (V.—7), was greater — because of the narrowness of the RGB sequences and the stability of the quadratie fits — at +£0.01 mag."," The accuracy with which we could measure $V_{{\rm HB}}$ was generally $\pm 0.05$ mag, while that for $(V-I)_g$ was greater – because of the narrowness of the RGB sequences and the stability of the quadratic fits – at $\pm 0.01$ mag."367" Ten thousand new fits per cluster were calculated. each time using a value of Vu chosen randomly from a distribution with @=0.05 about the genuine measurement of μυ. and a new value of (V—7), selected randomly from a distribution with 0=0.01 about the genuine measurement of (1I1),."," Ten thousand new fits per cluster were calculated, each time using a value of $V_{{\rm HB}}$ chosen randomly from a distribution with $\sigma = 0.05$ about the genuine measurement of $V_{{\rm HB}}$, and a new value of $(V-I)_g$ selected randomly from a distribution with $\sigma = 0.01$ about the genuine measurement of $(V-I)_g$."368 The standard deviations in the new sets of (V—£) and Fe H] detined the random errors in these quantities., The standard deviations in the new sets of $E(V-I)$ and $[$ $/$ $]$ defined the random errors in these quantities.369 The final reddening and metallicity values are recorded in Table 2. along with the estimated errors., The final reddening and metallicity values are recorded in Table \ref{t:metred} along with the estimated errors.370 NGC 1939 is a metal- cluster € Fe/H]= 2.10). while Reticulum is somewhat more metal-rich (Fe/H]= 1.66).," NGC 1939 is a metal-poor cluster $[$ $/$ $] = -2.10$ ), while Reticulum is somewhat more metal-rich $[$ $/$ $] = -1.66$ )."371 In contrast. NGC 1928 is significantly more metal-rich again with Fe/H] =1.27 - rendering it the most metal-rich of the known old LMC bar clusters.," In contrast, NGC 1928 is significantly more metal-rich again with $[$ $/$ $] = -1.27$ – rendering it the most metal-rich of the known old LMC bar clusters."372 Examination of the clean CMD for NGC 1928 supports thisresult. as there is a clear RGB luminosity function bump at approximately Vu.," Examination of the clean CMD for NGC 1928 supports thisresult, as there is a clear RGB luminosity function bump at approximately $V_{{\rm HB}}$."373 Such a bump is characteristic of clusters with intermediate metal abundance (see e.g.. Sarajedini Forrester (1995))).," Such a bump is characteristic of clusters with intermediate metal abundance (see e.g., Sarajedini Forrester \shortcite{sarajedini:95}) )."374 Our new results are all consistent with previous measurements and estimates. where these are available.," Our new results are all consistent with previous measurements and estimates, where these are available."375 NGC 1928 and 1939 uve been poorly studied. with each possessing only one previous metallicity estimate.," NGC 1928 and 1939 have been poorly studied, with each possessing only one previous metallicity estimate."376 These are from Dutra et al., These are from Dutra et al.377 (1999). who compared their integrated spectra of NGC 1928 and 1939 to those ‘or three Galactic globular clusters toestimate that Fe/H]=—1.2 or NGC 1928. and Fe/H]=—2.0 for NGC 1939.," \shortcite{dutra} who compared their integrated spectra of NGC 1928 and 1939 to those for three Galactic globular clusters toestimate that $[$ $/$ $] \approx -1.2$ for NGC 1928, and $[$ $/$ $] \approx -2.0$ for NGC 1939."378 According o Burstein Heiles (1982). the foreground reddening in the direction of both is (D1)=0.09. which corresponds o E(V1)=0.12 (see e.g. Mackey Gilmore (2003¢))).," According to Burstein Heiles \shortcite{dust}, the foreground reddening in the direction of both is $E(B-V) = 0.09$, which corresponds to $E(V-I) \approx 0.12$ (see e.g., Mackey Gilmore \shortcite{fnx}) )."379 Reticulum has been more extensively. studied., Reticulum has been more extensively studied.380 Walker (1992) ‘ound that Fe/H]=—L7+0.1 by studying the RR. Lyrae stars in the cluster. while Suntzeff et al.," Walker \shortcite{walker:ret}381 found that $[$ $/$ $] = -1.7 \pm 0.1$ by studying the RR Lyrae stars in the cluster, while Suntzeff et al."382 (1992) obtained a Spectroscopic measurement of Fe/H]=—1.71+0.1., \shortcite{suntzeff} obtained a spectroscopic measurement of $[$ $/$ $] = -1.71 \pm 0.1$.383 Both of these measurements are in excellent agreement with our photometric determination that Fe/H]=—1.66+0.12., Both of these measurements are in excellent agreement with our photometric determination that $[$ $/$ $] = -1.66 \pm 0.12$.384 On the reddening front. we measured (V.I)=0.07+0.02.," On the reddening front, we measured $E(V-I) = 0.07 \pm 0.02$."385 Walker (1992). found that 01)=0.03+0.02 (he. LA[)= 0.040.083) but notes that the colours of his RR Lyrae sample at minimum light could imply a slightly higher reddening: οV)e0.05z0.2 (e. E(V£)=0.07 0.03).," Walker \shortcite{walker:ret} found that $E(B-V) = 0.03 \pm 0.02$ (i.e., $E(V-I) = 0.04 \pm 0.03$ ) but notes that the colours of his RR Lyrae sample at minimum light could imply a slightly higher reddening: $E(B-V) = 0.05 \pm 0.02$ (i.e., $E(V-I) = 0.07 \pm 0.03$ )."386 Marconi et al., Marconi et al.387 (2002) suggest that the reddening towards Reticulum could be twice as large as that suggested in the literature (le. 0.05).," \shortcite{marconi} suggest that the reddening towards Reticulum could be twice as large as that suggested in the literature (i.e., $E(V-I) \sim 0.08$ )."388 All of these estimates are in good agreement with our new measurement., All of these estimates are in good agreement with our new measurement.389 As a final consistency check. if we adopt the calibration between intrinsic RR Lyrae brightness and metallicity of Chaboyer (1999): we can calculate distance moduli 1) for the three clusters.," As a final consistency check, if we adopt the calibration between intrinsic RR Lyrae brightness and metallicity of Chaboyer \shortcite{chaboyer}: we can calculate distance moduli $\mu$ ) for the three clusters."390 We find that. with ely=2.37E(V—D) (e.g. Mackey Gilmore (2003c))). po=18.470.19 for NGC 1928 and j/=18.480.16 for NGC 1939. where the errors represent only the effect of random measurement errors from Vp. (1£) and Fe/H].," We find that, with $A_V = 2.37E(V-I)$ (e.g., Mackey Gilmore \shortcite{fnx}) ), $\mu = 18.47 \pm 0.12$ for NGC 1928 and $\mu = 18.48 \pm 0.16$ for NGC 1939, where the errors represent only the effect of random measurement errors from $V_{{\rm HB}}$, $E(V-I)$ and $[$ $/$ $]$."391 For Reticulum we tind j;=18.39+0.12., For Reticulum we find $\mu = 18.39 \pm 0.12$.392 All these estimates are in good agreement with the canonical distance to the LMC: parcom18.50., All these estimates are in good agreement with the canonical distance to the LMC: $\mu_{{\rm LMC}} \approx 18.50$ .393 Given the uncertainties in the (approximate) photometric transformations detailed in Section 3.2.. it is important to discuss briefly the potential effect of these on our metallicity and reddening measurements.," Given the uncertainties in the (approximate) photometric transformations detailed in Section \ref{ss:cmdgood}, it is important to discuss briefly the potential effect of these on our metallicity and reddening measurements."394 The metallicity determination is obtained from a purely differential process (Eq., The metallicity determination is obtained from a purely differential process (Eq.395" + in Sarajedini (1994) shows Fe/H] to be dependent only on AV) 2) and is thus affected only by anysecond or higher order distortion over the range V,» in V and 12(VLD,inV 1.", 4 in Sarajedini \shortcite{s94} shows $[$ $/$ $]$ to be dependent only on $\Delta V_{1.2}$ ) and is thus affected only by anysecond or higher order distortion over the range $\Delta V_{1.2}$ in $V$ and $1.2 - (V-I)_g$in $V-I$.396 Since bothof these. especially the latter. are relatively small values. these distortions are unlikely to be large. and we estimate the systematic error so introduced to be less than 0.05 dex.," Since bothof these, especially the latter, are relatively small values, these distortions are unlikely to be large, and we estimate the systematic error so introduced to be less than $0.05$ dex."397 Since the distortion apparently produces an RGB which is slightly redder than appropriate (see Fig. 59).," Since the distortion apparently produces an RGB which is slightly redder than appropriate (see Fig. \ref{f:retmatch}) ),"398 the bias is towards measurements which are too metal-rich., the bias is towards measurements which are too metal-rich.399" The reddening estimates are dependent on both (τὸ, and Fe/H] (Sarajedini Eq.", The reddening estimates are dependent on both $(V-I)_g$ and $[$ $/$ $]$ (Sarajedini Eq.400 3)., 3).401 The dependence on Fe/H] is weak. so the primary error is introduced through (Vo 2). which could be ~0.02 mag too red (see Section 3.23).," The dependence on $[$ $/$ $]$ is weak, so the primary error is introduced through $(V-I)_g$ , which could be $\sim 0.02$ mag too red (see Section \ref{ss:cmdgood}) )."4023 This would be transferred directly tothe (V £) estimate. so it is possible these are too high by ~0.02.," This would be transferred directly to the $E(V-I)$ estimate, so it is possible these are too high by $\sim 0.02$."403 Nonetheless. the consistency of our estimates with both literature measurements and the LMC distance scale lead us to have contidence in the accuracy and validity of our results.," Nonetheless, the consistency of our estimates with both literature measurements and the LMC distance scale lead us to have confidence in the accuracy and validity of our results."404 Although we have images at only one epoch. and therefore no stellar variability information. it is possible to calculate a quantitative measure of each clusters HB morphology now that accurate reddening values are known.," Although we have images at only one epoch, and therefore no stellar variability information, it is possible to calculate a quantitative measure of each cluster's HB morphology now that accurate reddening values are known."405 As part of their study of 197 RR Lyrae stars in four globular clusters belonging to the Fornax dwarf. galaxy. Mackey Gilmore (2003c) provided accurate measurements of the intrinsic V/ colours of the red and blue edges of the instability strip at the level of the horizontal branch.," As part of their study of $197$ RR Lyrae stars in four globular clusters belonging to the Fornax dwarf galaxy, Mackey Gilmore \shortcite{fnx}406 provided accurate measurements of the intrinsic $V-I$ colours of the red and blue edges of the instability strip at the level of the horizontal branch."407 They found (VlHep=0.28+0.02 and (V.Hee59+ 0.02., They found $(V-I)_{{\rm BE}} = 0.28 \pm 0.02$ and $(V-I)_{{\rm RE}} = 0.59 \pm 0.02$ .408 These values can be used to count the number of blue HB stars. red HB stars. and stars on the instability strip.," These values can be used to count the number of blue HB stars, red HB stars, and stars on the instability strip."409 The HB morphology is usually parametrized by the index (7RB|VB) of Lee. Demarque Zinn (1994)... where £5 is 1e number of BHB stars. V the number of variable HB stars. and I the number of RHB stars.," The HB morphology is usually parametrized by the index $(B-R)/(B+V+R)$ of Lee, Demarque Zinn \shortcite{ldz}, where $B$ is the number of BHB stars, $V$ the number of variable HB stars, and $R$ the number of RHB stars."410 Because we have only single epoch observations it is possible that some variables might lie outside ye adopted instability strip edges (although this will not affect 1e morphology indices significantly. especially for NGC 1928 and 1939).," Because we have only single epoch observations it is possible that some variables might lie outside the adopted instability strip edges (although this will not affect the morphology indices significantly, especially for NGC 1928 and 1939)."411 In addition. because of the difficult field star subtractions necessary for NGC 1928 and NGC 1939. our number counts are commensurately uncertain.," In addition, because of the difficult field star subtractions necessary for NGC 1928 and NGC 1939, our number counts are commensurately uncertain."412 It is nonetheless worthwhile to make an attempt to calculate the HB morphology for these clusters since no previous estimates exist., It is nonetheless worthwhile to make an attempt to calculate the HB morphology for these clusters since no previous estimates exist.413 For NGC 1928 we counted /?=2 1.1=3 te and b— ne including the putativeextended BHB (—11 stars).," For NGC 1928 we counted $R = 2^{+1}_{-2}$, $V = 3^{+1}_{-3}$ , and $B = 111^{+13}_{-11}$ , including the putativeextended BHB $\sim 11$ stars)."414 For the more heavily populated NGC 1939 HB we counted /?=3 T3. V5 Land B=173. 12.," For the more heavily populated NGC 1939 HB we counted $R = 3 \pm 3$ , $V = 5^{+1}_{-5}$ , and $B = 173^{+10}_{-12}$ ."415 These star counts result in a HB index οLV|R)90.94.(ru for both clusters. confirming their status as having almost exclusively blue HB. morphologies.," These star counts result in a HB index of $(B-R)/(B+V+R) = 0.94^{+0.06}_{-0.04}$ for both clusters, confirming their status as having almost exclusively blue HB morphologies."416This racliation is therefore unobservable in the case of the known ogalactic superluminals. which are both observed with large viewing angles. but may be very important for sources with oL1 (see also Sikora οἱ al..,"This radiation is therefore unobservable in the case of the known galactic superluminals, which are both observed with large viewing angles, but may be very important for sources with $\delta\sim \Gamma \gg 1$ (see also Sikora et al.,"417. 1997)., 1997).418 The value of the magnetic field needed to carry Ly in the vicinity of the black hole is equal to equation (11). if the bulk of the magnetic field is moving with E. while the 5 before acceleration is a factor E &reater. corresponding to B3s10 Gat R=10° cm.," The value of the magnetic field needed to carry $L_{k}$ in the vicinity of the black hole is equal to equation (11), if the bulk of the magnetic field is moving with $\G$ , while the $B$ --value before acceleration is a factor $\G$ greater, corresponding to $B\sim 3\times 10^8$ G at $R=10^7$ cm."419" It must be remarked that the standard theory of accretion disks (Shakura Sunvaey 1973) predicts that the masxiniun possible magnetic field at a given A/Rs (where Rs is the Sehwarzshild radius) in à radiation dominate disk is Box(AMÁM.)297, so that microquasars will have magnetic fields ~10 stronger than those in quasars."," It must be remarked that the standard theory of accretion disks (Shakura Sunyaev 1973) predicts that the maximum possible magnetic field at a given $R/R_S$ (where $R_S$ is the Schwarzshild radius) in a radiation dominated disk is $B\propto (M/M_{\odot})^{-1/2}$, so that microquasars will have magnetic fields $\sim 10^4$ stronger than those in quasars."420" ""Therefore. the theoreticalestimate B~105101 G obtaine with the Blanclford Payne model (Blancllord Payne 1982) near the massive black holes in active galactic nuclei. clearly show that in microquasars 2~107 € can casily be attained."," Therefore, the theoretical estimate $B\sim 10^2 - 10^4$ G obtained with the Blandford Payne model (Blandford Payne 1982) near the massive black holes in active galactic nuclei, clearly show that in microquasars $B\sim 10^8$ G can easily be attained."421" Note that this value of the magnetic. field. would be of the same magnitude of the magnetie field. required. by the Blandford.Znajek (1977) process to produce Li by extracting the rotational energv of a 10 solar mass Werr black hole: a=onthere B=10°Bs C and AJ=1034, solar masses.", Note that this value of the magnetic field would be of the same magnitude of the magnetic field required by the Blandford–Znajek (1977) process to produce $L_{k}$ by extracting the rotational energy of a 10 solar mass Kerr black hole: where $B=10^9 B_9$ G and $M=10 M_1$ solar masses.422" 5 true em From the above arguments we conclude that (C oor relativistic electrons with <+- greater than m/m, cannot carry Ly in the inner region of the jet. while protons and the Povnting vector can."," 0.5 true cm From the above arguments we conclude that $e^\pm$ or relativistic electrons with $<\g>$ greater than $m_p/m_e$ cannot carry $L_{k}$ in the inner region of the jet, while protons and the Poynting vector can."423 An alternative solution could be that the energy. carie in the inner region by “normal” cold. plasma or toroicla magnetic field. is converted in e pairs at. large distance [rom the black hole and accretion disk.," An alternative solution could be that the energy, carried in the inner region by “normal"" cold plasma or toroidal magnetic field, is converted in $e^\pm$ pairs at large distance from the black hole and accretion disk."424 Pairs are produce most efficiently through photon collisions. but this requires a powerful 7. rav continuum.," Pairs are produced most efficiently through photon–photon collisions, but this requires a powerful $\gamma$ –ray continuum."425" since the maximum ellicieney in converting pairs in this way is of the order of 10 per cent (Svensson LOST). the high energy. Iuminosity jas to exceed 107i ODE S to produce a kinetic power of Daun ""E ⇂↥∢⋅∪↓⋅∠⇂⋖⋅↓⋅∪⇂↓∪⋟∢⋅↓⋅⋏∙≟⊳∖↓"," Since the maximum efficiency in converting pairs in this way is of the order of 10 per cent (Svensson 1987), the high energy luminosity has to exceed $10^{40}$ erg $^{-1}$, to produce a kinetic power of the order of $10^{39}$ erg $^{-1}$."426⊳∐∐⊳∖↓⊔⊔∐⊔∪≱∖↓↿∙∖⇁↓≱∖⊔∪↥∪∣⋡≱∖∢⋅↓⋅, This luminosity is not observed.427∖⇁⋖⋅∠⇂⋡⋠⋠⋠ Therefore we conclude that e pairs do not play any role as energv carriers along the jet and the minimun kinetic uminosity involved in major ejection events is given by the value estimated forep plasma (73.107eres 1)., Therefore we conclude that $e^\pm$ pairs do not play any role as energy carriers along the jet and the minimun kinetic luminosity involved in major ejection events is given by the value estimated for $e-p$ plasma $\sim 3\times 10^{40}~{\rm erg~ s^{-1}}$ ).428 There are no strong observational arguments to decide »etween protons and the Povnting vector. unless we observe a new galactic superluminal at a small viewing angle.," There are no strong observational arguments to decide between protons and the Poynting vector, unless we observe a new galactic superluminal at a small viewing angle."429 Note rowever that if Li is initially carried. by a Large magnetic ield there is the possibility to tap a great reservoir of energy (the rotational energv. of the black hole) and to accelerate he plasma to relativistic speeds., Note however that if $L_{k}$ is initially carried by a large magnetic field there is the possibility to tap a great reservoir of energy (the rotational energy of the black hole) and to accelerate the plasma to relativistic speeds.430 We therefore conclude that the kinetic power carried initially by the magnetic field is the most economic way to explain the observed. energeties., We therefore conclude that the kinetic power carried initially by the magnetic field is the most economic way to explain the observed energetics.431 Dillerential accretion disk rotation or rotating black holes can amplify magnetic fields to the required. values. and. the magnetic field. will then accelerate particles to relativistic speeds.," Differential accretion disk rotation or rotating black holes can amplify magnetic fields to the required values, and the magnetic field will then accelerate particles to relativistic speeds."432 The amount of matter present at the base of the jet mav not be negligible. especially if magnetic field. lines help to channel particles from the disk to the jet.," The amount of matter present at the base of the jet may not be negligible, especially if magnetic field lines help to channel particles from the disk to the jet."433" We can compare the inflow rate Aj, of the accretion process with the outllow rate Miu; necessary to account for the kinetic power. in particles. of the radio blob."," We can compare the inflow rate $\dot M_{in}$ of the accretion process with the outflow rate $\dot M_{out}$ necessary to account for the kinetic power, in particles, of the radio blob."434" LE we write the accretion Luminosity. as usually. as Li...=Misc. and the kinetic power as L,=(EDALwe. we derive Since ypOL and Ly~LOL... we have that the the inflowing5 and the outllowing5 mass rates are comparable."," If we write the accretion luminosity, as usually, as $L_{acc}=\eta \dot M_{in} c^2$, and the kinetic power as $L_{k} = (\Gamma-1) \dot M_{out} c^2$, we derive Since $\eta\sim 0.1$ and $L_{k}\sim 10 L_{acc}$ we have that the the inflowing and the outflowing mass rates are comparable."435 This in turn suggests that most of the matter in the jet may come from the accretion disk., This in turn suggests that most of the matter in the jet may come from the accretion disk.436 Another important question concerns the duration of the ejection events., Another important question concerns the duration of the ejection events.437 When the blob becomes visible in. the radio. it has a size of a few light days.," When the blob becomes visible in the radio, it has a size of a few light days."438 Lt seems unlikely hat it corresponds to an ejection duration lasting more han that. while a shorter ejection time may. be possible.," It seems unlikely that it corresponds to an ejection duration lasting more than that, while a shorter ejection time may be possible."439 In the latter case the requirement on the initial kinetic power Correspondingly increases., In the latter case the requirement on the initial kinetic power correspondingly increases.440 Note that. direct. racio observations of [lare events do not clirectly constrain the ejection time. since the radio flux eventually produced. in he first. parts of the jet is heavily sel. absorbed.," Note that direct radio observations of flare events do not directly constrain the ejection time, since the radio flux eventually produced in the first parts of the jet is heavily self absorbed."441 Again. he minimum power requirements criterium favours ejection events which last for four few clavs.," Again, the minimum power requirements criterium favours ejection events which last for $t_{out}\sim$ few days."442" This corresponds to ~10""Rs where sao Is the Schwarzchild radius for a 10 solar mass black hole."," This corresponds to $\sim 10^9~R_{S,10}/c$, where $R_{S,10}$ is the Schwarzchild radius for a 10 solar mass black hole."443 Scaling for a superluminal active ealactic nucleus. we would have. for a 10 solar mass black hole. an ection phase lasting for 2«LO” vears.," Scaling for a superluminal active galactic nucleus, we would have, for a $10^9$ solar mass black hole, an ejection phase lasting for $2\times 10^5$ years."444 We have obtained a reliable lower limit to the kinetic power Corresponding to major ejection events in superluminal galactic sources. in particular for GIUS 1915|105.," We have obtained a reliable lower limit to the kinetic power corresponding to major ejection events in superluminal galactic sources, in particular for GRS 1915+105."445" This limit is of the order of 3107"" erg + much greater than the observed. radiative luminosity. which is probably. Eddington limitedMM to values of] the order of 10739 erg 1. corresponding. to à black hole of 10 solar masses."," This limit is of the order of $3\times 10^{40}$ erg $^{-1}$, much greater than the observed radiative luminosity, which is probably Eddington limited to values of the order of $^{39}$ erg $^{-1}$, corresponding to a black hole of 10 solar masses."446 This by itself suggests that the jet acceleration mechanism cannot be radiative., This by itself suggests that the jet acceleration mechanism cannot be radiative.447 We have investigated the role of ο pairs. of normal plasma and of the magnetic Ποια as οποιον carriers. of the kinetic power in the inner jet regions. excluding an important role for the e pairs. ancl favouring àscenario," We have investigated the role of $e^\pm$ pairs, of normal plasma and of the magnetic field as energy carriers of the kinetic power in the inner jet regions, excluding an important role for the $e^\pm$ pairs, and favouring ascenario"448Planetary epliemerides are used lor multipe purposes inclucing dynamical mass determination or solar system bodies. pulsar timine. high-preCision tests of geueral relativity. and inter-planetary spacecralt navigation.,"Planetary ephemerides are used for multiple purposes including dynamical mass determination for solar system bodies, pulsar timing, high-precision tests of general relativity, and inter-planetary spacecraft navigation."449 During the past several «ecacles a series of iucreasiugly accurate epliemerides iive been developed at the Jet Propulsion Laboratory (JPL) by adding new data types such as Very Large Array (VLA) astrometry (Muhlema1etal. (1985):: Mublemanetel. (LO8G))). spacecrali racking (Duxbury&Callahan1989).. and radar range meastwements (Campbeletal.LOTS) to ustorical aud modern optic‘al observations.," During the past several decades a series of increasingly accurate ephemerides have been developed at the Jet Propulsion Laboratory (JPL) by adding new data types such as Very Large Array (VLA) astrometry \citet{Muhleman85}; ; \citet{Muhleman86}) ), spacecraft tracking \citep{Duxbury89}, and radar range measurements \citep{Campbell78} to historical and modern optical observations."450 Accurate ephemericdes are one of the basic tools of observational astronomy. in he same sense as star catalogs and redshift surveys.," Accurate ephemerides are one of the basic tools of observational astronomy, in the same sense as star catalogs and redshift surveys."451 They represeut a comauimuity resource wliose valie is proportional to their accuracy. amd whose accuracy requires regular observational support O inalntain aud improve.," They represent a community resource whose value is proportional to their accuracy, and whose accuracy requires regular observational support to maintain and improve."452 A specilic exampe is the great. improvement between timine distauces and kinematic distauces for pulsars when wine the newer DE105 ephemeris (Standish2001) coupared with the older DE200 ephemerisεις. Verbiestetal. (2008))).," A specific example is the great improvement between timing distances and kinematic distances for pulsars when using the newer DE405 ephemeris \citep{Standish04} compared with the older DE200 ephemeris, \citet{Verbiest08}) )."453" The orbits of the inne ‘planets are very accurately tied together with the «""urrent data set.", The orbits of the inner planets are very accurately tied together with the current data set.454 For example. the angular edhemeris errors [or Mars with respect to Earth are typically 0.2 (mas) or 1 nrad (LAU2009).," For example, the angular ephemeris errors for Mars with respect to Earth are typically 0.2 milli-arcsecond (mas) or 1 nrad \citep{IAU09}."455. However. the outer planets are not as well tied to the inuer planets (or each other) because there Lave been fewer opportunities to supplement optical observations with high precision spacecraft radio tracking data.," However, the outer planets are not as well tied to the inner planets (or each other) because there have been fewer opportunities to supplement optical observations with high precision spacecraft radio tracking data."456 The Pioneer and Voyager missions provided essentially single data points during their flybys of the outer planets. aud the Calileo uission to Jupiter was severely coustrained by the lossof its high. eain antenna.," The Pioneer and Voyager missions provided essentially single data points during their flybys of the outer planets, and the Galileo mission to Jupiter was severely constrained by the lossof its high gain antenna."457 This restricted, This restricted458enhancements without a mocel for the stream: trajectory.,enhancements without a model for the stream trajectory.459 In particular. at stream ingress there is no information on which parts of the stream are cclipsecd at which phases.," In particular, at stream ingress there is no information on which parts of the stream are eclipsed at which phases."460 We can use an eclipse mapping method to create a moclel accretion stream. by placing model stream. points along a oedetermined trajectory. consisting of a ballistic part from. he Ly point. coupling to a magnetically confined. section where the material is threaded. by the field. lines of the white dwark," We can use an eclipse mapping method to create a model accretion stream by placing model stream points along a predetermined trajectory, consisting of a ballistic part from the $_{1}$ point, coupling to a magnetically confined section where the material is threaded by the field lines of the white dwarf."461" Ehe distance from the white chwarl where this ransition occurs is the threading radius £),. ancl is a user input to the ποσο,"," The distance from the white dwarf where this transition occurs is the threading radius $R_{\mu}$, and is a user input to the model."462 The model svstem is rotated while the toche lobe filling secondary eclipses the stream