ReadingTimeMachine/rtm-sgt-ocr-v1

1source,target2"⇂⊳∖↥∩∖∖↽⋯⋯⇂≺↵2i 2EE 24: ⋅ ⋅ frequencies⋅ are oeiven⋅ by we.fis7 Ὀίωτ-,een>οαπ)τε0ο-⇁(ωρα/aAστ—kheie.12 where wy7=ck> ancl =í(k-.b)/p."," The fast and slow mode frequencies are given by $\omega^2_{f,s} =.5(\omega_b^2+\omega_s^2) \pm 0.5 \left(3(\omega_b^2+\omega_s^2)^2 - 4\omega_s^2 \omega_a^2 \right)^{1/2}$ where $\omega_s^2=c_s^2k^2$ and $\omega_a^2=(\kvec \cdot \bvec)^2/\rho$."4We7g- evolvedH the waves for one. period., We evolved the waves for one period.5" TheJ results for the"" fast andwy slow waves are shown in figures 3. aud. L. respectively."," The results for the fast and slow waves are shown in figures \ref{fig:fast}6 and \ref{fig:slow}, respectively."7 The slow wave is subject to substantial diffusion as compared to the [ast wave siuce its [requency isso uch lower for these extreme values of 5»., The slow wave is subject to substantial diffusion as compared to the fast wave since its frequency isso much lower for these extreme values of $\beta$.8 These 1d tests of the code involve a shock tube along the x-axis. as in fig.2a.b of ?..," These 1d tests of the code involve a shock tube along the x-axis, as in fig.2a,b of \citet{1998ApJ...509..244R}."9 We used continuous boundary coucditious aud 1021 grkl points for both tests., We used continuous boundary conditions and 1024 grid points for both tests.10" The initial conditions for lig.5 are (p.ey.cy.t:.pb,by.b.)=(1.10.0.0.20.5/νax.5/V15.0) for the left side and (1.10.0.0.1.5/VIm.15.0) for the right side."," The initial conditions for \ref{fig:shock1}11 are $(\rho,v_x,v_y,v_z,p,b_x,b_y,b_z)=12(1,10,0,0,20,5/\sqrt{4\pi},5/\sqrt{4\pi},0)$ for the left side and $(1,-10,0,0,1,5/\sqrt{4\pi},5/\sqrt{4\pi},0)$ for the right side."13 The code is run for a time 0.08L., The code is run for a time $0.08 L$.14 The result agrees well with ποσα of ?.., The result agrees well with fig.2a of \citet{1998ApJ...509..244R}.15 The following features cau be seen., The following features can be seen.16" The steep discontinulties atorQoL aud ar0.82 are fast shock frouts where the incoming flow couverts its kinetic energy into thermal energy aid compresses the trausverse field b,.", The steep discontinuities at $x\sim 0.1$ and $x\sim 0.85$ are fast shock fronts where the incoming flow converts its kinetic energy into thermal energy and compresses the transverse field $b_y$.17 As new matter [alls on. this shock is regenerated and maintains it’s steep profile as it moves outward.," As new matter falls on, this shock is regenerated and maintains it's steep profile as it moves outward."18 At ic~0.6 and pc90.2 are a slow shock aud W.slow rarefaction. respectively.," At $x\simeq 0.6$ and $x \simeq 0.5$ are a slow shock and slow rarefaction, respectively."19 The slow shock again compresses the fluicl but decreases the transverse field., The slow shock again compresses the fluid but decreases the transverse field.20 At ar20.55 the two phases of the initial gas configuration with different eutropies form a contact discontinuity., At $x\simeq 0.55$ the two phases of the initial gas configuration with different entropies form a contact discontinuity.21 Pressure. magnetic fiekl auc velocity are continuous while density aud thermal enerey experience a discontinuity.," Pressure, magnetic field and velocity are continuous while density and thermal energy experience a discontinuity."22 This discontuity moves rightward across the grid. aud the TVD advection of such discoutinuities results in some smeariug or diffusion of the structure.," This discontuity moves rightward across the grid, and the TVD advection of such discontinuities results in some smearing or diffusion of the structure."23 No pliysical mechauisma steepeus this contact. discontiuuitv once it sinears. aud a slow numerical diffusion is visible in this. aud all generic TVD codes which do uot introduce explicit contact steepeners.," No physical mechanism steepens this contact discontinuity once it smears, and a slow numerical diffusion is visible in this, and all generic TVD codes which do not introduce explicit contact steepeners."24 There are no significant oscillations., There are no significant oscillations.25" Both our aud ?""s solution have a slight overshoot in some variables in the first postshock cell. but this effect does uot persist onto subsequent cells."," Both our and \citet{1998ApJ...509..244R}' 's solution have a slight overshoot in some variables in the first postshock cell, but this effect does not persist onto subsequent cells."26 The initial couditiou for Ge.6 has velocity and maguetic field components in all directions. aud hence exhibits additional structures such asrotational discontinuities.," The initial condition for \ref{fig:shock2} has velocity and magnetic field components in all directions, and hence exhibits additional structures such asrotational discontinuities."27 The values are (p.ty.espbby.b.) = (1.08.1.2.0.01.0.5.0.05.ήνE.3.6/V/Ex.2/Ix) on the left side and (1.0.0.0.1.2//Ez.L/v/E.VDc) ou tlie right hand side.," The values are $(\rho,v_x,v_y,v_z,p,b_x,b_y,b_z)$ = $(1.08,1.2,0.01,0.5,280.95,2/\sqrt{4\pi},3.6/\sqrt{4\pi},2/\sqrt{4\pi})$ on the left side and $(1,0,0,0,1,2/\sqrt{4\pi},4/\sqrt{4\pi},2/\sqrt{4\pi})$ on the right hand side."29 The code is run for a time 0.2L., The code is run for a time $0.2 L$.30 The results again agreewith ?.., The results again agreewith \citet{1998ApJ...509..244R}.31 The following features may be seen: fast shocksator20.3 aud 0.9. rotational discontiuuity at ο220.53 right uext to a slow shock at ο2 0.55. contact. discontiuulty at or2 0.6. slow shock aud. rotational discontinuity at 0.68 and 0.70 respectively.," The following features may be seen: fast shocksat$x\simeq 0.3$ and $0.9$ , rotational discontinuity at $x\simeq 0.53$ right next to a slow shock at $x \simeq 0.55$ , contact discontinuity at $x \simeq 0.6$ , slow shock and rotational discontinuity at $0.68$ and $0.70$ respectively."32Excluding those clusters whose position angles suller [rom large uncertainties. we end up with a smaller subsample of 13 clusters and redetermined (he number Iraction distribution as a funetion of ó.,"Excluding those clusters whose position angles suffer from large uncertainties, we end up with a smaller subsample of $13$ clusters and redetermined the number fraction distribution as a function of $\phi$ ."33 Figure 4. plots the results., Figure \ref{fig:compare2} plots the results.34 As it can be seen. the distribution has a hieher peak at (he second bin but süll deviates significantly from (he numerical result. based on a ACDAL cosmology and the semi-analvtie galaxy formation model.," As it can be seen, the distribution has a higher peak at the second bin but still deviates significantly from the numerical result based on a $\Lambda$ CDM cosmology and the semi-analytic galaxy formation model."35 The recaleulation of V for this case rejects the hypothesis that the observational result. [rom the 13 clusters is consistent with the numerical result is rejected at the 95%. confidence level., The recalculation of $\chi^{2}$ for this case rejects the hypothesis that the observational result from the $13$ clusters is consistent with the numerical result is rejected at the $95\%$ confidence level.36 lt is worth mentioning the differences in the redshill range between the numerical ancl observational data used for the above comparison: The munerical result has been obtained al 2=0 while the observational results have been drawn [rom the galaxy. clusters al 0.3., It is worth mentioning the differences in the redshift range between the numerical and observational data used for the above comparison: The numerical result has been obtained at $z=0$ while the observational results have been drawn from the galaxy clusters at $0.1<z<0.3$ .37 This difference in the redshift range. however. would even worsen the disagreement between the munerical and the observational result for the following5 reason.," This difference in the redshift range, however, would even worsen the disagreement between the numerical and the observational result for the following reason."38 As mentioned in 82 and as shown by N-bocly simulations (e.g..Dailin&Steinmetz2005:etal.AltayAltavetal.2006:2006;Lee&KangΊναπο 2006).. 0the correlationsrrelations between the major axes of[dark dark matter and satellite galaxy distributions tend to be stronger at higher redshifts.," As mentioned in 2 and as shown by N-body simulations \citep[e.g.,][]{BS05,bailin-etal05,atlay-etal06,LK06}, the correlations between the major axes of dark matter and satellite galaxy distributions tend to be stronger at higher redshifts."39 In other words. the predicted strength of the correlations used lor the comparison with the observational result is underestimated.," In other words, the predicted strength of the correlations used for the comparison with the observational result is underestimated."40 One might think that the selection bias in the measurements of galaxy distributions should be responsible for the disagreement between theory and observation since in the analvsis of Oeurietal.(2010) only those bright galaxies with mag222 al r-band are used unlike in the numerical analvsis., One might think that the selection bias in the measurements of galaxy distributions should be responsible for the disagreement between theory and observation since in the analysis of \citet{Oguri-etal10} only those bright galaxies with $mag > 22$ at r-band are used unlike in the numerical analysis.41 Recall. however. that we used the Iuminositv-weighted ealaxv distributions in the numerical analysis to determine the major axes. which should minimize (he expected selection bias.," Recall, however, that we used the luminosity-weighted galaxy distributions in the numerical analysis to determine the major axes, which should minimize the expected selection bias."42 Another difference lies in the values of the cosmological parameters used for the Run simulations., Another difference lies in the values of the cosmological parameters used for the mili-Millennium Run simulations.43 Especially. the value of σς chosen by the Millennium Run simulation has been known to be higher than the WALAP value (IxXomatsuetal.2010).," Especially, the value of $\sigma_{8}$ chosen by the Millennium Run simulation has been known to be higher than the WMAP value \citep{wmap7}."44. The correlations between dark matter and satellite galaxy distributions in (riaxial clusters. however. are unlike to be significantly affected by the initial cosmological conditions. since il represents a nonlinear observable rather than a linear one.," The correlations between dark matter and satellite galaxy distributions in triaxial clusters, however, are unlike to be significantly affected by the initial cosmological conditions, since it represents a nonlinear observable rather than a linear one."45 Now that we have found (the observed misalignments of the projected major axes of dark matter and galaxy distributions in the galaxy. clusters to be inconsistent with the numerical prediction based on a ACDMcosmology and (he semi-analvtic galaxy. lormation model. we," Now that we have found the observed misalignments of the projected major axes of dark matter and galaxy distributions in the galaxy clusters to be inconsistent with the numerical prediction based on a $\Lambda$ CDMcosmology and the semi-analytic galaxy formation model, we"46We detected 7 min continuum emission towards each of the three observed sources.,We detected 7 mm continuum emission towards each of the three observed sources.47 The position. flux densities. and angular size of the detected radio sources are given in Table 2..," The position, flux densities, and angular size of the detected radio sources are given in Table \ref{tbl-obspar}."48 In what follows we present the results of our continuum observations and discuss the nature of the detected. sources in each of the regions. imdividuallv.," In what follows we present the results of our continuum observations and discuss the nature of the detected sources in each of the regions, individually."49 For the derivation of plivsical parameters we used (he distances given by Sridharan et al. (, For the derivation of physical parameters we used the distances given by Sridharan et al. (502002) and listecl in Table 3.,2002) and listed in Table 3.51 Figure | shows a contour map of the 7 mm continuum emission observed towards IRAS 18470-0044., Figure \ref{fig-18470maps} shows a contour map of the 7 mm continuum emission observed towards IRAS 18470-0044.52 The emission arises from two distinct compact sources separated by ((labelecd A and D)., The emission arises from two distinct compact sources separated by (labeled A and B).53 Both sources were also detected at 3.6 em and 6.0 em wavelengths., Both sources were also detected at 3.6 cm and 6.0 cm wavelengths.54 A contour map of the 3.6 em emission is shown in the lower panel of Fig. 1.., A contour map of the 3.6 cm emission is shown in the lower panel of Fig. \ref{fig-18470maps}.55 Component A is associated with a massive dust core detected at 350 and 450 jim by Williams et al. (, Component A is associated with a massive dust core detected at 850 and 450 $\mu$ m by Williams et al. (562004) and at 1200 jan by Deuther et al. (,2004) and at 1200 $\mu$ m by Beuther et al. (5720028).,2002a).58 At 1.2 mm the core has major and minor axis of 1T and12”.. respectivelv. implving a core radius. estimated [rom the geometric mean of the axis. of 0.29 pe (assuming a distance of 8.2 kpc).," At 1.2 mm the core has major and minor axis of 17 and, respectively, implying a core radius, estimated from the geometric mean of the axis, of 0.29 pc (assuming a distance of 8.2 kpc)."59 The mass of the core determined [rom the 850. jan observations is 720AL., The mass of the core determined from the 850 $\mu$ m observations is 720.60.. The peak position of the core is marked with a cross in Fig. 1.., The peak position of the core is marked with a cross in Fig. \ref{fig-18470maps}.61 The spectral index of the emission between 5.0 ancl 43.4 Giz are —0.1250.1 ancl —O0.140.1 for the east (A) ancl west (D) components. respectively. indicating that the emission in this frequency range is optically thin thermal emission.," The spectral index of the emission between 5.0 and 43.4 GHz are $-0.1\pm0.1$ and $-0.1\pm0.1$ for the east (A) and west (B) components, respectively, indicating that the emission in this frequency range is optically thin thermal emission."62 We conclude (hat the emission from these two objects is [ree-free emission from ionized gas., We conclude that the emission from these two objects is free-free emission from ionized gas.63 Table 3. lists the distance [col. (, Table \ref{tbl-derived} lists the distance [col. (642)]. the derived parameters of the regions of ionized gas: diameter [col. (,"2)], the derived parameters of the regions of ionized gas: diameter [col. ("653)]. emission measure (col. (,"3)], emission measure [col. ("664)]. and electron density |col. (,"4)], and electron density [col. ("675)]. the minimum number of ionizing photons required to maintain the ionization of the nebula [col. (,"5)], the minimum number of ionizing photons required to maintain the ionization of the nebula [col. ("686)]. and inferred spectral type of the exciting star icol. (,"6)], and inferred spectral type of the exciting star [col. ("690)].,7)].70 They were caleulated following the formulation of Mezger and Henderson (1967). assuming that the gas has constant electron density and an electron temperature of 107 Ix. The regions of ionized eas have radii of 0.021 and 0.029 pc. in the range of those of UC ILL regions. and densities of 4.3x10% and 2.5x10* . much lower than those of UC I] regions.," They were calculated following the formulation of Mezger and Henderson (1967), assuming that the gas has constant electron density and an electron temperature of $10^4$ K. The regions of ionized gas have radii of 0.021 and 0.029 pc, in the range of those of UC HII regions, and densities of $4.3\times10^3$ and $2.5\times10^3$ $^{-3}$, much lower than those of UC HII regions."71 We suggest that these small regions of ionized gas are deeply embedded within molecular cloud cores with high densities and large turbulent motions. and have already reached pressure ecquilibrium with the dense ambient gas (e.e.. De Pree. guez. Goss 1995; Xie et al.," We suggest that these small regions of ionized gas are deeply embedded within molecular cloud cores with high densities and large turbulent motions, and have already reached pressure equilibrium with the dense ambient gas (e.g., De Pree, guez, Goss 1995; Xie et al."72 1996)., 1996).73 The equilibrium radius is given by (see Garay Lizano, The equilibrium radius is given by (see Garay Lizano74"where R 6 are the cylindrical radius and polar angle, respectively, is the characteristic width of thejet sheath, no and bo are wiethe density and field strength scaling (and are to the question of the RM asymmetry), β is the ultimatelyvelocity and unimportantαι and o; are the velocity and magnetic field pitch angles, respectively.","where $R$ $\phi$ are the cylindrical radius and polar angle, respectively, $w_{\rm jet}$ is the characteristic width of thejet sheath, $n_0$ and $b_0$ are the density and field strength scaling (and are ultimately unimportant to the question of the $\RM$ asymmetry), $\beta$ is the velocity and $\alpha_u$ and $\alpha_b$ are the velocity and magnetic field pitch angles, respectively."75" Finally, we define the angle between the line of sight and the jet axis to be O, i.e. ke2cosO, =cosó and ke= Th"," Finally, we define the angle between the line of sight and the jet axis to be $\Theta$, i.e. $76\hat{k}^z = \cos\Theta77$, $78\hat{k}^R = \sin\Theta \cos\phi79$ and $80\hat{k}^\phi = -\sin\Theta\sin\phi/R81$."82"us, O=0° and ©=90° sinOcorrespond to lines of sight —sinOsing/R.along and orthogonal to the jet axis, respectively."," Thus, $\Theta=0^\circ$ and $\Theta=90^\circ$ correspond to lines of sight along and orthogonal to the jet axis, respectively."83" For a variety of values for these we compute the RM as defined in (6)) as a function parameters,of transverse position, thereby constructing Equationprofiles across the jet."," For a variety of values for these parameters, we compute the $\RM$ as defined in Equation \ref{eq:RM}) ) as a function of transverse position, thereby constructing profiles across the jet."84 The spatial variations in the density and orientation of the magnetic field necessarily lead to variation in the RM across the jet., The spatial variations in the density and orientation of the magnetic field necessarily lead to variation in the $\RM$ across the jet.85" In the limit of a static jet, where the plasma is at rest in the observer frame, the RM profile is shown in Figure 1 for a variety of magnetic pitch angles, as viewed from ©=60°."," In the limit of a static jet, where the plasma is at rest in the observer frame, the $\RM$ profile is shown in Figure \ref{fig:static}86 for a variety of magnetic pitch angles, as viewed from $\Theta=60^\circ$."87" For purely toroidal magnetic fields (a,=90°, blue), the RM profile is symmetric and approximately linear, only departing from a line at the sheath boundaries due to the decrease in theelectron "," For purely toroidal magnetic fields $\alpha_b=90^\circ$, blue), the $\RM$ profile is symmetric and approximately linear, only departing from a line at the sheath boundaries due to the precipitous decrease in theelectron density."88"In contrast, for magnetic precipitousfields nearly parallel to the jet density.(αν= 0°, red) the background density variation is clearly imprinted in the RM profile."," In contrast, for magnetic fields nearly parallel to the jet $\alpha_b=0^\circ$ , red) the background density variation is clearly imprinted in the $\RM$ profile."89" Due solely to geometry, the degree to which this occurs upon O, with the deviations at small O and αρ. depend"," Due solely to geometry, the degree to which this occurs depends upon $\Theta$, with the largest deviations at small $\Theta$ and $\alpha_b$."90"sHowever, the absolute variationlargest in the RM across the jet in this case is considerably reduced, and in the limit of a,=0? vanishes completely."," However, the absolute variation in the $\RM$ across the jet in this case is considerably reduced, and in the limit of $\alpha_b=0^\circ$ vanishes completely."91" More importantly, polarization maps of jets typically imply Rb?/b?