ancl white chvarl. with the brightness of the visible model stream points at cach phase summed to form a model light curve.," The model system is rotated while the Roche lobe filling secondary eclipses the stream and white dwarf, with the brightness of the visible model stream points at each phase summed to form a model light curve."463 The resultant light curve is optimized with the genetic algorithin (CLA) evolving the best fit light. curve., The resultant light curve is optimized with the genetic algorithm (GA) evolving the best fit light curve.464" The ""goodness of fit of à model light curve is measured with a fitness function! (see Llarrop-Allin 119992 for a full description).", The `goodness of fit' of a model light curve is measured with a `fitness function' (see Harrop-Allin 1999a for a full description).465 The CA adjusts the brightness points along the stream in an attempt to minimise this function. which consists of a X7 term. and. à. maximum entropy term. which ensures the problem is not uncler-constrained.," The GA adjusts the brightness points along the stream in an attempt to minimise this function, which consists of a $\chi^2$ term and a maximum entropy term, which ensures the problem is not under-constrained."466 After the final stages of the CX. a more conventional line-minimisation routine (Powell's method) is used to reach the final minimum of the solution.," After the final stages of the GA, a more conventional line-minimisation routine (Powell's method) is used to reach the final minimum of the solution."467 The aceretion stream itselfis taken to be physically thin in that it does not eclipse the primary. ancl so features such as the pre-eclipse dip (e.g. Watson 1995) are not reproduced bv the model.," The accretion stream itself is taken to be physically thin in that it does not eclipse the primary, and so features such as the pre-eclipse dip (e.g. Watson 1995) are not reproduced by the model."468 However. the brightness contribution of each stream point is taken as the sine of the angle between the line of sight and the tangent to the stream at that point. essentially a projection elfect. thus optically thick.," However, the brightness contribution of each stream point is taken as the sine of the angle between the line of sight and the tangent to the stream at that point, essentially a projection effect, thus optically thick."469 We also exclude the white dwarl from the model. although the ceress of the white chwarl can be seen in the light curves inumeciately before the ceress of the accretion region.," We also exclude the white dwarf from the model, although the egress of the white dwarf can be seen in the light curves immediately before the egress of the accretion region."470 The exact method we apply for the modelling. is dillerent to that of Llarrop-Allin ((1999b. 2001) in that we are not applying the technique to the complete eclipse light curves. nor can we interpret. the results in the same manner.," The exact method we apply for the modelling is different to that of Harrop-Allin (1999b, 2001) in that we are not applying the technique to the complete eclipse light curves, nor can we interpret the results in the same manner."471 Phere are a number of reasons for this., There are a number of reasons for this.472 Firstly. and importantly. our observations are all truncated. either in the ingress or the egress of the accretion stream.," Firstly, and importantly, our observations are all truncated, either in the ingress or the egress of the accretion stream."473 For observations where the egress is truncated (cycle 29995). the model has cilliculty breaking the ambiguity which exists when assigning brightness to points eclipsed in the same phase interval. be. the brightness can be either in the magneticallv confined. region. or the ballistic.," For observations where the egress is truncated (cycle 29995), the model has difficulty breaking the ambiguity which exists when assigning brightness to points eclipsed in the same phase interval, i.e. the brightness can be either in the magnetically confined region or the ballistic."474 bor observations where the pre-eclipse light curve is missing. we lack information on the accretion region. and. parts of the stream towards the secondary (evele 29993).," For observations where the pre-eclipse light curve is missing, we lack information on the accretion region, and parts of the stream towards the secondary (cycle 29993)."475 A further clifliculty lies in. determining the nature of the variable emission. from the aceretion region., A further difficulty lies in determining the nature of the variable emission from the accretion region.476" ""This is particularly important at ceress. where the brightness of the spot can ercally alfect the brightness distribution towards the white chwarl."," This is particularly important at egress, where the brightness of the spot can greatly affect the brightness distribution towards the white dwarf."477 After the egress of the accretion region the light curve consists of a variable component. plus the stream. which changes rapidly over the course of the observation.," After the egress of the accretion region the light curve consists of a variable component, plus the stream, which changes rapidly over the course of the observation."478 We have therefore chosen to use a restricted. modelling technique. which relies on the ingress of the accretion stream alone.," We have therefore chosen to use a restricted modelling technique, which relies on the ingress of the accretion stream alone."479 This means that we have truncated the light curves. removing all phases up to and including the ingress of the accretion region. and those after ó=1.0.," This means that we have truncated the light curves, removing all phases up to and including the ingress of the accretion region, and those after $\phi=1.0$."480 This is the only part of the light curve unalleeted by the variable emission from the accretion region., This is the only part of the light curve unaffected by the variable emission from the accretion region.481 We still have the problem of the ambiguity of the stream points. but we can make some progress in interpreting our results by referring back to the light curves and the colour ratios.," We still have the problem of the ambiguity of the stream points, but we can make some progress in interpreting our results by referring back to the light curves and the colour ratios."482 A number of parameters is required to produce a mocel light curve and. reproduce the stream brightness. distribution., A number of parameters is required to produce a model light curve and reproduce the stream brightness distribution.483 These fall into two tvpes: physical parameters such as the masses of the two component stars. and geometric parameters such as the location of the accretion region on the white dwarl (see Larrop-Allin 11999a for details).," These fall into two types: physical parameters such as the masses of the two component stars, and geometric parameters such as the location of the accretion region on the white dwarf (see Harrop-Allin 1999a for details)."484" The mocel is particularly. sensitive to the exact value chosen for the parameter Z,. but we can constrain the value using the mocel stream geometry."," The model is particularly sensitive to the exact value chosen for the parameter $R_{\mu}$, but we can constrain the value using the model stream geometry."485 H£ the value is too large then the model needs to assign a large amount of brightness to a few points., If the value is too large then the model needs to assign a large amount of brightness to a few points.486 Conversely if {1 ds too small then no emission is assigned by the model to the points in the threading region., Conversely if $R_{\mu}$ is too small then no emission is assigned by the model to the points in the threading region.487" From brightness maps for à range of values of J, we can determine the end. point of the ballistic trajectory and so provide a constraint on the value of /?,.", From brightness maps for a range of values of $R_{\mu}$ we can determine the end point of the ballistic trajectory and so provide a constraint on the value of $R_{\mu}$.488 We have found from our model fits of the light curves used here that the technique depends heavily on the data being of a sullicicntly high signal-to-noise ratio. which is important. because of the sensitivity to the value of Z2.," We have found from our model fits of the light curves used here that the technique depends heavily on the data being of a sufficiently high signal-to-noise ratio, which is important because of the sensitivity to the value of $R_{\mu}$."489 Therefore. in order to determine the best fit value to use we further restrict the application of our model technique o eveles 29993 and 29995 (Figure 2)).," Therefore, in order to determine the best fit value to use we further restrict the application of our model technique to cycles 29993 and 29995 (Figure \ref{fig:huaqr04colours}) )."490" Figure 6. shows model fits to the ""blue Leht curve of cvcle 29995 for different values of 2).", Figure \ref{fig:rmu29995} shows model fits to the `blue' light curve of cycle 29995 for different values of $R_{\mu}$.491 Lhe stream. maps ughlieht the dependence of the fits on a correct value for ἐν., The stream maps highlight the dependence of the fits on a correct value for $R_{\mu}$.492" For a value of 4/4,=0.18a the brightness of the threading region is low.", For a value of $R_{\mu}=0.18a$ the brightness of the threading region is low.493" This ack of emission. or ""hole. is caused by £2), ing too small - 10 data are incompatible with emission at the end part ofthe resulting long ballistic stream."," This lack of emission, or `hole', is caused by $R_{\mu}$ being too small - the data are incompatible with emission at the end part of the resulting long ballistic stream."494" On the other hand. if £2), is too large. so that the mocel ballistic stream is shorter wan it is in reality. a pile up of excess rightness at the tireacding region is seen. as in the stream. mapfor 2),=0.26."," On the other hand, if $R_{\mu}$ is too large, so that the model ballistic stream is shorter than it is in reality, a pile up of excess brightness at the threading region is seen, as in the stream mapfor $R_{\mu}=0.26$."495" The inappropriateness of the latter can xe deduced: from. re poor fit to the region at ó=0.98 (corresponding to he threading region) for values of 2), which are too large (insets to Figure 6)).", The inappropriateness of the latter can be deduced from the poor fit to the region at $\phi=0.98$ (corresponding to the threading region) for values of $R_{\mu}$ which are too large (insets to Figure \ref{fig:rmu29995}) ).496 For all our modelling. we used. fixed. values of VOM... g¢=0.25 and ¢=85.07 (Llarrop-Allin 11999b. Schwope 22001).," For all our modelling we used fixed values of $M_1=0.9M_{\odot}$ , $q=0.25$ and $i=85.0^{\circ}$ (Harrop-Allin 1999b, Schwope 2001)."497" Table 2 gives the values of Z4, and the field orientation parameters for cach evele.", Table \ref{tab:freeparams} gives the values of $R_{\mu}$ and the field orientation parameters for each cycle.498 We estimate the range on the values of 3 and ¢ as I0 (10)., We estimate the range on the values of $\beta$ and $\zeta$ as $\pm10^\circ (1\sigma)$ .499 The values of the three parameters in Table 2/— are different from those found by Llarrop-Allin, The values of the three parameters in Table \ref{tab:freeparams} are different from those found by Harrop-Allin500sequence from Bannister&Jameson(2007).. and was obviously incorrect.,"sequence from \citet{bannister07}, and was obviously incorrect."501 The sequence shown in Figure 2 of Jamesonetal.(2008b) crossed that for the Hyades. and the gradient of 2.88. did not fit. with the gradients of the other clusters. which had approximately parallel sequences. all with gradients of ~ 1.98. the value that was suggested by the authors as being more appropriate.," The sequence shown in Figure 2 of \citet{jameson08b} crossed that for the Hyades, and the gradient of 2.88, did not fit, with the gradients of the other clusters, which had approximately parallel sequences, all with gradients of $\sim$ 1.98, the value that was suggested by the authors as being more appropriate."502 Using our new L dwarfs. and those found by (20082)... we used the colour conversions of Stephens&Leggett(2004) to recalculate the relationship on the MKO system.," Using our new L dwarfs, and those found by \citet{jameson08}, we used the colour conversions of \citet{stephens04} to recalculate the relationship on the MKO system."503 Our new values are m=2.0746£0.28 |. 20.448 |. which is more in keeping with the values for the other clusters.," Our new values are $\pm$ 0.281, $\pm$ 0.4481, which is more in keeping with the values for the other clusters."504 The relationship in the 2MASS colour system is plotted on Figure 2.. as well as the sequence as detined by the Bannister&Jameson(2007) dwarfs.," The relationship in the 2MASS colour system is plotted on Figure \ref{mg_ursa}, as well as the sequence as defined by the \citet{bannister07} dwarfs."505 The Pleiades cluster is 125 Myr old and is situated at a distance of 130 pe (Stauffer.Schultz&Kirkpatrick1998)., The Pleiades cluster is 125 Myr old and is situated at a distance of 130 pc \citep{stauffer98}.506.. As a cluster it has been studied in depth and has been found to contain many brown dwarfs (Casewelletal.2007:Lodieu2007b:Bihainetal.2006:Moraux 2003).," As a cluster it has been studied in depth and has been found to contain many brown dwarfs \citep{casewell07, lodieu07a,bihain06,moraux03}."507. The Pleiades moving group has a convergent point of 85.04°+3.67. 0.932 (Madsen 2002)..," The Pleiades moving group has a convergent point of $^{\circ}$$\pm$ 3.67, $-$ $^{\circ}$$\pm$ 6.92 \citep{madsen02}. ."508 This convergent point is very —.close to that of many other moving groups such as Alpha Persei (96 .783:1.96. -23°.2743.67: Madsenetal.2002.. 50 Myr: Lynga.G 19879). Tucana/Horologium (30 Myr: Zuckerman&Song 20043) and the AB Dor moving group (SO Myr: Zuckerman&Song 20043) (see Zuckerman for a review). and it has been theorised that many of these moving groups have a common origin (Ortegaetal.2007).," This convergent point is very close to that of many other moving groups such as Alpha Persei $^{\circ}$ $\pm$ 1.96, $^{\circ}$ $\pm$ 3.67; \citealt{madsen02}, 50 Myr; \citealt{lynga87}) ), Tucana/Horologium (30 Myr; \citealt{zuckerman04}) ) and the AB Dor moving group (50 Myr; \citealt{zuckerman04}) ) (see \citealt{zuckerman04} for a review), and it has been theorised that many of these moving groups have a common origin \citep{ortega07}."509. Thirteen new candidate members were found using the moving group method., Thirteen new candidate members were found using the moving group method.510 6 objects with declinations <-30° and 7 objects with declinations L-307 (Figure 3.. Table 85.," 6 objects with declinations $<$ $^{\circ}$ and 7 objects with declinations $>$ $^{\circ}$ (Figure \ref{mg_plds}, Table \ref{pleiadestab}) )."511 As with the Hyades and Ursa Major clusters. the Pleiades is old enough to expect that some mass segregation has occurred. and thus it is not unreasonable to search the whole skv for members of the moving group.," As with the Hyades and Ursa Major clusters, the Pleiades is old enough to expect that some mass segregation has occurred, and thus it is not unreasonable to search the whole sky for members of the moving group."512 This is not the case however for many of the younger. southern moving groups.," This is not the case however for many of the younger, southern moving groups."513 The new moving group members are detailed in Table 8.., The new moving group members are detailed in Table \ref{pleiadestab}.514 Many of the southern moving groups have similar convergent points and velocities., Many of the southern moving groups have similar convergent points and velocities.515 To determine if any of our southern dwarfs are members of these moving groups. we have used the moving group method as for the Hyades. Ursa Major and Pleiades moving groups. but have then used the isochrone for Upper Scorpius as developed by Jamesonetal.(2008b).," To determine if any of our southern dwarfs are members of these moving groups, we have used the moving group method as for the Hyades, Ursa Major and Pleiades moving groups, but have then used the isochrone for Upper Scorpius as developed by \citet{jameson08b}."516. This can be then used as an age indicator for the vounger clusters., This can be then used as an age indicator for the younger clusters.517 If the selected dwarfs fall on or near the isochrone. then they are young (age «10 Myr) and are considered candidate members.," If the selected dwarfs fall on or near the isochrone, then they are young (age $<$ 10 Myr) and are considered candidate members."518 Radial velocity measurements are needed to confirm the membership of these objects however., Radial velocity measurements are needed to confirm the membership of these objects however.519 Simply by using the moving group method. we have found «]0 candidate members of the TW Hydra. Tucana/Horlogium. Beta Pictoris. AB. Doradus and #7) Chamaeleon moving groups.," Simply by using the moving group method, we have found $<$ 10 candidate members of the TW Hydra, Tucana/Horlogium, Beta Pictoris, AB Doradus and $\eta$ Chamaeleon moving groups."520 Because these clusters all have similar convergent points and velocities (Zuckerman&Song2004) some of the candidate members are found in more than one cluster., Because these clusters all have similar convergent points and velocities \citep{zuckerman04} some of the candidate members are found in more than one cluster.521 When plotted on the My. -/ἐν colour magnitude diagram. using Stephens&Leggett(2004) to convert the colours into the MKO system. with the Upper Scorpius and Alpha Perseus cluster isochrones from Jamesonetal.(2008b).. all of the candidate members sit lower then Alpha Per. indicating that these dwarfs cannot be moving group members at the calculated distances.," When plotted on the $_K$, $J-K$ colour magnitude diagram, using \citet{stephens04} to convert the colours into the MKO system, with the Upper Scorpius and Alpha Perseus cluster isochrones from \citet{jameson08b}, all of the candidate members sit lower then Alpha Per, indicating that these dwarfs cannot be moving group members at the calculated distances."522 This paper continues the work presented in Jamesonetal.(2008a).. which presented proper motions of 143 L and T dwarfs.," This paper continues the work presented in \citet{jameson08}, which presented proper motions of 143 L and T dwarfs."523 This paper presents a further 126 proper motions., This paper presents a further 126 proper motions.524 Thus the large majority of field L and T dwarfs discovered by 2MASS. DENIS and the SDSS now have known proper motions.," Thus the large majority of field L and T dwarfs discovered by 2MASS, DENIS and the SDSS now have known proper motions."525 From these data we tind a further 2 wide binary L dwarfs. both with M dwarf companions.," From these data we find a further 2 wide binary L dwarfs, both with M dwarf companions."526 A further 3 high velocity L dwarfs have been discovered. which we assume are old thick dise L dwarfs.," A further 3 high velocity L dwarfs have been discovered, which we assume are old thick disc L dwarfs."527 Finally. we find 7 more potential members of the Hyades moving group. 4 members of the Ursa Major moving group and 13 potential members of the Pleiades moving group.," Finally, we find 7 more potential members of the Hyades moving group, 4 members of the Ursa Major moving group and 13 potential members of the Pleiades moving group."528 We have found no members of the young southern moving groups. TW Hydra. Tucana/Horologium. Beta Pictoris. AB Doradus or 7 Chamaeleon.," We have found no members of the young southern moving groups, TW Hydra, Tucana/Horologium, Beta Pictoris, AB Doradus or $\eta$ Chamaeleon."529 We have also used these new members of the Ursa Major moving group to refine the L dwarf sequence for the group that was defined by Jamesonetal.(2008b)., We have also used these new members of the Ursa Major moving group to refine the L dwarf sequence for the group that was defined by \citet{jameson08b}.530. SLC was supported by STFC for the duration of this work., SLC was supported by STFC for the duration of this work.531 MBU is supported by a STFC Advanced Fellowship., MBU is supported by a STFC Advanced Fellowship.532 Observations were made at the United Kingdom Infrared Telescope. which is operated by the Joint Astronomy Centre on behalf of the U.K. Particle Physics and Astronomy Research Council-," Observations were made at the United Kingdom Infrared Telescope, which is operated by the Joint Astronomy Centre on behalf of the U.K. Particle Physics and Astronomy Research Council."533Observations were also made a the New Technology Telescope which is operatec by ESO.,Observations were also made a the New Technology Telescope which is operated by ESO.534 This publication makes use of data products from the Two Micron All Sky Survey. which is a joint project of the University of Massachusetts and the Infrared Processing anc Analysis Center/California Institute of Technology. funded by the National Aeronautics and Space Administration and the Nationa Science Foundation.," This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation."535 Research has benefited from the M. L. and T dwarf compendium housed at DwarfArchives.organd maintained by Chris Gelino. Davy Kirkpatrick. and Adam Burgasser.," Research has benefited from the M, L, and T dwarf compendium housed at DwarfArchives.organd maintained by Chris Gelino, Davy Kirkpatrick, and Adam Burgasser."536 This research has made use of NASA's. Astrophysics Data System Bibliographic Services., This research has made use of NASA's Astrophysics Data System Bibliographic Services.537is similar to [Y Tuc (see below) while the younger age would suggest that there is a considerable overlap in the ages of the thin aud thick disks.,is similar to 47 Tuc (see below) while the younger age would suggest that there is a considerable overlap in the ages of the thin and thick disks.538 However. we are reluctant to reach such a conclusion based only ou oue star.," However, we are reluctant to reach such a conclusion based only on one star."539 Two other stars which might be thick disk stars (HD 11007 and 67105) are also [αν young (6.6£0.5 aud. 6.5=1.0)., Two other stars which might be thick disk stars (HD 11007 and 67458) are also fairly young $6.6\pm 0.5$ and $6.5\pm 1.0$ ).540 However. oue could argue that the kinematics aud orbital parameters of these two stars are not too different from the thin disk. aud so there identification as thick disk stars is debateable.," However, one could argue that the kinematics and orbital parameters of these two stars are not too different from the thin disk, and so there identification as thick disk stars is debateable."541 Further age determinations of more metal-poor stars ([Fe/H]< —0.25) are needed before one can conclude that their is a significant spread in the age of the thick clisk., Further age determinations of more metal-poor stars $\feh < -0.25$ ) are needed before one can conclude that their is a significant spread in the age of the thick disk.542 Ixochroue fitting ages were determined for the thick disk globular cluster 17 Tuc., Isochrone fitting ages were determined for the thick disk globular cluster 47 Tuc.543 The photometric data for the cluster was obtained from Ilxaluzuy.etal.(1998)., The photometric data for the cluster was obtained from \citet{Kal98}.544. Heavy element abuudauces in the literature indicate values of [Fe/H]=—0.7040.07 (Carretta&Gratton1997).. and [Fe/H]=—0.81 (Brown&Wallerstein1992).," Heavy element abundances in the literature indicate values of $\feh = -0.70\pm0.07$ \citep{Crr97}, and $\feh =545-0.81$ \citep{Bro92}."546. Additionally. Brown&Wallerstein(1992) indicate an enhancement in a-capture elements of [a/Fe]=0.22.," Additionally, \citet{Bro92} indicate an enhancement in $\alpha$ -capture elements of $\afe = 0.22$."547 However. for the stellar models used in this study. opacities were only available for [a/Fe]=0.00 aud 0.10.," However, for the stellar models used in this study, opacities were only available for $\afe = 0.00$ and $0.40$."548 Thusisochrones were fit for abundances of and —0.80 both with[a/Fe]= , Thus isochrones were fit for abundances of $\feh = -0.70$ and $-0.80$ both with $\afe = 0.40$.549Isochroues were fit iu a manner identical to NCC 155. simutaneously in B-V aud V-L The value oL reddening was fixed at ECB—V)=0.01 (Harris1996) and Εν)=1.25«ECB—V)0.05.," Isochrones were fit in a manner identical to NGC 188, simutaneously in B-V and V-I. The value of reddening was fixed at $\ebv = 0.04$ \citep{Har96} and $\evi = 1.25*\ebv = 0.05$."550 The distance modulus was varied around ηνM)y:=11.37 (Harris1996) in order to d ea nain sequence fit., The distance modulus was varied around $\dmv = 11.37$ \citep{Har96} in order to obtain a good main sequence fit.551" Figure 9 shows the isochrone lits for [Fe/H]=—0.70 and [a/Fe]=""0.10.", Figure \ref{fig47tuc-070} shows the isochrone fits for $\feh = -0.70$ and $\afe = 0.40$.552 The »oor simultaneous fit is likely due to the dillerence iu a-euliaucemenut by nearly 0.2 dex ween the iterature value and the models., The poor simultaneous fit is likely due to the difference in $\alpha$ -enhancement by nearly 0.2 dex between the literature value and the models.553" The fits for [Fe/H]=—0.30 and [a/Fe]=""0.10. shown in Figure 8.. likewise indicate a poor simultaneous Π to ΕΝ aud. V-L In order to rellect the total jeavy element abundance (Z) in the cluster. isochrones were generated with [Fe/H]=—0.95 and a/Fe|=0.10."," The fits for $\feh =554-0.80$ and $\afe = 0.40$, shown in Figure \ref{fig47tuc-080}, , likewise indicate a poor simultaneous fit to B-V and V-I. In order to better reflect the total heavy element abundance $Z$ ) in the cluster, isochrones were generated with $\feh = -0.95$ and $\afe = 0.40$."555 This abundance was chosen to match the heavy element mass [Traction lor the values of aad Ποια in Brown&Wallerstein(1992).. correspoudiug to Z=0.0010.," This abundance was chosen to match the heavy element mass fraction for the values of and found in \citet{Bro92}, corresponding to $Z556= 0.0040$."557 The result. shown in Figure 10.. was an acceptable fit which indicated an age of 12.540.5 Gyr for a reddening of ECG—V)=0.01 auc distauce modulus of (00—M)q4:= 11.35.," The result, shown in Figure \ref{fig47tuc-095}, , was an acceptable fit which indicated an age of $12.5\pm 0.5$ Gyr for a reddening of $\ebv = 0.04$ and distance modulus of $\dmv =55811.35$ ."559 Both the reddeniug ancl distance modulus were iu good agreement with the values quoted in Harris(1996)., Both the reddening and distance modulus were in good agreement with the values quoted in \citet{Har96}.560. Uncertainty due to recdclening was determined by producing fits with ECB—V)=0.03 aud 0.05., Uncertainty due to reddening was determined by producing fits with $\ebv = 0.03$ and $0.05$.561 These fits inclicatecl ages of LL40.5 aud 11.520.5 Gyr. respectively.," These fits indicated ages of $14\pm 0.5$ and $11.5\pm 0.5$ Gyr, respectively."562 Table L πια{σος the isochrone sets aud parameters used in fitting to [7 Tuc., Table \ref{tab47tuc} summarizes the isochrone sets and parameters used in fitting to 47 Tuc.563The age used for comparison to the other clusters and field stars was 12.541.5Gyr. as iudicated and includes the uncertainty dueto reddening.,"The age used for comparison to the other clusters and field stars was $12.5\pm1.5$Gyr, as indicated and includes the uncertainty dueto reddening."564where the subscripteof denotes whistler growth in a clistribution function stabilized by binary collisions only. not by the whistlers themselves.,"where the subscript denotes whistler growth in a distribution function stabilized by binary collisions only, not by the whistlers themselves."565 Some rough estimates may be obtained from eq. 20.., Some rough estimates may be obtained from eq. \ref{eq:maxw_gro_coll}.566 Phe first is that. provided οthy7:3.1. we have 5ο0. in a narrow cone along the axis.," The first is that, provided $\epsilon^{th} \beta_{e}>1$, we have $\gamma^{w}> 0$, in a narrow cone along the axis."567" The width of ⋅⋠this anglecone is. roughly estimated. to bette"")Hte1.", The width angle of this cone is roughly estimated to be $ \beta_{e}^{-1}(\epsilon^{th})^{-1} < 1$.568 To obtain the quantitative conditions we note that the integral in eq., To obtain the quantitative conditions we note that the integral in eq.569 20. can be written in terms of tabulated functions. where Alarginal stability of the plasma is found numerically in GpE] space at The validity of the latter solution is subject to the condition where which is the range in which the whistler mode exists.," \ref{eq:maxw_gro_coll} can be written in terms of tabulated functions, where Marginal stability of the plasma is found numerically in $\beta_{e}\epsilon_{th}, \tilde{k}_{\parallel}, \chi$ space at The validity of the latter solution is subject to the condition where which is the range in which the whistler mode exists."570 A numerical study. of the properties of eq., A numerical study of the properties of eq.571 21. shows that there is a distinct range of ky for which ον> 0., \ref{eq:matz_a} shows that there is a distinct range of $\tilde{k}_{\parallel}$ for which $\gamma^{w}_{coll}>0$ .572 Ehis value is bounded. between 0.22<Ay0.7 for 1000., This value is bounded between $0.22<\tilde{k}_{\parallel}<0.7$ for $0.0001<\epsilon^{th}\beta_{e}<1000$ .573" Por &,=0.22. one finds For ky=0.7 instead of 0.22 we find that: The underlving physical interpretation of this range of dis as follows: Lf 2 is too large. the waves that resonate with thermal electrons can exclotron resonate with ions as well. which complicates things beyond the scope of this paper."," For $\tilde{k}_{\parallel}=0.22$, one finds For $\tilde574k_{\parallel}=0.7$ instead of $0.22$ we find that: The underlying physical interpretation of this range of $\beta$ is as follows: If $\beta$ is too large, the waves that resonate with thermal electrons can cyclotron resonate with ions as well, which complicates things beyond the scope of this paper."575 For 3 too small. the phase velocity of the whistlers exceeds the thermal electron velocity by a sullicient margin that the resonant particles are far out on the tail of the Maxwellian distribution Function. and the excitation is too weak to be interesting.," For $\beta$ too small, the phase velocity of the whistlers exceeds the thermal electron velocity by a sufficient margin that the resonant particles are far out on the tail of the Maxwellian distribution function, and the excitation is too weak to be interesting."576 In any case. condition eq.," In any case, condition eq."577 27. is met in clusters of galaxies. and condition 26 at the ISM.," \ref{eq:wis_beta_cond_mod} is met in clusters of galaxies, and condition \ref{eqq:wis_beta_cond_mod} at the ISM."578 The angular dependence of 5 on eq., The angular dependence of $\gamma$ on eq.579" 21. on x is roughly linear. with a maximum at X—1: the slope depends on c""."," \ref{eq:matz_a}580 on $\chi$ is roughly linear with a maximum at $\chi=1$; the slope depends on $\epsilon^{th}\beta_{e}$."581 ‘Thus. at v€L. condition eq.," Thus, at $\chi<1$, condition eq."582 27. or condition eq., \ref{eq:wis_beta_cond_mod} or condition eq.583 26. are somewhat relaxed by a [actor of order unity., \ref{eqq:wis_beta_cond_mod} are somewhat relaxed by a factor of order unity.584 The critical condition for whistlers present in a collision dominated hydrogen plasma (cf., The critical condition for whistlers present in a collision dominated hydrogen plasma (cf.585 the last line of eq., the last line of eq.586 19. ) is found from eq., \ref{eq:P_Q} ) is found from eq.587 23.5y to be: provided that :3 is in the range given by eqs. 2 ," \ref{eq:mar_coll} to be: provided that $\beta$ is in the range given by eqs. \ref{eq:wis_beta_cond_mod}, \ref{eqq:wis_beta_cond_mod}."588There are a lew more conditions for the validity of eq. 28.., There are a few more conditions for the validity of eq. \ref{eq:krit_krit}.589 One of them is and it stems from the validity of the πόσοι expansion., One of them is and it stems from the validity of the Knudsen expansion.590 The latter constraint is so weak that it can be ignored., The latter constraint is so weak that it can be ignored.591 The last condition to be considered is merely a formal one and it stems from the validity of eq. 10..," The last condition to be considered is merely a formal one and it stems from the validity of eq. \ref{eq:wisgro0},"592 namely: This condition is rather strong and it requires that CU.H<10., namely: This condition is rather strong and it requires that $\epsilon^{th}\beta_{e}<10$.593" However. even ifpano: this is not the case if"" when whistlers dominate the plasma. the value of vac. is sulliciently high and ¢ can be maintained much smaller than unity."," However, even if this is not the case if when whistlers dominate the plasma, the value of $\nu_{w,s}$ is sufficiently high and $\zeta$ can be maintained much smaller than unity."594 The conclusion of this section. is that any werodyvnamical model in which 3>»—001. and 103«dx gives rise to whistlers due to an excess of perpendicular momentum in the hotward. velocity jemisphere., The conclusion of this section is that any hydrodynamical model in which $\beta>0.01$ and $10^{-4}<\epsilon^{th}<10^{-2}$ gives rise to whistlers due to an excess of perpendicular momentum in the hotward velocity hemisphere.595" The unstable on-axis whistlers propagate in 1e colchward direction,", The unstable on-axis whistlers propagate in the coldward direction.596 Note that the hotward part of the distribution function. which has excess perpendicular momentum is not the par mt carries the heat.," Note that the hotward part of the distribution function, which has excess perpendicular momentum is not the part that carries the heat."597 The coldward. particles. which carry ie heat from hot to cokl have an excess of paralle momentum. and are stable to all on-axis whistlers Thus. the heat carrying. particles cannot. resonantly excite on-axis whistlers that propagate parallel to the fiel ines and on-axis whistlers that propagate parallel to the ield lines do not significantly inhibit heat Uusx.," The coldward particles, which carry the heat from hot to cold, have an excess of parallel momentum, and are stable to all on-axis whistlers Thus, the heat carrying particles cannot resonantly excite on-axis whistlers that propagate parallel to the field lines and on-axis whistlers that propagate parallel to the field lines do not significantly inhibit heat flux."598 Whistlors hat propagate olf the axis. on the other hand. can inhibi reat flux.," Whistlers that propagate off the axis, on the other hand, can inhibit heat flux."599 These oll-axis waves have right-handed. elliptica x»blaritv which can be represented as a superposition of eft-handed: and right-handed cireular polarity., These off-axis waves have right-handed elliptical polarity which can be represented as a superposition of left-handed and right-handed circular polarity.600 “Phe Left-wunided circular polarity allows for whistler emission. in perpendicular momentum deficient regions in. phase space., The left-handed circular polarity allows for whistler emission in perpendicular momentum deficient regions in phase space.601 Although at marginal. stability of a collision dominated Xxasma only on-axis whistlers are excited. it is incorrect. to ooceed. under theassumption that these on-axis whistlers can lead to heat Hux inhibition.," Although at marginal stability of a collision dominated plasma only on-axis whistlers are excited, it is incorrect to proceed under theassumption that these on-axis whistlers can lead to heat flux inhibition."602 Rather. we argue. any on- waves merely mocily the distribution function in such a wav that the marginal stability is transferred to oll-axis Waves.," Rather, we argue, any on-axis waves merely modify the distribution function in such a way that the marginal stability is transferred to off-axis waves."603of which the stars form is preserved. causes à steepening of the “O/T O gradient and a more pronounced. decrease. of the ratio in the solar neighbourhood in the last 4.5 Cyr.,"of which the stars form is preserved, causes a steepening of the $^{16}$ $^{17}$ O gradient and a more pronounced decrease of the ratio in the solar neighbourhood in the last 4.5 Gyr."604 Obviously. in the case of Aloclel we need also to further reduce the production. of⋅ newly formed⋅ Ly7 O in. order not to overestimate its solar abundance.," Obviously, in the case of Model we need also to further reduce the production of newly formed $^{17}$ O in order not to overestimate its solar abundance."605 We choose to lower the vields of ο from intermecdiate-mass stars (see ‘Lable 1)., We choose to lower the yields of $^{17}$ O from intermediate-mass stars (see Table 1).606 In this paper we discuss the problem of the evolution of the CNO isotopes in both the solar vicinity and the disc of the Galaxy., In this paper we discuss the problem of the evolution of the CNO isotopes in both the solar vicinity and the disc of the Galaxy.607 In particular. we analyse the implications of updated: results. from. stellar nucleosvnthesis stuclics (including nova nucleosynthesis).," In particular, we analyse the implications of updated results from stellar nucleosynthesis studies (including nova nucleosynthesis)."608 Our main conclusions can be summarized as follows:, Our main conclusions can be summarized as follows:609"(lower triangle and diamond) depends on the exact time of formation of the first structure, which is largely unknown.","(lower triangle and diamond) depends on the exact time of formation of the first structure, which is largely unknown."610" The duration of this episode is only a few tens of Myr, which also corresponds to the uncertainty on the redshift of formation of those stars."," The duration of this episode is only a few tens of Myr, which also corresponds to the uncertainty on the redshift of formation of those stars."611" Finally, all stars observed in the ESO-LP are found to form at redshift below 10, except CS 22949-037 whose abundances are very similar to HE 13004-0157 4.2))."," Finally, all stars observed in the ESO-LP are found to form at redshift below 10, except CS 22949-037 whose abundances are very similar to HE 1300+0157 )."612 The observed oxygen abundance in the UMP star HE 0107-5240 (diamond in upper panel of 5)) seems to be lower than the predicted abundances., The observed oxygen abundance in the UMP star HE 0107-5240 (diamond in upper panel of ) seems to be lower than the predicted abundances.613" This discrepancy points to the very special stars where C, O abundances are not explained by standard predictions (??).."," This discrepancy points to the very special stars where C, O abundances are not explained by standard predictions \citep{2006NuPhA.777..424N,2007ApJ...660..516T}."614 It is clear that the yields of the massive stars at zero metallicity are poorly known., It is clear that the yields of the massive stars at zero metallicity are poorly known.615" For example, new calculations concerning the effect of rotation on the evolution of primordial stars can modify considerably the abundance of C and O, and their corresponding ratio (?).."," For example, new calculations concerning the effect of rotation on the evolution of primordial stars can modify considerably the abundance of C and O, and their corresponding ratio \citep{2008A&A...489..685E}."616 They would then allow for a decrease of about 1 dex required for the oxygen abundance of HE 0107-5240 to be reproduced., They would then allow for a decrease of about 1 dex required for the oxygen abundance of HE 0107-5240 to be reproduced.617 We now study the influence of uncertainties on stellar abundances on the overall results., We now study the influence of uncertainties on stellar abundances on the overall results.618" We have performed the same full analysis using the abundances derived from 1D model atmospheres (given in 1)), yielding new envelopes for the Dtrans--[Fe/H] plane, abundance evolution, optical depth evolution and SFR of PoplIII stars."," We have performed the same full analysis using the abundances derived from 1D model atmospheres (given in ), yielding new envelopes for the -[Fe/H] plane, abundance evolution, optical depth evolution and SFR of PopIII stars."619" In the following figures, the same symbols as above are used for each CEMP star."," In the following figures, the same symbols as above are used for each CEMP star."620" We do not show ESO-LP stars in the figures, as their positions are unchanged."," We do not show ESO-LP stars in the figures, as their positions are unchanged."621" The main effect of the correction applied to abundances derived from 1D model atmospheres is to lower all abundances by about 0.1 dex for [Fe/H], and up to 1 dex for C and O abundances."," The main effect of the correction applied to abundances derived from 1D model atmospheres is to lower all abundances by about 0.1 dex for [Fe/H], and up to 1 dex for C and O abundances."622 This can be seen in by comparing filled and open symbols (abundances derived from 3D and 1D model atmospheres respectively)., This can be seen in by comparing filled and open symbols (abundances derived from 3D and 1D model atmospheres respectively).623" Given the predicted path of Dtrans--[Fe/H], this does not modify much the envelope in the intermediate redshift range."," Given the predicted path of -[Fe/H], this does not modify much the envelope in the intermediate redshift range."624" At high redshift, the effect is strong and displaces the envelope towards lower values ofDtrans."," At high redshift, the effect is strong and displaces the envelope towards lower values of."625". In both cases, PopllI stars are required and a very similar pattern is displayed."," In both cases, PopIII stars are required and a very similar pattern is displayed."626" As for the SFR, the best fit model assuming abundances derived from 1D model atmosphere extends slowly down to about 1077 Mo yr! Mpc? at z~4."," As for the SFR, the best fit model assuming abundances derived from 1D model atmosphere extends slowly down to about $10^{-7}$ $_\odot$ $^{-1}$ $^{-3}$ at $z\sim4$."627" However, the global envelope (including all possible shapes) is almost identical in both cases, although a bit more extended assuming 1D model atmospheres."," However, the global envelope (including all possible shapes) is almost identical in both cases, although a bit more extended assuming 1D model atmospheres."628" The evolution of optical depth is also not modified in a significant way, since the contribution of PopIII stars to reionization is marginal."," The evolution of optical depth is also not modified in a significant way, since the contribution of PopIII stars to reionization is marginal."629" Finally, we consider how our estimates for the redshift of formation of CEMP stars are affected."," Finally, we consider how our estimates for the redshift of formation of CEMP stars are affected."630 displays the envelope for the evolution of abundances with redshift allowed in the two cases., displays the envelope for the evolution of abundances with redshift allowed in the two cases.631" It appears even more clearly that the discrepancy occurs only at high redshift, while the transition from CEMP to standard poor stars is required in both cases."," It appears even more clearly that the discrepancy occurs only at high redshift, while the transition from CEMP to standard metal-poor stars is required in both cases."632 The stars are not located in this figure for clarity., The stars are not located in this figure for clarity.633 The different ranges of estimates for their redshift of formation are summarised in2., The different ranges of estimates for their redshift of formation are summarised in.634". Again, only the two stars at the highest redshift are affected by this uncertainty; while the range of allowed redshift is larger in the case of abundances derived from 1D model atmospheres (this is not visible in 7))."," Again, only the two stars at the highest redshift are affected by this uncertainty; while the range of allowed redshift is larger in the case of abundances derived from 1D model atmospheres (this is not visible in )."635" Following the approach developed in ?,, we have modeled the evolution of individual element abundances in the ISM assuming homogeneous star formation and stellar yields."," Following the approach developed in \citet{2004ApJ...617..693D}, we have modeled the evolution of individual element abundances in the ISM assuming homogeneous star formation and stellar yields."636" Recent observations at z~ 7-8 (?) were used to better constrain one ingredient of the model, namely the SFR for PoplI/I at high redshift."," Recent observations at $\sim$ 7-8 \citep{2007ApJ...670..928B} were used to better constrain one ingredient of the model, namely the SFR for PopII/I at high redshift."637" We have shown that a homogeneous scenario of hierarchical structure formation reproduces many different observations, from reionisation and first star abundances to local abundance observations."," We have shown that a homogeneous scenario of hierarchical structure formation reproduces many different observations, from reionisation and first star abundances to local abundance observations."638" We found that using the most recent results on the optical depth from WMAP, a massive mode is not absolutely required."," We found that using the most recent results on the optical depth from WMAP, a massive mode is not absolutely required."639" Nevertheless, the data can accommodate a PoplII contribution, responsible for the gradual reionization starting from z-20."," Nevertheless, the data can accommodate a PopIII contribution, responsible for the gradual reionization starting from $z\simeq 20$."640" Although the cosmological importance of PopllI stars cannot be fully constrained by the integrated Thomson optical depth, this question may be better tackled in the future with the help of accurate measurements of the CMB polarization data (?).."," Although the cosmological importance of PopIII stars cannot be fully constrained by the integrated Thomson optical depth, this question may be better tackled in the future with the help of accurate measurements of the CMB polarization data \citep{2009ApJS..180..306D}."641" We have also considered stellar constraints, in particular the MDF and the evolution of"," We have also considered stellar constraints, in particular the MDF and the evolution of"642 (Parketal.2000).. Walker(1956)... Suneetal.(1997)... Flaccomioetal.(1999)... (2008):," \citet{Herbig}. \citep{Park}. \citep{Herbig}. \citet{Walker}, \citet{Sung}, \citet{Flaccomio}, \citet{Mayne2008};"643 Dahlin(2008) 1989).. ," \citet{Dahm} \citep{Strom1971,Perez1989}, \citep[e.g., ][]{Anthony-Twarog1982}."644star formation in the Milkv Was. a better estimate of the age of NGC 2261 would further our understanding of processes relevant to early stellar evolution such as angular momentum transfer and the Dfetime of circumstellar disks.," star formation in the Milky Way, a better estimate of the age of NGC 2264 would further our understanding of processes relevant to early stellar evolution such as angular momentum transfer and the lifetime of circumstellar disks."645 Tn this paper. we determine the distance to NGC 2261. using a statistical technique that relies on measured projected rotation velocitics. rotation periods. Iuimuinosities and effective temperatures of the low mass I AL type cluster members.," In this paper, we determine the distance to NGC 2264 using a statistical technique that relies on measured projected rotation velocities, rotation periods, luminosities and effective temperatures of the low mass K M type cluster members."646 The technique was first developed by ITeudryetal.(1993). aud has subsequently been used to fud distauces to the Pleiades. the Taurus star forming regiou. and the Orion Nebula Cluster (O'Dellctal.1991:Preihisch&Sinith1997:Jeffries 2007).," The technique was first developed by \citet{Hendry} and has subsequently been used to find distances to the Pleiades, the Taurus star forming region, and the Orion Nebula Cluster \citep{Odell, Preibisch, Jeffries}."647. This method has the advantage of beiug nearly independent of stellar evolutionary models., This method has the advantage of being nearly independent of stellar evolutionary models.648 Tn bref. we first measure the projected rotational velocities of cluster members. esin/ (where ο is the angential velocity of the stellar surface at the equator and { is the inclination of the stellar rotational axis ou he skv such that ¢=907 implies au edge on oricutation and {=07 implies a pole on orientation) frou existiug Hel-vesolition spectra of NGC 2261 members (Firészetal. 2006).," In brief, we first measure the projected rotational velocities of cluster members, $v \sin i$ (where $v$ is the tangential velocity of the stellar surface at the equator and $i$ is the inclination of the stellar rotational axis on the sky such that $i = 90^{\circ}$ implies an edge on orientation and $i = 0^{\circ}$ implies a pole on orientation) from existing high-resolution spectra of NGC 2264 members \citep{Furesz}."649. An effective temperature. Ty5. is estimated or cach star from cither its spectral type or dereddeued photometry.," An effective temperature, $T_{eff}$, is estimated for each star from either its spectral type or dereddened photometry."650" Luninosities. L. are estimated for cluster ΠΟΡΟΣ frou, nmieasured magnitudes byw assuniusg a ronuinal value for the cluster distance. a prescription or the cluster reddening. and a standard bolometric correction."," Luminosities, $L$, are estimated for cluster members from measured magnitudes by assuming a nominal value for the cluster distance, a prescription for the cluster reddening, and a standard bolometric correction."651 Stellay radi are then calculated from the estimated Iuninosities aud effective temperatures using he Stefan-Boltzmann relation., Stellar radii are then calculated from the estimated luminosities and effective temperatures using the Stefan-Boltzmann relation.652 The final datauceded forhedistance deteriination are rotation periods obtaimed roni fits to periodic variations m the stellar light curves., The final dataneeded forthedistance determination are rotation periods obtained from fits to periodic variations in the stellar light curves.653Blazars ave characterized by fast variability iu cüffereut wavebauds frou radio to eanuna and iu few cases by TeV radiation (Urrv Paclovani 1995: Puuch 1992).,Blazars are characterized by fast variability in different wavebands from radio to gamma and in few cases by TeV radiation (Urry Padovani 1995; Punch 1992).654 Alauv of the objects reveal “superluuinal” jets. which indicate that matter of the jet moves ucarly toward us with relativistic speed (Blandford Rees 1975).," Many of the objects reveal “superluminal” jets, which indicate that matter of the jet moves nearly toward us with relativistic speed (Blandford Rees 1978)."655 The variability of the objects may be connected with outbursts of matter and cnerey frou the uucleus aud propagation of shocks alone the collimated relativistic jet (Blaudtord Ikónuiel 1979: Marscher 1980)., The variability of the objects may be connected with outbursts of matter and energy from the nucleus and propagation of shocks along the collimated relativistic jet (Blandford Könnigl 1979; Marscher 1980).656 This model was further developed for investigation of different radio properties of radiogalaxies aud quasars (Aller. Aller Ilushes 1985: Ilushes. Aller Aller 1985).," This model was further developed for investigation of different radio properties of radiogalaxies and quasars (Aller, Aller Hughes 1985; Hughes, Aller Aller 1985)."657 The back extrapolated time of VLBI outbursts apoxoxinatelv coincides with strong optical. Xrav and gamarav flares (παπα 1977: Belokon 1988: Wrichbamm et al.," The back extrapolated time of VLBI outbursts approximately coincides with strong optical, X–ray and gamma–ray flares (Kinman 1977; Belokon 1988; Krichbaum et al."658 1995: Otterbein ct al., 1995; Otterbein et al.659 1998) which is in favor of this model., 1998) which is in favor of this model.660 The idea of matter outbursts from centers of galaxies was first proposed by Απιζαιμιμμαι (1958). aud this has Όσοι confirmed bv miuerous observations.," The idea of matter outbursts from centers of galaxies was first proposed by Ambartsumian (1958), and this has been confirmed by numerous observations."661 The outbursted matter nav be a normal electrondon asma. or it oma consist mainly of electronpositrou ors.," The outbursted matter may be a normal electron–ion plasma, or it may consist mainly of electron–positron pairs."662 Prior to the Compton Observatory measurements. xediction of strong. collimated eanunaray eniüssion aud electron/positron cascades in ACN relativistic jets was uade bv the model of Lovelace. MacáAuslau Durus (1979): Durus Lovelace (1982).," Prior to the Compton Observatory measurements, prediction of strong, collimated gamma–ray emission and electron/positron cascades in AGN relativistic jets was made by the model of Lovelace, MacAuslan Burns (1979); Burns Lovelace (1982)."663 More receutly. a number of theoretical models have been developed ) explain the observed eanuuaray oenmuüsson of ACNs.," More recently, a number of theoretical models have been developed to explain the observed gamma–ray emission of AGNs."664 Iu most of the models the gammarav radiation is ascribed to imvorse Compton (IC) scattering of relativistic electrous and possibly positrous (Lorentz factors 5~107— 107) of a jet having relativistic bulk motion (Lorentz factor D 10) with soft photons (energies 1103 eV}., In most of the models the gamma–ray radiation is ascribed to inverse Compton (IC) scattering of relativistic electrons and possibly positrons (Lorentz factors $\gamma \sim 10^2-10^5$ ) of a jet having relativistic bulk motion (Lorentz factor $\Gamma \sim 10$ ) with soft photons (energies $\sim 1-10^2$ eV).665 The soft photons cau arise from the svuchrotron enission ofthe relativistic clectrous in the jet as in the (SSC) models (Maraschi. (ακομα Celotti 1992: XMLhwscher Bloor 1992). or from the direct or scattered thermal radiatiou from au accretiou disk (Denuer. Schlickeiser Masticliadis 1992: Dlaudford 1993: Sikora. Degeliuau Rees 1991). or from a sinele cloud. (ποπ Madau 1996).," The soft photons can arise from the synchrotron emission of the relativistic electrons in the jet as in the (SSC) models (Maraschi, Ghisellini Celotti 1992; Marscher Bloom 1992), or from the direct or scattered thermal radiation from an accretion disk (Dermer, Schlickeiser Mastichiadis 1992; Blandford 1993; Sikora, Begelman Rees 1994), or from a single cloud (Ghisellini Madau 1996)."666 Iu a very different class of models. ultra higheucrev protons (Lorentz factors >105) are postulated to cause a cascade. the product particles of which produce the observed radiation λα] Biermamun 1992: Protheroe Biermann 1997).," In a very different class of models, ultra high--energy protons (Lorentz factors $>10^6$ ) are postulated to cause a cascade, the product particles of which produce the observed radiation (Mannheim Biermann 1992; Protheroe Biermann 1997)."667 The idea of ονπας flux outmusts of cherey to the jet is based ou the fact that the| central regions of the disk and a black hole may acciiulate strong poloidal magnetic field of the order B—(1P10)G., The idea of Poynting flux outbursts of energy to the jet is based on the fact that the central regions of the disk and a black hole may accumulate strong poloidal magnetic field of the order $B\sim (10^3 - 10^4)~{\rm G}$.668 Rotation of this configuration leads to generation of the Povuting fiux. which is a “permanent machine” for matter acceleration (Blandford Zuajek 1977: Lovelace. Wang Sullsaucn 1987: Livio. Ovilvio Pringle 1998).," Rotation of this configuration leads to generation of the Poynting flux, which is a “permanent machine” for matter acceleration (Blandford Znajek 1977; Lovelace, Wang Sulkanen 1987; Livio, Ogilvio Pringle 1998)."669 Receutly. this idea was further developed aud applied to gammarav Blazars by Romanova Lovelace (1997) (hereafter ΙΤ). Coleate Li (1998) aud by Levinson (1998).," Recently, this idea was further developed and applied to gamma–ray Blazars by Romanova Lovelace (1997) (hereafter RL97), Colgate Li (1998) and by Levinson (1998)."670 RL97 proposed that the main driviug force for the observed superlininual jet compoucuts is a finite amplitude discoutinuity in a Povuting flux jet., RL97 proposed that the main driving force for the observed superluminal jet components is a finite amplitude discontinuity in a Poynting flux jet.671" A rapid change iu the Povutiug jet outflow from a disk can result from iuplosive accretion iu a disk with an ordered magnetic field (Lovelace. Romanova Newman 1991, hereafter LRN91)."," A rapid change in the Poynting jet outflow from a disk can result from implosive accretion in a disk with an ordered magnetic field (Lovelace, Romanova Newman 1994, hereafter LRN94)."672 Propagation of newly expelled electromagnetic feld aud matter from the disk with higher velocity than the old jet can lead to the formation ofa pair of shock waves as in the non.relativistic hydrodynamic flows in optical jet iu protostellar svstenis (Raga ct al., Propagation of newly expelled electromagnetic field and matter from the disk with higher velocity than the old jet can lead to the formation of a pair of shock waves as in the non–relativistic hydrodynamic flows in optical jet in protostellar systems (Raga et al.673 1990)., 1990).674 Particle acceleration iun the frout lav result from the shocks aud/or from amulilation and reconnection of oppositely directed macuetic fields iu the front (Romanova Lovelace 1992. hereafter RL92: Lovelace. Newnan Romanova 1997. hereafter LNR97).," Particle acceleration in the front may result from the shocks and/or from annihilation and reconnection of oppositely directed magnetic fields in the front (Romanova Lovelace 1992, hereafter RL92; Lovelace, Newman Romanova 1997, hereafter LNR97)."675 Tere. we consider the differcut aspects of the flares," Here, we consider the different aspects of the flares"676BHMFs estimated by using the correlation of the black hole mass with host galaxy luminosity are adopted in this work details).,BHMFs estimated by using the correlation of the black hole mass with host galaxy luminosity are adopted in this work .677. The continuity equation (133) for black hole number density is integrated from 2=zx by using Eqs. (2))-(4)), The continuity equation \ref{bhmevol2}) ) for black hole number density is integrated from $z=z_{\rm max}$ by using Eqs. \ref{nagn}) \ref{barlambda}) )678 and assuming the duty cycle is 0.5 at σι., and assuming the duty cycle is 0.5 at $z_{\rm max}$.679 The final results are insensitive to the initial conditions at cy..., The final results are insensitive to the initial conditions at $z_{\rm max}$.680 In all our calculations. cy.