>1 (2).."," More importantly, polarization maps of jets typically imply $R b^\phi/b^z\gtrsim 1$ \citep{Lyut-Pari-Gabu:05}."92" Jet sheaths with relativistic bulk motion along the jetaxis, but without any helical motion, are similar to their static"," Jet sheaths with relativistic bulk motion along the jetaxis, but without any helical motion, are similar to their static counterparts."93" In this case the of the motion for counterparts.the RM profiles, apart from primarythe drastic consequencereduction in the net RM, is relativistic aberration, which effectively results in observers at oblique angles viewing the jet from behind."," In this case the primary consequence of the motion for the $\RM$ profiles, apart from the drastic reduction in the net $\RM$, is relativistic aberration, which effectively results in observers at oblique angles viewing the jet from behind."94" This is seen explicitly for an extreme case in Figure 2,, in which the RM profiles are nearly identical to those for the static jet though rotated 180°."," This is seen explicitly for an extreme case in Figure \ref{fig:vertical}, in which the $\RM$ profiles are nearly identical to those for the static jet though rotated $180^\circ$."95" Most importantly, the sense of the RM gradient does not reverse as a consequence of the bulktion?."," Most importantly, the sense of the $\RM$ gradient does not reverse as a consequence of the bulk."96". The RM profiles do not significantly differ from the case shown for y>3, and for smaller velocities become even more degenerate in αν."," The $\RM$ profiles do not significantly differ from the case shown for $\gamma>3$, and for smaller velocities become even more degenerate in $\alpha_b$ ."97" Therefore, generally, within the context of symmetric models, magnetic fields with moderate pitch axiallyangles are incapablejet of producing strong asymmetric features in the RM profiles, though o; and jet Lorentz factor do play a substantial role in determining the absolute RM."," Therefore, generally, within the context of axially symmetric jet models, magnetic fields with moderate pitch angles are incapable of producing strong asymmetric features in the $\RM$ profiles, though $\alpha_b$ and jet Lorentz factor do play a substantial role in determining the absolute $\RM$."98" In stark contrast, even moderately relativistic helical motion easily produces dramatic asymmetric features in RM profiles, independent of the magnetic field pitch angle, and in some cases reversing the sense of the RM gradient."," In stark contrast, even moderately relativistic helical motion easily produces dramatic asymmetric features in $\RM$ profiles, independent of the magnetic field pitch angle, and in some cases reversing the sense of the $\RM$ gradient."99" As seen in Figure 3,, this occurs both for trans-relativistic and ultra-relativistic jets, and for velocity pitch angles as low as 30°."," As seen in Figure \ref{fig:helical}, this occurs both for trans-relativistic and ultra-relativistic jets, and for velocity pitch angles as low as $30^\circ$."100 Generic of relativistic helical motion is the noticeable bow in the RM , Generic of relativistic helical motion is the noticeable bow in the $\RM$ profiles.101"This feature is only weakly dependent upon ué and present profiles.for oy,230? for u>1.", This feature is only weakly dependent upon $u^z$ and present for $\alpha_u\gtrsim30^\circ$ for $u^z\gtrsim1$.102" Unlike similar features for non- jets, this occurs for a wide range of absolute rotation measures."," Unlike similar features for non-rotating jets, this occurs for a wide range of absolute rotation measures."103" When the revolving plasma in the jet sheath is approaching almost directly, ie. 9 is within an angle y! of É, the direction in which relativistic aberration rotates the magnetic field rapidly changes (see the dotted lines in Figure 3))."," When the revolving plasma in the jet sheath is approaching almost directly, i.e., $\bmath{\beta}$ is within an angle $\gamma^{-1}$ of $\bmath{\hat{k}}$, the direction in which relativistic aberration rotates the magnetic field rapidly changes (see the dotted lines in Figure \ref{fig:helical}) )."104" As a result, the RM evolves rapidly with a,."," As a result, the $\RM$ evolves rapidly with $\alpha_u$ ."105" At the same time, the Doppler shift reaches its maximum, producing dramatic enhancements in the absolute RM, andfor a, very close to O, complex RM profiles."," At the same time, the Doppler shift reaches its maximum, producing dramatic enhancements in the absolute $\RM$ , andfor $\alpha_u$ very close to $\Theta$ , complex $\RM$ profiles."106" However,for all but the slowestjets, this is restricted to such a small regime in viewing angle that it is relatively unlikely to be observed in practice."," However,for all but the slowestjets, this is restricted to such a small regime in viewing angle that it is relatively unlikely to be observed in practice."107 A much, A much108At the solar surface it is ¢@=0.3 and f=0.5 (Howard et al. 1983)).,At the solar surface it is $a\simeq 0.3$ and $f\simeq 0.5$ (Howard et al. \cite{HAB83}) ).109 The latitudinal shear varies only slightly with depth in the bulk of the convection zone but it shows a characteristic change near its base (Charbonneau et al. 1999))., The latitudinal shear varies only slightly with depth in the bulk of the convection zone but it shows a characteristic change near its base (Charbonneau et al. \cite{CDG99}) ).110 The amplitude a(1—f) of the cos?4 term remains almost constant up to the base and starts decreasing in the deeper tachocline only while the fraction f of cost6 contribution drops to practically zero near the base (cf., The amplitude $a(1-f)$ of the $\cos^2\theta$ term remains almost constant up to the base and starts decreasing in the deeper tachocline only while the fraction $f$ of $\cos^4\theta$ contribution drops to practically zero near the base (cf.111 Fig., Fig.112 10 of Charbonneau et al. 1999))., 10 of Charbonneau et al. \cite{CDG99}) ).113 The stratification. 1s characterized by the buoyancy frequency N. where g is the gravity. cp is the specific heat at constant pressure. and s is the specific entropy.," The stratification is characterized by the buoyancy frequency $N$, where $g$ is the gravity, $c_\mathrm{p}$ is the specific heat at constant pressure, and $s$ is the specific entropy."114 We address the linear stability problem with the small disturbances depending on time as exp(-tewr)., We address the linear stability problem with the small disturbances depending on time as $\mathrm{exp}(-\mathrm{i}\omega t)$.115 À positive imaginary part of the eigenvalue co means an instability., A positive imaginary part of the eigenvalue $\omega$ means an instability.116 The radial scales of the disturbances are assumed small compared to the stellar radius while the equations are global in both the horizontal dimensions., The radial scales of the disturbances are assumed small compared to the stellar radius while the equations are global in both the horizontal dimensions.117 The dependencies on radius and longitude ὁ are taken as Fourier modes exp+kr).," The dependencies on radius and longitude $\phi$ are taken as Fourier modes $\mathrm{exp}(\mathrm{i}m\phi +118\mathrm{i}kr)$."119 The linear equations for small perturbations in differentially rotating fluids with toroidal magnetic fields are already given by Kitchatinov Riiddiger (2008))., The linear equations for small perturbations in differentially rotating fluids with toroidal magnetic fields are already given by Kitchatinov Rüddiger \cite{KR08}) ).120 Here. the nonmagnetic version of the equations 1s considered im detail.," Here, the nonmagnetic version of the equations is considered in detail."121 The equations are formulated for normalized parameters (the rules of conversion to physical variables are given below)., The equations are formulated for normalized parameters (the rules of conversion to physical variables are given below).122" The equation for the potential W of the toroidal flow reads where ©=w/Q, 1s the normalized eigenvalue. Q=Q/Qp is the normalized rotation rate. jj=cos8. V is the poloidal flow potential. is the angular part of the Laplacian operator. and is the key parameter for the influence of the stratification."," The equation for the potential $W$ of the toroidal flow reads where $\hat{\omega} = \omega/\Omega_0$ is the normalized eigenvalue, $\hat{\Omega} = \Omega/\Omega_0$ is the normalized rotation rate, $\mu =123\cos\theta$, $V$ is the poloidal flow potential, is the angular part of the Laplacian operator, and is the key parameter for the influence of the stratification."124 The diffusion terms are characterized by the parameters where v and y are the microscopic viscosity ard the thermal conductivity., The diffusion terms are characterized by the parameters where $\nu$ and $\chi$ are the microscopic viscosity and the thermal conductivity.125 Apart from the Eq. (3)), Apart from the Eq. \ref{3}) )126 for the toroidal flow. the complete system of three equations includes the equatior for poloidal flow. and the equation for the normalized entropy S. The equations (3). (7) and (8) form an eigenvalue problem which we solved numerically.," for the toroidal flow, the complete system of three equations includes the equation for poloidal flow, and the equation for the normalized entropy $S$, The equations \ref{3}) ), \ref{7}) ) and \ref{8}) ) form an eigenvalue problem which we solved numerically."127" The diffusion parameters (6)) for the upper radiative core of the Sun are e,=107 and &=2x107!° which are used in the calculations."," The diffusion parameters \ref{6}) ) for the upper radiative core of the Sun are $\epsilon_\chi128= 10^{-4}$ and $\epsilon_\nu = 2\times 10^{-10}$ which are used in the calculations."129" The disturbances in physical units follow from. their normalized values by The velocity field can be restored from the potentials of poloidal (P,,) and toroidal (Τη) flows. (Chandrasekhar 1961)). where e,. ej. and e, are unit vectors in the radial. meridioral and longitudinal directions."," The disturbances in physical units follow from their normalized values by The velocity field can be restored from the potentials of poloidal $P_u$ ) and toroidal $T_u$ ) flows, (Chandrasekhar \cite{C61}) ), where $\vec{e}_r$, $\vec{e}_\theta$, and $\vec{e}_\phi$ are unit vectors in the radial, meridional and longitudinal directions."130 Without rotation (Q— 0) and for small diffusion the equations (3)). (7)) and (8)) reproduce the spectrum of g-modes.," Without rotation $\Omega\rightarrow 0$ ) and for small diffusion the equations \ref{3}) ), \ref{7}) ) and \ref{8}) ) reproduce the spectrum of $g$ -modes."131"poke More related to the stability problem is the limit of very large 2-parameter (5)) which leads to the following 2D approximation,", More related to the stability problem is the limit of very large $\hat\lambda$ -parameter \ref{5}) ) which leads to the following 2D approximation.132 The ratio of ΑΛΩΣ in stars can be so large (~10° in the upper radiative core of the Sun) that  (51) can also be large in spite of short-wave approximation in radius. Ar>>I.," The ratio of $N^2/\Omega^2$ in stars can be so large $\sim 10^5$ in the upper radiative core of the Sun) that $\hat{\lambda}^2$ \ref{5}) ) can also be large in spite of short-wave approximation in radius, $kr \gg 1$."133 In the limit of large 2? the above equation system reduces to its 2D approximation., In the limit of large $\hat{\lambda}^2$ the above equation system reduces to its 2D approximation.134 In leading order of this parameter Eq. (7)), In leading order of this parameter Eq. \ref{7}) )135 gives S=0., gives $S = 0$.136 Then it follows from (8)) that V=0 and Eq. (3)), Then it follows from \ref{8}) ) that $V = 0$ and Eq. \ref{3}) )137 reduces to the standard equation of 2D theory of Watson (1981)). describing toroidal flows on spherical surfaces.," reduces to the standard equation of 2D theory of Watson \cite{W81}) ), describing toroidal flows on spherical surfaces."138 The2D approximation 15 justified for stable oscillations with not too short radial scales so that 2 remains large., The2D approximation is justified for stable oscillations with not too short radial scales so that $\hat{\lambda}$ remains large.139 Its validity for stability problem 15 less certain because the radial scales of most rapidly growing modes are not know in advance and the value of kr for those modes is normally so large that | (Kitehatinov Rüddiger 2008)).," Its validity for stability problem is less certain because the radial scales of most rapidly growing modes are not know in advance and the value of $kr$ for those modes is normally so large that $}1401$ (Kitchatinov Rüddiger \cite{KR08}) )."141 For rigid rotation Eq. (12)), For rigid rotation Eq. \ref{12}) )142 4 jd., provides the eigenvalue spectrum of the r-modes (Papaloizou Pringle \cite{PP78}) ).143 chan, Instabilities can emerge with nonuniform rotation.144ges its sign (Watson 1981)).," The condition for instability is that the second derivative, $\mathrm{d}^2((1-\mu^2)\hat{\Omega})/\mathrm{d}\mu^2$ , changes its sign (Watson \cite{W81}) )."145 For the angular velocity profile, For the angular velocity profile146Many statistics have been put forward to characterize the 2lem emission from the ΕΟΚ. the power spectrum probably being the most frequently studied (222?.tochoosesomerecent examples)...,"Many statistics have been put forward to characterize the 21cm emission from the EoR, the power spectrum probably being the most frequently studied \citep[][to choose some recent147examples]{BAR08,LID08,PRI08,SET08}."148 We have suggested that higher-order statistics may be useful not only to characterize a CS cube that has been cleaned of oregrounds. noise and instrumental effects. but also to extract the signature of reionization from these corrupting influences in the first place.," We have suggested that higher-order statistics may be useful not only to characterize a CS cube that has been cleaned of foregrounds, noise and instrumental effects, but also to extract the signature of reionization from these corrupting influences in the first place."149 The skewness of the one-point distribution of brightness emperature. measured as a function of observed frequency (or equivalently as a function of redshift). is one such promising statistic.," The skewness of the one-point distribution of brightness temperature, measured as a function of observed frequency (or equivalently as a function of redshift), is one such promising statistic."150 The three detailed simulations of reionization which we have studied show a strong evolution of the skewness with redshift., The three detailed simulations of reionization which we have studied show a strong evolution of the skewness with redshift.151 Some of the features of this evolution appear to be generic and can be readily understood: in the early stages of reionization the skewness drops below that of the underlying density field as the first ionized bubbles. from which the emission is negligible. are formed.," Some of the features of this evolution appear to be generic and can be readily understood: in the early stages of reionization the skewness drops below that of the underlying density field as the first ionized bubbles, from which the emission is negligible, are formed."152 As reionization progresses. the majority of the volume becomes ionized and the skewness increases again. becoming very large at low redshift when the distributionof brightness temperature is peaked at zero. with a tail extending to large values.," As reionization progresses, the majority of the volume becomes ionized and the skewness increases again, becoming very large at low redshift when the distribution of brightness temperature is peaked at zero, with a tail extending to large values."153 In simulation f250C there is a well defined dip in the skewness with a width Am]., In simulation f250C there is a well defined dip in the skewness with a width $\Delta z\approx 1$.154 Our other simulation in which the Universe is reionized entirely by stars CI-star) shows a more gradual change. with the epoch of reionization extending throughout the redshift range probed by LOFAR.," Our other simulation in which the Universe is reionized entirely by stars (T-star) shows a more gradual change, with the epoch of reionization extending throughout the redshift range probed by LOFAR."155 A third simulation. T-QSO. in which QSOs reionize the Universe. shows an intermediate behaviour.," A third simulation, T-QSO, in which QSOs reionize the Universe, shows an intermediate behaviour."156 Bv combining these simulations with models of the foregrounds. noise and instrumental response. we have generated datacubes which are intended to simulate the output of the LOFAR EoR experiment.," By combining these simulations with models of the foregrounds, noise and instrumental response, we have generated datacubes which are intended to simulate the output of the LOFAR EoR experiment."157 We have studied two cases: firstly. one in which we smooth the foregrounds and signal to the resolution of the telescope using a Gaussian kernel. then add uncorrelated Gaussian noise: secondly. one in which we degrade the foregrounds and noise to the resolution of the telescope using a realistic PSF. and add noise which is uncorrelated in the Fourier plane rather than the image plane. producing what we refer to as ‘dirty’ images.," We have studied two cases: firstly, one in which we smooth the foregrounds and signal to the resolution of the telescope using a Gaussian kernel, then add uncorrelated Gaussian noise; secondly, one in which we degrade the foregrounds and noise to the resolution of the telescope using a realistic PSF, and add noise which is uncorrelated in the Fourier plane rather than the image plane, producing what we refer to as `dirty' images."158 In the former case. we can see the signature of reionization in the skewness by fitting out the foregrounds to obtain residual images. and then denoising these images with a simple smoothing operation.," In the former case, we can see the signature of reionization in the skewness by fitting out the foregrounds to obtain residual images, and then denoising these images with a simple smoothing operation."159 The skewness in these images as a function of redshift shows significant evidence of reionization., The skewness in these images as a function of redshift shows significant evidence of reionization.160 The result is quite robust to the details of the foreground fitting and the smoothing. Under-, The result is quite robust to the details of the foreground fitting and the smoothing. Under-161 or over-fitting the foregrounds affects the recovered skewness less severely than the recovered variance., or over-fitting the foregrounds affects the recovered skewness less severely than the recovered variance.162 Extracting a signal from the dirty cubes requires a more sophisticated denoising scheme., Extracting a signal from the dirty cubes requires a more sophisticated denoising scheme.163 In an optimistic scenario where the correlation matrices of the original signal and of the noise are known. we can again recover the evolution of the skewness quite cleanly using Wiener deconvolution.," In an optimistic scenario where the correlation matrices of the original signal and of the noise are known, we can again recover the evolution of the skewness quite cleanly using Wiener deconvolution."164 We have touched upon some areas for improvement: simulations which remain realistic but extend to larger scales and exhibit an even greater range of reionization histories: taking into account the polarization of the foregrounds and the instrumental response. and incorporating new observational constraints as they arrive: testing the minimal assumptions we must make about the signal in order for our extraction scheme to work. for example whether a poor estimate of the correlation matrix. of the CS seriously affects the extracted skewness: and studying a wider range of statistics beyond the variance and power spectrum.," We have touched upon some areas for improvement: simulations which remain realistic but extend to larger scales and exhibit an even greater range of reionization histories; taking into account the polarization of the foregrounds and the instrumental response, and incorporating new observational constraints as they arrive; testing the minimal assumptions we must make about the signal in order for our extraction scheme to work, for example whether a poor estimate of the correlation matrix of the CS seriously affects the extracted skewness; and studying a wider range of statistics beyond the variance and power spectrum."165 All of these will be areas for future work., All of these will be areas for future work.166 Even at this stage. however. our results justify some optimism that the new generation of radio telescopes can detect the signature of reionization using order statistics.," Even at this stage, however, our results justify some optimism that the new generation of radio telescopes can detect the signature of reionization using higher-order statistics."167 GH is supported by a grant from the Netherlands Organisation for Scientitic Research (NWO)., GH is supported by a grant from the Netherlands Organisation for Scientific Research (NWO).168 As LOFAR members. the authors are partially funded by the European Union. European. Regional Development Fund. and by 'Samenwerkingsverband Noord-Nederland’. EZ/KOMPAS.," As LOFAR members, the authors are partially funded by the European Union, European Regional Development Fund, and by `Samenwerkingsverband Noord-Nederland', EZ/KOMPAS."169 GM and IT acknowledge that this study was supported in part by Swiss National Science Foundation grant 200021-116696/1 and Swedish Research Council grant 60336701., GM and II acknowledge that this study was supported in part by Swiss National Science Foundation grant 200021-116696/1 and Swedish Research Council grant 60336701.170Finally. collecting (3.22)) and (3.23)). we get that there exists a constant C=C(T.Mj) independent of 0<2X1 such that: which gives the announced result.,"Finally, collecting \ref{EM:I_1}) ) and \ref{EM:I_2}) ), we get that there exists a constant $C=C(T,M_0)$ independent of $0<\e\le 1$ such that: which gives the announced result."171 This Corollary is a straightforward consequence of Remark 2.1.. Theorem 2.2.. estimate (3.21)) and Lemma 3.3.. In this section. we prove (hat (he svstem (1.1))-(1.2)) admits solutions « in the distributional sense.," $\hfill\Box$ This Corollary is a straightforward consequence of Remark \ref{molli_est}, Theorem \ref{EM:theo:exip_regu}, estimate \ref{L1_estimate}) ) and Lemma \ref{EM:lem:etem}.. In this section, we prove that the system \ref{EM:burger}) \ref{EM:initialdata}) ) admits solutions $u$ in the distributional sense."172 They are the limits of vw given by Theorem 2.2. when 7— 0. To do this. we will justify the passage to the limit as z tends to 0 in Che svstem (2.14)) by using some compactniess tools that are presented in a first subsection.," They are the limits of $u^{\e}$ given by Theorem \ref{EM:theo:exip_regu} when $\e\rightarrow1730$ To do this, we will justify