=d is adopted. because the Eddington ratio distributions are calculated from a sample of AGN with 2<+2006).," In all our calculations, $z_{\rm681max}=4$ is adopted, because the Eddington ratio distributions are calculated from a sample of AGN with $z<4$."682".. The resulted BHMFs of AGN relies at low redshifts are insensitive to the value of zi,4«. because the fraction of local black hole mass accreted at high redshifts can be neglected."," The resulted BHMFs of AGN relics at low redshifts are insensitive to the value of $z_{\rm max}$, because the fraction of local black hole mass accreted at high redshifts can be neglected."683 We plot our results with different values of ρω in the upper panel of Fig. 3..," We plot our results with different values of $\eta_{\rm rad}$ in the upper panel of Fig. \ref{fig3},"684 which indicates that the measured local BHMF cannot be fitted with any values of tcp., which indicates that the measured local BHMF cannot be fitted with any values of $\eta_{\rm rad}$.685 This is due to the mean Eddington ratios derived in this work being ~0.1.—0.3. which deviates significantly from A~| suggested in most of the previous works2004).," This is due to the mean Eddington ratios derived in this work being $\sim 0.1-0.3$, which deviates significantly from $\lambda \sim 1$ suggested in most of the previous works."686. In our calculations. we only consider the uncertainty of the number density in the bolometric LF given by(2007).," In our calculations, we only consider the uncertainty of the number density in the bolometric LF given by."687" effticiency. in which μαι remains constant for Aij,«107 and increases as a power-law with black hole mass for Adi,22107: in our calculations."," fficiency, in which $\eta_{\rm rad}$ remains constant for $M_{\rm bh}< 10^8$ and increases as a power-law with black hole mass for $M_{\rm bh}\ge 10^8$: in our calculations."688 We find that the measured local BHMF can be roughly reproduced by the BHMF of AGN relies provided sno=0.08 and g=0.36 are adopted (see the lower panel in Fig. 35.," We find that the measured local BHMF can be roughly reproduced by the BHMF of AGN relics provided $\eta_{\rm689rad,0}=0.08$ and $q=0.36$ are adopted (see the lower panel in Fig. \ref{fig3}) )."690 tried to derive the BHMFs with redashifts up to 2~1 from the spheroid LF of early-type galaxies using the correlation between the spheroid luminosity and black hole mass (see their paper for the details). which provide further constraints on the model calculations for the cosmological evolution of massive black holes.," tried to derive the BHMFs with redashifts up to $z\sim6911$ from the spheroid LF of early-type galaxies using the correlation between the spheroid luminosity and black hole mass (see their paper for the details), which provide further constraints on the model calculations for the cosmological evolution of massive black holes."692" The model calculations performed with this ij, dependent radiative efficiency (Equation 16)) are compared with the spheroid-BHMFs derived by in Fig. 4..", The model calculations performed with this $M_{\rm bh}$ -dependent radiative efficiency (Equation \ref{etarad}) ) are compared with the spheroid-BHMFs derived by in Fig. \ref{fig4}. .693 We find that calculated BHMFs of AGN relics can roughly reproduce the spheroid-BHMFs at different redshifts either for luminosity-dependent or luminosity-independent corrections for the thick AGN., We find that calculated BHMFs of AGN relics can roughly reproduce the spheroid-BHMFs at different redshifts either for luminosity-dependent or luminosity-independent corrections for the Compton-thick AGN.694 As inthe most previous works. we implicitly assume that the black hole growth is dominated by mass accretion in bright AGN. while some inactive black holes may still be accreting gases. though their mass accretion rates are very low.," As in the most previous works, we implicitly assume that the black hole growth is dominated by mass accretion in bright AGN, while some inactive black holes may still be accreting gases, though their mass accretion rates are very low."695 If the duration of the accretion in these objects is as long as the Hubbletimescale.," If the duration of the accretion in these objects is as long as the Hubbletimescale,"696Parameters of the four sets aro given du Table 1...,Parameters of the four sets are given in Table \ref{sim}.697 All siuul:Vols included 128? dark matter particles. au equal Πιο of baryonic cells on a quasi-Laerangian moving mesh. and about 3 wullion steHar particles that formed continuously during the simulation.," All simulations included $128^3$ dark matter particles, an equal number of baryonic cells on a quasi-Lagrangian moving mesh, and about 3 million stellar particles that formed continuously during the simulation."698 The nominal PAvatial resolution of simulations with the box size of Ui.1Mpe was fixed at 172 conioviue kpc. with re real resolution beige a actor of two worse.," The nominal spatial resolution of simulations with the box size of $4h^{-1}\dim{Mpc}$ was fixed at $1h^{-1}$ comoving kpc, with the real resolution being a factor of two worse."699 Simulations with the box size of Sh.tMpe had je twice worse spatial resolution., Simulations with the box size of $8h^{-1}\dim{Mpc}$ had the twice worse spatial resolution.700 Iu all CHSCRS a Hat cosmology was assumed. with Qxy=|Qa. iixl normalization of je primordial fluctuations was determined either roni theWAZAP data (Sperecl et 22003) for sets Al aud A&. or from theCODE data (White Bunn 1995).," In all cases a flat cosmology was assumed, with $\Omega_{\Lambda,0} =7011-\Omega_{m,0}$, and normalization of the primordial fluctuations was determined either from the data (Spergel et 2003) for sets A4 and A8, or from the data (White Bunn 1995)."702 Notice that a small change iu he slope of the prinordial power-hwe spectrum D nuakes a siguificaut effect ou the amount of the siuall-scale power due to a large leverage ari from ΑΠΟ scales to the teus-of-kpe scales which are Huportanut for reionization., Notice that a small change in the slope of the primordial power-law spectrum $n$ makes a significant effect on the amount of the small-scale power due to a large leverage arm from CMB scales to the tens-of-kpc scales which are important for reionization.703 Star formation is incorporated in the simulations using a phenomenological Schliaid law. which introduces two free parameters: the star formation cficieucy egg (as defined by ((1) of Cnediu 2000) and the ioniziue radiation efficicney ειν (defined as the energev iu ionizing photous per uuit of the rest euergy of stellar particles).," Star formation is incorporated in the simulations using a phenomenological Schmidt law, which introduces two free parameters: the star formation efficiency $\epsilon_{\rm SF}$ (as defined by (1) of Gnedin 2000) and the ionizing radiation efficiency $\epsilon_{\rm UV}$ (defined as the energy in ionizing photons per unit of the rest energy of stellar particles)."704 The star formatioi efficiency egg is Chosen so as to normalize the elobalo star formation rate iu the simulation at 2=| to the observed value from Steidel et ((2OL). whereas the ultraviolet radiation efficiency ec vds only weakly constrained bv the (hiehlv uncertain) mean plotoionization rate at oloL.," The star formation efficiency $\epsilon_{\rm SF}$ is chosen so as to normalize the global star formation rate in the simulation at $z=4$ to the observed value from Steidel et (2001), whereas the ultraviolet radiation efficiency $\epsilon_{\rm UV}$ is only weakly constrained by the (highly uncertain) mean photoionization rate at $z\sim4$."705 The reslift of reionization strongly depends on eps aud is not in fact predicted in a sinulation. but can be changed over a reasonable range depending on the assunued value of ep.," The redshift of reionization strongly depends on $\epsilon_{\rm UV}$ and is not in fact predicted in a simulation, but can be changed over a reasonable range depending on the assumed value of $\epsilon_{\rm UV}$."706 Each of the simulatious sets included in Table 1 in fact included several iudividual sinmlatious with different values of ειν., Each of the simulations sets included in Table \ref{sim} in fact included several individual simulations with different values of $\epsilon_{\rm UV}$.707 However. since the simulations are quite expensive. it is not possible to cover a large rauge of ei iu a eiven set.," However, since the simulations are quite expensive, it is not possible to cover a large range of $\epsilon_{\rm UV}$ in a given set."708 Typically. only 2 or 3 simulations per set have been performed aud the results are then interpolated between the simulations.," Typically, only 2 or 3 simulations per set have been performed and the results are then interpolated between the simulations."709 This procedure is fully described in &1L.., This procedure is fully described in \ref{results}.710 Reiouization is a process. not an event.," Reionization is a process, not an event."711 Iu fact. whole process of reiouization is quite extende GN.05. 10). and can be generically separate iuto three stages: (1) tlestage. iu which individual rregious around the sources of ionization expan and merece in the low density ICAL (1) thestage. in which all individual rregious overlap. aud last remnants of the neutra low density eas quickly clisappear. aud (ii) thestage. iu which remaining ligh density gas is being ionized frou he outside. until neutral eas remains only iu some of the highest density regions. which would o identified as Lyviiuilinit svstem in the absorption spectra," In fact, whole process of reionization is quite extended $\Delta z\sim5-10$ ), and can be generically separated into three stages: (i) the, in which individual regions around the sources of ionization expand and merge in the low density IGM, (ii) the, in which all individual regions overlap, and last remnants of the neutral low density gas quickly disappear, and (iii) the, in which remaining high density gas is being ionized from the outside, until neutral gas remains only in some of the highest density regions, which would be identified as Lyman-limit system in the absorption spectra"712sharp gradieut iu modified opacity over this narrow region (or equivaleutly a sharp eracicut iu the Z profile) it will (e possible to obain composition profiles which are not Hat just below the convection zone.,sharp gradient in modified opacity over this narrow region (or equivalently a sharp gradient in the $Z$ profile) it will be possible to obtain composition profiles which are not flat just below the convection zone.713 If the exadieu in Z xofile were to be iicreased by a factor of five over tha iu Proffitt (1991)). i Wolld be possible to get au VY xofile with eradieut simuar to that in Model ο at the ase of he convection zone.," If the gradient in $Z$ profile were to be increased by a factor of five over that in Proffitt \cite{pro94}) ), it would be possible to get an $X$ profile with gradient similar to that in Model S at the base of the convection zone."714 TMIS. ος1uposition profiles obtained using simular treat11011 of diflusion for both helium ancl LCAVV elements are no COIsistent with inverted profiles unless the eradieut vaUshes as in the case of turbule wining (Richard et al. | 006)).," Thus, composition profiles obtained using similar treatment of diffusion for both helium and heavy elements are not consistent with inverted profiles unless the gradient vanishes as in the case of turbulent mixing (Richard et al. \cite{ric96}) )."715" These results are cousiste with couchsions drawn from the oscillatory signal iu the Yequenicies (Basu Aitia 1001: Basu 1997)). which also supports the oresence of tur»ileut imixiug in this reei"""," These results are consistent with conclusions drawn from the oscillatory signal in the frequencies (Basu Antia \cite{ba94}; Basu \cite{b97}) ), which also supports the presence of turbulent mixing in this region."716 οαν evidence is also sueeestedsuge by the inversion of sotnd speed (Cough ot al. 1996)]., Similar evidence is also suggested by the inversion of sound speed (Gough et al. \cite{dog96}) ).717 All this seems to indicate that the region just be owt1ο colVecion zone 1s probaY mixed (Richard et al. |9906) ), All this seems to indicate that the region just below the convection zone is probably mixed (Richard et al. \cite{ric96}) )718 by some process., by some process.719 Tn contrast. iu the central region around r=0251. —16 Composition profile iu the Sun aypears to be steeper —iui that in the solar modol. perhaps sugeesting that musing is walisely to have occurred i1 this region of solar oeterior.," In contrast, in the central region around $r=0.25R_\odot$ the composition profile in the Sun appears to be steeper than that in the solar model, perhaps suggesting that mixing is unlikely to have occurred in this region of solar interior."720 Frou Fie., From Fig.721 3 1 can he seen that AN las a negative eracicut iu tjo lnuer COLO around r=OLR... which would iuplv hat the WN prcMle in the Sun is smoother thau that iu he ioccl.," \ref{invtx} it can be seen that $\delta X$ has a negative gradient in the inner core around $r=0.1R_\odot$, which would imply that the $X$ profile in the Sun is smoother than that in the model."722 This difference has. prestumalbly been considered as a lint of nuxiug 1i the core (Coug[um et al. | 996))., This difference has presumably been considered as a hint of mixing in the core (Gough et al. \cite{dog96}) ).723 Tlowever. consideriis the fact hat the .X eracdicut Is very stee) in tlUs reelou. the «iffereuce 1ρα extremely sinall and mixing if any. colId only have taken place iu the very carly historv of solar evolution or the nüxiug process Is extroniclv slow.," However, considering the fact that the $X$ gradient is very steep in this region, the difference is extremely small and mixing if any, could only have taken place in the very early history of solar evolution or the mixing process is extremely slow."724 A more likely cause of this difference is the errors iu nuccar reaction rates., A more likely cause of this difference is the errors in nuclear reaction rates.725 It is also possible that this clifferenee could arise from uncertainties in the primary inversion in the core., It is also possible that this difference could arise from uncertainties in the primary inversion in the core.726 Using the inverted T aud NX profies it is possible to estimate the neutrino fluxes., Using the inverted $T$ and $X$ profiles it is possible to estimate the neutrino fluxes.727 From the results in Table 1. --- appears that these neutijuo fluxes are significantly lower than those in the staridard solar model of BPO. with dithsion of helium aud reavy clements.," From the results in Table 1, it appears that these neutrino fluxes are significantly lower than those in the standard solar model of BP95, with diffusion of helium and heavy elements."728 Some of the iference could be due to xnnewhat lower cross-section for pp reaction used bv BPS)5., Some of the difference could be due to somewhat lower cross-section for pp reaction used by BP95.729 A part of the difference will also arise from the diffslo of heavy. elements;, A part of the difference will also arise from the diffusion of heavy elements.730 As areued earlier there are £ooc reasons to believe that the region inunuediatelv below the convection zo1ο ds mixed and ποιος the heavy elemeit abundance will not increase as steeply as in the iode ο| BPO., As argued earlier there are good reasons to believe that the region immediately below the convection zone is mixed and hence the heavy element abundance will not increase as steeply as in the model of BP95.731 A reduction iu Z value inside the core wi] reduce. the opacities and hence the eniperature and the correspoucliig neutrino fluxes., A reduction in $Z$ value inside the core will reduce the opacities and hence the temperature and the corresponding neutrino fluxes.732 However. the compfcxd icutrino fluxes ni seismic models are sienificantly larecv than the observed values.," However, the computed neutrino fluxes in seismic models are significantly larger than the observed values."733 Iu fact. it its been found (Awla Chitre 1997)) that even if arbitrary variations 1n opacities are allowed it is not possible to reduce the ueutriuo fluxes iu any two solar neutrino experiments siiuultauecouslv to the observed values.," In fact, it has been found (Antia Chitre \cite{ac97}) ) that even if arbitrary variations in opacities are allowed it is not possible to reduce the neutrino fluxes in any two solar neutrino experiments simultaneously to the observed values."734 Thus. it appears that he solution of solar neutriuo problemi should be sought iu crlus of neutrino properties. thoieh the seisnic models can be used to constrain these solutions.," Thus, it appears that the solution of solar neutrino problem should be sought in terms of neutrino properties, though the seismic models can be used to constrain these solutions."735 Since the neutiiuo fiuxes in the standard. solar encl of DP95 are somewlha clifferent from those in the seismic models. the coustraiuts on the particle physics solution (c.g. Tata Lausacker 1997)) could chauge when seine models are usec.," Since the neutrino fluxes in the standard solar model of BP95 are somewhat different from those in the seismic models, the constraints on the particle physics solution (e.g., Hata Langacker \cite{hat97}) ) could change when seismic models are used."736 We have demonstrated tiif our inversion technique procuces reasonably well the thermal aud composition profiles in the Suus intenor. with the knowlecexορ of the sound speed aac σαςτν inferred fou the accurately observed. frequecies. based on the mechanical and thermal equilibriuni constraints goveruiug the SOLO structure.," We have demonstrated that our inversion technique produces reasonably well the thermal and composition profiles in the Sun's interior, with the knowledge of the sound speed and density inferred from the accurately observed frequencies, based on the mechanical and thermal equilibrium constraints governing the solar structure."737 These seiswically determined temperatirea xd hydrogen abunudauce profies in the Sun turu out to IO close to those obtained with a standard solar nodel., These seismically determined temperature and hydrogen abundance profiles in the Sun turn out to be close to those obtained with a standard solar model.738 T1C sxnall departures cot14 he due to a variety of processes arising fron diffusion acl ncertaiuties mn nuclear reaction rates. equation of state. jieavy clement abuidances or even the presence o |a dnagnetic feld.," The small departures could be due to a variety of processes arising from diffusion and uncertainties in nuclear reaction rates, equation of state, heavy element abundances or even the presence of a magnetic field."739 It is remarkable that the neutrino fhxes in the framework of he seiuuic inodel come out to be close to those prediced bv the standard solar model. assuniue that the opacilos are not very different from the cuenutlv accepted OPAL values.," It is remarkable that the neutrino fluxes in the framework of the seismic model come out to be close to those predicted by the standard solar model, assuming that the opacities are not very different from the currently accepted OPAL values."740 There is thus a strong hint of the particle plivsics solution of the solar neutrino puzzle!, There is thus a strong hint of the particle physics solution of the solar neutrino puzzle!741"Weak aabsorbers are defined to be those with rest frame equivalent widths HW,«0.3A and represent a dillerent population than strong aabsorbers (Righyetal.2002:Nestor2005).","Weak absorbers are defined to be those with rest frame equivalent widths $W_r < 0.3~\Ang$ and represent a different population than strong absorbers \citep{Rig02, Nest05}."742". Strong, aabsorbers are known (o be associated. with huninous galaxies (within ~38h!(L/L*) kpc) (Bergeron&Doissé1991:Bergeronοἱal.1997:Steidel 1995).. while weak aabsorbers are not tvpically seen within a 50/5+ kpe impact parameter of a huninous ealaxv (Rigbyetal.2002.butseeChurchill(2005). [or someexceptions)."," Strong absorbers are known to be associated with luminous galaxies (within $\sim 38 h^{-1} (L/L^*)^{0.15}$ kpc) \citep{Berg91, Berg92, LeBrun93, Steid94, Steid97, Steid95}, while weak absorbers are not typically seen within a $50 h^{-1}$ kpc impact parameter of a luminous galaxy \citep[but see \citet{Church05} for some."743 The exact environment(s) and process/processes that give rise to weak aabsorbers is not vet known. but they may arise in dwarf galaxy environments. in the cosmic web surrounding galaxies. and/or in hieh velocity clouds.," The exact environment(s) and process/processes that give rise to weak absorbers is not yet known, but they may arise in dwarf galaxy environments, in the cosmic web surrounding galaxies, and/or in high velocity clouds."744 Weak aabsorbers generally correspond to sub-Lynian limit svstems (15.8<logΕΠ)16.5[em. 7]) (Churchilletal.1999b:Rigbyοἱ2002:Churchill2000). ancl (they have metallicities of at least solar and as high as solar or even supersolar 2003:Simcoeetal. 2006).," Weak absorbers generally correspond to sub-Lyman limit systems $15.8 < \log{N(\HI)} < 16.8 [\cmsq]$ ) \citep{Church99b,Rig02,Church00} and they have metallicities of at least solar and as high as solar or even supersolar \citep{Rig02,Char03,Sim05}."745. In addition. the rratio of some absorbers does not allow for a-enhancement. (hus Tvpe Ia supernovae mist contribute as well as Type II.," In addition, the ratio of some absorbers does not allow for $\alpha$ -enhancement, thus Type Ia supernovae must contribute as well as Type II."746 Because Type Ia supernovae cannot eject metals to large distances. metals must be produced situ.," Because Type Ia supernovae cannot eject metals to large distances, metals must be produced ”."747 The number statisties and kinematics of single cloud weak aabsorbers lend themselves best to a flattened geometry and suggest that the absorbers may be produced by higher density regions in (he cosmic web (Milutinoviéetal.2005)., The number statistics and kinematics of single cloud weak absorbers lend themselves best to a flattened geometry and suggest that the absorbers may be produced by higher density regions in the cosmic web \citep{Milni05}.748. aabsorption (vpically arises in a high density region ~ 1100 pes thick which is often surrounded by a lower density region that gives rise to high ionization aabsorption centered at the same velocity as the citepChar03.Sim05..," absorption typically arises in a high density region $\sim$ 1–100 pcs thick which is often surrounded by a lower density region that gives rise to high ionization absorption centered at the same velocity as the \\citep{Char03,Sim05}."749 Additional low density regions producing aabsorption. that are detected at different velocities (han.Mglt.. often exist.," Additional low density regions producing absorption, that are detected at different velocities than, often exist."750 While most weakaabsorbers can be fit by a single Voiet prolile component. about one third have multiple components (Churchilletal.2000:Lynch 2006)..," While most weakabsorbers can be fit by a single Voigt profile component, about one third have multiple components \citep{Church00,Lynch06}. ."751 Some of these multiple cloud weak, Some of these multiple cloud weak752xoduce slightly αποο line profiles. ie. curved sectors with a shape that depends on the depth of line ornation (c.g. Dravius 1987)).,"produce slightly asymmetric line profiles, i.e. curved bisectors with a shape that depends on the depth of line formation (e.g. Dravins \cite{dra87}) )."753 The question is therefore if the atinospiere velocity broadening determined from he two lines is also vedid for the lue., The question is therefore if the atmospheric velocity broadening determined from the two lines is also valid for the line.754 Due to the low excitation potential of the ΠΕ resonance line it is probably formed somewhat higher in the atmosphere than the irom hues., Due to the low excitation potential of the lithium resonance line it is probably formed somewhat higher in the atmosphere than the iron lines.755 Iu the case of a «rastic increase of Ee; to Husteacl of the value derived from the ]liues. ) decreases fi9Li) to about zero.," In the case of a drastic increase of $\Gamma_G$ to instead of the value derived from the lines, ) decreases $f(\Lisix)$ to about zero."756 One could. also inaeime that the σαiue in Hxd has a red asvaiuuetrv that mumics the ddoublet although no such asviunietry is secu du the profiles of the lines., One could also imagine that the line in and has a red asymmetry that mimics the doublet although no such asymmetry is seen in the profiles of the lines.757" Towever, such possible effects have to occur for and oulv. because we cau not allow a reduction of F(PLA) for the other three stars which have FLA)~0.00. when the atinospheric velocity broadening of the ]lines is adoped."," However, such possible effects have to occur for and only, because we can not allow a reduction of $f(\Lisix)$ for the other three stars which have $f(\Lisix) \simeq 0.00$, when the atmospheric velocity broadening of the lines is adopted."758 As seen from Table 1 there are indeed siguificaut differences in the atmospheric parameters of the two “ITD stars and the three CIIRO stars that could induce some differential effects in the broadening of the aud ines., As seen from Table 1 there are indeed significant differences in the atmospheric parameters of the two `HD' stars and the three `HR' stars that could induce some differential effects in the broadening of the and lines.759 has a lower eravity and has a üeher than the other three stars., has a lower gravity and has a higher than the other three stars.760 A lint that there may be systematic differeuces m the convective pattern between he two eroups of stars cones from the small changes of he laboratory wavelenetls uceded to optimize tle 4? fit of the aud ies (seo Table 5)., A hint that there may be systematic differences in the convective pattern between the two groups of stars comes from the small changes of the laboratory wavelengths needed to optimize the $\chi^2$ fit of the and lines (see Table 5).761 The apparent helioceutrie radial velocities Gucliding eravitational redshift aud convective dueshift) is deteriuiued from the two ines., The apparent heliocentric radial velocities (including gravitational redshift and convective blueshift) is determined from the two lines.762 Deuce. the sum of the wavelength shifts for these wo lines is zero by definition.," Hence, the sum of the wavelength shifts for these two lines is zero by definition."763 As secu. the waveleneth slüft of the LB1ο is always positive.," As seen, the wavelength shift of the line is always positive."764 The average value is ({corresponding to a redshift of oof the lime relative to the limes) aud the rims scatter is3., The average value is (corresponding to a redshift of of the line relative to the lines) and the rms scatter is.765luauA. This is more iui the expected error of the laboratory wavelenueths., This is more than the expected error of the laboratory wavelengths.766 Iu particular. we note that the recshift for aud are lower than the redshift for the other three PAars.," In particular, we note that the redshift for and are lower than the redshift for the other three stars."767 Although this couk be accidental. it is a warning that there may be differential effects in the couvective lue broadening.," Although this could be accidental, it is a warning that there may be differential effects in the convective line broadening."768 Clearly. this problem should be further studied by applying receulv consructed Inhomogeneous 3D hvdioclvnauuical iiod ‘Latinospheres (Asplund et al. 19993) ," Clearly, this problem should be further studied by applying recently constructed inhomogeneous 3D hydrodynamical model atmospheres (Asplund et al. \cite{asp99}) )"769in he analvsis oftje line., in the analysis of the line.770 According to standard stellar models the depletion. of lithium is a stroug function of stellar mass (Piusouucault, According to standard stellar models the depletion of lithium is a strong function of stellar mass (Pinsonneault771llere. we present an alternative moment-based approach to solving the realistic coagulation kernel in which the integer moments appear directly.,"Here, we present an alternative moment-based approach to solving the realistic coagulation kernel in which the integer moments appear directly."772 Unlike the previous case of8 2.2.1. where the double integral of Eq. (," Unlike the previous case of 2.2.1, where the double integral of Eq. ("7735) is used to get the functions of my. Dy ancl D». we only integrate over one mass variable (i.e.. only integrate one of the integrals). defining the functions where the form of the kernel A(m.iml) is the same that in 2.2.1.,"5) is used to get the functions of $m_L$ , $\Gamma_0$ and $\Gamma_2$, we only integrate over one mass variable (i.e., only integrate one of the integrals), defining the functions where the form of the kernel $K(m,m^\prime)$ is the same that in 2.2.1."774 We then fit Cy and C» with a finite series in fractional powers of m in the same manner as given in Eq. (, We then fit $C_0$ and $C_2$ with a finite series in fractional powers of $m$ in the same manner as given in Eq. (77515).,15).776 Substituting these functions in place of one of the integrals (sav over /). we may integrate over m. (o gel where we have made use of equations (8) and (9) to express the solution in ternis of the integer moments ο=0.1.2.," Substituting these functions in place of one of the integrals (say over $m^\prime$ ), we may integrate over $m$ to get where we have made use of equations (8) and (9) to express the solution in terms of the integer moments $k = 0,1,2$."777" Here. ji,=(ο)Αθ) Up,4=My,400)/M3(0). Mí=Ιλιον and 0Xp;€1."," Here, $\mu_{p_i} = M_{p_i}(0)/778M_0(0)$, $\nu_{p_i+1} = M_{p_i+1}(0)/M_2(0)$, $M^\prime_k = M_k(t)/M_k(0)$, and $0\leq p_i \leq 1$."779" The C, are fairly smooth functions over a large range of particle radii: however. (he accuracy. of fitting a sinele series in [fractional moments over a very broad range of particle sizes (ie.. over many orders of magnitude) may drop olf sienificantlv as the broadness of the range increases."," The $C_k$ are fairly smooth functions over a large range of particle radii;, however, the accuracy of fitting a single series in fractional moments over a very broad range of particle sizes (i.e., over many orders of magnitude) may drop off significantly as the broadness of the range increases."780 This issue may be cireiumvented by elploving a piecewise fit to the integrated kernels Cy., This issue may be circumvented by employing a piecewise fit to the integrated kernels $C_k$.781 It is interesting (o note that bv this definition of Ορ. we have effectively. accomplished what we set out (o do in our discussion at the beginning of 2.2. that is. defining the coagulation kernel in terms of finite series in powers of the mass m.," It is interesting to note that by this definition of $C_k$, we have effectively accomplished what we set out to do in our discussion at the beginning of 2.2, that is, defining the coagulation kernel in terms of finite series in powers of the mass $m$."782 The difference here is that wehave done so through the first integral of the kernel. and not the kernel itself.," The difference here is that wehave done so through the first integral of the kernel, and not the kernel itself."783 This, This784Preprint Oue of the more surprising results of the Conptou Camuna-Ray Observatory (CORO) was the EGRET discovery of au 18 CoV photon associated with CRB 910217 (Ihulev 1991)., One of the more surprising results of the Compton Gamma-Ray Observatory (CGRO) was the EGRET discovery of an 18 GeV photon associated with GRB 940217 (Hurley 1994).785 About a half-dozeu bursts were seen over the course of the CORO iiission with photons above 100 MeV (Catelli 1998. Diugus 2003).," About a half-dozen bursts were seen over the course of the CGRO mission with photons above 100 MeV (Catelli 1998, Dingus 2003)."786 Since the GRD spectral energy. distribution at lower energies has jen well characterized by a imodifed power law with oeak fluxes at enereies of the order of 200 IeV. the existence of photous at energies 105 times higher puts a senificaut constraint on any viable model of the CRB xXienomenon.," Since the GRB spectral energy distribution at lower energies has been well characterized by a modified power law with peak fluxes at energies of the order of 200 KeV, the existence of photons at energies $10^4$ times higher puts a significant constraint on any viable model of the GRB phenomenon."787 This has been a subject of ereat interest or niüssous that followed ECRET., This has been a subject of great interest for missions that followed EGRET.788 Prior to launch of he Fermi Camuna-ray Space Telescope. it was possible o speculate that the LAT instrmucut would detect nore than 200 CRD eveuts per vear (Dineus. 2003).," Prior to launch of the Fermi Gamma-ray Space Telescope, it was possible to speculate that the LAT instrument would detect more than 200 GRB events per year (Dingus, 2003)."789" Iu the two wear period since the launch of the Fermi CGauunaray Space Telescope. the Canmunarayv Durst Monitor (GDM) has reported approximately 175 CRBs. ic,"," In the two year period since the launch of the Fermi Gamma-ray Space Telescope, the Gamma-ray Burst Monitor (GBM) has reported approximately 475 GRBs, ie."790 a rate of about 250 per νους., a rate of about 250 per year.791 Over essentiallv the sale period. only 17 bursts have been identified by the Fermi/LAT.," Over essentially the same period, only 17 bursts have been identified by the Fermi/LAT."792 We now see that the range of CRB photon energies extends over a scale of LO® but the physical dynamics of these phenomena are still not. understood., We now see that the range of GRB photon energies extends over a scale of $10^6$ but the physical dynamics of these phenomena are still not understood.793 This is coupled to the question of whether high energy photons are associated with all GRBs or only with a snuadl sub-class., This is coupled to the question of whether high energy photons are associated with all GRBs or only with a small sub-class.794 Since the Ferma müssionu is unlikely to be duplicated any time soon. there is some urgenev to assuiues that the mnaxiuuni information is bee extracted from this valuable facility.," Since the Fermi mission is unlikely to be duplicated any time soon, there is some urgency to assuring that the maximum information is being extracted from this valuable facility."795 Thus. our group has set about developiug techniques for chlareine the number of οπλο bursts identified with high energy photon enission. 1e.," Thus, our group has set about developing techniques for enlarging the number of gamma-ray bursts identified with high energy photon emission, ie."796 above LOO MeV. The first result of this effort has established the correlation of two Sav ft/XRT-localized bursts. CRB O80905À. and CRB 091208D. with high cucrey photons in the Ferm//LAT detector (Akerlof cl al. (," above 100 MeV. The first result of this effort has established the correlation of two $Swift$ /XRT-localized bursts, GRB 080905A and GRB 091208B, with high energy photons in the $Fermi$ /LAT detector (Akerlof el al. ("7972010). hereafter ALO).,"2010), hereafter A10)."798 The statistical technique enploved is the matehedfilter: method. most familar to those detecting signals in the time domain.," The statistical technique employed is the $matched~filter$ method, most familiar to those detecting signals in the time domain."799 The uuderliug assunrptiou is that the characteristics of both the signal and background are eprior; known functions of one or amore variables., The underlying assumption is that the characteristics of both the signal and background are $a~priori$ known functions of one or more variables.800 Since the matched filter maximizes the signal-to-noise ratio. moderate departures from optimality degrade the filter performance relatively slowly. making this a valuable tool for investigatiug the possible existence of faint signals.," Since the matched filter maximizes the signal-to-noise ratio, moderate departures from optimality degrade the filter performance relatively slowly, making this a valuable tool for investigating the possible existence of faint signals."801 The details of the filter aleorithin are explicitly described in ALO., The details of the filter algorithm are explicitly described in A10.802 In this paper. we take the next harder step of dropping our reliance on precision burst coordinates provided bv Swift or other simular hieh resolution iustruiments.," In this paper, we take the next harder step of dropping our reliance on precision burst coordinates provided by Swift or other similar high resolution instruments."803 Instead. weuse the approxinate localization of the Feriiz/GDM to map a reeion of interest on the Fermi//LAT field of view.," Instead, weuse the approximate localization of the $Fermi$ /GBM to map a region of interest on the $Fermi$ /LAT field of view."804 Dx identifving high energy photon clusters. provisional burst coordinates can be determined with siguificautlv sinaller errors than available from the G@BAL," By identifying high energy photon clusters, provisional burst coordinates can be determined with significantly smaller errors than available from the GBM."805 From there. the burst identification follows aloug lines set out in ALO.," From there, the burst identification follows along lines set out in A10."806 As a first step in this program. a list of all CDM trigecrs was obtained from the fermghrst catalog maiutaimed by the Ferini Scieuce SupportCeuter?®.," As a first step in this program, a list of all GBM triggers was obtained from the $fermigbrst$ catalog maintained by the $Fermi$ Science Support."807. The catalog contains 197 GRB triggers from launch to July 9. 2010.," The catalog contains 497 GRB triggers from launch to July 9, 2010."808 This list was cross-matched with Table 1 in Guetta Pian (2009) and Table 2 in Caretta ct al. (, This list was cross-matched with Table 1 in Guetta Pian (2009) and Table 2 in Guetta et al. (8092010) to identity the burst GCN designations aud the low energv Huencees.,2010) to identify the burst GCN designations and the low energy fluences.810 For trigecrs occuring after February 18. 2010. Huences were obtained from individual CCN circulars.," For triggers occuring after February 18, 2010, fluences were obtained from individual GCN circulars."811 GBAL triggers were also checked against NRT locations Yon Swift! to remove events already cousidered in A10., GBM triggers were also checked against XRT locations from $Swift$ to remove events already considered in A10.812 Usiug data from the Fermi spacecraft attitude file. we urther selected those triggers with a boresight angle ess than 52° and an estimated CBAL error circle less hau 107.," Using data from the Fermi spacecraft attitude file, we further selected those triggers with a boresight angle less than $^\circ$ and an estimated GBM error circle less than $^\circ$ ."813 Events without (BAL fluence information or, Events without GBM fluence information or814excludes [rom the sample. very luminous X-ray selected normal galaxies.,excludes from the sample very luminous X-ray selected normal galaxies.815 For example about 20 per cent of the Fabbiano et al. (, For example about 20 per cent of the Fabbiano et al. (8161992) sample have logLx/Lg2.,"1992) sample have $\log L_X /L_B817>-2$."818 The vast majority of these svstems are also luminous with Lyzz107eres +.," The vast majority of these systems are also luminous with $L_X819\ga 10^{42} \rm \, erg \, s^{-1}$ ."820 Excluding E/S0 galaxies with logLx/Lg>2 from that sample we find a [latter slope of z1.5 for the LxLg relation in agreement with the value estimated here.," Excluding E/S0 galaxies with $\log L_X821/L_B >-2$ from that sample we find a flatter slope of $\approx 1.5$ for the $L_X - L_B$ relation in agreement with the value estimated here."822 Alternative the Hatter Ly relation may indicate that the A-band. provides a better proxy to galaxy mass., Alternative the flatter $L_X - L_K$ relation may indicate that the $K$ -band provides a better proxy to galaxy mass.823 For example. Shapley ct al. (," For example, Shapley et al. ("8242001) used Z-band: near-infrared data ancl find a flatter slope for the LyLu relation of spirals compared to the Ly relation for the same systems.,2001) used $H$ -band near-infrared data and find a flatter slope for the $L_X - L_H$ relation of spirals compared to the $L_X - L_B$ relation for the same systems.825 Although comparing the X-ray properties of ellipticals and spirals is not appropriate it suggests that the Hatter slope we are estimating may be partly due to the use of near-infrarecl rather than optical luminosities., Although comparing the X-ray properties of ellipticals and spirals is not appropriate it suggests that the flatter slope we are estimating may be partly due to the use of near-infrared rather than optical luminosities.826 In this paper we demonstrate the power of the First Serendipitous Source Catalog for studies of N-rav selected normal galaxies., In this paper we demonstrate the power of the First Serendipitous Source Catalog for studies of X-ray selected normal galaxies.827 Our sample is compiled. froma X-rav sources detected onNew/on pointings that have (i) EPLO-PN detector as prime instrument operated in full-[rame mode. (ij) exposure time Tkks. Git) declinations DIEC(J2000)>10deg. (iv) galactic latitude [bi]z20deg and (v) right ascension. RA(J2000)> 4hhours.," Our sample is compiled from X-ray sources detected on pointings that have (i) EPIC-PN detector as prime instrument operated in full-frame mode, (ii) exposure time $>7$ ks, (iii) declinations $\rm DEC(J2000) > - 10 \, deg$, (iv) galactic latitude $\rm |b_{II}|>20 \, deg$ and (v) right ascension $\rm828RA(J2000)>4$ hours."829 A total of 5] fields fulfil the above criteria. covering a total area. of zGdee? to the kkeV band. limit [x(0.5.2keV)zm10herestem? ," A total of 51 fields fulfil the above criteria, covering a total area of $\approx \rm 6\, deg^2$ to the keV band limit $f_X(\rm 0.5 - 2 \, keV) \approx 10^{-15} \, erg \,830s^{-1} \, cm^{-2}$ ."831"The USNO A2.0 catalogue. provides a homogeneous platform that allows identification of X-ray selected. normal galaxy candidates on the basis of the low Nav.tooptical lux ratios of these sources. ουνων,<2."," The USNO A2.0 catalogue provides a homogeneous platform that allows identification of X-ray selected normal galaxy candidates on the basis of the low X-ray–to–optical flux ratios of these sources, $\log f_X832/f_{opt} < -2$."833 Reliable μαar/galaxy separation is available from the APAL. allowing us to exclude Galactic stars that also have logfx/fii 2.," Reliable star/galaxy separation is available from the APM, allowing us to exclude Galactic stars that also have $\log f_X834/f_{opt} < -2$ ."835 Optical spectroscopy is then used. to identity systenis ju show evidence for AGN activity resulting in a sample of 23 normal galaxy candidates: 9 with narrow emission lines. 12 with absorption lines only and 2 without optical spectroscopic information.," Optical spectroscopy is then used to identify systems that show evidence for AGN activity resulting in a sample of 23 normal galaxy candidates: 9 with narrow emission lines, 12 with absorption lines only and 2 without optical spectroscopic information."836 Future releases of the Serendipitous Source. Catalog will provide much wider areal coverage resulting in significantly larger low-2 normal galaxy samples., Future releases of the Serendipitous Source Catalog will provide much wider areal coverage resulting in significantly larger $z$ normal galaxy samples.837 At present we increase our sample size by combining it with X-ray selected. normal galaxy candidates from the Needles in the Lavstack Survey (Georgantopoulos et al., At present we increase our sample size by combining it with X-ray selected normal galaxy candidates from the Needles in the Haystack Survey (Georgantopoulos et al.838 2005)., 2005).839 This provides a total of 46 z£z;0.2 X-ray. detectec normal galaxies. the largest low-z sample vet available.," This provides a total of 46 $z840\la 0.2$ X-ray detected normal galaxies, the largest $z$ sample yet available."841 Such a large number of sources provides à unique opportunity to constrain the normal galaxy ουνlog* at brigh fluxes (lOL.10+8Creslem 7).," Such a large number of sources provides a unique opportunity to constrain the normal galaxy $\log N - \log S$ at bright fluxes $\rm 10^{-15} -10^{-13} \, erg \, s^{-1} \, cm^{-2}$ )."842 We estimate a slope of 1.460.19 consistent with the euclidean prediction and in agreement with previous determinations (Llornschemeicr e al., We estimate a slope of $-1.46\pm0.13$ consistent with the euclidean prediction and in agreement with previous determinations (Hornschemeier et al.843 2003: Tajer et al., 2003; Tajer et al.844 2005), 2005).845sstaudards.,standards.846"PSR J1911—6000C in NGC 6752, though, is located outside this radius so that we expanded the search region Του this cluster to 3 aremin.","PSR $1911-6000$ C in NGC 6752, though, is located outside this radius so that we expanded the search region for this cluster to 3 arcmin."847" The resulting identifications, counting rates and chance probabilities for finding an X-ray source by chance at the radio pulsar position are listed in Table 5.."," The resulting identifications, counting rates and chance probabilities for finding an X-ray source by chance at the radio pulsar position are listed in Table \ref{t:xraydetections}."848 In total 31 X-ray sources in nine globular clusters were found to be coincident with the radio timing position of known millisecond pulsars., In total 31 X-ray sources in nine globular clusters were found to be coincident with the radio timing position of known millisecond pulsars.849 Among them are the 19 millisecond pulsars previously identified in 47 Tuc (Grindlayetal.2001:Bogdanoval...2006).. the millisecond pulsar PSR J1824-2452A in NGC 6626 (Beckeretal.2003).. PSR 195341846AÀ in NGC 6838 (Elsneretal.2008).. PSR J1701-3006B in NGC 6266(Cocozzaetal.2008).. PSR 5340 in NGC 6397 (Huang&Becker2010) and few more for which an association has been assigned in the literature (cf.," Among them are the 19 millisecond pulsars previously identified in 47 Tuc \citep{Grindlay2001, Bogdanov2006}, the millisecond pulsar PSR J1824-2452A in NGC 6626 \citep{Becker2003}, PSR 1953+1846A in NGC 6838 \citep{Elsner2008}, PSR J1701-3006B in NGC 6266\citep{Cocozza2008}, PSR J1740-5340 in NGC 6397 \citep{HunangBecker2010} and few more for which an association has been assigned in the literature (cf."850 Table 6.9 in Becker 2009 and references therein)., Table 6.9 in Becker 2009 and references therein).851 Pulsars for which X-ray counterparts are newly detected are PSR J1824-2452G and PSR J1824-2452H in NGC 6626 and PSR J1701-3006C in NGC 6266., Pulsars for which X-ray counterparts are newly detected are PSR J1824-2452G and PSR J1824-2452H in NGC 6626 and PSR J1701-3006C in NGC 6266.852" The tentative assignment of the X-ray counterparts for PSR J2140-3310A in M30 (Ransometal.2004) and PSR J1910-5959B 2002) could not be confirmed by our analysis, albeit additional data were available tor the latter pulsar compared to their analysis."," The tentative assignment of the X-ray counterparts for PSR J2140-3310A in M30 \citep{Ransom2004} and PSR J1910-5959B \citep{DAmico2002} could not be confirmed by our analysis, albeit additional data were available for the latter pulsar compared to their analysis."853 Counting rate upper limits were computed for those pulsars for which no X-ray counterpart could be detected., Counting rate upper limits were computed for those pulsars for which no X-ray counterpart could be detected.854" For this we measured the number of counts recorded at the radio pulsar position and computed the 36 upper limits according to Cy,20.5x(S/N)y/etst0.25(S/N."," For this we measured the number of counts recorded at the radio pulsar position and computed the $3\sigma$ upper limits according to $C_{3\sigma}=0.5 \times 855(S/N)^2+(S/N) \times \sqrt{cts+0.25 \times (S/N)^{2}}$."856 Here S/N=3 is the signal-to-noise ratio and cts the counts obtained within a circle of 1 aresec radius centered on the position of the radio pulsar., Here $S/N=3$ is the signal-to-noise ratio and $cts$ the counts obtained within a circle of 1 arcsec radius centered on the position of the radio pulsar.857 All upper limits are summarized in Table 6 along with the exposure time of the observation and the number of counts recorded at the pulsar position., All upper limits are summarized in Table \ref{t:upperlimits} along with the exposure time of the observation and the number of counts recorded at the pulsar position.858 Figures 2 to 10. show ACIS-S and/or HRC-I images of all globular clusters considered in this work., Figures \ref{figure2} to \ref{figure10} show ACIS-S and/or HRC-I images of all globular clusters considered in this work.859 The location of the millisecond pulsars and the cluster half-mass radius are indicated., The location of the millisecond pulsars and the cluster half-mass radius are indicated.860 For about ten years the 3.05 ms pulsar PSR J1824-2452A in M28 was the only globular cluster pulsar from which pulsed X-ray emission had been detected., For about ten years the 3.05 ms pulsar PSR J1824-2452A in M28 was the only globular cluster pulsar from which pulsed X-ray emission had been detected.861 Timing observations were performed with ROSAT (Danner et al., Timing observations were performed with ROSAT (Danner et al.862" 1997), ASCA (Saito et al."," 1997), ASCA (Saito et al."863" 1997), BeppoSax (Minco et al."," 1997), BeppoSax (Mineo et al."864 2004) and the Rossi X-ray Timing Explorer (c.g. Rots 2006)., 2004) and the Rossi X-ray Timing Explorer (e.g. Rots 2006).865" XMM-Newton lists the pulsar as calibration target, although it was never scheduled tor observations so far."," XMM-Newton lists the pulsar as calibration target, although it was never scheduled for observations so far."866 Chandra observed PSR J1824-2452A in 2002 and 2006 for a total of ~90.440 ksee using the HRC-S with the timing flag enabled.," Chandra observed PSR J1824-2452A in 2002 and 2006 for a total of $\sim 90,440$ ksec using the HRC-S with the timing flag enabled."867 The temporal resolution of the HRC-S in this mode is 15.625 jes.," The temporal resolution of the HRC-S in this mode is $15.625\,\mu s$ ."868 It is sensitive in the, It is sensitive in the869lines [rom SN ejecta appear only about day. 40 after the discovery (Fassia et al.,lines from SN ejecta appear only about day 40 after the discovery (Fassia et al.870 2001)., 2001).871 Remarkably. the outer shock is radiatiave in both models for zz20 days.," Remarkably, the outer shock is radiatiave in both models for $\approx 20$ days."872" As a result on Alarch 6 with z9 clays passed after the explosion the outer postshock eas should cool very. quickly resulting in a very thin outer postshock region. ""NI<0.1."," As a result on March 6 with $\approx 9$ days passed after the explosion the outer postshock gas should cool very quickly resulting in a very thin outer postshock region, $\Delta R/R < 0.1$."873" We consider only the Ho line. although a similar approach may be applied to any other line. including WR. lines. observed. in carly-time spectra of SN. 19988. “Phe model suggests a sharp photosphere with a radius 2,=fj). in a fully ionised. isothermal CS gas (r Hy) with an electron temperature ἐν=Zr Clable 1)."," We consider only the $\alpha$ line, although a similar approach may be applied to any other line, including WR lines, observed in early-time spectra of SN 1998S. The model suggests a sharp photosphere with a radius $R_{\rm p}=R_{\rm s}$ in a fully ionised isothermal CS gas $r>R_{\rm p}$ ) with an electron temperature $T_{\rm e}=T_{\rm eff}$ (Table 1)."874 Any cllects related. to. the outer shock are omitted: they are of a minor importance for the line profile., Any effects related to the outer shock are omitted; they are of a minor importance for the line profile.875 The wind velocity law PΞtwasfry?DPΌμμι is taken to mimic a radiative acceleration of the wind by the SN radiation., The wind velocity law $v=v_{\rm max}(R_{\rm p}/r)^2 + v_{\rm min}$ is taken to mimic a radiative acceleration of the wind by the SN radiation.876 We adopt Cada=40 km + for the distant wind (Fassia et al., We adopt $v_{\rm min}=40$ km $^{-1}$ for the distant wind (Fassia et al.877 2001) and cua=1000 km at the photosphere. a rough guess based upon the extrapolated behavior of the maximal velocities of the fast CS gas on March. 20 and April SN (Fassia et al.," 2001) and $v_{\rm max}=1000$ km $^{-1}$ at the photosphere, a rough guess based upon the extrapolated behavior of the maximal velocities of the fast CS gas on March 20 and April 8 (Fassia et al."878 2001)., 2001).879 Phe result. actually. is not. very much sensitive to μις unless it significantly exceeds. 1000. kina L.," The result, actually, is not very much sensitive to $v_{\rm max}$ unless it significantly exceeds 1000 km $^{-1}$ ."880"C7phe wind emissivity in Lla is assumed to scale as à recombination enmüssivitv j=μπλαΠΗΓΗ) (org tem ? Dy where oa» is the cllective recombination cocllicient for the Ho. emission (case D). while C4, is an emission correction factor. which allows for uncertainties in the distance. exctinction. electron. temperature. hydrogen abundance. as well as for à wind clumpiness ancl a possible deviation from the recombination case D. The scattering in the wind is essentially conservative. but the photons struck the photosphere will be considered. lost."," The wind emissivity in $\alpha$ is assumed to scale as a recombination emissivity $j=C_{\rm em}(h\nu/4\pi)\alpha_{32}n_{\rm e}n(\mbox{H}^{+})$ (erg $^{-1}$ $^{-3}$ $^{-1}$ ), where $\alpha_{32}$ is the effective recombination coefficient for the $\alpha$ emission (case B), while $C_{\rm em}$ is an emission correction factor, which allows for uncertainties in the distance, exctinction, electron temperature, hydrogen abundance, as well as for a wind clumpiness and a possible deviation from the recombination case B. The scattering in the wind is essentially conservative, but the photons struck the photosphere will be considered lost."881 “The resonance scattering is neglected., The resonance scattering is neglected.882 This approximation is justified. by our simulations. which do not show a dependence on the resonance scattering at the considered epoch.," This approximation is justified by our simulations, which do not show a dependence on the resonance scattering at the considered epoch."883 The emergent line spectrum is computed. using the Alonte Carlo technique., The emergent line spectrum is computed using the Monte Carlo technique.884 The photon frequency at each scattering is randomly chosen adopting the svmmetric angle-averaged. frequency redistribution. function (cf, The photon frequency at each scattering is randomly chosen adopting the symmetric angle-averaged frequency redistribution function (cf.885 Mihalas 19785), Mihalas 1978).886 Note. computations with both angle-averaged and anele-depencent frequency redisribution functions are mutually consistent with a high precision even in the case of Tp& Las Hüllier (1991) has shown in his studs of electron-scattering cllects in WI stars.," Note, computations with both angle-averaged and angle-dependent frequency redisribution functions are mutually consistent with a high precision even in the case of $\tau_{\em T}\approx 1$ as Hillier (1991) has shown in his study of electron-scattering effects in WR stars."887 The relativistic correction to the Doppler ellect anc Compton recoil produce a net blue shift AvivΑΔ(21:.Av)μις (Wevmann 1970). where No isthe average number of scatterings.," The relativistic correction to the Doppler effect and Compton recoil produce a net blue shift $\Delta \nu/\nu = N_{\rm s}(3kT_{\rm e}-h\nu)/mc^2$ (Weymann 1970), where $N_{\rm s}$ is the average number of scatterings."888 This elfect. although small. is included in the profile modeling.," This effect, although small, is included in the profile modeling."889 The Ho line broadening ellect in the case of the high Thomson optical depth is illustrated in Fig., The $\alpha$ line broadening effect in the case of the high Thomson optical depth is illustrated in Fig.890 3 with mocel parameters given in Table 2. which presents the electron temperature. the linear wind density. ey. and the Thomson optical depth.," 3 with model parameters given in Table 2, which presents the electron temperature, the linear wind density $w_1$ , and the Thomson optical depth."891" In all the cases the photospherie radius is R,=4107 em. the wind velocity is à—40|1000(4,DE ius andthe CS density distribution is defined by Eq. (1) "," In all the cases the photospheric radius is $R_{\rm p}=4\times10^{14}$ cm, the wind velocity is $u=40+1000(R_{\rm p}/r)^2$ km $^{-1}$ and the CS density distribution is defined by Eq. \ref{eq:cs}) )"892with we»20. 