the passage to the limit as $\e$ tends to $0$ in the system \ref{EM:burgersapp}) ) by using some compactness tools that are presented in a first subsection."174First. for all open interval J of R. wedenote by,"First, for all open interval $I$ of $\R$ , wedenote by"175"27.5 and 22.5 Me remains, but these merge at t£~1.1x105.","27.5 and 22.5 $\mearth$ remains, but these merge at $t\sim 1.1\times 10^5$."176 The final state of the system is then a 50 Me planet orbiting at r~1.5., The final state of the system is then a 50 $\mearth$ planet orbiting at $r\sim 1.5$.177" A similar outcome is obtained in Model3 in which the long-term evolution resulted in a 15 Me planet evolving in a high-eccentricity orbit with a semi-major axis of a,~2.", A similar outcome is obtained in Model3 in which the long-term evolution resulted in a 15 $\mearth$ planet evolving in a high-eccentricity orbit with a semi-major axis of $a_p\sim 2$.178" At earlier times, the increase in eccentricities following disc dispersal led to a collision between the 12.5 and 22.5 Μο bodies, thereby forming a new 35 Mg planet."," At earlier times, the increase in eccentricities following disc dispersal led to a collision between the 12.5 and 22.5 $\mearth$ bodies, thereby forming a new 35 $\mearth$ planet."179" At t~2x10°, the latter is observed to undergo a close encounter with the cental binary, leading to this body being completely ejected from the system."," At $t\sim 2\times18010^5$, the latter is observed to undergo a close encounter with the cental binary, leading to this body being completely ejected from the system."181" Interestingly, the three-planet system in Model2 appears to be dynamically stable over long time scales, with the planets maintaining their commensurabilities."," Interestingly, the three-planet system in Model2 appears to be dynamically stable over long time scales, with the planets maintaining their commensurabilities."182" This indicates that multiplanet resonant systems could potentially be found in circumbinary discs, where the existence of the resonance helps to maintain the stability of the system."," This indicates that multiplanet resonant systems could potentially be found in circumbinary discs, where the existence of the resonance helps to maintain the stability of the system."183 In this paper we have presented the results of hydrodynamic simulations aimed at studying the evolution of multiple planets embedded in a circumbinary disc., In this paper we have presented the results of hydrodynamic simulations aimed at studying the evolution of multiple planets embedded in a circumbinary disc.184 We first focused on a system consisting of a pair of planets interacting with each other., We first focused on a system consisting of a pair of planets interacting with each other.185" We assumed that one body is trapped at the edge of the inner cavity formed by the binary, while the other migrates inward from outside the orbit of the innermost body."," We assumed that one body is trapped at the edge of the inner cavity formed by the binary, while the other migrates inward from outside the orbit of the innermost body."186" Our calculations show different outcomes, depending on the planet mass ratio q=m;/mpo. "," Our calculations show different outcomes, depending on the planet mass ratio $q=m_i/m_o$ "187of the core-collapse supernovae (CC-SNe: Woosley(1993))) and mergers of neutron stars with another neutron star (NS-NS) or wilh a companion black hole hole (BII-NS: Paczviski (1991)))the currently. favored astronomical progenitors of cosmological ganmuna-ray bursts (GRBs).,of the core-collapse supernovae (CC-SNe; \cite{woo93}) ) and mergers of neutron stars with another neutron star (NS-NS) or with a companion black hole hole (BH-NS; \cite{pac91}) )–the currently favored astronomical progenitors of cosmological gamma-ray bursts (GRBs).188 While all short GRD are probably produced by mergers. the converse need not hold in general.," While all short GRB are probably produced by mergers, the converse need not hold in general."189 Black holes with a neutron star companion should have a diversity in spin 1999)., Black holes with a neutron star companion should have a diversity in spin \citep{van99}.190. These mixed binaries can be short and long lived. depending on the angular velocily of the black hole.," These mixed binaries can be short and long lived, depending on the angular velocity of the black hole."191 It predicts that some of the short GRBs. produced by slowly spinning black holes. also feature X-ray aftereglows (vanPutten90014) as in GRD050509D (Gehrelsetal.2005). ancl GRBOS50709 (Villasenoretal.2005:Foxal. 2005).," It predicts that some of the short GRBs, produced by slowly spinning black holes, also feature X-ray afterglows \citep{van01a} as in GRB050509B \citep{geh05} and GRB050709 \citep{vil05,fox05,hjo05}."192. Long GRBs. produced by rapidly rotating black holes. ave expected to form in CC-SNe trom short. intra-«dayv. period binaries (Paczviski(1998):vanPutten (2004))). but also [rom mergers wilh a companion neutron star (wanPutten1999). or out of the merger of (wo neutron stars (Daiottietal.2008:vanPutten2009)..," Long GRBs, produced by rapidly rotating black holes, are expected to form in CC-SNe from short, intra-day period binaries \cite{pac98,van04}) ), but also from mergers with a companion neutron star \citep{van99} or out of the merger of two neutron stars \citep{bai08,van09b}."193 A diversity in the origin of long GRBs in CC-SNe and mergers naturally accounts for evenis wilh and without supernovae. notably. GIRDOGOGId (vanPutten2008:Caitoetal. 2009).. with and without pronounced X-ray allerelows (vanPullen&Gupta2009) and in wind versus constant densitv host environments. that are relevant to recent studies of extraordinary. and. FermiLAT events (Cenkoetal.2010a.b).," A diversity in the origin of long GRBs in CC-SNe and mergers naturally accounts for events with and without supernovae, notably GRB060614 \citep{van08a,caito09}, with and without pronounced X-ray afterglows \citep{van09} and in wind versus constant density host environments, that are relevant to recent studies of extraordinary and -LAT events \citep{cen10,cen10b}."194. Rapidly rotating black holes can sweep up surrounding matter and induce the formation of mulüpole mass-moments., Rapidly rotating black holes can sweep up surrounding matter and induce the formation of multipole mass-moments.195 La (his process. spin energv is catalviicallv converted to a long duration gravitational wave burst (GWD: vanPutten (2003))).," In this process, spin energy is catalytically converted to a long duration gravitational wave burst (GWB; \cite{van01b,van03a}) )."196 For stellar mass black holes. (his output max be detected by advanced gravitational wave detectors for events in the local Universe.," For stellar mass black holes, this output may be detected by advanced gravitational wave detectors for events in the local Universe."197 As candidate inner engines to long GRBs. evidence for the associated spin down of the black hole has been found in the normalized light curve of 600 long GRBs in the DATSE catalogue (vanPutten&Gupta2009).," As candidate inner engines to long GRBs, evidence for the associated spin down of the black hole has been found in the normalized light curve of 600 long GRBs in the BATSE catalogue \citep{van09}."198. The high Irequency range of the planned aclvanced detectors LIGO-Vireo (Barish&Weiss1999;Arceseetal. 2004).. the Large-scale Crvogenic Gravitalional-wave Telescope (LCGT. Ixurodaetal. (2010))) and the Einstein Telescope (ET. Hild.Chelkowski (2008))) covers the «quadrupole emission spectrum of orbital motions around stellar mass black holes. thus establishing a window to rigorously probe (the inner most workings of GRBs and some of the CC-SNe.," The high frequency range of the planned advanced detectors LIGO-Virgo \citep{bar99,arc04}, the Large-scale Cryogenic Gravitational-wave Telescope (LCGT, \cite{lcgt}) ) and the Einstein Telescope (ET, \cite{et08}) ) covers the quadrupole emission spectrum of orbital motions around stellar mass black holes, thus establishing a window to rigorously probe the inner most workings of GRBs and some of the CC-SNe."199 We anticipate an event rate for long GWDs of 0.4-2 per vear within a distance of LOO Alpe from the local event rate of long GRBs (Guetta&DellaValle2007)., We anticipate an event rate for long GWBs of 0.4-2 per year within a distance of 100 Mpc from the local event rate of long GRBs \citep{gue07}.200. It compares favorably with that of mergers of binary neutron stars (e.g O'Shaughnessy (2010))).," It compares favorably with that of mergers of binary neutron stars (e.g \cite{osh08,aba10}) )."201 Since the local event rate of type Ib/c supernovae is ~80 per vear within a cdistauce of 100 Mpe. the branching ratio of Type Ib/c supernovae into long GRBs is therefore rather," Since the local event rate of type Ib/c supernovae is $\sim 80$ per year within a distance of 100 Mpc, the branching ratio of Type Ib/c supernovae into long GRBs is therefore rather"202Due to the changing shape the SPL solution in this case requires some artificial viscosity in order to prevent particle interpenetration during the compression phase.,Due to the changing shape the SPH solution in this case requires some artificial viscosity in order to prevent particle interpenetration during the compression phase.203 We apply this using the switch as discussed in relscc:sph.., We apply this using the switch as discussed in \\ref{sec:sph}.204 The particle distribution during the evolution of the exact. non-axisymimetric mode is shown in Figure 16.. where initially Vp= Vio=1/2. Ve;=1 and Vo»=1/4.," The particle distribution during the evolution of the exact, non-axisymmetric mode is shown in Figure \ref{fig:teqmnonaxi}, , where initially $V_{11} = 1$, $V_{12}=1/2$, $V_{21}=1$ and $V_{22} = 1/4$."205 For comparison with the exact solution we solve. (55))- (62)) using a simple second order modified Euler predictor-corrector method. using the conservation of mass (64)) asa checkon the quality of the integration.," For comparison with the exact solution we solve \ref{eq:dV11dt}) \ref{eq:dBdtnonaxi}) ) using a simple second order modified Euler predictor-corrector method, using the conservation of mass \ref{eq:massnonaxi}) ) as a checkon the quality of the integration."206 The solid line shown in Figure 16. is the curve corresponding to the edge of the ‘Tov Star (ic., The solid line shown in Figure \ref{fig:teqmnonaxi} is the curve corresponding to the edge of the Toy Star (ie.207 where p= 0) at the appropriate times., where $\rho=0$ ) at the appropriate times.208 The SPL particles adjust to the changing shape quite well apart from a damping of the amplitude with time caused by the application of artificial viscosity., The SPH particles adjust to the changing shape quite well apart from a damping of the amplitude with time caused by the application of artificial viscosity.209 We have performed a range of simulations using cllferent values of the initial parameters which in general show very similar results., We have performed a range of simulations using different values of the initial parameters which in general show very similar results.210 For simulations with very strong compression the particles can clump together in the manner described in refsee:static due to the force being zero at the origin of the cubic spline kernel used in the caleulations. despite using h=1.2(mp2," For simulations with very strong compression the particles can clump together in the manner described in \\ref{sec:static} due to the force being zero at the origin of the cubic spline kernel used in the calculations, despite using $h=1.2 (m/\rho)^{1/2}$."211 This is because a strong compression can push the particles neighbours close enough to be in the region of the kernel where the force decreases towards the origin. causing a clumping instability for positive pressures in compression similar in its clleet to the well known instability for negative stresses in tension(?).," This is because a strong compression can push the particles neighbours close enough to be in the region of the kernel where the force decreases towards the origin, causing a clumping instability for positive pressures in compression similar in its effect to the well known instability for negative stresses in tension."212. As discussed in& ro[secistatie the remedy for this is to use a kernel with non- derivative at the origin. an investigation of which will be performed elsewhere.," As discussed in \\ref{sec:static} the remedy for this is to use a kernel with non-zero derivative at the origin, an investigation of which will be performed elsewhere."213 The primary aim of this paper has been to provide a set of benchmarks For simulations of gaseous disks of the kind that arise in star formation., The primary aim of this paper has been to provide a set of benchmarks for simulations of gaseous disks of the kind that arise in star formation.214 Phe svstems. which we call ‘Tov Stars. are similar to their astrophysical counterparts in that they consist of compressible gas. held together by an attractive force which results in the gas having an outer surface where the density ancl pressure fall to zero.," The systems, which we call Toy Stars, are similar to their astrophysical counterparts in that they consist of compressible gas, held together by an attractive force which results in the gas having an outer surface where the density and pressure fall to zero."215 They therefore provide. tests which are quite different to the usual tests based. on Dow in periodic rectangular regions., They therefore provide tests which are quite different to the usual tests based on flow in periodic rectangular regions.216 Furthermore. not only can the linear modes be found. in terms of known functions. but non linear solutions can be [ound in terms of a small number of dillerential equations.," Furthermore, not only can the linear modes be found in terms of known functions, but non linear solutions can be found in terms of a small number of differential equations."217 The results described. and discussed in this paper can be summarized as follows: DIP is supported by a PPARC postcloctoral research [ellowship., The results described and discussed in this paper can be summarized as follows: DJP is supported by a PPARC postdoctoral research fellowship.218 Lle also acknowledges the support) of the Commonwealth Scholarship Commission and the Cambridge Commonwealth Trust., He also acknowledges the support of the Commonwealth Scholarship Commission and the Cambridge Commonwealth Trust.219 DJP also wishes to thank Monash Universityfor their hospitality during a visit., DJP also wishes to thank Monash Universityfor their hospitality during a visit.220 lor the axisvnunetric modes s= 0., For the axisymmetric modes $s=0$ .221 Phe lowest axisvnimetric mode has j=2 and setting we find, The lowest axisymmetric mode has $j=2$ and setting we find222radius of ag=1«109 un we can estimate the total dust mass. AM. of the cloud using Tuscrting the scattering cross-section we nieasure for Schiila’s dust cloud. we tls obtain an approximate dust mass of Ma~3«101 ke.,"radius of $a_d=1\times10^{-6}$ m, we can estimate the total dust mass, $M_d$, of the cloud using Inserting the scattering cross-section we measure for Scheila's dust cloud, we thus obtain an approximate dust mass of $M_d\sim3\times10^7$ kg."223 This estimate is of course based ol nuuerous assuuptious. particularly average dust erain size and bulk density. as specified above. and is only computed to provide approximate plysical contest to the photometric excess that was measured.," This estimate is of course based on numerous assumptions, particularly average dust grain size and bulk density, as specified above, and is only computed to provide approximate physical context to the photometric excess that was measured."224" For reference. cluploving the differeut erain size distribution and deusitv assunptious made bv Jewittetaf(2011) (p=2000 kein Pag=110 9) andBodewitsefal.(2011) (p=2500 ke Frayὃν10tan). we would instead obtain AZ~1«10° ke and AL,~5«10? ke. respectively."," For reference, employing the different grain size distribution and density assumptions made by \citet{jew11} $\rho=2000$ kg $^{-3}$; $a_d=1\times10^{-6}$ m) and\citet{bod11} $\rho=2500$ kg $^{-3}$; $a_d=1\times10^{-4}$m), we would instead obtain $M_d\sim4\times10^7$ kg and $M_d\sim5\times10^9$ kg, respectively."225" For comparison. Larson(2010) imeasured 1.24 mag on 2010 December 3. while Bodewitsefal,(2011) measured Aimy=0.66 mag on 2010 December LELS and Jewittetef(2011) measured Any=1.26 mag on 2010 December 28 and Ani=1.00 1uag ou 2011 January 5."," For comparison, \citet{lar10} measured $\Delta m_V=1.24$ mag on 2010 December 3, while \citet{bod11} measured $\Delta m_V=0.66$ mag on 2010 December 14-15 and \citet{jew11} measured $\Delta m_V=1.26$ mag on 2010 December 28 and $\Delta m_V=1.00$ mag on 2011 January 5."226 However. given the differeut observational and instrumental circumstances ivolved (especially given the technical difficulty of observiug the extremely bright nucleus aud comparatively extremely faint dust cloud simultancously). with the exception of the decline between the two measurements by Jewittct (2011).. we do not consider auv dust nass fluctuations nuplied by comparing these disparate data sets to he reliable.," However, given the different observational and instrumental circumstances involved (especially given the technical difficulty of observing the extremely bright nucleus and comparatively extremely faint dust cloud simultaneously), with the exception of the decline between the two measurements by \citet{jew11}, we do not consider any dust mass fluctuations implied by comparing these disparate data sets to be reliable."227" VoR color measurements (Table 1)) of the dust-contaiuinated nucleus iudicate that it is redder than the Sun. with the entire dust cloud with uucleus flux subtracted (""Dust4 in Table 1)) having au effectively identical red. color. simular to colors measured for other active comoets and active Centaurs (Bodewitsefo£2011:Jewitt 2009).."," $V-R$ color measurements (Table \ref{photom}) ) of the dust-contaminated nucleus indicate that it is redder than the Sun, with the entire dust cloud with nucleus flux subtracted $_{\rm A}$ ” in Table \ref{photom}) ) having an effectively identical red color, similar to colors measured for other active comets and active Centaurs \citep{bod11,jew09b}."228 Assunüug that the dust contaminating our uucleus photometry has a scatteriug cross-section larger than that of the nucleus (estimated above) aud the same color as the dust cloud as a whole. we fud a dust-subtracted color for the nucleus of VRocOL mag. consistent with a D-type spectral classification (FornasieretaL2007).," Assuming that the dust contaminating our nucleus photometry has a scattering cross-section larger than that of the nucleus (estimated above) and the same color as the dust cloud as a whole, we find a dust-subtracted color for the nucleus of $V-R\approx0.44$ mag, consistent with a D-type spectral classification \citep{for07}."229". To test whether the northern aud southern phunes of Scheila’s dust cloud exhibit any compositional differences. we mcasiure their colors individually παμε aud ""Ότο). but within estimated uncertainties. find no significant color cüffereuces."," To test whether the northern and southern plumes of Scheila's dust cloud exhibit any compositional differences, we measure their colors individually $_{\rm B}$ ” and $_{\rm C}$ ”), but within estimated uncertainties, find no significant color differences."230 The iost sensitive probe of sublimating eas in a comet is CN omission at38s0A., The most sensitive probe of sublimating gas in a comet is CN emission at.231. We show the spectral iuage of Scheila from 3700A to LLOOA in Figure Jaa. Iu this tage. the horizoutal continumu corresponds to reflected light from the nucleus.," We show the spectral image of Scheila from $3700{\rm \AA}$ to $4100{\rm \AA}$ in Figure \ref{keck_obs}a a. In this image, the horizontal continuum corresponds to reflected light from the nucleus."232 OIT sky: cmission lines are visible as vertical bands; aud dark Eraunuhofer lines in the Solar spectrum aud promincut Ca II (3933À)) and Ik (3966A)) absorption lines are also visible.," OH sky emission lines are visible as vertical bands, and dark Fraunhofer lines in the Solar spectrum and prominent Ca H ) and K ) absorption lines are also visible."233 Iu a two-dimensional spectral image. the intensity. ο. of a cometary cluission lines should be highest near the ceuter of the σοιπμ and eradually decrease with increasing distance frou the coutinuun. moving iu the spatial direction.," In a two-dimensional spectral image, the intensity, $I_e$, of a cometary emission lines should be highest near the center of the continuum and gradually decrease with increasing distance from the continuum, moving in the spatial direction."234 No spectral features near 3880À exhibit such behavior. and we therefore conclude that no gas is detected.," No spectral features near ${\rm\AA}$ exhibit such behavior, and we therefore conclude that no gas is detected."235 We also search for CN cussion iu a one-dimensional spectrum extracted frou the spectral inaee using a UO.S71 rectangular aperture centered ou the continu., We also search for CN emission in a one-dimensional spectrum extracted from the spectral image using a $1\farcs0\times8\farcs1$ rectangular aperture centered on the continuum.236" Sky backeround was measured aud subtracted using flanking regions 10"" to 16"" from the nucleus.", Sky background was measured and subtracted using flanking regions $''$ to $''$ from the nucleus.237 Calibration was performed using a nearby fux standard star aud a solar analog star (Fig., Calibration was performed using a nearby flux standard star and a solar analog star (Fig.238" το),", \ref{keck_obs}b b).239 Shaded regious in Figures ?bb and Tec indicate where CN omission is expected. but we again find no evidence of enission. consistent with work by Bodewitsefaf.(2011).. Howell&Lovell(2011)..aud Jehinetaf.(2011).," Shaded regions in Figures \ref{keck_obs}b b and \ref{keck_obs}c c indicate where CN emission is expected, but we again find no evidence of emission, consistent with work by \citet{bod11}, , \citet{how11},and \citet{jeh11}."240. To estimate Scheila’s CN production rate. we remove the continui using a scaled solar analog spectruui (Fie.," To estimate Scheila's CN production rate, we remove the continuum using a scaled solar analog spectrum (Fig."241 του). which should then leave ouly gas cussion.," \ref{keck_obs}c c), which should then leave only gas emission."242" Standard errors in three wavelength reeious in the residual spectrum 3830Ar 3900A.. where CN cinission is expected: andΙΟΡΟΑ:: each in width) are 2.7«10.L0, 2.0&«104) and Laslo!orgcn 2s! A!vespectively (Fig."," Standard errors in three wavelength regions in the residual spectrum;, where CN emission is expected; and; each in width) are $2.7\times10^{-17}$, $2.0\times10^{-17}$, and $1.8\times10^{-17}~{\rm erg~cm}^{-2}$ $^{-1}$ $^{-1}$,respectively (Fig."243 Tec)., \ref{keck_obs}c c).244 We choose 2.7.10 cre ? s| At as a conservative estimate of the wneertainty in the CN baud., We choose $2.7\times10^{-17}$ erg $^{-2}$ $^{-1}$ $^{-1}$ as a conservative estimate of the uncertainty in the CN band.245 Since 9P/Tempel 1 observations (Aleechetad.WwH1) utilized the same iustruuicutal settings used here. we assume that any CN band iu Scheila’s spectu will have the same profile as in 9P's spectrmm.," Since 9P/Tempel 1 observations \citep{mee11}246 utilized the same instrumental settings used here, we assume that any CN band in Scheila's spectrum will have the same profile as in 9P's spectrum."247" We therefore fud a peak value of any CN baud of (2.7s10PL ee en2 1A 1) or oe 2s PAL,"," We therefore find a peak value of any CN band of $3\times(2.7\times10^{-17}$ erg $^{-2}$ $^{-1}$ $^{-1}$ ), or $\sim8\times10^{-17}$ erg $^{-2}$$^{-1}$ $^{-1}$."248 We calculate the inteerated CN baud fux. fox. by sunning the cmission flux iu the shaded region. obtaining foxSS1019 erg 72 1.," We calculate the integrated CN band flux, $f_{\rm CN}$ by summing the emission flux in the shaded region, obtaining $f_{\rm CN}=8.8\times10^{-16}$ erg $^{-2}$ $^{-1}$."249" We then convert fex to the total παπανο of CN molecules. Ver. usine where A and ry, are in cm aud AU. respectively. and g(7) is the resonance fluorescence efficiency. which describes the wmmber of photous scattered per second per radical. in cre s +."," We then convert $f_{\rm CN}$ to the total number of CN molecules, $N_{\rm CN}$, using where $\Delta$ and $r_h$ are in cm and AU, respectively, and $g(l)$ is the resonance fluorescence efficiency, which describes the number of photons scattered per second per radical, in erg $^{-1}$ $^{-1}$."250 Diving our observations. Scheila had a radial velocity of ὃν=2.5 km lofor which g(lrj)=2.7«101 eve st + when the Swings effect is taken iuto account(Schleicher 2010)..," During our observations, Scheila had a radial velocity of $\dot{r}_h=2.5$ km $^{-1}$ , for which $g(l,r_h)=2.7\times10^{-13}$ erg $^{-1}$ $^{-1}$ when the Swings effect is taken into account\citep{sch10}. ."251" Substituting fex=s.8«1016 ere 2s ο, we obtain Nox=5.33s1025."," Substituting $f_{\rm CN}=8.8\times10^{-16}$ erg $^{-2}$ $^{-1}$, we obtain $N_{\rm CN}=5.33\times10^{26}$."252 A simple Haser(1957) model is used to derive the CN production rate. Qox. from New. assuming isotropic outgassing.constant radial expansion of the gas coma. aud a 2-step exponeutial decay process.," A simple \citet{has57} model is used to derive the CN production rate, $Q_{\rm CN}$, from $N_{\rm CN}$ , assuming isotropic outgassing,constant radial expansion of the gas coma, and a 2-step exponential decay process."253" We use 7,=τον and p,-223«4102 as the effective Haser scale leugthbs af rj=1 AU (AIlemetαἱ. 1995).. and adopt a eas volocitv of (Diverctal. 1997).."," We use $l_{p}=1.3\times10^{4}$ and $l_{p}=2.2\times10^{5}$ as the effective Haser scale lengths at $r_{h}=1$ AU \citep{ahe95}, , and adopt a gas velocity of \citep{biv97}. ."254 Integratiug the computed spatial cohunn density model over a rectangle 1800 Ίαν « , Integrating the computed spatial column density model over a rectangle 1800 km $\times$ 255ddo not differ too ereatly from those obtained with he red continu measured from the Fabry-Perot data cubes.,do not differ too greatly from those obtained with the red continuum measured from the Fabry-Perot data cubes.256 The typical difference is 3 wwhich fs within the typical uncertainties for our uecasureinenuts., The typical difference is 3 which fits within the typical uncertainties for our measurements.257 This sugecsts that star formation rigecring effects. although locally nuportaut. do mot change the overall weights applied to the velocities. (," This suggests that star formation triggering effects, although locally important, do not change the overall weights applied to the velocities. ("258IT) We consider velocity deviations due to density waves by naking sure that we derive consistent values whem we nove along a given slit or across the disk.,II) We consider velocity deviations due to density waves by making sure that we derive consistent values when we move along a given slit or across the disk.259 This strongly sugeests that such velocity deviations do cancel to first order., This strongly suggests that such velocity deviations do cancel to first order.260 The ideal form of the Tremaine-Weinberg method uses he luninosity-weighted velocities and the distances in he full radial range of the galaxy disk. ic. the iutegrals ranee from κ. to ox.," The ideal form of the Tremaine-Weinberg method uses the luminosity-weighted velocities and the distances in the full radial range of the galaxy disk, i.e. the integrals range from $-\infty$ to $\infty$."261 Observations. ou the other haud. cover oulv a limited radial range. aud ours reach typically he ος radius of the galaxy disk.," Observations, on the other hand, cover only a limited radial range, and ours reach typically the $r_{25}$ radius of the galaxy disk."262 It is thus important to see whether our observations are deep enough so that hey do not vield correct, It is thus important to see whether our observations are deep enough so that they do not yield incorrect.263 We uote that the method gives pattern speeds strictly when the nuits of the integrals reach well bevoud the bar., We note that the method gives pattern speeds strictly when the limits of the integrals reach well beyond the bar.264 However. iu lis test. we restrict the radial range of integration iu xogressive steps. starting from au inucrimost radius of LO jxxels and increasing in steps of LO pixels uutil the eutire observed disk is covered (see Fig. 62).," However, in this test, we restrict the radial range of integration in progressive steps, starting from an innermost radius of 10 pixels and increasing in steps of 10 pixels until the entire observed disk is covered (see Fig. \ref{fig:radialdependency}) )."265 Each derivation vields a differeut. (V2/6X5 value. treated as if it were a n for ;(see Fig. ον 7)).," Each derivation yields a different $\langle V \rangle$ $\langle X \rangle$ value, treated as if it were a value for (see Fig. \ref{fig:radialOpvalues}) )."266 As shown in the detailed analvsis by these values decrease asviuptotically as the disk coverage increases., As shown in the detailed analysis by \citet{Zimmeretal2004} these values decrease asymptotically as the disk coverage increases.267 In particular the differences between he outermost values of these trials and the values obtained using the complete disks are much simaller than hose between the values obtained linitine the feld to a few tens of pixels aud those fouud when using the full disk region., In particular the differences between the outermost values of these trials and the values obtained using the complete disks are much smaller than those between the values obtained limiting the field to a few tens of pixels and those found when using the full disk region.268 Furthermore. we confini that by using all the jxxels inside the slit G.c.. without the radial truication as shown in Fig. 6)).," Furthermore, we confirm that by using all the pixels inside the slit (i.e., without the radial truncation as shown in Fig. \ref{fig:radialdependency}) ),"269" the derived. Q,s are unich inore stable.", the derived s are much more stable.270 This is in support of the result by ? who found that uost of the variation in the derived patteri speed occurs within au inner radius which they set to Tor their observations., This is in support of the result by \citet{Zimmeretal2004} who found that most of the variation in the derived pattern speed occurs within an inner radius which they set to for their observations.271 A pattern speed derived over a radial. rauge sienificautly shorter than the bar leneth will not eive a ucaningful value since the integrals do not converge. so we do not wish to justify here any variations (or indeed absence of variations) calculated within these ranges.," A pattern speed derived over a radial range significantly shorter than the bar length will not give a meaningful value since the integrals do not converge, so we do not wish to justify here any variations (or indeed absence of variations) calculated within these ranges."272" Moreover. as foundbv ? for 551. quasi-steady state continuity is uot satisfiedby a single valued pattem speed. so it is nuaportaut to analyse the derived vvariatious to male sure they converge on a unique ονvalue, which cau then be taken as the main value for a single and dominant i)=2 perturbation (2).."," Moreover, as found by \citet{Shettyetal2007} for 51, quasi-steady state continuity is not satisfied by a single valued pattern speed, so it is important to analyse the derived variations to make sure they converge on a unique value, which can then be taken as the main value for a single and dominant $m=2$ perturbation \citep{Henryetal2003}."273 In our work we have used integrations over the full observed field for all ealaxies to derive the pattern speeds preseuted in Table and Fig. 1, In our work we have used integrations over the full observed field for all galaxies to derive the pattern speeds presented in Table \ref{tab:patternspeeds} and Fig. \ref{fig:allmaps}.274 Iu an ongoing study of the uuuethod based ou N-body SPI uunerical simmlatious carried out by Isabel Pérez |(Pérezctal.inpreparation.seealso7). we find that in the case of oue constant pattern speed ina disk. scans of uutruucated pseudo-slits in the Tuner regions as well as outer regions. all recover the input oofthe simmlatious.," In an ongoing study of the method based on N-body + SPH numerical simulations carried out by Isabel Pérrez \citep[P\'erez et al. in preparation, see also ][]{Beckmanetal2008} we find that in the case of one constant pattern speed in a disk, scans of untruncated pseudo-slits in the inner regions as well as outer regions, all recover the input of the simulations."275"©, When truncating the slits to cut the outer sections of the disk (compare with Fie. 6))."," When truncating the slits to cut the outer sections of the disk (compare with Fig. \ref{fig:radialdependency}) ),"276 the inteerals applied to immer truncated slits result in different (V2d /C6X5 values when compared with using the full ίατο ealaxy., the integrals applied to inner truncated slits result in different $\langle V \rangle$ $\langle X \rangle$ values when compared with using the full simulated galaxy.277 This i$ a clear demonstration of the necessity of using full slit coverage aud deep observations (even in the iuner regious) due to the non-convereius integrals., This is a clear demonstration of the necessity of using full slit coverage and deep observations (even in the inner regions) due to the non-converging integrals.278 However. as expected. we have found. that as soon as the radial disk section is comparable with or larger than the size of the bar. the input iuto the simulations can be recovered.," However, as expected, we have found that as soon as the radial disk section is comparable with or larger than the size of the bar, the input into the simulations can be recovered."279Ὃν This feature is shared by real data as well as by umuerical simulations., This feature is shared by real data as well as by numerical simulations.280 Furthermore. we have applied the nuuethod using the simulated velocity ficld weighted by the simulated density maps as well as the simulated star-formation maps and found that although using the density iaps provide more accurate results. the star-formation maps also deliver comparable (to within the errors) pattern speeds. Πρίντις that the vvolocities are reliable when applying the uuuethod.," Furthermore, we have applied the method using the simulated velocity field weighted by the simulated density maps as well as the simulated star-formation maps and found that although using the density maps provide more accurate results, the star-formation maps also deliver comparable (to within the errors) pattern speeds, implying that the velocities are reliable when applying the method."281 For the galaxies preseuted here. Table 1 shows that the aad coutiuuun deliver comparable (note that the continuum maps used for this exercise also conie from our data cubes).," For the galaxies presented here, Table \ref{tab:patternspeeds} shows that the and continuum deliver comparable (note that the continuum maps used for this exercise also come from our data cubes)."282" The exception is NGC L519. where the contimuuu nuage assigns higher weights to the velocities imside the bar. and thereby iutroduces significaut difference between the dderived using the contiuuuuau and2, nunaps."," The exception is NGC 4519, where the continuum image assigns higher weights to the velocities inside the bar, and thereby introduces significant difference between the derived using the continuum and maps."283" The higher pattern speed of the bar. using the οὐΠτα image delivers a higher total£,."," The higher pattern speed of the bar, using the continuum image delivers a higher total."284. Tn the presence of multiple structures with different patteru speeds. when deriving the VW) /CN) for au inner component. such as an inner bar inside a large bar. by applving the notional slits on the iuner parts of a two-dimensional map. the majority of the pixels will belong to he disk region outside the bar.," In the presence of multiple structures with different pattern speeds, when deriving the $\langle V \rangle$ $\langle X \rangle$ for an inner component, such as an inner bar inside a large bar, by applying the notional slits on the inner parts of a two-dimensional map, the majority of the pixels will belong to the disk region outside the bar."285 These pixels will therefore affect the derived: pattern speed of the immer structure., These pixels will therefore affect the derived pattern speed of the inner structure.286" This effect was tested by c.g. ?.theirFie.7 who fouud hat once the slit coverage is comparable with the size of he main bar. the inethod delivers reliable. Q,s. Moreover. cutting the disk in radial bius secuis to reveal the presence of multiple ottern speeds when the disk section is comparable to enu with a correspondingly distinct pattern speed."," This effect was tested by e.g., \citet[][ their Fig.~7 ]{Zimmeretal2004} who found that once the slit coverage is comparable with the size of the main bar, the method delivers reliable s. Moreover, cutting the disk in radial bins seems to reveal the presence of multiple pattern speeds when the disk section is comparable to structure with a correspondingly distinct pattern speed."287 Iu Fig. ," In Fig. \ref{fig:allmaps}, ,"288we illustrate the (V5. CX poiuts from the Inner regions of two galaxies where this 5effect can be seen.," we illustrate the $\langle V \rangle$, $\langle X \rangle$ points from the inner regions of two galaxies where this effect can be seen."289 ILowever. as the derivation of secondary pattern speeds Is nore complicated (seee.g...2).. this test is to be used with caution iu those cases.," However, as the derivation of secondary pattern speeds is more complicated \citep[see e.g., ][]{Meidtetal2008}, this test is to be used with caution in those cases."290" Finally. we contirui that the dadiffereunces using the continu©, maages instead of the ssurface briehtuess maps. does not significantly chauge the location of the resonances throughout our analysis."," Finally, we confirm that the differences using the continuum images instead of the surface brightness maps, does not significantly change the location of the resonances throughout our analysis."291 Morphologically. the bar radius r(bar)is commonly determined by analysing cllipse fitting profiles," Morphologically, the bar radius r(bar)is commonly determined by analysing ellipse fitting profiles"292may contribute to future growth in massive galaxies.,may contribute to future growth in massive galaxies.293" We are also pursuing a companion project on the IRAM 30m telescope, COLDGASS?,, which will obtain accurate and homogeneous molecular gas masses for a subset of ~300 galaxies from the GASS sample."," We are also pursuing a companion project on the IRAM 30m telescope, COLD, which will obtain accurate and homogeneous molecular gas masses for a subset of $\sim 300$ galaxies from the GASS sample."294" These data will allow us to characterize the balance between atomic and molecular gas in the galaxies in our sample, and understand the physical processes that determine how the condensed baryons are partitioned into stars, HI and Hg in the local Universe."," These data will allow us to characterize the balance between atomic and molecular gas in the galaxies in our sample, and understand the physical processes that determine how the condensed baryons are partitioned into stars, HI and $_2$ in the local Universe."295" In this paper, we report on UGC8802, an extraordinary galaxy blindly selected for inclusion in the GASS sample (under the catalog name GASS35981, used hereafter), which contains a reservoir of HI >1010 Mo, at least equal in mass to the galaxy's entire stellar content."," In this paper, we report on UGC8802, an extraordinary galaxy blindly selected for inclusion in the GASS sample (under the catalog name GASS35981, used hereafter), which contains a reservoir of HI $>10^{10}$ $_\odot$, at least equal in mass to the galaxy's entire stellar content."296 This galaxy contains less than one tenth this mass in H5 and also has a rather modest star formation rate (SFR)., This galaxy contains less than one tenth this mass in $_2$ and also has a rather modest star formation rate (SFR).297 We describe the spectroscopic follow-up that enables us to conclude that the outer disk of this galaxy is currently forming from gas that has likely accreted from the external environment., We describe the spectroscopic follow-up that enables us to conclude that the outer disk of this galaxy is currently forming from gas that has likely accreted from the external environment.298" In the following, we adopt a standard ACDM cosmology with Hg= 70km s! Mpc-!, Qm=0.3 and Q4=0.7."," In the following, we adopt a standard $\Lambda$ CDM cosmology with $_0=70$ km $^{-1}$ $^{-1}$, $\Omega_m=0.3$ and $\Omega_\Lambda=0.7$."299" GASS35981 (also SDSS J135308.36+354250.5, in addition to UGC8802), was selected for inclusion in the GASS parent sample because it has photometry from both SDSS and GALEX, is located ina region of sky accessible to Arecibo, and has stellar mass of M,=2x10!°Mo and redshift of z=0.0411 that fit into our targeted range."," GASS35981 (also SDSS $+$ 354250.5, in addition to UGC8802), was selected for inclusion in the GASS parent sample because it has photometry from both SDSS and GALEX, is located ina region of sky accessible to Arecibo, and has stellar mass of $_*=2 \times 10^{10} {\rm M}_\odot$ and redshift of $z=0.0411$ that fit into our targeted range."300 GASS35981 has pre-existing HI observations available from the Cornell HI Digital Archive (Springob et al., GASS35981 has pre-existing HI observations available from the Cornell HI Digital Archive (Springob et al.301 2005)., 2005).302" The mass of HI in GASS35981 is estimated from the line flux tobe 2.1x 10!