8.129.l0 em. s.2. νι10.," with $w_2=0$, $R_{\rm c,1}=9\times10^{14}$ cm, $s_1=-2$, $p_1=10$."893 All the xoliles are normalized to unity at maximum., All the profiles are normalized to unity at maximum.894 A gaussian smoothing with FWLIAI=6.7 is applied henceforth to the computed profile to allow for the inite resolution in the spectrum on 1998 March 6 (Fassia et al., A gaussian smoothing with FWHM=6.7 is applied henceforth to the computed profile to allow for the finite resolution in the spectrum on 1998 March 6 (Fassia et al.895 2001)., 2001).896 Results show that the emplate model DI with he Thomson optical depth rr=4 produces strong nearly svmmetric electron-scattering wings., Results show that the template model D1 with the Thomson optical depth $\tau_{\rm T}=4$ produces strong nearly symmetric electron-scattering wings.897 Le should be emphasised that the line profile from the expanding electron scattering wind with the opaque core is the result. of the combination of several factors inclucüng. (1) single scattering xoadening related. to. the outmost lavers with zrX1: (ii) broadening due to multiple scattering. which may be interpreted as a dillusion in the frequency. space: (iii) the redshift’ acquired. in the course of multiple scattering in he expanding medium: (iv) the photon absorbtion by the opaque photosphere.," It should be emphasised that the line profile from the expanding electron scattering wind with the opaque core is the result of the combination of several factors including, (i) single scattering broadening related to the outmost layers with $\tau_{\rm T}\leq 1$; (ii) broadening due to multiple scattering, which may be interpreted as a diffusion in the frequency space; (iii) the redshift acquired in the course of multiple scattering in the expanding medium; (iv) the photon absorbtion by the opaque photosphere."898 Le should. be emphasised. that. the resulting redshift essentially depends on the wind expansion kinematics., It should be emphasised that the resulting redshift essentially depends on the wind expansion kinematics.899 “Phe model D2 with ten times lower optical depth compared. to the model D1 clearly shows the blue shift due to the occultation of the wind by the photosphere and the enhanced red wing due to the expansion cllect., The model D2 with ten times lower optical depth compared to the model D1 clearly shows the blue shift due to the occultation of the wind by the photosphere and the enhanced red wing due to the expansion effect.900 A primary reason. why the expansion elfect is not so apparent in the model D1 relates to the adopted: wind. kinematics with the velocity dropping outward.," A primary reason, why the expansion effect is not so apparent in the model D1 relates to the adopted wind kinematics with the velocity dropping outward."901 In the optically jiick situation the contribution of the outer slow expanding eas dominates. which thus account for the small expansion effect in the model D1.," In the optically thick situation the contribution of the outer slow expanding gas dominates, which thus account for the small expansion effect in the model D1."902 Obviously. this οσο does not operate in the transparent case D2. where fast inner scattering wind essentially contributes in the line profile.," Obviously, this effect does not operate in the transparent case D2, where fast inner scattering wind essentially contributes in the line profile."903 Note. the mentioned bias to the red wing in the model D2 very much resembles the appearence of electron-scattering wings in WI stars (Auer van Dlerkom 1972: Hillier 1991).," Note, the mentioned bias to the red wing in the model D2 very much resembles the appearence of electron-scattering wings in WR stars (Auer van Blerkom 1972; Hillier 1991)."904 The mocel D3 with rr=5 has markedly stronger wings compared to the model DI in a wide range of velocities., The model D3 with $\tau_{\rm T}=5$ has markedly stronger wings compared to the model D1 in a wide range of velocities.905 The higher electron. temperature. (model D4) slightly increases high velocity wings., The higher electron temperature (model D4) slightly increases high velocity wings.906 Such an effect is practically on the verge of detectabilitv., Such an effect is practically on the verge of detectability.907 In this regard we note. that the uncertainty of Zr in the light curve model is of zz20%. which is thus insignificant for the line modeling.," In this regard we note, that the uncertainty of $T_{\rm eff}$ in the light curve model is of $\approx 20\%$, which is thus insignificant for the line modeling."908 The spectrum of Lla on 1998 March 6 (Fassia οἱ al., The spectrum of $\alpha$ on 1998 March 6 (Fassia et al.909" 2001) with two ""best/ fit versions of the line prolile based. upon models A and. D. are. ahown in Fig.", 2001) with two 'best' fit versions of the line profile based upon models A and B are ahown in Fig.910 d., 4.911 Jo makethe plot the emission. lines are placed upon the appropriate continuum., To makethe plot the emission lines are placed upon the appropriate continuum.912 Asnoted. before. (section 3). parameters of models A anc B are found: using itterative," Asnoted before (section 3), parameters of models A and B are found using itterative"913number of narrow lines and consequently have larger values of AL,number of narrow lines and consequently have larger values of ${\cal A}$.914 Note. however. that the dependence on the slope + is also quite strong. but this may be partly. a consequence of using the mean density as the pivot. point around. which we change the slope.," Note, however, that the dependence on the slope $\gamma$ is also quite strong, but this may be partly a consequence of using the mean density as the pivot point around which we change the slope."915 We have also superposed the mixed-temperature model. which stays close to the hot component for small values of 4 before veering away to the locus of the cold component for large values of the amplitudo.," We have also superposed the mixed-temperature model, which stays close to the hot component for small values of ${\cal A}$ before veering away to the locus of the cold component for large values of the amplitude."916 Lavine shown that the mean cumulative distribution CCA) depends on the equation. of state. we now want to characterise how well cilferent models can be clistinguisheel [rom each other. based on a spectrum.," Having shown that the mean cumulative distribution $\bar C({\cal A})$ depends on the equation of state, we now want to characterise how well different models can be distinguished from each other, based on a spectrum."917 Hence. we want to characterise to what extent the cumulative distribution CCA) for a single spectrum of mocel j differs [rom the mean. C'i. For model 7.," Hence, we want to characterise to what extent the cumulative distribution $C_j({\cal A})$ for a single spectrum of model $j$ differs from the mean, $\bar C_i$, for model $i$."918 Fo this end. we compute the dispersion For a single realisation of a spectrum of model j. 07; is just a number.," To this end, we compute the dispersion For a single realisation of a spectrum of model $j$, $\sigma_{ij}^2$ is just a number."919 In order to be able to distinguish between two models { and jf based on a single spectrum. it is necessary that the dispersion. o7;2 be much smaller than the mean difference στ between the models.," In order to be able to distinguish between two models $i$ and $j$ based on a single spectrum, it is necessary that the dispersion $\sigma_{ii}^2$ be much smaller than the mean difference $\sigma_{ij}^2$ between the models."920creating Figure 20.. and J. Bailin for helpful coments on the manuscript.,"creating Figure \ref{fig:GLIMPSE_image}, and J. Bailin for helpful comments on the manuscript."921 IL. A. F. thanks the National Radio Astronomy Observatory for support under its Graduate Studeut Iuteruship Program., H. A. F. thanks the National Radio Astronomy Observatory for support under its Graduate Student Internship Program.922 The National Badio Astronomy Observatory is operated by. Associated Universities. Iuc.. uncer a cooperative aerecment with the National Science Foundation.," The National Radio Astronomy Observatory is operated by Associated Universities, Inc., under a cooperative agreement with the National Science Foundation."923"0, or Os) o. the potential we left [ree [or each point of a grid. (ο. A).",$\theta_a$ or $\theta_s$ ) of the potential we left free for each point of a grid $(\Omega_m$ $\Omega_\lambda)$.924" The likelihood of the result is obaimed"" via. a > X-miuimizatiou.. where the 47o is computed iu. the source plane."," The likelihood of the result is obtained via a $\chi^2$ -minimization, where the $\chi^2$ is computed in the source plane."925 ‘To recover the parameters of the potential ( ie oy. 04. 0 aud adjusted leus parameters). we venerated 3 families of images with regularly distributed source redshifts.," To recover the parameters of the potential ( ie $\sigma_0$, $\theta_a$, $\theta_s$ and adjusted lens parameters), we generated 3 families of images with regularly distributed source redshifts."926 For starting values (QU.QV)(0.3.0.7) we obtained the Fig.," For starting values $(\Omega_m^0,\Omega_\lambda^0)=(0.3,0.7)$ we obtained the Fig."927 2. coufideuce levels., \ref{3fam} confidence levels.928" The uethod puts forward a good coustraint. better ou Q,, than ou OQ). aud the cleg@eueracy is the expected one (Fig. 1))."," The method puts forward a good constraint, better on $\Omega_m$ than on $\Omega_\lambda$, and the degeneracy is the expected one (Fig. \ref{F_zs}) )."929 Coucerning the free paramete*. we also recovered iu a rather good way he potential. the variations being Aq~150 kin/s. Ade~ 3and AQ.~20 ," Concerning the free parameters, we also recovered in a rather good way the potential, the variations being $\Delta\sigma_0\sim150$ km/s, $\Delta\theta_a\sim3$ ”and $\Delta\theta_s\sim20$ ”."930This is an “ideal” case. of course. because we trie| to recover the same type of potential we isecl to generate the images. the morphology of the €uster beiug quite regular aud the redshift ange of the sources being wide enough to check each yart of the F curve.," This is an “ideal” case, of course, because we tried to recover the same type of potential we used to generate the images, the morphology of the cluster being quite regular and the redshift range of the sources being wide enough to check each part of the $F$ curve."931 Such simple approach cau be applied to regular clusters like MS2137-23. which shows at least 3 Lamiuilies of multiple images including a radial oue.," Such simple approach can be applied to regular clusters like MS2137-23, which shows at least 3 families of multiple images including a radial one."932 But the spectroscopic redshifts are still missing for the moment., But the spectroscopic redshifts are still missing for the moment.933" Folowing the work of LP9S. we discussed a method to obtain informations on the cosmological paraleters QO,, auc QG while recoustructing the leus gravitational potential of clusters witli lutltiple inage systel sat different redsils."," Following the work of LP98, we discussed a method to obtain informations on the cosmological parameters $\Omega_m$ and $\Omega_\lambda$ while reconstructing the lens gravitational potential of clusters with multiple image systems at different redshifts."934" This tech.ique gives degenerate conusralnts. Q,, aud £2 being negatively correlaed. with a beter COLstraint oftie matter density."," This technique gives degenerate constraints, $\Omega_m$ and $\Omega_\lambda$ being negatively correlated, with a better constraint of the matter density."935" With a siugle cluster in a typical leising configuration we Call exvec the follOwlug er‘or bars: QQ,=0.34:0.21. X=0.70.5."," With a single cluster in a typical lensing configuration we can expect the following error bars: $\Omega_m=0.3{\pm 0.24}$, $\Omega_\lambda=0.7{\pm 0.5}$."936" To pe‘form that. seve‘al eeneral οςclitions must1 be fiHillecl: acuster wl hoa rather 'e8lar morphology. ""nulinerots systems of iniltiple inlages. a σοος spallil resolution (HST) atxl spectroscopi€ precision for t different. recshifts that should je also regularly clisributed. fro uz 9 "," To perform that, several general conditions must be fulfilled: a cluster with a rather regular morphology, “numerous” systems of multiple images, a good spatial resolution (HST) and spectroscopic precision for the different redshifts that should be also regularly distributed, from $z_l$ \ref{3fam} "937discussed below in some detail. of nuclear star formation in a substantial fraction of brightest cluster galaxies (Bildfelletal.2008:Reichardetal. 2009)... which will cause the innermost bin ο be significantly higher for this distribution than that for the blue star-forming galaxies.,"discussed below in some detail, of nuclear star formation in a substantial fraction of brightest cluster galaxies \citep{bildfell,reichard}, which will cause the innermost bin to be significantly higher for this distribution than that for the blue star-forming galaxies."938 It is interesting to note that the fraction of blue passive galaxies also show a minor increment around ους., It is interesting to note that the fraction of blue passive galaxies also show a minor increment around $_{200}$.939 Other studies have shown that in clusters. particularly those that are ed by filaments. there is an enhancement of nuclear star formation in the infalling galaxies beyond rouo (e.g. oreparation)..," Other studies have shown that in clusters, particularly those that are fed by filaments, there is an enhancement of nuclear star formation in the infalling galaxies beyond $_{200}$ \citep[e.g.][]{p2,p08,mrp09}."940 One of the objectives in this paper will be to examine the hypothesis that the galaxy populations can indeed be divided. on the basis of a single parameter. into two classes: passive and star-forming. and that the incidence of red star-forming or blue passive galaxies is merely due to the scatter in the measured parameters within reasonable errors.," One of the objectives in this paper will be to examine the hypothesis that the galaxy populations can indeed be divided, on the basis of a single parameter, into two classes: passive and star-forming, and that the incidence of red star-forming or blue passive galaxies is merely due to the scatter in the measured parameters within reasonable errors."941 As we show below. this hypothesis fails to hold.," As we show below, this hypothesis fails to hold."942 Star-forming regions in a galaxy are often surrounded by dust. which can significantly affect quantitative analyses based on optical light.," Star-forming regions in a galaxy are often surrounded by dust, which can significantly affect quantitative analyses based on optical light."943 Conversely. the presence of dust in a galaxy would imply the presence of star-forming regions therein.," Conversely, the presence of dust in a galaxy would imply the presence of star-forming regions therein."944 In the absence of infrared observations. which are often used to quantify the effect of dust in star-forming systems (e.g.Calzetti1997).. optical photometry can also be used to constrain the internal extinction in a galaxy (also see Fig. 9)).," In the absence of infrared observations, which are often used to quantify the effect of dust in star-forming systems \citep[e.g.][]{cal97}, optical photometry can also be used to constrain the internal extinction in a galaxy (also see Fig. \ref{o-i-r}) )."945 In one such attempt. Kauffmannetal.(2003b) have estimated the degree of dust attenuation in the SDSS z-band. by comparing model colours to the measured colours to estimate the reddening for each galaxy.," In one such attempt, \citet{kauff03b} have estimated the degree of dust attenuation in the SDSS $z$ -band, by comparing model colours to the measured colours to estimate the reddening for each galaxy."946 The shape of the attenuation curve from observations is found to resemble a power law with slope ~—0.7 over a wavelength range from 1250-8000 citepcal94.., The shape of the attenuation curve from observations is found to resemble a power law with slope $\sim\! -0.7$ over a wavelength range from 1250-8000 \\citep{cal94}.947 A standard attenuation curve. of the form τνXAhe is then extrapolated to obtain the extinction in the SDSS -z-band.," A standard attenuation curve, of the form $\tau_\lambda \propto \lambda^{-0.7}$, is then extrapolated to obtain the extinction in the SDSS $z$ -band."948 We use the ;A. values from Kauffmannetal.(2003b).. expressed in magnitudes. in this section.," We use the $A_z$ values from \citet{kauff03b}, expressed in magnitudes, in this section."949 The typical lo error on the estimated ele is ~0.12 mag., The typical $\sigma$ error on the estimated $A_z$ is $\sim\! 0.12$ mag.950 They also note that comparison of gr and r.4 colours yield similar extinction values for most galaxies if the colours are corrected for nebular emission., They also note that comparison of $g\! -\! r$ and $r\! -\! i$ colours yield similar extinction values for most galaxies if the colours are corrected for nebular emission.951 The reddening of a galaxy is the result of a combination of several factors. involving the presence of dust and/or metals in the interstellar medium and of old stars.," The reddening of a galaxy is the result of a combination of several factors, involving the presence of dust and/or metals in the interstellar medium and of old stars."952 In our attempt to interpret the apparent evidence of star formation in the fibre spectra of some red galaxies (red SF’). and the lowvalues of SFR in the spectra of some blue galaxies (blue passive’). we plot. in Fig. 4..," In our attempt to interpret the apparent evidence of star formation in the fibre spectra of some red galaxies (`red SF'), and the lowvalues of SFR in the spectra of some blue galaxies (`blue passive'), we plot, in Fig. \ref{dust},"953 the distribution of internal extinction ;1. of the galaxies in the four populations as classified in Fig. 2.., the distribution of internal extinction $A_z$ of the galaxies in the four populations as classified in Fig. \ref{ssf-gr}.954" As expected. the ""red sequence’ galaxies. most of which are passively evolving massive galaxies in the cores of clusters. show very little extinction (negative values of ;l. being interpreted as zero here)."," As expected, the `red sequence' galaxies, most of which are passively evolving massive galaxies in the cores of clusters, show very little extinction (negative values of $A_z$ being interpreted as zero here)."955 However. even among passive galaxies. there is a small fraction that constitutes a tail extending to non-negligible extinction values.," However, even among passive galaxies, there is a small fraction that constitutes a tail extending to non-negligible extinction values."956 The blue star-forming galaxies. on the other hand. show a clear sign of attenuation going upto 1.0 mag in the z-band. with most galaxies having extinction values around 0.6 mag for the blue star-forming galaxies and 0.35. mag for the blue passive galaxies respectively.," The blue star-forming galaxies, on the other hand, show a clear sign of attenuation going upto $1.9$ mag in the $z$ -band, with most galaxies having extinction values around $0.6$ mag for the blue star-forming galaxies and $0.35$ mag for the blue passive galaxies respectively."957 In contrast. the red star-forming galaxies show a mix of at least two different populations: about half of them are unattenuated (similar to the red sequence galaxies). and the other half contributing to the skewed high extinction end of the distribution.," In contrast, the red star-forming galaxies show a mix of at least two different populations: about half of them are unattenuated (similar to the red sequence galaxies), and the other half contributing to the skewed high extinction end of the distribution."958 We employ the KMM algorithm (Ashman.Bird&Zepf1994) to quantify the existence of bimodality in our data., We employ the KMM algorithm \citep{kmm} to quantify the existence of bimodality in our data.959 The KMM algorithm fits a user specitied number of Gaussian distributions to the dataset. calculates the maximum likelihood estimate of their means and variances. and assesses the improvement of the fit over that provided by a single Gaussian.," The KMM algorithm fits a user specified number of Gaussian distributions to the dataset, calculates the maximum likelihood estimate of their means and variances, and assesses the improvement of the fit over that provided by a single Gaussian."960 The KMM likelihood ratio test statistics (LRTS) used here is a measure of improvement in using two Gaussian distributions (since we are testing bimodality) over a -mode fit., The KMM likelihood ratio test statistics (LRTS) used here is a measure of improvement in using two Gaussian distributions (since we are testing bimodality) over a 1-mode fit.961 For the distribution of extinction. in the red star-forming galaxies the KMM test gives the value of likelihood ratio (LRTS) o be 75. when using a bimodal fit to the data than using a unimodal tit. with nil probability of the null hypothesis being satistied.," For the distribution of extinction, in the red star-forming galaxies the KMM test gives the value of likelihood ratio (LRTS) to be 75, when using a bimodal fit to the data than using a unimodal fit, with nil probability of the null hypothesis being satisfied."962 The 2-modes of the internal extinction distribution are found to be centred around .—-0.06 (read zero extinction) and 0.72 mag respectively or the sample of cluster galaxies., The 2-modes of the internal extinction distribution are found to be centred around $_{z}$ =-0.06 (read zero extinction) and 0.72 mag respectively for the sample of cluster galaxies.963 Interestingly. we tind that even by changing the selection criteria for detining the red star-forming galaxies to a higher value of log SFR/M* = -10 +. the KMM est still vields statistically signiticant result in favour of a bimodal fit to the data (LRTS221 at a significance level 5«.10.7.," Interestingly, we find that even by changing the selection criteria for defining the red star-forming galaxies to a higher value of log $^*$ = -10 $^{-1}$, the KMM test still yields statistically significant result in favour of a bimodal fit to the data (LRTS=21 at a significance level $5\times 10^{-5}$ )."964 Along with the distribution of extinction. values for the cluster galaxies. we also show the corresponding distributions or 2300.000 galaxies. with the same magnitude and redshift range as our cluster sample. drawn from the entire SDSS DR4 spectroscopic catalogue (grey thin lines).," Along with the distribution of extinction values for the cluster galaxies, we also show the corresponding distributions for $>$ 300,000 galaxies, with the same magnitude and redshift range as our cluster sample, drawn from the entire SDSS DR4 spectroscopic catalogue (grey thin lines)."965 For this much larger P4ample. the histograms of extinction values are not significantly different from those for the cluster sample. except for the red star- galaxies. where cluster galaxies seem to have relatively fewer galaxies with high extinction values than similar galaxies in the larger all-SDSS sample.," For this much larger sample, the histograms of extinction values are not significantly different from those for the cluster sample, except for the red star-forming galaxies, where cluster galaxies seem to have relatively fewer galaxies with high extinction values than similar galaxies in the larger all-SDSS sample."966" In order to probe the presence of young (<| Gyr old) stellar populations among galaxies with an unusual. combination of SFR/M* and colour. we plot the distributions of the EW of the Hs absorption line. and of the D, 4000 values in Figs."," In order to probe the presence of young $<1$ Gyr old) stellar populations among galaxies with an unusual combination of $^*$ and colour, we plot the distributions of the EW of the $_\delta$ absorption line, and of the $_n$ 4000 values in Figs."967 5. and 6 respectively., \ref{hd} and \ref{d4000} respectively.968" The D, 4000 is the strongest discontinuity occurring in the optical spectrum of a galaxy. mainly due to the presence of ionised metals."," The $_n$ 4000 is the strongest discontinuity occurring in the optical spectrum of a galaxy, mainly due to the presence of ionised metals."969 On the other hand. Hs absorption is detected after most of the massive hot stars have finished evolving on the main sequence. aat least O.1-1 Gyr after a starburst is truncated.," On the other hand, $_\delta$ absorption is detected after most of the massive hot stars have finished evolving on the main sequence, at least 0.1-1 Gyr after a starburst is truncated."970 Thus the Hs EW is a measure of the age of the youngest stellar population in a galaxy. and has been extensively used to estimate the mean stellar ages as well (Worthey&Ottaviani1997).," Thus the $_\delta$ EW is a measure of the age of the youngest stellar population in a galaxy, and has been extensively used to estimate the mean stellar ages as well \citep{wo}."971. Even though several studies have shown that the Balmer emission dueto HIT regions. AGN and/or planetary nebulae can fill in the underlying Balmer absorption lines. causing age estimates to be spuriously high (Trageretal.2000:Prochaska 2007).. the Hs EW remains a popular stellar age indicator because it is less affected than the lower order Balmer lines. due to the steep Balmer decrement in emission (Osterbrock1989:Worthey&Ottaviani 1997)..," Even though several studies have shown that the Balmer emission dueto HII regions, AGN and/or planetary nebulae can fill in the underlying Balmer absorption lines, causing age estimates to be spuriously high \citep{trager00,prochaska07}, , the $_\delta$ EW remains a popular stellar age indicator because it is less affected than the lower order Balmer lines, due to the steep Balmer decrement in emission \citep{osterbrock89,wo}. ."972 Here we use the measured values of the (emission corrected), Here we use the measured values of the (emission corrected)973Dorucki. W.. Koch. D.. Dasri. 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E.B.. et al..," 2010 ApJ, 711, L1 Mandel, K., Agol, E. 2002, ApJ, 580, Maness, H.L, Marcy, G.W., Ford, E.B., et al.,"981 2007. Pub.," 2007, Pub."982 Ast., Ast.983 Soc., Soc.984 Pac..," Pac.,"985 119. 90," 119, 90"986"where p, is the fraction (by mass) of newly produced aud ejected oxveen by a star of mass i.",where $p_o$ is the fraction (by mass) of newly produced and ejected oxygen by a star of mass $m$.987" We used for p, the expression given by Woosley aud Weaver (1995) whereas for m4, the expression eiven by Tinsley (1980).", We used for $p_o$ the expression given by Woosley and Weaver (1995) whereas for $m_{rem}$ the expression given by Tinsley (1980).988 Iu our model the eas aud stellar masses are related by ads Now we want to relate the previous quantities to the observedi metallicity distribution of G-dawarts ΕΦ} in eq. (, In our model the gas and stellar masses are related by ds Now we want to relate the previous quantities to the observed metallicity distribution of G-dwarfs $f(\Phi)$ in eq. (9892)) in order to fud an equation for y(n.ft).,"2)) in order to find an equation for $\varphi(m,t)$."990 We have: LJ )) where (Qn.