°Mo, and the rest-frame velocity width of the HI line is Wso=360+25 km s! (Figure 1))."," The mass of HI in GASS35981 is estimated from the line flux tobe $2.1\times 10^{10}$ $_\odot$, and the rest-frame velocity width of the HI line is $W_{50}=360\pm25$ km $^{-1}$ (Figure \ref{gas_prof}) )."303 We display the HI archive spectrum in Figure 1.., We display the HI archive spectrum in Figure \ref{gas_prof}.304" We note that there is no evidence for contamination from possible companion galaxies within the 3.5’ Arecibo beam: one nearby galaxy has a spectroscopic redshift of 0.14, and two additional faint companions have SDSS photometric redshifts consistent with z=0.14."," We note that there is no evidence for contamination from possible companion galaxies within the $\arcmin$ Arecibo beam: one nearby galaxy has a spectroscopic redshift of 0.14, and two additional faint companions have SDSS photometric redshifts consistent with $z=0.14$."305 The lower panel of Figure 1 shows that GASS35981 (blue star) lies near the extreme end of HI fractions observed by GASS., The lower panel of Figure \ref{gas_prof} shows that GASS35981 (blue star) lies near the extreme end of HI fractions observed by GASS.306" Indeed, its gas fraction is comparable to the highest values measured for all galaxies in this stellar mass range (e.g., Giovanelli et al."," Indeed, its gas fraction is comparable to the highest values measured for all galaxies in this stellar mass range (e.g., Giovanelli et al."307 2007)., 2007).308" Indeed, even in Hl-selected samples, which are biased towards objects like GASS35981, galaxies in this stellar mass range >1010 with such high gas fractions are quite (M,uncommon Mo)(e.g., the “HI Giants” described by Garcia-Appadoo et al."," Indeed, even in HI-selected samples, which are biased towards objects like GASS35981, galaxies in this stellar mass range $_*>10^{10}$ $_\odot$ ) with such high gas fractions are quite uncommon (e.g., the “HI Giants” described by Garcia-Appadoo et al."309 2009)., 2009).310" It is also clear that GASS35981 lies significantly above the best-fit ‘gas fundamental plane’ (dotted line) relating stellar mass surface density,NUV-r color, and gas fraction, as described in Catinella et al. ("," It is also clear that GASS35981 lies significantly above the best-fit `gas fundamental plane' (dotted line) relating stellar mass surface density, color, and gas fraction, as described in Catinella et al. ("3112010).,2010).312" Because this galaxy was an interesting outlier and a presumed easy target, GASS35981 was selected for inclusion in our initial COLD GASS pilot program to obtain molecular gas measurements with the IRAM 30m telescope."," Because this galaxy was an interesting outlier and a presumed easy target, GASS35981 was selected for inclusion in our initial COLD GASS pilot program to obtain molecular gas measurements with the IRAM 30m telescope."313" Observations of GASS35981 in the J—1-0 rotational transition of CO were made at 3mm with the IRAM 30m telescope, in three different pointings: one at the galaxy center, and one each to the north and south, one beam-width (22"") away along the galaxy major axis."," Observations of GASS35981 in the J=1–0 rotational transition of CO were made at 3mm with the IRAM 30m telescope, in three different pointings: one at the galaxy center, and one each to the north and south, one beam-width $\arcsec$ ) away along the galaxy major axis."314" Data were taken in June and August 2009, using the WILMA and 4MHz backends simultaneously to record the data, and the software to process them."," Data were taken in June and August 2009, using the WILMA and 4MHz backends simultaneously to record the data, and the software to process them."315" Individual scans were examined, and a linear baseline subtracted from each of them."," Individual scans were examined, and a linear baseline subtracted from each of them."316" After rejection of scans with unstable baselines due to, e.g., poor atmospheric conditions, the data were combined and binned to a spectral resolution of 21 km s-!."," After rejection of scans with unstable baselines due to, e.g., poor atmospheric conditions, the data were combined and binned to a spectral resolution of 21 km $^{-1}$ ."317" 'The CO line is detected in the central pointing with S/N= 5.8, for an integrated line flux of"," The CO line is detected in the central pointing with $=5.8$ , for an integrated line flux of"318(AMaceroni BRuciuski 1997: Maceroni \Toutalban 2001).,(Maceroni Rucinski 1997; Maceroni Montalban 2004).319 This was modelled: as cousisting of two ALS dwarfs which are aluost. but not quite in contact. with masses of WLAL. aud 0.11AZ...," This was modelled as consisting of two M3 dwarfs which are almost, but not quite in contact, with masses of $0.44~M_\odot$ and $0.41~M_\odot$."320 This object is not wesent in the SuperWASP database owing to its füntuess., This object is not present in the SuperWASP database owing to its faintness.321 Iun preseutius the short-period end of the coutact dnarv period distribution based ou the Al-Sky Automated Survey (ASAS). Rucinski (2007) found only τος systems in the period range 0.200 d <P« 1225 d (and none at shorter periods).," In presenting the short-period end of the contact binary period distribution based on the All-Sky Automated Survey (ASAS), Rucinski (2007) found only three systems in the period range 0.200 d $< P <$ 0.225 d (and none at shorter periods)."322 The oulv one of these they dist as a confined W UAla svstem is ASAS JUSS128]|1953.1. with a period of 0.2178 d. Rucnuski Pribulla (2008) subsequently presented further photoimetrc and spectroscopic observations of this system and argued the case for this svsteni as the shortest period field contact binary., The only one of these they list as a confirmed W UMa system is ASAS J083128+1953.1 with a period of 0.2178 d. Rucinski Pribulla (2008) subsequently presented further photometric and spectroscopic observations of this system and argued the case for this system as the shortest period field contact binary.323 This object is iudeed preseut iu the SuperWASP database (ax 15SWASP JOS3127.87|195303.5). with the same period. but 1e licht curve js poorly samplec (fewer than 1000 data poiuts) iid προς between two bnghtuess levels. presuuably as a result of another star sometimes fallhius within the iotonietrie aperture.," This object is indeed present in the SuperWASP database (as 1SWASP J083127.87+195303.5), with the same period, but the light curve is poorly sampled (fewer than 1000 data points) and jumps between two brightness levels, presumably as a result of another star sometimes falling within the photometric aperture."324 It nonetheless displavs a broadly sinusoidal modulation when folded at this period (see Figure Ta)., It nonetheless displays a broadly sinusoidal modulation when folded at this period (see Figure 7a).325 Since the modulation profile did uot match hat of a classic contact binary. it was selected as a candidate eclipsing binary by the current exercise.," Since the modulation profile did not match that of a classic contact binary, it was selected as a candidate eclipsing binary by the current exercise."326 More recently Pribulla. Vauko ILuubalek (2009) ooked at two of the candidate short period svstenis isted by Ruciuski (2007).," More recently, Pribulla, Vanko Hambalek (2009) looked at two of the candidate short period systems listed by Rucinski (2007)."327" They found that one of hese stars (ASAS JI130310101.9) in fact has a perioc ouecr than that originally sugeested (0.2710 d instead of 1,2131 d).", They found that one of these stars (ASAS J113031–0101.9) in fact has a period longer than that originally suggested (0.2710 d instead of 0.2131 d).328 The other candidate (CASAS JO7TLS290336.7) Was confirmed as a contact binary with a period of 42113 d. As with the object. discussed by. Ruciuksi Pribulla. this oue too is present in the SuperWASP database (as ISWASP JOrIs25.67.033639.5). but the ligh curve is very poorly suupled (fewer than LOO data poiuts).," The other candidate (ASAS J071829–0336.7) was confirmed as a contact binary with a period of 0.2113 d. As with the object discussed by Rucinksi Pribulla, this one too is present in the SuperWASP database (as 1SWASP J071828.67–033639.5), but the light curve is very poorly sampled (fewer than 100 data points)."329 Nonetheless. when the SuperWASP data are folded at the ASAS period. a profile characteristic of a W UMa star is revealed (sce Figure 7b).," Nonetheless, when the SuperWASP data are folded at the ASAS period, a profile characteristic of a W UMa star is revealed (see Figure 7b)."330 However. eiven the few data points. this object was not included in the sample that were examined here.," However, given the few data points, this object was not included in the sample that were examined here."331 A survey of a 0.25 square deeree region of the Galactic plane using the ESO-2.21 telescope x Miller et al (2010) vielded more than half a million light curves down to YN> 21.5., A survey of a 0.25 square degree region of the Galactic plane using the ESO-2.2m telescope by Miller et al (2010) yielded more than half a million light curves down to $R \sim 24.5$ .332 Amonest this set they found 1318 variable stars. 533 of which were W UM—a stars.," Amongst this set they found 1318 variable stars, 533 of which were W UMa stars."333 This included seven candidate contact binaries with periods less than 0.23 ᾱ three of which have periods at or below the period cut-off: V-737 (0.2109 d). V-301 (0.2113 d) and V-1085 (0.2199 d).," This included seven candidate contact binaries with periods less than 0.23 d, three of which have periods at or below the period cut-off: V-737 (0.2109 d), V-301 (0.2143 d) and V-1085 (0.2199 d)."334 Each ofthese stars is relatively faint (2 iuaguitudes in the range ~19 22) and so thev are not amenable to detailed follow-up., Each of these stars is relatively faint $R$ magnitudes in the range $\sim 19 - 22$ ) and so they are not amenable to detailed follow-up.335 Noue of these are present iu the SuperWASP database. owing to their location auc füutness.," None of these are present in the SuperWASP database, owing to their location and faintness."336 As noted in the introduction. all of the stars discussed above have recently been superseded as the shortest oeriod eclipsing binary with main sequence coniponeuts x GSC 23110530 (= ISWASP JO022050.85|332017.6) with a period of 0.1926 d (Norton ct al 2007: Dimitrov Igurkchieva 2010). as shown in Figure 3 of the prescut oper.," As noted in the introduction, all of the stars discussed above have recently been superseded as the shortest period eclipsing binary with main sequence components by GSC 2314–0530 (= 1SWASP J022050.85+332047.6) with a period of 0.1926 d (Norton et al 2007; Dimitrov Kjurkchieva 2010), as shown in Figure 3 of the present paper."337 As n result of our work. however. Figure 5 aud Table l show that we can now add a further 22 candidates o the set of eclipsing binaries with the shortest periods 200 d 0.225 d).," As a result of our work, however, Figure 5 and Table 1 show that we can now add a further 22 candidates to the set of eclipsing binaries with the shortest periods (0.200 d – 0.225 d)."338 Four of these are brighter than uaenitude 13. so nüeht have been accessible to ASAS.," Four of these are brighter than magnitude 13, so might have been accessible to ASAS."339 Iu addition we fiud a further 30 candidates iu the period range at which the sharp cut-off occurs (0.225 d 1230 d). Ithoueh four of this latter set were already known. two of them had the wroue perio previously recorded.," In addition we find a further 30 candidates in the period range at which the sharp cut-off occurs (0.225 d – 0.230 d), although four of this latter set were already known, two of them had the wrong period previously recorded."340 Ruciuski 2007) conunented at the time of ιο ASAS work that the statistics of the sample at such short periods were very limited. despite the fact that ASAS covered around 3/l of the skv anc extended down ο nmaeguitude ~123.," Rucinski (2007) commented at the time of the ASAS work that the statistics of the sample at such short periods were very limited, despite the fact that ASAS covered around 3/4 of the sky and extended down to magnitude $\sim 13$."341 SuperWASP covers a similar fraction of the sky (avoiding the Galactic plane) but is scusitive down to magnitude 1S. Le. over sx times faüuter. aud as a result increases the sample by a factor of wore thia six.," SuperWASP covers a similar fraction of the sky (avoiding the Galactic plane) but is sensitive down to magnitude $\sim 15$, i.e. over six times fainter, and as a result increases the sample by a factor of more than six."342 Deb Singh (2010) have τοσο presented au analysis of the light curves of 62 binary stars (inostlv contact binaries) from the ASAS-3 survey., Deb Singh (2010) have recently presented an analysis of the light curves of 62 binary stars (mostly contact binaries) from the ASAS-3 survey.343 In particular they show that there is a rather tight correlation between the period and (FIV) colour of the coutact binarics in their sample (sce their Figure 11)., In particular they show that there is a rather tight correlation between the period and $J-K$ ) colour of the contact binaries in their sample (see their Figure 11).344 The relationship is parameterized by where P is in days., The relationship is parameterized by where $P$ is in days.345 Although their relationship is well constrained. the majority of their sample have periods around 0.1 d and they iuclude relatively few objects close to the period cut-off.," Although their relationship is well constrained, the majority of their sample have periods around 0.4 d and they include relatively few objects close to the period cut-off."346 In Figure 8 we show the 241ÀSS (7 A) colours of our salple. against period. with Equation 1 over-plotted.," In Figure 8 we show the 2MASS $J-K$ ) colours of our sample, against period, with Equation 1 over-plotted."347 Although the fit is reasonably eood. there is significant scatter iu the colours of these short period svstenis.," Although the fit is reasonably good, there is significant scatter in the colours of these short period systems."348 Gazeas Stepicen (2008) and CGazeas Niarclios (2006) demonstrated that there aro clear correlations between the masses of the components of contact binaries aud their orbital periods. aud also between the radii of the coniponeuts and their orbital periods.," Gazeas Stepien (2008) and Gazeas Niarchos (2006) demonstrated that there are clear correlations between the masses of the components of contact binaries and their orbital periods, and also between the radii of the components and their orbital periods."349 Iu particular. the period cut-off of around 0.22 d corresponds to primary aud secondary masses of around 0:55AL. and 0.3A. and radii of around 0.7.AL. and 0.5AZ. respectively.," In particular, the period cut-off of around 0.22 d corresponds to primary and secondary masses of around $0.85~M_\odot$ and $0.3~M_\odot$ and radii of around $0.7~M_\odot$ and $0.5~M_\odot$ respectively."350 These masses radii correspond to stars of spectral type I& aud thus match the observed V...AN. colours we see in our sample (Figure 6)., These masses and radii correspond to stars of spectral type K and thus match the observed $V-K$ colours we see in our sample (Figure 6).351 The mass aud radius estimates of Gazeas Stepien (2008) are good to around accuracy., The mass and radius estimates of Gazeas Stepien (2008) are good to around accuracy.352 However. the short period cud of these correlations is defined by ouly three stars: CC Com (0.2211 d). V523 Cas (0.2337 d) alu RW Cou (025753 οἱ). and there is considerable scatter between their parameters.," However, the short period end of these correlations is defined by only three stars: CC Com (0.2211 d), V523 Cas (0.2337 d) and RW Com (0.2373 d), and there is considerable scatter between their parameters."353 Increasing the number, Increasing the number354Snowdenetal. (1998))). we estimate ils electron density.,"\citet{snowden_etal_98}) ), we estimate its electron density."355" The temperature is not well known. but most of the lions are likely to be near their ionizational equilibrium temperature (3.2xLO? IK). and the enission equation is relatively insensitive to temperature for 1.x10~T—ο. An VI-rich plasma. with the above column density. a temperature of 6.3xLO? IX. and a thermal pressure of 15.000 IX 7? emits 450 photons 7s J|1 |, which is within the observational 2 sigma upper limit on the intensitv."," The temperature is not well known, but most of the ions are likely to be near their ionizational equilibrium temperature $3.2 \times 10^5$ K), and the emission equation is relatively insensitive to temperature for $1 \times 10^5 \stackrel{<}{\sim} 356T \stackrel{<}{\sim} 1 \times 10^6$ K. An -rich plasma, with the above column density, a temperature of $6.3 \times 10^5$ K, and a thermal pressure of 15,000 K $^{-3}$ emits 450 photons $^{-2}$ $^{-1}$ $^{-1}$, which is within the observational 2 sigma upper limit on the intensity."357" Similar plasmas will temperatures as low as c1x10"" Ix emit even less intense rracliiation.", Similar plasmas with temperatures as low as $\sim 1 \times 10^5$ K emit even less intense radiation.358 Thus. a (wo phase model could meet (he observational constraints without requiring unobserved astroplivsies or unusual conditions.," Thus, a two phase model could meet the observational constraints without requiring unobserved astrophysics or unusual conditions."359 In this section. we examine the multi-phase bubble simulations of and (he evaporating cloud simulations of Slavin(1989)..," In this section, we examine the multi-phase bubble simulations of \citet{smith_cox} and the evaporating cloud simulations of \citet{slavin}."360 In the models of (2001).. the Local Bubble resulted rom two or (11ος supernova explosions occurring up lo several million vears ago.," In the models of \citet{smith_cox}, the Local Bubble resulted from two or three supernova explosions occurring up to several million years ago."361" The interior of the structure consists of hot (~10"" IX). nearly collisional ionizational equilibrium: plasma. while (he periphery of the structure consists of an intermediate temperature transition zone."," The interior of the structure consists of hot $\sim 10^6$ K), nearly collisional ionizational equilibrium plasma, while the periphery of the structure consists of an intermediate temperature transition zone."362 Although the simulations do not explicitly: include the transition zones surrounding the embedded cool elouds. such zones are thought to harbor lions (Slavin1989:Oegerleetal.2002) and so should contribute to the Πακ of rresonance line photons.," Although the simulations do not explicitly include the transition zones surrounding the embedded cool clouds, such zones are thought to harbor ions \citep{slavin,oegerle_etal} and so should contribute to the flux of resonance line photons."363 Here. we will use the simulations of Slavin(1989).. which predict their intensity.," Here, we will use the simulations of \citet{slavin}, which predict their intensity."364 After performing several hvdrocwnamical simulations. Smith&Cox(2001) decided that the best model lies intermediate between their various simulations.," After performing several hydrodynamical simulations, \citet{smith_cox} decided that the best model lies intermediate between their various simulations."365 Their simulations vield predicted intensities ranging from 190 to more than 9.500 photons 7s | LH (alter the extra [actor ol 4x im their Figure 19 (Smith. private communication) is divided out).," Their simulations yield predicted intensities ranging from 190 to more than 9,500 photons $^{-2}$ $^{-1}$ $^{-1}$, (after the extra factor of $4\pi$ in their Figure 19 (Smith, private communication) is divided out)."366 To this intensity must be added the intensity emitted by the transition zone on the local cloud aud. possibly. transition zones on other cool clouds embedded in the Local Bubble.," To this intensity must be added the intensity emitted by the transition zone on the local cloud and, possibly, transition zones on other cool clouds embedded in the Local Bubble."367 For the transition zone on the cool cloud surrounding (he Sun. Slavin(1989). predicted an ddoublet intensity of 250 photons 7s | |.," For the transition zone on the cool cloud surrounding the Sun, \citet{slavin} predicted an doublet intensity of 250 photons $^{-2}$ $^{-1}$ $^{-1}$."368 The sium of the Smith&Cox(2001). and Slavin(1989). predictions (440 to >9800 photons 7s ! 1) marginally overlaps the 2 signia upper limit reported in this paper., The sum of the \citet{smith_cox} and \citet{slavin} predictions (440 to $\geq9800$ photons $^{-2}$ $^{-1}$ $^{-1}$ ) marginally overlaps the 2 sigma upper limit reported in this paper.369 If other cool clouds reside along the line of sight. then the predicted intensity would be even higher.," If other cool clouds reside along the line of sight, then the predicted intensity would be even higher."370 Thus. this particular model is heavily constrained by the null results.," Thus, this particular model is heavily constrained by the null results."371 We would have lost confidence in this (vpe of model had it not been possible to, We would have lost confidence in this type of model had it not been possible to372We thank Lars Hernquist. Chris McKee. Phil Chang. Pedro Aarronetti. Leo Blitz. Jay Gallagher. Risa. Wechsler. and Daniel Holz for helpful discussions.,"We thank Lars Hernquist, Chris McKee, Phil Chang, Pedro Marronetti, Leo Blitz, Jay Gallagher, Risa Wechsler, and Daniel Holz for helpful discussions."373" Banerjee. A. Jog. ο, 2011. ΑΡΗ 732L. 8B Bigiel, E; Leroy, A. Seibert, M., et al."," Banerjee, A. Jog, C., 2011, ApJL, 732L, 8B Bigiel, F., Leroy, A., Seibert, M., et al.,"374" 2010.Journal, 140, 94 UJiz. L.. ApJ. 1979. 231. L115 Bullock. J.. Dekel, Αν. Kolatt, T.S.. et al;"," 2010, 140, 1194 Blitz, L., ApJ, 1979, 231, L115 Bullock, J., Dekel, A., Kolatt, T.S., et al.,"375" 2001, ApJ. 555, 240 Chakrabarti. 5. Blitz L.. 2009,AINRAS, 399, L1I8 [CBO9] e»hakrabarti, 5. Blitz L.. 2011,ApJ. 731. 40€ Chang.P. Chakrabarti, S.. 2011. MNRAS, 416, 618C e»hakrabarti. Bigtel. Chang Blitz 2011. ApJ. 743. 35 [CBCB] Jebattista. V... Moore, D.. Quinn, T., et al."," 2001, ApJ, 555, 240 Chakrabarti, S. Blitz L., 2009, 399, L118 [CB09] Chakrabarti, S. Blitz L., 2011, 731, 40C Chang,P. Chakrabarti, S., 2011, MNRAS, 416, 618C Chakrabarti, Bigiel, Chang Blitz 2011, ApJ, 743, 35 [CBCB] Debattista, V., Moore, B., Quinn, T., et al.,"376" 2004, ApJ, 681. 1076 dobbs, C.L.. et al.2010.403. 625 Jubinski. J., Mihos. C. Hernquist. L.. 1996, ApJ, 462. 576 Gnedin, O., Kravtsov, Αι. Klvpin, A. Nagai, D., 2004. ApJ. 616. 16 Hernquist 1990. ApJ, 356, 359H Mihos. C.. Dubinski. J. Hernquist. L.. 1998, ApJ. 494. 183 Maccio, A. et al,"," 2004, ApJ, 681, 1076 Dobbs, C.L., et al.2010,, 625 Dubinski, J., Mihos, C. Hernquist, L., 1996, ApJ, 462, 576 Gnedin, O., Kravtsov, A., Klypin, A. Nagai, D., 2004, ApJ, 616, 16 Hernquist 1990, ApJ, 356, 359H Mihos, C., Dubinski, J. Hernquist, L., 1998, ApJ, 494, 183 Maccio, A. et al.,"377" 2008.391, 1940 Navarro, J.. Frenk. C.S. White; S.D.M.. 1996. ApJ. 462. 563 [NFW96] Rubin. V.. Thonnard. N. Ford. KW. 1977. ApJL. 217. ΕΙ Salo. H. Laurtkainen, Ἐν, 2000."," 2008,, 1940 Navarro, J., Frenk, C.S. White, S.D.M., 1996, ApJ, 462, 563 [NFW96] Rubin, V., Thonnard, N. Ford, K.W., 1977, ApJL, 217, L1 Salo, H. Laurikainen, E., 2000,"378LLL respectively). and the closely-related76-11 sample.,"III respectively), and the closely-related sample."379 “Phis lattor sample was selected at a frequency of 151 MlZ using the 7€ survey data of Lacy et ((1995) with a flux limi chosen to maximise overlap with the SC sample., This latter sample was selected at a frequency of 151 MHz using the 7C survey data of Lacy et (1995) with a flux limit chosen to maximise overlap with the 8C sample.380 Phis sample is defined in Section 2. and will be described in more detai in a future paper (Lacy et 11999h).," This sample is defined in Section 2, and will be described in more detail in a future paper (Lacy et 1999b)."381 A further paper wil discuss spectroscopy of the GC sample of Eales (1985). ane details of the and samples are presented in Willot (1998. ancl papers in preparation).," A further paper will discuss spectroscopy of the 6C sample of Eales (1985), and details of the and samples are presented in Willott (1998, and papers in preparation)."382 The properties of these samples are sunimarised in Table 1. and the coverage of the racio-Iuminositv — redshift plane is illustrated in. of Blundell. Rawlines Willott (1999).," The properties of these samples are summarised in Table 1, and the coverage of the radio-luminosity – redshift plane is illustrated in, 1 of Blundell, Rawlings Willott (1999)."383 Samples such as these are very valuable for studying the cosmic evolution of the radio source population. in particular the question of the evolution of source size. D. with recdshilt.," Samples such as these are very valuable for studying the cosmic evolution of the radio source population, in particular the question of the evolution of source size, $D$, with redshift."384 As redshift ancl radio luminosity are always strongly correlated within any flux-limited. sample. partial correlation cocllicients need to be calculated to investigate whether the true correlation is with redshift or luminosity.," As redshift and radio luminosity are always strongly correlated within any flux-limited sample, partial correlation coefficients need to be calculated to investigate whether the true correlation is with redshift or luminosity."385" Studies based. on low-frequeney selected: samples. typically show a weak correlation with redshift only. parameterised as Dx(112)"" where nzLT1.0 tthe ος sample. Eales 1985: Neeser ct 11995. and the and samples: Blundell. Rawlings Willott 1999). although samples selected at higher frequencies seem to have stronger dependences. with ;g3 (Oort. Ixatgert Windhorst LOST: Ixapahi 1989) combined with a radio luminosity dependence DxL' with e20.3."," Studies based on low-frequency selected samples typically show a weak correlation with redshift only, parameterised as $D\propto (1+z)^{-\eta}$ where $\eta \approx 3861.7-1.9$ the 6C sample, Eales 1985; Neeser et 1995, and the and samples; Blundell, Rawlings Willott 1999), although samples selected at higher frequencies seem to have stronger dependences, with $\eta \approx 3$ (Oort, Katgert Windhorst 1987; Kapahi 1989) combined with a radio luminosity dependence $D\propto L^{\epsilon}$ with $\epsilon \approx 0.3$."387 In Paper Lb we performed. a partial rank correlation on the SC-NEC sample using photometric redshifts., In Paper II we performed a partial rank correlation on the 8C-NEC sample using photometric redshifts.388 This showed that the funcamental correlation was between size and redshift. but having only recshilts based. on /-bancl magnitudes we were forced to only consider ο<1.1 objects and to accept the uncertainties associated with photomoetric redshifts.," This showed that the fundamental correlation was between size and redshift, but having only redshifts based on $R$ -band magnitudes we were forced to only consider $z<1.1$ objects and to accept the uncertainties associated with photometric redshifts."389 We also investigated. the four-way correlation coefficients. of redshift. luminosity. size and spectral index. finding that spectral index at 2GIz in the rest frame was most stronely correlated with redshift. ancl any correlation with luminosity was weak.," We also investigated the four-way correlation coefficients of redshift, luminosity, size and spectral index, finding that spectral index at 2GHz in the rest frame was most strongly correlated with redshift, and any correlation with luminosity was weak."390 Since then. independent: work on the GC. and surveys has been carried. out by Blunclell et (1999) with results that are broadly consistent with he Neeser et rresult and. the results of Paper LL.," Since then, independent work on the 6C, and surveys has been carried out by Blundell et (1999) with results that are broadly consistent with the Neeser et result and the results of Paper II."391 They ind. however. a significant correlation of spectral index with uminosity at a rest-frame frequenev of 1 GllIz. although a correlation with redshift is seen at higher frequencies.," They find, however, a significant correlation of spectral index with luminosity at a rest-frame frequency of 1 GHz, although a correlation with redshift is seen at higher frequencies."392 In his paper we use the redshifts for the and SC-NEC samples to study the size-redshift relation further., In this paper we use the redshifts for the and 8C-NEC samples to study the size-redshift relation further.393 We assume Jo=50kms!Mpe. and an Einstein. — de Sitter (O3;=1. O4— 0) cosmology unless otherwise stated.," We assume $H_0=50 \, {\rm kms^{-1}Mpc^{-1}}$ and an Einstein – de Sitter $\Omega_{\rm M} = 1$, $\Omega_{\Lambda}=0$ ) cosmology unless otherwise stated."394 Positions are all epoch D1950.0., Positions are all epoch B1950.0.395" Spectral indices. both radio and optical are defined in the sense that S,x&mm "," Spectral indices, both radio and optical are defined in the sense that $S_{\nu} \propto \nu^{-\alpha}$."396The SC-NEC sample has been formally defined in Paper I. ancl some refinements described in Paper HI.," The 8C-NEC sample has been formally defined in Paper I, and some refinements described in Paper III."397 It consists of all raclio sources with 38-Mllz flux densities Saszc1.3 Jv within 3° o£ 18 OO. 66° in the survey of Rees (1990)., It consists of all radio sources with 38-MHz flux densities $S_{38} \geq 1.3$ Jy within $3^{\circ}$ of $^{\rm h}$ $^{\rm m}$ $^{\circ}$ in the survey of Rees (1990).398" Phe sample consists of all TC objects from the mini-survey of Lacy et ((1995) with 151-MllIz ux densities Sy.)20.5 Jy. again within 3° of 18""00"". |667."," The sample consists of all 7C objects from the mini-survey of Lacy et (1995) with 151-MHz flux densities $S_{151}\geq 0.5$ Jy, again within $3^{\circ}$ of $18^{\rm h} 00^{\rm m}$ $+66^{\circ}$."399 Lhe Dux density limits are deliberately chosen to maximise the overlap of the two samples. thus most sources are common to both samples.," The flux density limits are deliberately chosen to maximise the overlap of the two samples, thus most sources are common to both samples."400 The sample will be more fully described in Lacey et 11999b. but the positions and radio properties of the objects which are present only in the sample (and which therefore have not appeared in Papers LLL) are presented in Table 2. for completeness.," The sample will be more fully described in Lacy et 1999b, but the positions and radio properties of the objects which are present only in the sample (and which therefore have not appeared in Papers I-III) are presented in Table 2, for completeness."401 number of objects have been excluded: from the samples on the basis of confusion by bright nearby sources., A number of objects have been excluded from the samples on the basis of confusion by bright nearby sources.402 7€ 1732|6715 (SC. 1732|672) has avery bright radio source nearby and has been temporarily removed from the sample pending an improved radio image., 7C 1732+6715 (8C 1732+672) has a very bright radio source nearby and has been temporarily removed from the sample pending an improved radio image.403 το 182116442 (SC 1821646) has a star on top of the ID position MMeMahon.. personal. communication).," 7C 1821+6442 (8C 1821+646) has a star on top of the ID position McMahon, personal communication)."404 TC 182716517 (SC 18271652) has been excluded as there is à very bright. star nearby., 7C 1827+6517 (8C 1827+652) has been excluded as there is a very bright star nearby.405 TFhis has reduced. the total number of objects in the sample from 57 to 54 and for the SC-NEC sample from 61 to 58., This has reduced the total number of objects in the sample from 57 to 54 and for the 8C-NEC sample from 61 to 58.406 As these objects were removed for reasons unconnected with their intrinsic radio or optical properties their omission should not alfect the sample statistics., As these objects were removed for reasons unconnected with their intrinsic radio or optical properties their omission should not affect the sample statistics.407 Apart [rom these. all objects in the sample have spectroscopic data.," Apart from these, all objects in the sample have spectroscopic data."408 In the SC-NISC sample. there are three objects for which spectra are vet to be obtained.," In the 8C-NEC sample, there are three objects for which spectra are yet to be obtained."409 Alost of the objects in both the SC-NEC ancl North Ecliptic Cap samples were observed. with the ISLS spectrograph on the Willian Llerschel Telescope. (IUE)., Most of the objects in both the 8C-NEC and North Ecliptic Cap samples were observed with the ISIS spectrograph on the William Herschel Telescope (WHT).410 Most observations were mace on the nights of 1995 July 28 to 31. though observations of a few objects were made by on the nights of 1993 August 20-21 and 19983 June 15-19.," Most observations were made on the nights of 1995 July 28 to 31, though observations of a few objects were made by on the nights of 1993 August 20-21 and 1993 June 18-19."411 Observations of brighter objects in the sample were mace with the IGI on the MeDonalel Observatory LOT telescope on the nights of 1993 July 27-28., Observations of brighter objects in the sample were made with the IGI on the McDonald Observatory $^{''}$ telescope on the nights of 1993 July 27-28.412 Pwo objects were observed using the Ixast spectrograph on the Shane 32m telescope at, Two objects were observed using the Kast spectrograph on the Shane 3-m telescope at413According to the theory of cliffusive shock acceleration or SNRs. the maximum attainable energy for cosmic ravs is determined by the size of accelerator. the magnetic field of the CSAL and the energy. losses resulting from acdiabatic oocesses and svnchrotron. processes.,"According to the theory of diffusive shock acceleration for SNRs, the maximum attainable energy for cosmic rays is determined by the size of accelerator, the magnetic field of the CSM and the energy losses resulting from adiabatic processes and synchrotron processes."414 The size depends on he explosion evolution of SNR., The size depends on the explosion evolution of SNR.415 According to Ixirk(1904).. he explosion includes three phases: frec-expansion. phase. Sedov-Tavlor. phase. ancl snow-plough phase.," According to \cite{Kirk1994}, the explosion includes three phases: free-expansion phase, Sedov-Taylor phase and snow-plough phase."416 During the rec-expansion phase. the kinetic energy of ejecta remains untapped. and the particle acceleration is not significant.," During the free-expansion phase, the kinetic energy of ejecta remains untapped, and the particle acceleration is not significant."417 Once the mass swept-up by the shock becomes comparable o the mass of the ejecta Adje. the explosion enters he Secov-Tavlor phase.," Once the mass swept-up by the shock becomes comparable to the mass of the ejecta $M_{\rm ejc}$, the explosion enters the Sedov-Taylor phase."418 The acceleration ellicieney is the lighest in this phase., The acceleration efficiency is the highest in this phase.419 The maximum energy for protons is approximately eiven by (Schurectal.2010) where Zis the charge number. e is the elementary electric charge. e is the speed of light and £5 is à relation between the compression ratio of the density and magnetic field.," The maximum energy for protons is approximately given by \citep{Schure2010}420 where $Z$is the charge number, $e$ is the elementary electric charge, $c$ is the speed of light and $\xi_{\sigma}$ is a relation between the compression ratio of the density and magnetic field."421 Here. we assume that the magnetic field is parallel to the shock normal. which means £4=20.," Here, we assume that the magnetic field is parallel to the shock normal, which means $\xi_{\sigma}=20$."422 D is the magnetic lield strength. and fp~Repτμ is the duration for which the particles stay in the Sedov-TFavlor phase. where Vy is the shock speed and Rep is the radius where the shock sweeps up the matter whose mass is equal to that of the ejecta.," $B$ is the magnetic field strength, and $t_{\rm ST}\sim R_{\rm ST}/V_{\rm sh}$ is the duration for which the particles stay in the Sedov-Taylor phase, where $V_{\rm sh}$ is the shock speed and $R_{\rm ST}$ is the radius where the shock sweeps up the matter whose mass is equal to that of the ejecta."423" 1n general. for SNRs. the magnetic Ποιά D of the CSAIL is  pCGauss. ancl fer is ~ pe due to the high mass of the ejecta (~ AL.) and the low particle density of CSM (Melee&""Truelove. 1995)."," In general, for SNRs, the magnetic field $B$ of the CSM is $\sim424\mu$ Gauss, and $R_{\rm ST}$ is $\sim$ pc due to the high mass of the ejecta $\sim M_\odot$ ) and the low particle density of CSM \citep{McKee1995}."425.. Typical fp is several hundred: vears., Typical $t_{\rm ST}$ is several hundred years.426 llowever. in svmbiotic novae like V407 Cvgni. there are some physical conditions which are greatly different from jose in σας: (i) Phe magnetic field of the CSAL is the magnetic field of the stellar wind from the RC. and it is given by Bodeοἱ(1985) where & is: Doltzmann's: constant. m=1021 eis the mean particle mass. and 7; is the temperature of the stellar wind.," However, in symbiotic novae like V407 Cygni, there are some physical conditions which are greatly different from those in SNRs: (i) The magnetic field of the CSM is the magnetic field of the stellar wind from the RG, and it is given by \cite{Bode1985}427 where $k$ is Boltzmann's constant, $\bar{m} = 10^{-24}$ g is the mean particle mass, and $T_{\rm g}$ is the temperature of the stellar wind."428 W407 ονου is a D-type 88 in which the BG has dust shells., V407 Cygni is a D-type SS in which the RG has dust shells.429 Phe temperature for the dust condensation zone is  1000 Ix Cail&Sedlmayr(1999)., The temperature for the dust condensation zone is $\sim$ 1000 K \cite{Gail1999}.430". Llere. we take 7;= 10001. The density p is given by where Ah, is the mass-loss rate of the RG. V is the stellar wind velocity. e is the binary separation. a distance Rand polar angle @ is from the WD center towards the tC."," Here, we take $T_{\rm g}=1000$ K. The density $\rho$ is given by where $\dot{M}_{\rm L}$ is the mass-loss rate of the RG, $V_{\rm w}$ is the stellar wind velocity, $a$ is the binary separation, a distance $R$ and polar angle $\theta$ is from the WD center towards the RG."431 For simplicity. we only consider 6=0°.," For simplicity, we only consider $\theta=0^{\rm o}$."432 As shown by Bodeetal.(L985)... Bis ~107 Gauss. which is 10° times ueher than that in the CSM of SN~ (," As shown by \cite{Bode1985}, $B$ is $\sim 10^{-2}$ Gauss, which is $10^{3}$ times higher than that in the CSM of SNR. ("433"i) Por a typical nova. the mass of ejecta is ~10.""AL. (Yaronetal.2005).. which is much less than that of the ejecta in a typical supernova.","ii) For a typical nova, the mass of ejecta is $\sim 10^{-6}434M_\odot$ \citep{Yaron2005}, which is much less than that of the ejecta in a typical supernova."435 Furthermore. we note that he duration of matter ejecting in a tvpical nova is  several davs or tens of davs. and the matter ejected has an average expansion velocity Vis over the whole ejecting matter phase and a maximal expansion velocity Vias.," Furthermore, we note that the duration of matter ejecting in a typical nova is $\sim$ several days or tens of days, and the matter ejected has an average expansion velocity $V_{\rm av}$ over the whole ejecting matter phase and a maximal expansion velocity $V_{\rm max}$."436 Fhis means that a part of the matter ejected has the high expansion. velocity Vas," This means that a part of the matter ejected has the high expansion velocity $V_{\rm437max}$."438 Phe shock in à nova is mainly produced by the matter ejected with high velocity., The shock in a nova is mainly produced by the matter ejected with high velocity.439 We assume that Via=Vis and use a parameter η to define a ratio of the mass ejected with a velocity of Vias to the whole ejecta.," We assume that $V_{\rm sh}=V_{\rm max}$, and use a parameter $\eta$ to define a ratio of the mass ejected with a velocity of $V_{\rm max}$ to the whole ejecta."440 Ler can be given by the following equation: where {νο is the racius of WD., $R_{\rm ST}$ can be given by the following equation: where $R_{\rm WD}$ is the radius of WD.441 Abdoetal. found that the peak [lux in 5-ravs was observed. after 3-4 davs of a nova outburst from V407 Cvgni on 10 March 2010., \cite{Abdo2010} found that the peak flux in $\gamma$ -rays was observed after 3-4 days of a nova outburst from V407 Cygni on 10 March 2010.4420 This implies that /p in V407 Cveni should shorter than 3 days.," This implies that $t_{\rm443ST}$ in V407 Cygni should shorter than 3 days."444 In our model fp depends on the parameter η.," In our model $t_{\rm445ST}$ depends on the parameter $\eta$."446 We find that fs¢~ days when qg 0.01., We find that $t_{\rm ST} \sim$ days when $\eta \sim$ 0.01.447 ‘The novae occurring in SSs are surrounded by the dense stellar winds from the Bs., The novae occurring in SSs are surrounded by the dense stellar winds from the RGs.448 They olfers an environment for high efficient. particle acceleration., They offers an environment for high efficient particle acceleration.449 Pherefore. they may be an important source of the high-energy 5-ravs in the Galaxy.," Therefore, they may be an important source of the high-energy $\gamma$ -rays in the Galaxy."450 In general. SSs are the detached interacting binaries in which the WDs accrete the matter of the RCs via stellar winds.," In general, SSs are the detached interacting binaries in which the WDs accrete the matter of the RGs via stellar winds."451 ὃν a population synthesis method. Lüetal.(2006). czuried out a detailed investigation of SSs.," By a population synthesis method, \cite{Lu2006} carried out a detailed investigation of SSs."452 They found. that. the occurrence rate of the novae in ος is greatly. alleeteck by common-envelope evolution and the stellar wind velocity Vi of theBC., They found that the occurrence rate of the novae in SSs is greatly affected by common-envelope evolution and the stellar wind velocity $V_{\rm w}$ of theRG.453 Following Lüetal.(2006) and Zhuetal.(2010).. [or common-envelope evolution in dilflerent. simulations we use an GQeeAce=0.5 in o-algorithm and 5=1.75 in a 5- algorithm. respectively: for the stellar wind. Vio=ieu where rece is the escape velocity and Vy is determined. by he relation between the mass-loss rates and the terminal wind velocities fitted by Wintersetal.(2003) às: In this work we consider three cases with different input xwameters: ((1) iin case 1. a4.=0.5 and V=NE (ii) lin case 2.5=1.75 and V—S6 ((iii) in case 3. eX.=0.5 and Vi taken as(5).," Following \cite{Lu2006} and \cite{Zhu2010}, , for common-envelope evolution in different simulations we use an $\alpha_{\rm ce}\lambda_{\rm ce}=0.5$ in $\alpha$ -algorithm and $\gamma=1.75$ in a $\gamma$ -algorithm, respectively; for the stellar wind, $V_{\rm w}=\frac{1}{2}v_{\rm454esc}$ where $v_{\rm esc}$ is the escape velocity and $V_{\rm w}$ is determined by the relation between the mass-loss rates and the terminal wind velocities fitted by \cite{Winters2003} as: In this work we consider three cases with different input parameters: (i) in case 1, $\alpha_{\rm ce}\lambda_{\rm ce}=0.5$ and $V_{\rm455w}=\frac{1}{2}v_{\rm esc}$ (ii) in case 2, $\gamma=1.75$ and $V_{\rm w}=\frac{1}{2}v_{\rm esc}$ (iii) in case 3, $\alpha_{\rm456ce}\lambda_{\rm ce}=0.5$ and $V_{\rm w}$ taken as."457" Using the model of SSs and erid for novae in Yaronetal. (2005).. we can estimate £7)luax in which 6=0"" and η=0.01 or every nova."," Using the model of SSs and grid for novae in \cite{Yaron2005}, we can estimate $E^{\rm p}_{\rm max}$ in which $\theta=0^{\rm o}$ and $\eta=0.01$ for every nova."458 According to Kamaeetal. (2006).. p.p interaction can occur when the energv. of proton is higher han 100 eV.κε which. results in. -rav emission.," According to \cite{Kamae2006}, , $p-p$ interaction can occur when the energy of proton is higher than $10^9$ eV, which results in $\gamma$ -ray emission."459.. sTherefore.. we assume that the novae in SSs are 5-rav sources if the £jULES.p in Eq. (1))," Therefore, we assume that the novae in SSs are $\gamma$ -ray sources if the $E^{\rm460p}_{\rm max}$ in Eq. \ref{eq:epmax}) )"461" is higher than 10"" eV. Using a population svnthesis method described in Luetal. 