Τ)ΕΠΗΕΓΗΗ because the stars iu our suauple are iu the range l.1A..," We have: _c ) where (m,t)mdm because the stars in our sample are in the range $0.8-1.1M_{\odot}$ ."991 Equatious (5) and (9) give: Qn” the other hand we cau derive1 Jig from- (5)in and (8)d in the following wav: is the iitial eas mass., Equations (5) and (9) give: On the other hand we can derive $lng$ from (5) and (8) in the following way: where $g_0$ is the initial gas mass.992"↽↽ Hence from (11) we⋉⊓↴⋖↕⊳⋖≖↕⊳↓↙⇢−≖⋥↥−≖↓ 02: − obtain: Tf we evaluate the previous equation at $=0 (that is f— 0) we have: where pp aud oso are the quantities in (6) and (10). respectively, with y(n.ft)=qoGn.0)."," Hence from (11) we obtain: - If we evaluate the previous equation at $\Phi=0$ (that is $t=0$ ) we have: where $p'_0$ and $\alpha_{c0}$ are the quantities in (6) and (10), respectively, with $\varphi(m,t)=\varphi(m,0)$."993 By differentiating eq. (, By differentiating eq. (99413) with respect to ® we obtain finally This is an iuteero-cdiffercutial equation for the function von.) with the initial condition given by (11).,"13) with respect to $\Phi$ we obtain finally = This is an integro-differential equation for the function $\varphi(m,\Phi)$ with the initial condition given by (14)."995 The previous problem las. of course. infinite solutious.," The previous problem has, of course, infinite solutions."996 Therefore to proceed further we have to make some assuniptiou on the behaviow of the yo.0).," Therefore to proceed further we have to make some assumption on the behaviour of the $\varphi(m,\Phi)$."997 In the next sectious we shall investigate IME. with one slope (Sect., In the next sections we shall investigate IMF with one slope (Sect.998 2.2) and with two slopes (Sect., 2.2) and with two slopes (Sect.999 2.3)., 2.3).1000" Let consider a single power-law IME. namely where My aud Ap ave respectivelv the smallest aud the largest stellar mass (that sve asstme do not depend on the time) aud the normalization is performed iu the above dass rango. Le, C=E""TSxl(dqT Substitutius eq. ("," Let consider a single power-law IMF, namely )= C where $M_L$ and $M_U$ are respectively the smallest and the largest stellar mass (that we assume do not depend on the time) and the normalization is performed in the above mass range, i.e. $C=\frac{1-x(\Phi)}1001{M_U^{1-x(\Phi)}-M_L^{1-x(\Phi)}}$ Substituting eq. ("100216) in (15) we find the followine μοι for αφ): “hich is a nonlinear T order differential equation with initial condition given by substituting (16) in (11).,16) in (15) we find the following equation for $x(\Phi)$: which is a nonlinear I order differential equation with initial condition given by substituting (16) in (14).1003" The functious in (17) are: ín, lup]; DM where Since Po(r)>0. eq. ("," The functions in (17) are: _c -lnp'] )= + ] Since $F_2(x)>0$, eq. ("100417) Is us that a constant IME fiy(ro. with a slope .e—ty ataiv fine) corresponds to a straight line for ΕΦ) with a negative slope (Iudeed. iu this case eq. (,"17) tells us that a constant IMF (i.e. with a slope $x=x_0$ at any time) corresponds to a straight line for $f(\Phi)$ with a negative slope (Indeed, in this case eq. ("100517) becomes F3(®)=ue Foot).,17) becomes $F_3(\Phi)=\frac{df}{d\Phi}=-F_2(x_0)$ ).1006 This is the rigit behaviour since our model becomes the Simple Model w1O1 14Ξμ., This is the right behaviour since our model becomes the Simple Model when $x=x_0$.1007" hp, kolutions «(®) are plotted in Fie.", The solutions $x(\Phi)$ are plotted in Fig.1008 2 for two different vaues of Ar and Ag., 2 for two different values of $M_U$ and $M_L$.1009 We fouud very flat IMES for low «Deyeen abundances (ie. at initial times)., We found very flat IMFs for low oxygen abundances (i.e. at initial times).1010 At the solar inetalicity (ῷ= 1) the slope is always steeper than a Salpeter (1955) Ge= 1.35)., At the solar metallicity $\Phi=1$ ) the slope is always steeper than a Salpeter (1955) $x=1.35$ ).1011 Decreasing Mrdecreases. of course. wie. the IMF becomes flatter.," Decreasing $M_U$decreases, of course, $x$, i.e. the IMF becomes flatter."1012" The effect of a change im fie Mr, valueis neelieible (especiallyat low d$).", The effect of a change in the $M_L$ valueis negligible (especiallyat low $\Phi$ ).1013 Let now consider the following IME: The above IME depends on the three parameters ηνο and A.," Let now consider the following IMF: The above IMF depends on the three parameters $x_1, x_2$ and $M$ ."1014 We shall investigate the three following cases:, We shall investigate the three following cases:1015Galaxy formation theories predict that baryous cool in dark matter halos in such a way as to provide counections between galaxy observables aud dark matter properties (White&Rees1978:Cole&Ixalser. 1989).,"Galaxy formation theories predict that baryons cool in dark matter halos in such a way as to provide connections between galaxy observables and dark matter properties \citep{whi78,col89}."1016. For example. the Tully-Fisher relation (Tully&Fisher1977) shows the connection between galaxy luminosity and circular velocity. where the circular velocity depeuS on the dark matter anc baryonic mass profiles.," For example, the Tully-Fisher relation \citep{tul77} shows the connection between galaxy luminosity and circular velocity, where the circular velocity depends on the dark matter and baryonic mass profiles."1017 A key tool in studying galaxy evolution is the semi-analvtic model approach to relating the observable properties of galaxies to the tucerlying formation physics (Elisenustein&Loeb1996:Moetal.—1998).," A key tool in studying galaxy evolution is the semi-analytic model approach to relating the observable properties of galaxies to the underlying formation physics \citep{eis96,mo98}."1018. Semi-aualytic iuodels of galaxy formation predict. observables such as the luninosity Duuction. radii. rotation curves. clustering statistics. colors. aud the stellar mass of galaxies.," Semi-analytic models of galaxy formation predict observables such as the luminosity function, radii, rotation curves, clustering statistics, colors, and the stellar mass of galaxies."1019 Cnedinetal.(2007) and have shown that semi-analytic inodels cau predict the joint distrinition of. galaxy. observables. with model parameters that depend ou the baryouic mass profile. where the baryonic mass prolile includes the stellar mass aud gas mass.," \cite{gne07} and \cite{dut07} have shown that semi-analytic models can predict the joint distribution of galaxy observables, with model parameters that depend on the baryonic mass profile, where the baryonic mass profile includes the stellar mass and gas mass."1020 Budgeting barvouic mass into stellar mass aid gas mass is au important tuuable parameter in the modeling (MeCGaugh2005)., Budgeting baryonic mass into stellar mass and gas mass is an important tunable parameter in the modeling \citep{mcg05}.1021. One major difficulty. lies in couvertiug multi-waveleneth imaging clea iuto the stellar mass. where the multi-wavelenetli imaging data is inherently. noisy.," One major difficulty lies in converting multi-wavelength imaging data into the stellar mass, where the multi-wavelength imaging data is inherently noisy."1022 Large surveys produce multi-waveleneth[n] maps of galaxies. which are used to measure the o»wvouic properties of tlie galaxy. population.," Large surveys produce multi-wavelength maps of galaxies, which are used to measure the baryonic properties of the galaxy population."1023 Large surveys produce large data sets. which are comparable in size to modern simulations (DeLucjaetal.2006:Bower2006).," Large surveys produce large data sets, which are comparable in size to modern simulations \citep{del06,bow06}."1024. Since moclels ol galaxy formation predict stellar mass and surface deusity. the multi-wavelength maps of galaxies must be couverted into stellar populatious sing svuthetic stellar population models (MarastonBrugual&Charlot 2003).," Since models of galaxy formation predict stellar mass and surface density, the multi-wavelength maps of galaxies must be converted into stellar populations using synthetic stellar population models \citep{mar05,bru03}."1025. In order to anaye the stellar populations in multi-wavelenetl lunages of galaxies. uoise-recuctiou techniques mus be employed.," In order to analyze the stellar populations in multi-wavelength images of galaxies, noise-reduction techniques must be employed."1026 Large surveys are key to auswerine these questions because they provide data unilorlity over a large area of tje sky., Large surveys are key to answering these questions because they provide data uniformity over a large area of the sky.1027 SDSS provides ugriz-band data over of the sky with a photometric calibratior accuracy good to 2001)..., SDSS provides $ugriz$ -band data over of the sky with a photometric calibration accuracy good to \citep{ive04}.1028 The existence of these noisy. but τιiform and large. data sets. along with the ueed for stellar population mocleling. requires a suooting techuique for multi-waveleugtli data sets.," The existence of these noisy, but uniform and large, data sets, along with the need for stellar population modeling, requires a smoothing technique for multi-wavelength data sets."1029 A study similar to this one is (Lanyou-Fosteretal.(2007): hereafter LOT). which studies the pixel color maguitucde relation [or nearby galaxies.," A study similar to this one is \cite{lan07}; hereafter L07), which studies the pixel color magnitude relation for nearby galaxies."1030 LOT noted the distinct difference of pixel color magnitude diagrams with different. Hubble types. where Early-type [n]galaxies liave redder pCDMIs.," L07 noted the distinct difference of pixel color magnitude diagrams with different Hubble types, where Early-type galaxies have redder pCDMs."1031 LOT uoted how morphological features were related to distinct features in the pCDML, L07 noted how morphological features were related to distinct features in the pCDM.1032 Scatter in a pCDNI was caused by extinction. showing the ueed for accurate ISM extinction models when mocleling observed colors.," Scatter in a pCDM was caused by extinction, showing the need for accurate ISM extinction models when modeling observed colors."1033 The W.study by LOT shows how pixel maps of galaxies are correlated with ealaxy type. and iight. reveal hidden features.," The study by L07 shows how pixel maps of galaxies are correlated with galaxy type, and might reveal hidden features."1034 LOT does not employ uoise-reduction techniques. stich as tlie oues presented in this paper. which may affect the structwe of the pixel diagratus.," L07 does not employ noise-reduction techniques, such as the ones presented in this paper, which may affect the structure of the pixel diagrams."1035 Another study similar to this one is Welikalaetal.(2008)., Another study similar to this one is \cite{wel08}.1036. Welikalaetal.(2008) used the pixel-z technique. which combines stellar population syvutlesis mocels with multi-waveleneth pixel photometry of galaxies to study the stellar population couteut of SDSS galaxies.," \cite{wel08} used the pixel-z technique, which combines stellar population synthesis models with multi-wavelength pixel photometry of galaxies to study the stellar population content of SDSS galaxies."1037"bar formation evaluated at the initial position and velocity—or, equivalently, at the initial orbit since the initial distribution function is time-independent.","bar formation evaluated at the initial position and velocity—or, equivalently, at the initial orbit since the initial distribution function is time-independent."1038" Since the Hercules stream is only apparent in the planar motions in the disk 2009b),, we only consider a two-dimensional model for the Galaxy."," Since the Hercules stream is only apparent in the planar motions in the disk , we only consider a two-dimensional model for the Galaxy."1039 We use a simple power-law rotation curve to model the axisymmetric Galactic potential where iis the distance from the Sun to the Galactic center., We use a simple power-law rotation curve to model the axisymmetric Galactic potential where is the distance from the Sun to the Galactic center.1040 For most of the simulations below we specify this model further to a flat rotation curve (3=0)., For most of the simulations below we specify this model further to a flat rotation curve $\beta = 0$ ).1041" The model for the bar is given by the following potential Here€) is the pattern speed of the bar andHj is the bar radius, which is fixed to be 80percent of the bar's corotation radius."," The model for the bar is given by the following potential Here is the pattern speed of the bar and is the bar radius, which is fixed to be 80 percent of the bar's corotation radius."1042" The bar is grown smoothly during a time t,, always set to half of the total integration time in what follows, using the prescription A comparison of the local velocity distribution obtained by using this simple bar potential with that resulting from the more realistic one of shows that this simple potential is sufficient to model the bar's influence on stellar orbits in the outer disk."," The bar is grown smoothly during a time $t_1$, always set to half of the total integration time in what follows, using the prescription A comparison of the local velocity distribution obtained by using this simple bar potential with that resulting from the more realistic one of shows that this simple potential is sufficient to model the bar's influence on stellar orbits in the outer disk."1043" For the distribution function of the stellar disk before bar formation, we use a Dehnen distribution function given by whereR,, L,, and Q(R,) are the radius, angular momentum, and angular frequency, respectively, of the circular orbit with energy E."," For the distribution function of the stellar disk before bar formation, we use a Dehnen distribution function given by where, , and $\Omega(\rE)$ are the radius, angular momentum, and angular frequency, respectively, of the circular orbit with energy $E$."1044" Using the procedure given in§ 3.2 of (1999a), we choose the X(R) and or(R) functions such that they reproduce a disk with exponential surface density andvelocity dispersionprofiles"," Using the procedure given in 3.2 of , we choose the $\Sigma(R)$ and $\sigmaR(R)$ functions such that they reproduce a disk with exponential surface density andvelocity dispersionprofiles"1045eeneral condition for a quark bubble formation in a neutron star core: The quark bubble formation rate essentially depends on the enthalpy difference in the two phases.,general condition for a quark bubble formation in a neutron star core: The quark bubble formation rate essentially depends on the enthalpy difference in the two phases.1046 In the density range of interest. all the neutron matter EOS can be very. well parameterized as polviropes. Nn;(Lugones.Benvenuto&Vucetich 1994).," In the density range of interest, all the neutron matter EOS can be very well parameterized as polytropes, }$ ."1047".. The corresponding energy density in the neutron. phase is —zlvn,,leadingto ."," The corresponding energy density in the neutron phase is }$ , leading to }$."1048 τι also assume that the formed quark bubble consist of wand d quarks in the ratio 1:2: only later weak interactions may change (he composition ilo an enereelically more favorable state., We also assume that the formed quark bubble consist of $u$ and $d$ quarks in the ratio $1:2$; only later weak interactions may change the composition to an energetically more favorable state.1049" The quarks chemical potentials are related bv pg=217pus and. assuming chemical equilibrium across the phase boundary. we also have Mn=qu2p(A1Ὁpu,1994)..."," The quarks chemical potentials are related by $\mu1050_{d}=2^{1/3}\mu _{u}$, and, assuming chemical equilibrium across the phase boundary, we also have $\mu _{n}=\mu _{u}+2\mu _{d}=\left( 1+2^{4/3}\right)1051\mu _{u}$."1052" Then the pressure in the quark phase is. (assuming. a simple. bag model). 2,=P.rhTnvto adc τα=3D,4 B1998). giving ie,=dou.πα—3B."," Then the pressure in the quark phase is (assuming a simple bag model) $P_{q}=\frac{\mu _{u}^{4}+\mu _{d}^{4}}{4\pi ^{2}}-B$ and $%1053\varepsilon _{q}=3P_{q}+ B, giving $w_{q}=\frac{\mu1054_{u}^{4}+\mu _{d}^{4}}{\pi ^{2}}-3B$."1055" Hence. the enthalpy difference- in the two phases can be approximated by Assuming that the enerev flow is provided by the viscous effects only. one obtains for the prefactor (he expression In the limit of zero barvon number. A,—0 and we obtain the result of(1992a)."," Hence, the enthalpy difference in the two phases can be approximated by Assuming that the energy flow is provided by the viscous effects only, one obtains for the prefactor the expression In the limit of zero baryon number, $\lambda _{n}\rightarrow 0$ and we obtain the result of."1056". If the matter is barvon-rich. but viscous damping is negligible. j,,.£,—0. and we obtain (he results of andIxat5."," If the matter is baryon-rich, but viscous damping is negligible, $\eta _{n},\xi1057_{n}\rightarrow 0$, and we obtain the results of and."1058. Therefore the condition of the formation of a quark bubble is given bv The transport properties of dense matter have been intensively investigated in both high enerev physics and astrophysical frameworks, Therefore the condition of the formation of a quark bubble is given by The transport properties of dense matter have been intensively investigated in both high energy physics and astrophysical frameworks1059known. we argue that reasonable estimates for all of their can be obtained. and thus infer that mach of the fibuneutary structure contaimiug the protoealactic uiedimu. was directly impacted by the expanding overpressured lobes of radio galaxies born duriug the quasar era (83).,"known, we argue that reasonable estimates for all of them can be obtained, and thus infer that much of the filamentary structure containing the protogalactic medium was directly impacted by the expanding overpressured lobes of radio galaxies born during the quasar era 3)."1060 The role iu trigecring the dramatic star formation activity seen at 2~ 12 should therefore be closely examined., Their role in triggering the dramatic star formation activity seen at $z \sim~$ 1–2 should therefore be closely examined.1061" As hiehliehted by BRW99. the depletion. of cucrectic articles due to adiabatic aud euliauced IC losses at > can lead to a ""youth-redshüft degeneracy (Dluudell Rawhues 1999)."," As highlighted by BRW99, the depletion of energetic particles due to adiabatic and enhanced IC losses at $z$ can lead to a “youth-redshift degeneracy” (Blundell Rawlings 1999)."1062 With increasing +. radio galaxies will oulv (0 observed in progressively earlier phases in any fiux indted survey.," With increasing $z$, radio galaxies will only be observed in progressively earlier phases in any flux limited survey."1063 Taking a fixed lifetime T. of 5«105 vr for he unclear activity. BRW99 have argued that at -=2h.a source with a fairly high beam power of 2« LOW would vecolme undetectable after only a few Myr. even in the deepest meter-waveleugth (151 MITZ) complete samples with redshift data.," Taking a fixed lifetime $T$, of $5 \times 10^8$ yr for the nuclear activity, BRW99 have argued that at $z = 2.5$, a source with a fairly high beam power of $2 \times 10^{38}$ W would become undetectable after only a few Myr, even in the deepest meter-wavelength (151 MHz) complete samples with redshift data."1064 We define the fractional duration of detectability. f;=το. with r the time for which the source remus above the flux deusitv Bait of the survey.," We define the fractional duration of detectability, $f_d \equiv \tau/T$, with $\tau$ the time for which the source remains above the flux density limit of the survey."1065 It should be noted that even after falling below the detection threshold. the lobes of such a radio source will coutiuue to eyYOW TL size.," It should be noted that even after falling below the detection threshold, the lobes of such a radio source will continue to grow in size."1066 Wilile wei have drawn upon the most recent and sophisticated imodels for beam dvuamics. which successfully reproduces ao lavee umber of slices in theobserved 1D. τα) parameter space. the poor uuderstanding of the hieh-: circumealactic medi introduces uucertaimties. as does the neutral asstuuption of a vedshift independent active lifetime. T.," While we have drawn upon the most recent and sophisticated models for beam dynamics, which successfully reproduces a large number of slices in theobserved $P,D,z,\alpha$ ] parameter space, the poor understanding of the $z$ circumgalactic medium introduces uncertainties, as does the neutral assumption of a redshift independent active lifetime, $T$."1067 Iu the DRW99 model. the total length of the source. D(f). is related to the power in cach beam. Qu: The ambicut density profile is paaí(r)=potrfag) with reasonable values being py=1.67«10κοm? «y=10 kpc. ο=L5. aud ey=Ls.," In the BRW99 model, the total length of the source, $D(t)$, is related to the power in each beam, $Q_0$: The ambient density profile is $\rho_{\rm ext}(r) = \rho_0 (r/a_0)^{-\beta}$, with reasonable values being $\rho_0 = 1.67 \times 10^{-23}{\rm kg}~{\rm m}^{-3}$, $a_0 = 10~$ kpc, $\beta = 1.5$, and $c_1 = 1.8$."1068 In the absence of a consensus ou the cosimological evolution of these paralucters. we follow BRW99 in makine the neutral assuniptioun that 09.7. py and T are independent of +: however. we allow for d€T/1Qv«€5.," In the absence of a consensus on the cosmological evolution of these parameters, we follow BRW99 in making the neutral assumption that $a_0, \beta$, $\rho_0$ and $T$ are independent of $z$; however, we allow for $1 \le T/10^8{\rm y} \le 5$."1069" ere we consider cosmolosies with fy=50kmsBITSlO,0 or 1. aud O4—0."," Here we consider cosmologies with $H_0 = 50~ {\rm km~ s}^{-1} 1070{\rm Mpc}^{-1}, \Omega_{\rm M} = 0$ or $1$, and $\Omega_{\Lambda} = 0$."1071 The nost recent determination of the cosmological evolution of the RLF is based on three fiux-lHinited samples derived frou surveys at low radio frequencies (151/178 AIIIz). the YCRS. 6CE. and 3CRR. which are complete above the fiux deusitv liuits ranging from 0.512 Jv at 151 MIIZ (Willott et 22001).," The most recent determination of the cosmological evolution of the RLF is based on three flux-limited samples derived from surveys at low radio frequencies (151/178 MHz), the 7CRS, 6CE, and 3CRR, which are complete above the flux density limits ranging from $0.5 - 12$ Jy at 151 MHz (Willott et 2001)."1072 Spectroscopic redshitts obtained for of the total of 357 sources in these samples provide an unprecedented coverage of the Poi plane. aud thereby cau resolve substantially the degeneracy between bIunünositv. P. aud 2.," Spectroscopic redshifts obtained for of the total of 357 sources in these samples provide an unprecedented coverage of the $P-z$ plane, and thereby can resolve substantially the degeneracy between luminosity, $P$, and $z$."1073 The selection at low frequencies minimizes the orientation bias due to relativistic beaming aud hence the morphological diversity of sources., The selection at low frequencies minimizes the orientation bias due to relativistic beaming and hence the morphological diversity of sources.1074 Note that the derived RLFs oulv reflect the sources that are visible above the 0.5 Jv Bit of the deepest sample. so the computed duratious of the visible phase at 151 MITz in the BRW99 inodel at can be directly applied to these RLFs in a self-consisteut manner.," Note that the derived RLFs only reflect the sources that are visible above the 0.5 Jy limit of the deepest sample, so the computed durations of the visible phase at 151 MHz in the BRW99 model at can be directly applied to these RLFs in a self-consistent manner."1075" The verv rapid cosmological evolution of the more powerful sources. of Panaroft-Rilev (1971. FR) Type IL with Piz,21οOWIIzlayPanakes the RLF at :—2.5 esseutiallv flat between that power and log P5;=27. above which the RLF declines rapidly."," The very rapid cosmological evolution of the more powerful sources, of Fanaroff-Riley (1974, FR) Type II, with $P_{151} \ge 10^{25.5} 1076{\rm W~Hz}^{-1}{\rm sr}^{-1}$ makes the RLF at $z \simeq 2.5$ essentially flat between that power and log $P_{151} = 27$, above which the RLF declines rapidly."1077 By ~2. the RLF of powerful sources has risen by nearly 3 dex above the local RLF. followed by a possible slow decline at higher redshifts (Willott et 22001: also Jarvis Rawlings 2000).," By $z \sim 2$, the RLF of powerful sources has risen by nearly 3 dex above the local RLF, followed by a possible slow decline at higher redshifts (Willott et 2001; also Jarvis Rawlings 2000)."1078 As our main concern is with the volume euconpassed by radio lobes diving the cutive quasar era. we shall cousider all powerful. i.c. all FR IL. radio sources. whether radio ealaxies or quasars.," As our main concern is with the volume encompassed by radio lobes during the entire quasar era, we shall consider all powerful, i.e., all FR II, radio sources, whether radio galaxies or quasars."1079" The comoving space deusitv of FR II sources around logP4;4,=25.5 is pon.&(6.3.3.1]N10*Mpe.""(AlogPis1) 1. where. throughout this paper. ors of values iu square brackets are for O4; = 1 and V respectively 33 of Willott et 22001)."," The comoving space density of FR II sources around $\log P_{151} = 25.5$ is $\rho_{\rm obs} \simeq [6.3,3.1] \times 10^{-7} ~{\rm Mpc}^{-3}1080(\Delta {\log} P_{151})^{-1}$ , where, throughout this paper, pairs of values in square brackets are for $\Omega_M$ = $1$ and $0$, respectively 3 of Willott et 2001)."1081" Tn order o correct these observed values of pop, for the sources which have fallen below the detection limit. they should )o divided by the appropriate value of fy."," In order to correct these observed values of $\rho_{\rm obs}$ for the sources which have fallen below the detection limit, they should be divided by the appropriate value of $f_d$."1082 The αμαιο- results presented iu BRW99 113 aud 11) permit a conservative useful estimate of the mean of fy at τς2., The simulation results presented in BRW99 13 and 14) permit a conservative useful estimate of the mean of $f_d$ at $z = 2$.1083 A nore detailed calculation is underway (Jxulkarui. Copal- Wiita 2001).," A more detailed calculation is underway (Kulkarni, Gopal-Krishna Wiita 2001)."1084" We infer that for a source to appear at all iu the BRW99 dataset it must have à Qu>LW= Q,. where it will have loePj5;=27.0 at an carly evolutionary stage (7~dMyr)."," We infer that for a source to appear at all in the BRW99 dataset it must have a $Q_0 > 7.5 \times 10^{37}{\rm W}1085\equiv Q_m$ , where it will have ${\log} P_{151} = 27.0$ at an early evolutionary stage $\tau \simeq 1~$ Myr)."1086" A source with Quy=2< 107W has 7~9 Myr. while one with Qu=13« LOW has z~70 Myr. so that. roughly. τν OW. for Qu>Q,,."," A source with $Q_0 = 2 \times 10^{38}$ W has $\tau \simeq 9$ Myr, while one with $Q_0 = 1.3 \times 10^{40}$ W has $\tau \simeq 70$ Myr, so that, roughly, $\tau \propto Q_0^{0.5}$ , for $Q_0 > Q_m$."1087 Assuming a fixed lifetime for all radio galaxies. Z5;=(σουMyr) (cf.," Assuming a fixed lifetime for all radio galaxies, $T_5 = (T/500~{\rm Myr})$ (cf."1088" DRW99). a source will coutiuue to expand its lobes for au extra factor of T/r=! times beyond the age at which it falls low the detectionf, threshold of their deepest sample."," BRW99), a source will continue to expand its lobes for an extra factor of $T/\tau = f_d^{-1}$ times beyond the age at which it falls below the detection threshold of their deepest sample."1089" Using the same probability distribution of beam powers as clupirically inferred by BRW99. p(Q)dQoxQy2), or Quin=5xΛα<Quy«107W—Qu and p(Qu)=0 otherwise. we find that. normalizing to Qi=1.3« 10. for which f;=0.11T,+ 113 of DRW99). (fj=061L£;~L5«10?Tet. This correction factor should be applied to the observed source deusifies at and above the luminosity where the RLF(2= 2) steepens. that is for logP4541=26.5 for Oy,= Land logePy,=27.0 for Oxy=0 (see 33 of Willott et 22001)."," Using the same probability distribution of beam powers as empirically inferred by BRW99, $p(Q) dQ_0 \propto Q_0^{-2.6}dQ_0$ for $Q_{\rm min} \equiv 5 \times 10^{37}{\rm W} < Q_0 < 10905 \times 10^{42}{\rm W} \equiv Q_{\rm max}$ and $p(Q_0) = 0$ otherwise, we find that, normalizing to $Q_0^* = 1.3 \times 10^{40}$ W, for which $f_d^* = 0.14~T_5^{-1}$ 13 of BRW99), $\langle f_d \rangle = 0.11f_d^* \simeq 1.5 \times 10^{-2}~T_5^{-1}.