2008).. we model10"" binary svstems which gives a statistical error for our Monte Carlo simulation lower than 5 percent for the svmbiotic novae."," is higher than $10^9$ eV. Using a population synthesis method described in \cite{Lu2006,462Lu2008}, , we model$10^6$ binary systems which gives a statistical error for our Monte Carlo simulation lower than 5 percent for the symbiotic novae."463 In order to estimate the occurrence rate of the x-ray sources like V407 Cvgni. we," In order to estimate the occurrence rate of the $\gamma$ -ray sources like V407 Cygni, we"464iaenetosphere above the polar cap.,magnetosphere above the polar cap.465 Low-level accretion. possibly of supernova fallback material. has been mvoked to ease the problem iu both cases.," Low-level accretion, possibly of supernova fallback material, has been invoked to ease the problem in both cases."466 This would point to the existence of a debris disk surrounding the INS (lich could be detected in the optical-intrared range). a long sought astrophysical object. so far possibly observed ouly in the case of the Anomalous N-rav Pulsar (ANP) 0112|61 (?).," This would point to the existence of a debris disk surrounding the INS (which could be detected in the optical-infrared range), a long sought astrophysical object, so far possibly observed only in the case of the Anomalous X-ray Pulsar (AXP) 0142+61 ."467. Very deep imaging of the field of hhave been performed both from the grouud with the ESO (VLT)) and with the (IEST))., Very deep imaging of the field of have been performed both from the ground with the ESO ) and with the ).468 Optical oobservatious (De Luca et al., Optical observations (De Luca et al.469" 2001) did not reveal any potential counterpart down to R~27.1 aud V~27.3 while observations iu the optical with the and in the near infrares (NIR) with the showed the preseuce of a faint source (hereafter ""source Z) close to the Nav position. with maguitudes Wess026.14 and Ks~20.7(77)."," 2004) did not reveal any potential counterpart down to $\sim$ 27.1 and $\sim$ 27.3 while observations in the optical with the and in the near infrared (NIR) with the showed the presence of a faint source (hereafter “source Z”) close to the X-ray position, with magnitudes $_{F555W}\sim26.4$ and $\sim$ 20.7."470" Ilowever. the association with wwas soon after questioned by ou the basis of precise absolute astrometry of he Ππμασος, which showed a positional offset of source Z with respect to the coordinates."," However, the association with was soon after questioned by on the basis of precise absolute astrometry of the images, which showed a positional offset of source Z with respect to the coordinates."471 The same source was observed in the NIR by?.. who reported very red colours. consistent with au AL dwarf. aud also questioned its possible association to bbecause of the inconsistency with the position.," The same source was observed in the NIR by, who reported very red colours, consistent with an M dwarf, and also questioned its possible association to because of the inconsistency with the position."472" also observed the field withSpitzerat L5jan aud at δρα, but did not detect auv source at the target position."," also observed the field withat $\mu$ m and at $\mu$ m, but did not detect any source at the target position."473 Tere we repor onu a different. iudependent test to assess the association of source Z to5209.. using multi-epoch data collected with the ((Sect. 2)).," Here we report on a different, independent test to assess the association of source Z to, using multi-epoch data collected with the (Sect. \ref{hst}) )."474 The same ddataset. completed by erouncd based data collected with theVLT.. is also used to derive strinecut constraints ou the optical/imtrared cussion from ((Sect. 3)).," The same dataset, completed by ground based data collected with the, is also used to derive stringent constraints on the optical/infrared emission from (Sect. \ref{phot}) )."475 Results ave discussed in Sect. L.., Results are discussed in Sect. \ref{disc}. .476 1296.5|10.0 has a remarkable. well defined bilatera sviunetre(27).," G296.5+10.0 has a remarkable, well defined bilateral symmetry."477 Very likely. the explosion site lies on the svinmnetry axis of the SNR. but the current position of 1s sigmificautly offset from the apparent ceuter of the host SNR.," Very likely, the explosion site lies on the symmetry axis of the SNR, but the current position of is significantly offset from the apparent center of the host SNR."478 Iudeed. the geometrical ceuter position evaliatec by is ~δ to the south west of the N-rav source(2)..," Indeed, the geometrical center position evaluated by is $\sim8\arcmin$ to the south west of the X-ray source."479 Assuming for the system au age of TOOOO years. such a displacement would tuaply a proper motion of ~TO amas ol. corresponding to a projected velocity of ~GIO kan 4. consistent with the observed. velocity distribution for radio pulsus(7).," Assuming for the system an age of 000 years, such a displacement would imply a proper motion of $\sim70$ mas $^{-1}$, corresponding to a projected velocity of $\sim640$ km $^{-1}$, consistent with the observed velocity distribution for radio pulsars."480. This offers a natura wav to test the putative identification: if iudeed associated with5209.. source Z should show a significant proper motion.," This offers a natural way to test the putative identification: if indeed associated with, source Z should show a significant proper motion."481 Thus. we used iuulti-epochi oobservations to search for an angular displacement of source Z. We observed the field of with the on May sth 2007 (Proeranune 10791).," Thus, we used multi-epoch observations to search for an angular displacement of source Z. We observed the field of with the on May 8th 2007 (Programme 10791)."482 Our observations were originally scheduled for execution with the (WEC) of the (CACS))(22)., Our observations were originally scheduled for execution with the ) of the ).483. Unfortunately. theACS/WEC was put in idle state on January 2007 due to a failure of the on-board electronics.," Unfortunately, the was put in idle state on January 2007 due to a failure of the on-board electronics."484 Our observations were re-scheduled aud executed with the C(WEPC'2))., Our observations were re-scheduled and executed with the ).485 A set of four 500s exposures were obtained duriug one spacecraft orbit. through the sliW filter (A=8OL2AÀ: AA=1539 Aj).," A set of four 500s exposures were obtained during one spacecraft orbit, through the 814W filter $\lambda= 8012$ ; $\Delta486\lambda=1539$ )."487 In order to exploit the maxinuun spatial resolution for the proper motion measurement. was placed at the ceutre of the (PC) Tip (00015/pixel).," In order to exploit the maximum spatial resolution for the proper motion measurement, was placed at the centre of the ) chip 045/pixel)."488 Our new data add up to observations collected with the oon July 28th and August 7th 2003 (Proeranuue 9872) and available in the public aarchives., Our new data add up to observations collected with the on July 28th and August 7th 2003 (Programme 9872) and available in the public archives.489 This first-epoch ddataset allowed to pick up Source Z as a possible couuterpart to5209., This first-epoch dataset allowed to pick up Source Z as a possible counterpart to.490. TheWEC (070050/pixel) was used in both visits., The 050/pixel) was used in both visits.491 Two SOGQUOLCOR of L aud 5 exposures were obtained through the broad-banud filters 555WN (A=531|GÀ:: AA=1193 Aj) and SIIW (A= S333A: AA=2511 ÀJ) for a total iuteeration time of 12800 s and 10200 x. respectively.," Two sequences of 4 and 5 exposures were obtained through the broad-band filters 555W $\lambda= 5346$; $\Delta \lambda=1193$ ) and 814W $\lambda= 8333$ ; $\Delta \lambda=2511$ ), for a total integration time of 12800 s and 10200 s, respectively."492 The complete dataset spans a time baselime of ~3.75 vears., The complete dataset spans a time baseline of $\sim3.75$ years.493 We downloaded the data from the Space Telescope European Coordinating Facility (ST-ECF) Scieuce DataArchivel., We downloaded the data from the Space Telescope European Coordinating Facility (ST-ECF) Science Data.494 Ou-the-fly data reduction (bias and flat- correction) and flux. calibration were applied usine theSoftware (STSDAS) through the ST-EC'F Data Archive pipeline., On-the-fly data reduction (bias and flat-field correction) and flux calibration were applied using the ) through the ST-ECF Data Archive pipeline.495 To filter cosimic rav hits. sinele eexposures were combined and averaged using the taskcombine. while single exposures were combined using which also produces a mosaic mage of the two cchips aud applies the correction for the geometric distortions of the camera.," To filter cosmic ray hits, single exposures were combined and averaged using the task, while single exposures were combined using which also produces a mosaic image of the two chips and applies the correction for the geometric distortions of the camera."496the surface density of galaxies at the inner edge of the extended radio relic.,the surface density of galaxies at the inner edge of the extended radio relic.497" Remarkably, the transverse extent of the wall is also comparable to the relic, ~2 Mpc."," Remarkably, the transverse extent of the wall is also comparable to the relic, $\sim$ 2 Mpc."498 Fig., Fig.499 7 shows a 1-D slice across the Coma halo and relic in radio (1.4 GHz) and brightnesses., \ref{slice} shows a 1-D slice across the Coma halo and relic in radio (1.4 GHz) and brightnesses.500 There is no significant X-ray emission beyond the relic., There is no significant X-ray emission beyond the relic.501" We also plot the surface density of SDSS galaxies in three velocity bins along the same slice, with a width of 2°."," We also plot the surface density of SDSS galaxies in three velocity bins along the same slice, with a width of $^{\circ}$."502" Moving away from the cluster, we find a sharp drop in the number of galaxies with 6600 < v < 8200 just as the relic radio emission increases."," Moving away from the cluster, we find a sharp drop in the number of galaxies with 6600 $<$ v $<$ 8200 just as the relic radio emission increases."503" The other velocity bins, as expected, are dominated by the cluster itself and drop off gradually without any special behaviour at the relic position."," The other velocity bins, as expected, are dominated by the cluster itself and drop off gradually without any special behaviour at the relic position."504" Several infalling groups of galaxies have been identified near this region (e.g., Adami et al."," Several infalling groups of galaxies have been identified near this region (e.g., Adami et al."505" 2005), but this is the first identification of a very broad transverse feature in the infall pattern into Coma."," 2005), but this is the first identification of a very broad transverse feature in the infall pattern into Coma."506 Rines et al., Rines et al.507" 2003 estimate a virial radius of 2.8 Mpc (using ~1.3rag9, Eke, Cole Frenk 1996, and converting to Hp=70), so the galaxy wall is already within the virialized region but can still be isolated in space and velocity."," 2003 estimate a virial radius of 2.8 Mpc (using $\sim$ $_{200}$, Eke, Cole Frenk 1996, and converting to $_0$ =70), so the galaxy wall is already within the virialized region but can still be isolated in space and velocity."508 The correspondence between the wall of galaxies and the inner edge of the radio relic suggests a causal link., The correspondence between the wall of galaxies and the inner edge of the radio relic suggests a causal link.509" This poses a problem for the association between the radio relic and the NAT radio source NGC 4789, which is a possible source of seed relativistic electrons (EnBlin et al."," This poses a problem for the association between the radio relic and the NAT radio source NGC 4789, which is a possible source of seed relativistic electrons lin et al."510 1998)., 1998).511" Given its radial velocity of 8365 km/s and the morphology of the bent jet, NGC 4789 is apparently on the back side of the cluster (moving away), while the wall of galaxies, if"," Given its radial velocity of 8365 km/s and the morphology of the bent jet, NGC 4789 is apparently on the back side of the cluster (moving away), while the wall of galaxies, if"512finds a maximum of 770+110rad m-?.,finds a maximum of $770\pm110$rad $^{-2}$.513" The maps are similar moving north across where the RM switches from positive to negative (0?15,0?4),values; Tsuboietal.(1986) measure RM—250rad m? while the present survey finds —220+130 rad m~?."," The maps are similar moving north across $(0\ddeg15,0\ddeg4)$, where the RM switches from positive to negative values; \citet{t86} measure $\approx-250$rad $^{-2}$ while the present survey finds $-220\pm130$ rad $^{-2}$."514" There is some agreement at the northwestern edge of the polarized emission of the Radio Arc, shown in Figure 5,, where the RM switches back to positive values."," There is some agreement at the northwestern edge of the polarized emission of the Radio Arc, shown in Figure \ref{rmcomp}, where the RM switches back to positive values."515 The exact location of this second RM sign change is slightly different and may reflect the different RM depths each survey is sensitive to., The exact location of this second RM sign change is slightly different and may reflect the different RM depths each survey is sensitive to.516 Yusef-Zadehetal.(1997) presented a detailed study of the polarization properties of the nonthermal filament G359.544-0.18 (RF-C3) at 6 and 3.6 cm., \citet{y97} presented a detailed study of the polarization properties of the nonthermal filament G359.54+0.18 (RF-C3) at 6 and 3.6 cm.517" Figure 3 of that work has a similar 6 cm brightness and RM distribution as the present work, both presented here and in Lawetal."," Figure 3 of that work has a similar 6 cm brightness and RM distribution as the present work, both presented here and in \citet{gcl_vla}."518" The RM map of the filament shows three distinct, (2008a)..bright clumps each having relatively uniform values."," The RM map of the filament shows three distinct, bright clumps each having relatively uniform values."519" The morphology seen in the present survey is similar to that of Yusef-Zadehetal.(1997),, although it had roughly three times better resolution ccompared to iin the present work)."," The morphology seen in the present survey is similar to that of \citet{y97}, although it had roughly three times better resolution compared to in the present work)."520" The first clump, at RA, Dec = -29:12:30) has RM&—2700 rad m-?, (B1950)compared to (17:40:41,—3960+1100 rad m~? in the present survey."," The first clump, at RA, Dec (B1950) = (17:40:41, –29:12:30) has $\approx-2700$ rad $^{-2}$ , compared to $-3960\pm1100$ rad $^{-2}$ in the present survey."521" The second clump, at (17:40:43, —29:12:40), has RM—2000 rad m~?, compared to —2200+440 rad m? in the present survey."," The second clump, at (17:40:43, –29:12:40), has $\approx-2000$ rad $^{-2}$, compared to $-2200\pm440$ rad $^{-2}$ in the present survey."522" The third clump, at (17:40:44,29:12:45), has RM—1500 rad m?, compared to —15404:660 rad m~? in the present survey."," The third clump, at (17:40:44,--29:12:45), has $\approx-1500$ rad $^{-2}$, compared to $-1540\pm660$ rad $^{-2}$ in the present survey."523" We conclude that, in general, there is good agreement between the RM of the present survey and that of Yusef-Zadehetal. (1997)."," We conclude that, in general, there is good agreement between the RM of the present survey and that of \citet{y97}."524". In summary, the polarized intensity and RM of the present 6 cm survey shows good agreement with those of other surveys."," In summary, the polarized intensity and RM of the present 6 cm survey shows good agreement with those of other surveys."525" This is consistent with the fact the polarimetric leakgage is expected to have relatively little frequency structure for the VLA feed design (Cotton1994,1999);; any systematic errors in the polarization angle are subtracted when forming the iimage."," This is consistent with the fact the polarimetric leakgage is expected to have relatively little frequency structure for the VLA feed design \citep{c94,c99}; any systematic errors in the polarization angle are subtracted when forming the image."526 It also shows that histogram fitting of the vvalues is a reasonable estimate of the RM and its uncertainty at 6 cm in this region., It also shows that histogram fitting of the values is a reasonable estimate of the RM and its uncertainty at 6 cm in this region.527 'The 6 cm polarized continuum intensity of the northern extension of the Radio Arc is several mJy beam~! and spans the entire eastern edge of the survey up to a latitude of b~0?8., The 6 cm polarized continuum intensity of the northern extension of the Radio Arc is several mJy $^{-1}$ and spans the entire eastern edge of the survey up to a latitude of $b\sim0\ddeg8$.528" To test for frequency structure in the polarized intensity, the polarized intensity maps in the two bands were differenced."," To test for frequency structure in the polarized intensity, the polarized intensity maps in the two bands were differenced."529 The lack of diffuse emission in the difference map shows that the two maps have similar diffuse emission within roughly 1 mJy., The lack of diffuse emission in the difference map shows that the two maps have similar diffuse emission within roughly 1 mJy.530 The comparable 20 cm mosaic of polarized continuum shows no extended emission down to a level of about 0.1 mJy beam! detailinLawetal.2008a)., The comparable 20 cm mosaic of polarized continuum shows no extended emission down to a level of about 0.1 mJy $^{-1}$ \citep[more detail in][]{gcl_vla}.531". For latitudes(more up to b=0°3, the polarized continuum emission seen in the 6 cm interferometric maps (Fig. 1))"," For latitudes up to $b=0\ddeg3$, the polarized continuum emission seen in the 6 cm interferometric maps (Fig. \ref{poln_polc}) )"532 has a total intensity counterpart in the same data., has a total intensity counterpart in the same data.533" However, north of b=0?3, the total intensity counterpart is too extended to be detected by the VLA 6 cm observations."," However, north of $b=0\ddeg3$, the total intensity counterpart is too extended to be detected by the VLA 6 cm observations."534" Since the polarized emission is broken into small spatial scales (as shown in Figure 2)), it is detected throughout the region and the apparent polarization fraction often exceeds100%."," Since the polarized emission is broken into small spatial scales (as shown in Figure \ref{canal}) ), it is detected throughout the region and the apparent polarization fraction often exceeds."535". 'To estimate the polarization fraction without the effect of missing flux, we compare the VLA polarized-intensity maps to continuum maps from the Green Bank Telescope (Lawetal.2008b).."," To estimate the polarization fraction without the effect of missing flux, we compare the VLA polarized-intensity maps to continuum maps from the Green Bank Telescope \citep{gcsurvey_gbt}."536" We convolve the VLA maps to the GBT resolution to estimate the polarization fraction; this will be a lower limit, since the VLA emission is laced with depolarized canals."," We convolve the VLA maps to the GBT resolution to estimate the polarization fraction; this will be a lower limit, since the VLA emission is laced with depolarized canals."537" At 6 cm, the peak polarization fraction is in the eastern half of the survey and in the western half of the survey."," At 6 cm, the peak polarization fraction is in the eastern half of the survey and in the western half of the survey."538" These values are consistent with other single-dish surveys (Tsuboietal.1986;Haynesetal. 