$ This correction factor should be applied to the observed source densities at and above the luminosity where the $z = 2$ ) steepens, that is for $\log P_{151} \ge 26.5$ for $\Omega_{\rm M} = 1$ and $\log P_{151} \ge 27.0$ for $\Omega_{\rm M} = 0$ (see 3 of Willott et 2001)."1091 For the remaining FR II sources. Lc. those appearing at lower huuinosities iu the RLF at ;D—2.fqds clearly expected to be still analler. iu that such sources will have 7<1 Myr (BRBW99).," For the remaining FR II sources, i.e., those appearing at lower luminosities in the RLF at $z = 2$, $f_d$ is clearly expected to be still smaller, in that such sources will have $\tau < 1$ Myr (BRW99)."1092" Furthermore. these estimates of fy for +=2 are conservative upper limits for 2= 2.5. close to the peak of the quasar era (6,0, Rawlines 20013. and where the CMDR is even strougcr."," Furthermore, these estimates of $f_d$ for $z=2$ are conservative upper limits for $z = 2.5$ , close to the peak of the quasar era (e.g., Rawlings 2001), and where the CMBR is even stronger."1093 Tn addition. there will be a larger population of radio sources at ;=2.5 which are simply not detected. because their powers are too low even atcarly stages. but which will also ciuuulatively inflate a substantial lobe voluue.," In addition, there will be a larger population of radio sources at $z = 2.5$ which are simply not detected, because their powers are too low even atearly stages, but which will also cumulatively inflate a substantial lobe volume."1094 It is known that starburst activity can occur along the, It is known that starburst activity can occur along the1095Never before in the nearly 14 vears of continuous research of large-scale coronal waves homologous EIT wave events were reported.,Never before in the nearly 14 years of continuous research of large-scale coronal waves homologous EIT wave events were reported.1096 We are the first to present a study of homologous EIT waves. emerging from the same AR within a short period of time.," We are the first to present a study of homologous EIT waves, emerging from the same AR within a short period of time."1097 Thev travel into the same direction and their fronts have similar shape and angular extent., They travel into the same direction and their fronts have similar shape and angular extent.1098 They propagate into a quiet Sun area. surrounded by ARs to the north and south aud a laree coronal hole close io the northern polar region mimovie 1).," They propagate into a quiet Sun area, surrounded by ARs to the north and south and a large coronal hole close to the northern polar region movie 1)."1099 As is expected for nonlinear magnetosonic waves. they do not penetrate into these regions of increased Alfvénn velocity (seealsoal.2003:Gopalswauivet 2009).," As is expected for nonlinear magnetosonic waves, they do not penetrate into these regions of increased Alfvénn velocity \citep[see also][]{veronig08,gopalswamy09}."1100. In our study we compared [ον the first time different methods of deriving (he wave kinematics. (he (rather subjective) visual method and the (more objective) profile method.," In our study we compared for the first time different methods of deriving the wave kinematics, the (rather subjective) visual method and the (more objective) profile method."1101 Both methods vield consistent results. i.e. the waves propagate at constant velocities ~220kms! for the weakest wave up to ~340kms for the strongest event.," Both methods yield consistent results, i.e. the waves propagate at constant velocities $\sim220\mathrm{\,km\,s}^{-1}$ for the weakest wave up to $\sim340\mathrm{\,km\,s}^{-1}$ for the strongest event."1102 Furthermore. we calculated the perturbation profiles to study. the physical characteristics and evolution of the disturbances.," Furthermore, we calculated the perturbation profiles to study the physical characteristics and evolution of the disturbances."1103 The strong imitial steepening of the perturbation amplitudes confirms that these features are indeed shocks. albeit only weak shocks. since (hev peak at low intensity values |<1.25. Assuming these coronal waves to constitute large-scale fast magnetosonie waves. the measured velocities lie well within the velocity range of 210—350kms.+ for fast magnetosonic waves lor quiet Sun conditions.," The strong initial steepening of the perturbation amplitudes confirms that these features are indeed shocks, albeit only weak shocks, since they peak at low intensity values $A < 1.25.$ Assuming these coronal waves to constitute large-scale fast magnetosonic waves, the measured velocities lie well within the velocity range of $210 - 350\mathrm{\,km\,s}^{-1}$ for fast magnetosonic waves for quiet Sun conditions."1104" In the MIID approach the quantities delining a shock wave in (he solar corona are: Ma, shock magnetosonic Mach number. AX. density jump al the shock front. J... angle between shock [ront and magnetic field. ων plasima-beta."," In the MHD approach the quantities defining a shock wave in the solar corona are: $M_{\mathrm{ms}}$ shock magnetosonic Mach number, $X_{\mathrm{c}}$ density jump at the shock front, $\vartheta$ angle between shock front and magnetic field, $\beta_{\mathrm{c}}$ plasma-beta."1105 Thev are related by (he Rankine-IIugoniot (RII) conditions for an oblique shock (¢.fPriest1982)., They are related by the Rankine-Hugoniot (RH) conditions for an oblique shock \citep[c.f.][]{priest82}.1106. Considering a perpendicular shock the RII relation reduces to with a polvivopic index 5 of 5/3., Considering a perpendicular shock the RH relation reduces to with a polytropic index $\gamma$ of $5/3$.1107 Studies of Visnaketal.(2002) indicate that ;2x0.1 in (he quiet Sun's low corona., Studies of \citet{vrsnak02} indicate that $\beta\approx0.1$ in the quiet Sun's low corona.1108" Using the previously calculated. density. jumps A, (cf.", Using the previously calculated density jumps $X_c$ (cf.1109 Sect. 3.2...," Sect. \ref{wavekin},"1110" Nox V/A). we derive for the peak magnetosonic Mach munbers M4, 1.06 (wave 1). 1.04 (wave 2). 1.05 (wave 3). and 1.09 (wave 4)."," $X_c \propto\sqrt{A}$ ), we derive for the peak magnetosonic Mach numbers $M_{\mathrm{ms}}$ = $1.06$ (wave 1), $1.04$ (wave 2), $1.05$ (wave 3), and $1.09$ (wave 4)."1111 With these observations of homologous waves. we can [or the first (me perform a «quantitative analvsis of the characteristic wave parameters without any. limiting factors like changing or unknown quiet Sun background conditions.," With these observations of homologous waves, we can for the first time perform a quantitative analysis of the characteristic wave parameters without any limiting factors like changing or unknown quiet Sun background conditions."1112 The top panel of Fig., The top panel of Fig.11135. shows the calculated magnetosonic Mach number versus the propagation velocities ὃς of the four waves. revealing a distinet correlation between the wave characteristics Af. and ve with a correlation coefficient of R?x 0.99. Such correlation is expected [or nonlinear [ast-mode,"\ref{fig5} shows the calculated magnetosonic Mach number versus the propagation velocities $v_{\mathrm{c}}$ of the four waves, revealing a distinct correlation between the wave characteristics $M_{\mathrm{ms}}$ and $v_{\mathrm{c}}$ with a correlation coefficient of $R^2\approx0.99$ Such correlation is expected for nonlinear fast-mode"1114Ellipsoicd mantle with axial ratio 432 and spherical nanodiamond core in three dilferent volume percentages as shown in Table 2 are taken.,Ellipsoid mantle with axial ratio 432 and spherical nanodiamond core in three different volume percentages as shown in Table 2 are taken.1115 No particle size distribution is chosen. as μια is a constant and the normalized exGnetion will be essentially the same for all the particle size distributions.," No particle size distribution is chosen, as $Q_{ext}/a$ is a constant and the normalized extinction will be essentially the same for all the particle size distributions."1116 The three components are linearly. combined with p. q and s contributory weights and resulting extinction is compared wilh the average galactic values (Whittet.2003)..," The three components are linearly combined with p, q and s contributory weights and resulting extinction is compared with the average galactic values \citep{whittet}."1117 The set ol reduced Y (Devington1969:Vaidyaetal.2001) are given by where pp is the degrees of freedom. 57(A;) is the model curve (j=! to 3 for silicate. eraphite and nanodiamoncd-eraphite p. q ancl s fractions respectively) and TZ;(A;) is the observed value at wavelength Aj.," The set of reduced $ \chi^2_j$ \citep{bevington69,vaidya01} are given by where pp is the degrees of freedom, $S^j_i(\lambda_i)$ is the model curve (j=1 to 3 for silicate, graphite and nanodiamond-graphite p, q and s fractions respectively) and $T_i(\lambda_i)$ is the observed value at wavelength $\lambda_i$."1118 The p. q. s combinations that give minimized 4? are shown in Table 2 with corresponding graphs in fig.3.," The p, q, s combinations that give minimized $\chi^2$ are shown in Table 2 with corresponding graphs in \ref{fig8}."1119. The 2175 peak modifications and the Eu-UV rise are simultauneouslv explained on incorporation of very small percentage of nanodiamondis., The 2175 peak modifications and the far-UV rise are simultaneously explained on incorporation of very small percentage of nanodiamonds.1120 For comparison Table 2 also shows the 0% nanodiamond. two component model. that eives 0.40 silicate and 0.49 eraphite fractions.," For comparison Table 2 also shows the $0\%$ nanodiamond, two component model, that gives 0.40 silicate and 0.49 graphite fractions."1121 This is well within estimated silicate aud eraphite grain abundances (Draine&Lee1984)., This is well within estimated silicate and graphite grain abundances \citep{draine-lee84}.1122. On adding nanodiamond-graphite nantle particles as the third component (he fit improves., On adding nanodiamond-graphite core-mantle particles as the third component the fit improves.1123 This verv small erain component is a small Traction of carbonaceous particles having even smaller nanocdiamond core., This very small grain component is a small fraction of carbonaceous particles having even smaller nanodiamond core.1124 That is much lower than the 1054 upper limit of ISM. nanodiamond reported by (1989)., That is much lower than the $10\%$ upper limit of ISM nanodiamond reported by \citet{lewis89}.1125. The core-amantle component also reduces the eraphite fraction slehtly and changes jeglieiblv the relative fraction of silicates., The core-mantle component also reduces the graphite fraction slightly and changes negligibly the relative fraction of silicates.1126 The 47 values increase wilh increasing percentage of nanodiamond in graphite mantle but its overall contribution (Iraction s) decreases., The $\chi^2$ values increase with increasing percentage of nanodiamond in graphite mantle but its overall contribution (fraction `s') decreases.1127 The Taction of nanodiamond-graphite is also much smaller than used by Aannestad(1995). for 5nm nanocdiamond grains., The fraction of nanodiamond-graphite is also much smaller than used by \citet{aannestad95} for $5~nm$ nanodiamond grains.1128 Considering nanocdiamond density of 3.52 em/ce the nanocdiamonds in our models are <0.154 fraction of carbonaceous particles., Considering nanodiamond density of 3.52 gm/cc the nanodiamonds in our models are $< 0.1\%$ fraction of carbonaceous particles.1129 The best fit. in the complete," The best fit, in the complete"1130approach to modelling the evolution of the emission due to accretion onto SMDlIs.,approach to modelling the evolution of the emission due to accretion onto SMBHs.1131 At low redshift (2<2) we use the well established observed X-ray luminosity functions. which extend to impressively faint luminosities.," At low redshift $z<2$ ) we use the well established observed X-ray luminosity functions, which extend to impressively faint luminosities."1132 At intermediate redshift. where the X-ray luminosity function becomes less reliable. we use a mereer-driven CDAI-like model with a range of assumptions for the decline of the accretion rate onto the central. BIL during a merger.," At intermediate redshift, where the X-ray luminosity function becomes less reliable, we use a merger-driven CDM-like model with a range of assumptions for the decline of the accretion rate onto the central BH during a merger."1133 Vhis model is calibrated: using the extensive optical data as well as the available X-ray cata., This model is calibrated using the extensive optical data as well as the available X-ray data.1134 In Section 4 we describe an extension of the merger-driven. model. as well as models for growth via continuous Eddington limited: accretion. with a range of cluty eveles. to very high. redshift. (2= 6).," In Section 4 we describe an extension of the merger-driven model, as well as models for growth via continuous Eddington limited accretion with a range of duty cycles, to very high redshift $z>6$ )."1135 Recently 7T. constructed. an observationally anchored: model for the evolution of the SMDBII population which indicates. that the quasar duty evele increases with increasing reclshilt. providing some empirical impetus for this approach.," Recently \citet{shankar2007b} constructed an observationally anchored model for the evolution of the SMBH population which indicates that the quasar duty cycle increases with increasing redshift, providing some empirical impetus for this approach."1136 We first discuss the ingredients of our merger-driven nmocel in some detail., We first discuss the ingredients of our merger-driven model in some detail.1137 Me assume that the aceretion of gas onto SMDIIS. is predominantly triggered by major galaxy mergers. (?222).. and take the merger rate of dark matter haloes in the standard ACOAL model for structure formation as a proxy for the rate of galaxy mergers.," We assume that the accretion of gas onto SMBHs is predominantly triggered by major galaxy mergers \citep{kh2000,dimatteo2005,1138hopkins2005b}, and take the merger rate of dark matter haloes in the standard $\Lambda CDM$ model for structure formation as a proxy for the rate of galaxy mergers."1139 This picture is acimitteclvy simple but has nevertheless been shown to vield a reasonably consistent. model for many of the properties of the observed QLE and its evolution at. intermediate: redshifts (e.g. 227222).," This picture is admittedly simple but has nevertheless been shown to yield a reasonably consistent model for many of the properties of the observed QLF and its evolution at intermediate redshifts \citep[e.g.][]{hnr1998,wyithe2002, wyithe2003,1140volonteri2003, croton2006, marulli2007}."1141 In a merger-driven model. new quasars continuously form ata redshift and. luminosity. dependent rate.," In a merger-driven model, new quasars continuously form at a redshift and luminosity dependent rate."1142" We assume that the quasars become active with an initial peak Luminosity Lye and then fade according to a “facing law”. dlogL""-"," We assume that the quasars become active with an initial peak luminosity $L_{\rm peak}$ and then fade according to a “fading law”, $\frac{dt}{dlogL}$."1143" For a given model for the rate of formation of sources with peak luminosity Lick. (Lenk)=TMogkdunyay” the luminosity function. di ""uma be wrltten as We assume that Lyeu is the Eddington luminosity of the final mass DII."," For a given model for the rate of formation of sources with peak luminosity $L_{\rm peak}$, $\dot{n}(L_{\rm peak}) = \frac{d^2n}{dlogL_{\rm1144peak}dt}$, the luminosity function, $\frac{dn}{dlogL}$, can be written as We assume that $L_{\rm peak}$ is the Eddington luminosity of the final mass BH."1145" We further assume thatdark matter halos host a central DII with mass Mi given by (c.g.7?) where (25,=Sou""m codτη land A=184|S2d—39d7 is the overdensitv of a virialised halo at redshift z."," We further assume thatdark matter halos host a central BH with mass $M_{\rm bh}$ given by \citep[e.g.][]{wyithe2003}1146 where $\Omega_m^z=\frac{\Omega_m(1+z)^3}{\Omega_m(1+z)^3+1147\Omega_\Lambda+\Omega_k(1+z)^2}$, $d \equiv \Omega_m^z-1$ and $\Delta_c=18\pi^2+82d-39d^2$ is the overdensity of a virialised halo at redshift $z$."1148" ""Fhis relationship is motivated by. the observed correlation between Ay and the velocity dispersion of the host galaxie's bulge. e (?77).."," This relationship is motivated by the observed correlation between $M_{\rm bh}$ and the velocity dispersion of the host galaxie's bulge, $\sigma$ \citep{ferrarese2002,1149shields2003}."1150 We assume that σ΄ may be approximated by eis V2. where ray is the virial velocity of the dark matter halo from. ?..," We assume that $\sigma$ may be approximated by $v_{\rm1151vir}/\sqrt{2}$ , where $v_{\rm vir}$ is the virial velocity of the dark matter halo from \citet{bl2001}."1152 Empirical estimates of a typically fallin the range 4...5., Empirical estimates of $\alpha$ typically fall in the range $4-5$.1153 We have chosen a=5 which is consistent with a simple scll-regulated growth scenario in which the DII grows until it radiates enough energy. to unbind the gas that is feeding it (e.g.2?7)..," We have chosen $\alpha = 5$ which is consistent with a simple self-regulated growth scenario in which the BH grows until it radiates enough energy to unbind the gas that is feeding it \citep[e.g.][]{silk1998,hnr1998,wyithe2003}."1154" Phe merger rate ση""m is taken as the merger rate of halos with final DII mass such that Lisa=Leavin)."," The merger rate $\frac{d^2n}{dlogL_{\rm peak}dt}$ is taken as the merger rate of halos with final BH mass such that $L_{\rm peak} = L_{\rm Edd}(M_{\rm1155bh})$."1156 Using equation (2)) to relate DII and host halo mass. we may write where the limits of integration ensure that we count only major mergers and NM.ANM.) is the merger rateof dark matter haloes of mass AJAAL and NM. per unit cosmic time /. Here JAGIGg— is the probability per unit time that a halo mass AAJMOM will merge with another halo to form a halo ∖∖↓↿↓↕⊔↓≼↧⊳∖⊳∖⇀∪⇂↓∪⊔↓≼⋃⊔⇂↕∣∖↼∖∣⊥∖∣↴↓⊳∖⇂↓∐⊳∖↓≻≼↧⊓∠⇂⋖⊔≱∖⊔∙∖E ; T ? 4 n 1 . ⋅⋆⇁ ∪⇂⋅↓⋯↓⇜∖∖⋰↓∣↓↕↿↓↕⋖⋅⋜↧↓≻↓≻↓⋅∪↓≻↓⋰↓⋜⋯⋅⊔↓⋜↧⊳∖⊳∖∠⇂⊀↓∐⋅∢⋅↓⋅⋖⊾⊔≼⇍⋖⋅∐⋅∪⊔↓⇀∙↗↿∖∖∖⋰∐↓↕ ⊔↓⋯∐∐≼⇍⋜⊔⊲↓∪↓↕∐⋅∪⊔↓⇀∙↗↦⊳∖⋖⋅∢⊾⇀∙↗⋜⋯∠⇂⇀∙↗⇂⋅∪↓⋅≻↕↓↥↓↕↓⋜↧↓⋅≼∼⋜↧↓≼∼⊔↓⋜∐⊲↓∪⊔⊳∖∃⊳," Using equation \ref{Mbh-Mhalo}) ) to relate BH and host halo mass, we may write where the limits of integration ensure that we count only major mergers and $\dot{N}(M, \Delta M, t)$ is the merger rateof dark matter haloes of mass $M-\Delta M$ and $\Delta M$ per unit cosmic time $t$ , Here $\left.\frac{d^2P}{d \Delta M dt} \right|_{M - \Delta1157M}$ is the probability per unit time that a halo mass $\Delta M$ will merge with another halo to form a halo with mass $M$ from \citet{lacey1993}, and $\frac{dn}{d(M- \Delta M)}$ is the space density of halos with the appropriate mass difference from \citet{ps1974} (with modification from \citet{sheth1999}, see \citet{rhook2006} and \citet{wyithe2003} for similarcalculations)."1158 Equation (3)) becomes inaccurate as hes⋅⋡∙∙ ∏≼↧↓≻↓≻↓⋖⋟≼↧≼the Llubble time at the relevant redshift., Equation \ref{bol_QLF}) ) becomes inaccurate as $\frac{dt}{dlogL}$ approaches the Hubble time at the relevant redshift.1159 Εις could. in principle be relevant at. high redshift. however at high redshift we are mainly concerned with the bright end of the OLE. for which the facing time-scale remains short (see Section ?7?)).," This could in principle be relevant at high redshift, however at high redshift we are mainly concerned with the bright end of the QLF for which the fading time-scale remains short (see Section \ref{fading_laws}) )."1160 Note that. for Toa(LeLos)constant (corresponding to an exponential lisht-curve) or apie(LeLye)x0LLys) (corresponding to a top-hat light-curve) the shape of the QLE is identical to that of MLyen).," Note that for $\frac{dt}{dlogL}(L,L_{\rm peak}) = {\rm constant}$ (corresponding to an exponential light-curve) or $\frac{dt}{dlogL}(L,L_{\rm peak}) \propto \delta(L-L_{\rm Lpeak})$ (corresponding to a top-hat light-curve) the shape of the QLF is identical to that of $\dot{n}(L_{\rm peak})$."1161 As discussed in the previous section. the faint end of the QLE is very sensitive to the assumed fading law.," As discussed in the previous section, the faint end of the QLF is very sensitive to the assumed fading law."1162 When two easerich ealaxies merge. the resulting tidal torques drive large amounts of gas into the central region. providing [uel for the rapid. growth of a SMDIL.," When two gas-rich galaxies merge, the resulting tidal torques drive large amounts of gas into the central region, providing fuel for the rapid growth of a SMBH."1163 Ehe facing of the quasar emission due the gas accretion onto a central SMDIL is governed. by the infall of gas to the centre and. its subsequent accretion onto the SALBLI during the late stages of the merger., The fading of the quasar emission due the gas accretion onto a central SMBH is governed by the infall of gas to the centre and its subsequent accretion onto the SMBH during the late stages of the merger.1164" ? used. numerical simulations of galaxy mergers. with a prescription for the subsequent accretion of gas onto a central SMDIL from ο, to obtain a physically motivated fading law."," \citet{hopkins2005b} used numerical simulations of galaxy mergers, with a prescription for the subsequent accretion of gas onto a central SMBH from \citet{dimatteo2005}, to obtain a physically motivated fading law."1165" ο present a power-law representation for this Facing law. dt which has been fit to the results of severalhundred: ""msimulations of mergers between equal mass galaxies resulting in quasars with peak bolometric luminosities between 107 and 1017 L.."," \citet{hopkins2005b} present a power-law representation for this fading law, $\frac{dt}{dlogL}$ , which has been fit to the results of severalhundred simulations of mergers between equal mass galaxies resulting in quasars with peak bolometric luminosities between $10^{8}$ and $10^{15}$ $_{\sun}$ ."1166 The power-law index depends on Lisa. withhigher luminosity quasars expected to spend relatively more time close to their IExddington limit.," The power-law index depends on $L_{\rm peak}$ , withhigher luminosity quasars expected to spend relatively more time close to their Eddington limit,"1167"At« 2h after energetic flares, whereas for At €[2h,4h] the number of observed flares is larger than the one expected for an uncorrelated process.","$\Delta t<2$ h after energetic flares, whereas for $\Delta t \in $ [2h,4h] the number of observed flares is larger than the one expected for an uncorrelated process."1168" The above results suggest that after a large flare a recovery time of about 2 hours takes place, when only a small number of flares is observed."," The above results suggest that after a large flare a recovery time of about $2$ hours takes place, when only a small number of flares is observed."1169 After this time the number of observed flares reaches a maximum value for At< 4h and then decreases to the background level for larger At., After this time the number of observed flares reaches a maximum value for $\Delta t \lesssim 4$ h and then decreases to the background level for larger $\Delta t$.1170" According to the dependence on e,, observed in Fig.4a, the recovery time can be a spurious effect related to obscuration."," According to the dependence on $e_{th}$ observed in Fig.4a, the recovery time can be a spurious effect related to obscuration."1171 The number of events n(t) occurring at the time ¢ after an energetic flare can be explicitly evaluated following the method of Lippiello (2008b))., The number of events $n(t)$ occurring at the time $t$ after an energetic flare can be explicitly evaluated following the method of Lippiello \cite{Lip2}) ).1172" More precisely, we define as a “main” flare an event with the energy E>E,4;=10E»o."," More precisely, we define as a “main” flare an event with the energy $E\ge E_{main}=10E_0$."1173" Indicating with f; the occurrence times of main-flares we compute the quantity N(t,Emain)=Din(t—t)8(ti44t), where @(x) is the Heaviside step function, and the sum extends over all main-flares."," Indicating with $t_i$ the occurrence times of main-flares we compute the quantity ${\cal N}(t,E_{main}) = \sum_{i} n(t-t_i)\Theta(t_{i+1}-t) 1174$, where $\Theta(x)$ is the Heaviside step function, and the sum extends over all main-flares."1175" Here n(t—tj) is the number of flares with an energy lower than 10 occurring during the time ¢—f; after the th main flare, and the sum extends over all main-flares in the catalog."," Here $n(t-t_i)$ is the number of flares with an energy lower than $10E_0$ occurring during the time $t-t_i$ after the i-th main flare, and the sum extends over all main-flares in the catalog."1176 Assuming that n(t—¢;) is time translationally invariant we obtain which represents the average number of flares occurring in a period of a duration ¢ after a mainflare.," Assuming that $n(t-t_i)$ is time translationally invariant we obtain, which represents the average number of flares occurring in a period of a duration $t$ after a mainflare."1177" The data (Fig.6a) agree with the previous results, with a maximum number of flares at f~ 4h, decaying at longer times."," The data (Fig.6a) agree with the previous results, with a maximum number of flares at $t\simeq 4$ h, decaying at longer times."1178" Notice that the asymptotic decay is consistent with a power law f? with p~1, reminiscent of the Omori law for seismic sequences (Omori 1894,, de Arcangelis et al 2006))."," Notice that the asymptotic decay is consistent with a power law $t^{-p}$ with $p\simeq 1$, reminiscent of the Omori law for seismic sequences (Omori \cite{Omo}, de Arcangelis et al \cite{deA}) )."1179 We now discuss the existence of correlations between energies of subsequent flares., We now discuss the existence of correlations between energies of subsequent flares.1180" In order to do so, we computed the energy distribution p(£) of the first πι flares occurring after a flare with a larger energy than a reference value E,."," In order to do so, we computed the energy distribution $\rho(E)$ of the first $m$ flares occurring after a flare with a larger energy than a reference value $E_r$ ."1181" Since the analysis is restricted to all flares with E>Eo, obviously p(£E) coincides with the flare energy distribution of the whole catalog pr(E), for E,=Eo."," Since the analysis is restricted to all flares with $E \ge E_0$, obviously $\rho(E)$ coincides with the flare energy distribution of the whole catalog $\rho_T(E)$ , for $E_r=E_0$."1182" In Fig.6b we plot óp(E)=p(E)—pr(E) for m=20 and different values of E,.", In Fig.6b we plot $\delta \rho (E)=\rho(E)-\rho_T(E)$ for $m=20$ and different values of $E_r$.1183 Similar results are obtained for other values of m., Similar results are obtained for other values of $m$.1184" Deviations from pr(E) become more and more evident for increasing values of Ε,.", Deviations from $\rho_T(E)$ become more and more evident for increasing values of $E_r$.1185" In particular, the higher E, is, the larger is the probability to have subsequent flares with higher energy and the lower is the probability to have small flares."," In particular, the higher $E_r$ is, the larger is the probability to have subsequent flares with higher energy and the lower is the probability to have small flares."1186" In order to get further insights in the correlations between flare energies, we computed the quantity óp(E;=AE;ΙΔ< T), ie. the difference between the conditional and the unconditional probability density to have the energy of the subsequent flare 2 times the previous one."," In order to get further insights in the correlations between flare energies, we computed the quantity $\delta p(E_{i}=\lambda E_{i-1}1187\vert \Delta t_i<T)$ , i.e. the difference between the conditional and the unconditional probability density to have the energy of the subsequent flare $\lambda$ times the previous one."1188" We found (Fig.7a) that for T= th, óp(E;=AE;At;«T) is significantly different from zero for all A values."," We found (Fig.7a) that for $T=1$ h, $\delta1189p(E_{i}=\lambda E_{i-1}1190\vert \Delta t_i<T)$ is significantly different from zero for all $\lambda$ values."1191 This indicates that the energies of two subsequent flares are correlated., This indicates that the energies of two subsequent flares are correlated.1192 Moreover we observed that these correlations depend on the time separation between the two flares and are practically zero for At; 10h (Fig.7a)., Moreover we observed that these correlations depend on the time separation between the two flares and are practically zero for $\Delta t_i>10$ h (Fig.7a).1193" We verified that this result is not affected by obscuration performing the same analysis for T= lh and different lower energy thresholds e,, (Fig.7b).", We verified that this result is not affected by obscuration performing the same analysis for $T=1$ h and different lower energy thresholds $e_{th}$ (Fig.7b).1194 We found that curves for different e;; coincide within statistical fluctuations., We found that curves for different $e_{th}$ coincide within statistical fluctuations.1195" This indicates that energy correlations and their dependence on time separation are a physical property, not a spurious effect due to obscuration."," This indicates that energy correlations and their dependence on time separation are a physical property, not a spurious effect due to obscuration."1196" Curves present a maximum for 2z1, indicating that it is more probable to find the next flare with ποπ βοΕυνιο]σσσ bot slightly higher than the previous one."," Curves present a maximum for $\lambda \gtrsim 1$, indicating that it is more probable to find the next flare with an energy close to but slightly higher than the previous one."1197" In conclusion, we presented a statistical analysis of the GOES catalog indicating the existence of time-energy correlations between successive events not to be attributed to obscuration effects."," In conclusion, we presented a statistical analysis of the GOES catalog indicating the existence of time-energy correlations between successive events not to be attributed to obscuration effects."1198" More precisely, we observed that for couples of events close in time (T« 1h), the second event tends to have a high energy."," More precisely, we observed that for couples of events close in time $T<1$ h), the second event tends to have a high energy."1199 Moreover couples of events distant in time between 1h and 10h have the first event with a highenergy., Moreover couples of events distant in time between 1h and 10h have the first event with a highenergy.1200 The analysis ofthe rate decay after large flares shows evidence that the largest number of events is detected about 4h after the occurrence, The analysis ofthe rate decay after large flares shows evidence that the largest number of events is detected about 4h after the occurrence

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