1992),, which confirms the validity of techniques and maps of the VLA survey."," These values are consistent with other single-dish surveys \citep{t86,h92}, which confirms the validity of techniques and maps of the VLA survey."539" At 20 cm, the upper limit on the polarization fraction is roughly of the total intensity measured by the GBT."," At 20 cm, the upper limit on the polarization fraction is roughly of the total intensity measured by the GBT."540 Figure 6 shows two maps of RM smoothed over 125-arcsec tiles with the histogram-fitting method., Figure \ref{padilg} shows two maps of RM smoothed over 125-arcsec tiles with the histogram-fitting method.541 The images show there is coherent structure on degree size scales., The images show there is coherent structure on degree size scales.542 The east side of the survey tends to have RM greater than zero and the west side less than zero., The east side of the survey tends to have RM greater than zero and the west side less than zero.543" 'The east-west structure is seen more clearly in averages calculated over all latitudes, as shown in Figure 7.."," The east-west structure is seen more clearly in averages calculated over all latitudes, as shown in Figure \ref{rmlong}."544" In the east, for 0°2<|—0°3, RM z4-330 rad τη”. then the RM changes rapidly for —0?3«| —0?55, and in the west, for —0°95«| —0?55, RM—880+50 rrad m~?."," In the east, for $0\ddeg2<l<-0\ddeg3$, RM $\approx+330$ rad $^{-2}$, then the RM changes rapidly for $-0\ddeg3<l<-0\ddeg55$ , and in the west, for $-0\ddeg95<l<-0\ddeg55$ , $\approx-880\pm50$ rad $^{-2}$ ."545" Averaging RM over the top half ofthe survey (0245«b 0?7) shows a similar structure as the average over all latitudes, but with a larger range."," Averaging RM over the top half ofthe survey $0\ddeg45<b<0\ddeg7$ ) shows a similar structure as the average over all latitudes, but with a larger range."546" The maximum RM is+660+75 rrad m~? nnear |=—0°25 oon the east side, while the minimum RM is —1320+τὸ rrad m7? nnear |——0?65 oon the west side."," The maximum RM is$+660\pm75$ rad $^{-2}$ near $l=-0\ddeg25$ on the east side, while the minimum RM is $-1320\pm75$ rad $^{-2}$ near $l=-0\ddeg65$ on the west side."547imply a cutolf in the spectrum of accelerated: protons at ~100 TeV. roughly a factor of 30 short of the knee.,"imply a cutoff in the spectrum of accelerated protons at $\sim 100$ TeV, roughly a factor of 30 short of the knee."548 [t is worth keeping in mind that in an expanding SNR. the highest cosmic rav energy is expected to be reached around the beginning of the Sedoy. phase., It is worth keeping in mind that in an expanding SNR the highest cosmic ray energy is expected to be reached around the beginning of the Sedov phase.549 Before and after that time the maximum energy of accelerated particles does not need to be as high as the knee energy., Before and after that time the maximum energy of accelerated particles does not need to be as high as the knee energy.550 Moreover. cilferent SNRs nueht accelerate to clilferent maximum energies because of the different environment in which they explode.," Moreover, different SNRs might accelerate to different maximum energies because of the different environment in which they explode."551 In this sense it is only natural that most SNRs do not show proton acceleration up to the energy of the knee., In this sense it is only natural that most SNRs do not show proton acceleration up to the energy of the knee.552 The strength. and. topology of the magnetic field. in the acceleration/radiation region regulate the clliciency of particle acceleration (nuclei and electrons) and the radiation losses of electrons., The strength and topology of the magnetic field in the acceleration/radiation region regulate the efficiency of particle acceleration (nuclei and electrons) and the radiation losses of electrons.553 The recent detection of marrow X-ray bright rims in several SNRs (Bambaetal.2003.2005:Lazen-dicetal.2003.2004:Vink&Laming2003) has allowed to infer the strength of the field. if the thickness of the rims is interpreted. as the svnehrotron loss length of the radiating electrons. (Ballet 2006)...," The recent detection of narrow X-ray bright rims in several SNRs \cite[]{bamba03, bamba05, laz03, laz04, vink03}554 has allowed to infer the strength of the field, if the thickness of the rims is interpreted as the synchrotron loss length of the radiating electrons \cite[]{ballet}. ."555 Typical values of. 501000507 have been inferred. which suggest. efficient. magnetic field amplification in the shock region.," Typical values of $50-1000\mu G$ have been inferred, which suggest efficient magnetic field amplification in the shock region."556 One more argument in favor of strong magnetic fields was made by Uchivamaetal.(2007) who interpreted the rapid time variability (of the orders of [ew vears) observed in some X-ray emitting regions Of RN J1713.7-3946 as due to rapid synchrotron cooling., One more argument in favor of strong magnetic fields was made by \cite{uch07} who interpreted the rapid time variability (of the orders of few years) observed in some X-ray emitting regions of RX J1713.7-3946 as due to rapid synchrotron cooling.557 The field strength inferred based on this interpretation is as high as ] mCG. The same ellect was also observed in some knots of Cas A (Uchivama&Aharonian2008)., The field strength inferred based on this interpretation is as high as $\sim 1$ mG. The same effect was also observed in some knots of Cas A \cite[]{uch08}.558. There is however a large source of ambiguity in that the narrow thickness of the X-ray rims might be due to damping of the magnetic field (for instance due to waveswave non-linear coupling) (Pohletal.2005)., There is however a large source of ambiguity in that the narrow thickness of the X-ray rims might be due to damping of the magnetic field (for instance due to wave-wave non-linear coupling) \cite[]{pohl05}.559. In this case the magnetic lield inferred. by assuming that the rims are due to severe svnchrotron losses might be overestimated., In this case the magnetic field inferred by assuming that the rims are due to severe synchrotron losses might be overestimated.560 We discuss this issue at several points throughout the paper., We discuss this issue at several points throughout the paper.561 Alagnetic field amplification could result from turbulent amplification (Ciacalone&Jokipii2007) or from cosmic rav induced streaming instability., Magnetic field amplification could result from turbulent amplification \cite[]{joki} or from cosmic ray induced streaming instability.562 An open question is whether the large magnetic fields present in the X-rav rims are widespread: throughout the remnant or are rather confined in thin filaments with a relatively small filling factor (this would be the case if damping plavs a role downstream of the shock)., An open question is whether the large magnetic fields present in the X-ray rims are widespread throughout the remnant or are rather confined in thin filaments with a relatively small filling factor (this would be the case if damping plays a role downstream of the shock).563 This dillerence might have important consequences on the interpretation of the observed. non-thermal emission [rom SNRs. as we discuss below.," This difference might have important consequences on the interpretation of the observed non-thermal emission from SNRs, as we discuss below."564 Interestingly enough. the magnetic field strength inforrec from N-rav. observations is of the same order of magnitude as that required. by the theory of shock acceleration in order to account for particle acceleration up to the knee region. provided the diffusion coellicient is ohm-like.," Interestingly enough, the magnetic field strength inferred from X-ray observations is of the same order of magnitude as that required by the theory of shock acceleration in order to account for particle acceleration up to the knee region, provided the diffusion coefficient is Bohm-like."565 From the theoretical point of view. a major improvement has been achieved in the last few vears in that the calculations are carried out in the context. of the so-called non-linear theory of particle acceleration.," From the theoretical point of view, a major improvement has been achieved in the last few years in that the calculations are carried out in the context of the so-called non-linear theory of particle acceleration."566 This theory allows us to calculate the spectrum ancl spatial distribution of accelerated: particles around the shock. their dynamical reaction on the shock and the magnetic field amplification that cosmic rays induce due to streaming instability.," This theory allows us to calculate the spectrum and spatial distribution of accelerated particles around the shock, their dynamical reaction on the shock and the magnetic field amplification that cosmic rays induce due to streaming instability."567 Although the non-linear theory has been previously applied to SNRs. this paper improves on previous attempts in two major aspects: 1) the magnetic field in the shock region is caleulated from. streaming instability ancl from conservation equations instead. of being inserted. in such a wav to fit the X-ray observations: 2) we include the dynamical reaction of the turbulent magnetic field on the shock. which is a very important elfect in shaping the shock precursor (C'apriolietal.(2008a.b))).," Although the non-linear theory has been previously applied to SNRs, this paper improves on previous attempts in two major aspects: 1) the magnetic field in the shock region is calculated from streaming instability and from conservation equations instead of being inserted in such a way to fit the X-ray observations; 2) we include the dynamical reaction of the turbulent magnetic field on the shock, which is a very important effect in shaping the shock precursor \cite{cap08,long}) )."568 The first point is of crucial importance in that it allows us to achieve a unified. picture of the spectra of X-ray and ganuna ray emission. together with the morphology of the X-ray emission. the strength of the magnetic field and finally the dilfusion properties of the accelerated particles.," The first point is of crucial importance in that it allows us to achieve a unified picture of the spectra of X-ray and gamma ray emission, together with the morphology of the X-ray emission, the strength of the magnetic field and finally the diffusion properties of the accelerated particles."569 Inclusion of the dynamical reaction of the field. then. as showed by Capriolietal.(2008a).. leads to à substantial reduction of the compression in the precursor. thereby also reducing the concavitv of the spectrum of accelerated. particles (C'apriolietal.(2008b))).," Inclusion of the dynamical reaction of the field, then, as showed by \cite{cap08}, leads to a substantial reduction of the compression in the precursor, thereby also reducing the concavity of the spectrum of accelerated particles \cite{long}) )."570 A reduced concavity of the spectrum should also be expected as a result of the enhanced. velocity of the scattering centers when the magnetic field is amplified (see for instance Zirakashvili&Ptuskin (2000)))., A reduced concavity of the spectrum should also be expected as a result of the enhanced velocity of the scattering centers when the magnetic field is amplified (see for instance \cite{zir08}) ).571 The large values of the magnetic field strength inferred from X-ray observations ancl confirmed by our calculations clearly favor a hacronie interpretation of the observed. ganima ray emission. because a subdominant population of electrons is sullicient to explain the spectrum and intensity of the observed X-ray. emission. but is insullicient to produce the observed. gamma ray emission through inverse Compton scattering (LCS) on the CMD and infrared/optical photons (IR|Opt).," The large values of the magnetic field strength inferred from X-ray observations and confirmed by our calculations clearly favor a hadronic interpretation of the observed gamma ray emission, because a subdominant population of electrons is sufficient to explain the spectrum and intensity of the observed X-ray emission, but is insufficient to produce the observed gamma ray emission through inverse Compton scattering (ICS) on the CMB and infrared/optical photons (IR+Opt)."572 The issue of whether the large fields are present in large fractions of the remnant volume or are rather confined in narrow filaments. remains however an open Issue.," The issue of whether the large fields are present in large fractions of the remnant volume or are rather confined in narrow filaments, remains however an open issue."573 For this reason we also investigate the possibility that he filaments have some alternative explanation. so that here is no constraint on the streneth of the magnetic ield clownstream.," For this reason we also investigate the possibility that the filaments have some alternative explanation, so that there is no constraint on the strength of the magnetic field downstream."574 We still use our non-linear calculations o derive the spectra of accelerated: protons and. electrons. oit. force. the injection to be low enough to avoid. large magnetic fields produced by streaming instability.," We still use our non-linear calculations to derive the spectra of accelerated protons and electrons, but force the injection to be low enough to avoid large magnetic fields produced by streaming instability."575 We find hat a marginal fit to the gamma ray and. X-ray data is »xossible. although a large density of Ht photons needs to be assumed. inside the remnant.," We find that a marginal fit to the gamma ray and X-ray data is possible, although a large density of IR photons needs to be assumed inside the remnant."576 The fit to the highest energy xwt of the gamma ray spectrum is not às good. as for the mielronic interpretation., The fit to the highest energy part of the gamma ray spectrum is not as good as for the hadronic interpretation.577 The general conclusion we draw is that although there are numerous indications that the observed. gamma. ravs may be of hadronic origin. a clear answer on this point may only come from: a) the extension of the gamma rav observationsto lower energies. and b) the detection of high energv neutrinos. which would be produced in the same haclronic interactions (Morlinoetal.2008).," The general conclusion we draw is that although there are numerous indications that the observed gamma rays may be of hadronic origin, a clear answer on this point may only come from: a) the extension of the gamma ray observationsto lower energies, and b) the detection of high energy neutrinos, which would be produced in the same hadronic interactions \cite[]{neutrinos}."578. The paper is organized as follows: in 82. we discuss in some detail the general lines of the calculations we carry out. including the non-linear theory of particle acceleration. the magnetic field amplification and the dillerent. channels of non-thermal emissions.," The paper is organized as follows: in \ref{sec:model} we discuss in some detail the general lines of the calculations we carry out, including the non-linear theory of particle acceleration, the magnetic field amplification and the different channels of non-thermal emissions."579 ln 83. we discuss the results we obtain by specializing the caleulations tothe case of the SN RN J1713.7-3946., In \ref{sec:results} we discuss the results we obtain by specializing the calculations tothe case of the SNR RX J1713.7-3946.580 We conclude in ΚΕ. , We conclude in \ref{sec:conc}. .581In this section. we discuss the technical aspects of the, In this section we discuss the technical aspects of the582The primary purpose of our archival search was to find. simultaneous observations of Ser A* at,The primary purpose of our archival search was to find simultaneous observations of Sgr A* at583communication),communication).584 In BATSE. the burst was observed. 64 above the horizon. implving that the source remained visible for at least ~15 min after the trigger: thus. E900 s is a conservative lower limit for the interval between two resolved bursts. (," In BATSE, the burst was observed $64^\circ$ above the horizon, implying that the source remained visible for at least $\sim 15$ min after the trigger; thus, $\pm900$ s is a conservative lower limit for the interval between two resolved bursts. ("585Also relevant are the data from. Ulysses which saw no burst consistent with the location of GRB 990123 [or a period of at least three days. before and. after the event (Ix. Hurley. private communication). although coverage was only about complete and we cannot completely exclude a second burst.),"Also relevant are the data from Ulysses which saw no burst consistent with the location of GRB 990123 for a period of at least three days before and after the event (K. Hurley, private communication), although coverage was only about complete and we cannot completely exclude a second burst.)"586 1L as we argue. Ls“fyfox900s is excluded. then so are magnilications 40<µου400.," If, as we argue, $1~s\leq t_3-t_2 \leq 900~s$ is excluded, then so are magnifications $40\leq \mu_{2,3} \leq 400$."587" Furthermore. we can use limits on additional point sources in the HSTT image within 2"" ⋠⋠⋅∕∕⋅of the afterglow⋅ to place constraints⋠ on. lensed images."," Furthermore, we can use limits on additional point sources in the HST image within $2^{\prime\prime}$ of the afterglow to place constraints on lensed images."588 Hf µου<40. then using yy=4 (from eq.," If $\mu_{2,3}<40$, then using $\mu_1=4$ (from eq."589 11). we find that burst Lo would have had a [luence »3510.7 ere  on or around Jan. 15.," 11), we find that burst 1 would have had a fluence $>3\times10^{-5}$ erg $^{-2}$ on or around Jan. 15."590 It is unlikely. though not completely exeluded. that this Failed to trigger any detector.," It is unlikely, though not completely excluded, that this failed to trigger any detector."591 However. the afterglow associated with burst 1 would have en brighter than V728.8 at the time ofthe LIST image even allowing for its additional [acing with time.," However, the afterglow associated with burst 1 would have been brighter than $V\sim28.8$ at the time of the HST image even allowing for its additional fading with time."592" We have »erformoed two-dimensional Gaussian fits (including sloping. Xanar baselines) to all local maxima within 2"" of the OT in the LIST image."," We have performed two-dimensional Gaussian fits (including sloping, planar baselines) to all local maxima within $2^{\prime\prime}$ of the OT in the HST image."593 The only feature consistent with the psf (derived from a similar fit to the OT as EWIIM = 3.240. Pixels) is the faint object located 14 north of the OT., The only feature consistent with the psf (derived from a similar fit to the OT as FWHM = $3.2 \pm 0.1$ pixels) is the faint object located $1.4^{\prime\prime}$ north of the OT.594 This ~le excess has a magnitude of approximately V~28.4 (scaled to the value of V—25.2 for the OT reported. by Bloom et al. (, This $\sim 4 \sigma$ excess has a magnitude of approximately $V \sim 28.4$ (scaled to the value of $V=25.2$ for the OT reported by Bloom et al. (5951999)).,1999)).596 We take this as an upper limit to the magnitude of the first afterglow., We take this as an upper limit to the magnitude of the first afterglow.597 We can therefore almos exclude µου<40.," We can therefore almost exclude $\mu_{2,3} \leq 40$."598 The remaining parameter space is described bv fols and pro&400.," The remaining parameter space is described by $t_{2,3} \leq 1~s$ and $\mu_{2,3} \geq 400$."599 In this case. the first afterglow will be uncdetectable.," In this case, the first afterglow will be undetectable."600 However. the finite size of the source becomes a factor at these high magnifications.," However, the finite size of the source becomes a factor at these high magnifications."601 For a source angular size Bit). the magnification is limited to This limit should not allect. the burst itself. although it will eventually influence the afterglow.," For a source angular size B(t), the magnification is limited to This limit should not affect the burst itself, although it will eventually influence the afterglow."602 Unfortunately. our lack of understanding of the ambient environment ancl the nature of the explosion precludes a confident expression for Bit).," Unfortunately, our lack of understanding of the ambient environment and the nature of the explosion precludes a confident expression for B(t)."603" However. a naive estimate for a spherical. relativistic blastwave with £~107 erg and m~1 cm? (eg. DBlandford and. Melxee 1977) gives D—20/1d)*""pas."," However, a naive estimate for a spherical, relativistic blastwave with $E\sim10^{52}$ erg and $n\sim 1$ ${\rm cm}^{-3}$ (e.g., Blandford and McKee 1977) gives $B\sim2(t/1{\rm d})^{5/8} \mu {\rm as}$."604" This limits the magnificationὃν to foaX6000/17d)""7."," This limits the magnification to $\mu_{2,3}\leq 600(t/17{\rm d})^{-0.3}$."605 After this inequality is violated. the afterglow emission. will decline correspondingly more steeply with time.," After this inequality is violated, the afterglow emission will decline correspondingly more steeply with time."606 In fact. just such an increase in the rate of decline has been reported. at |—ll d (Yadigaroglu Halpern 1999).," In fact, just such an increase in the rate of decline has been reported at $t=11$ d (Yadigaroglu Halpern 1999)."607 We therefore cannot confidently. exclude lensing with µου400 at this stage.," We therefore cannot confidently exclude lensing with $\mu_{2,3}\sim400$ at this stage."608" However. if it is possible to examine the subsecond time variations in the BATSE lishteurve of GRBOSOL23 and thereby limit f;9£5 to z10 ms. then fro, would have to exceed z1000. and all multiple imaging by a z;=1.6 dellector would ellectively be ruled out."," However, if it is possible to examine the subsecond time variations in the BATSE lightcurve of GRB980123 and thereby limit $t_3-t_2$ to $\approx10$ ms, then $\mu_{2,3}$ would have to exceed $\approx1000$, and all multiple imaging by a $z_d=1.6$ deflector would effectively be ruled out."609 In summary. three arguments (the high Αη of the galaxy. the implausibilitv of missing the first burst and of failing to detect. its afterglow) can already be marshalled against the lensing hypothesis.," In summary, three arguments (the high $M/L$ of the galaxy, the implausibility of missing the first burst and of failing to detect its afterglow) can already be marshalled against the lensing hypothesis."610 Vhree additional steps might ellectivelv eliminate it - searching for double structure on subsecond. timescales in the BATSE data. setting a better limit on the presence of additional afterglow images at the predicted locations and obtaining a reliable photometric or spectroscopic redshift for the galaxy.," Three additional steps might effectively eliminate it - searching for double structure on subsecond timescales in the BATSE data, setting a better limit on the presence of additional afterglow images at the predicted locations and obtaining a reliable photometric or spectroscopic redshift for the galaxy."611 C'ontrariwise. iit turns out that the burst was highly magnilied by lensing. then the burst energv would be reduced to ~9LOBpa1000)+ erg.," Contrariwise, if it turns out that the burst was highly magnified by lensing, then the burst energy would be reduced to $\sim9\times10^{51}{\cal B}(2\mu_{2,3}/1000)^{-1}$ erg."612 GRB 990123 serves as a reminder that multiple imaging of a gamma-ray burst is to be expected eventually in a large enough sample and the analysis of §22 should be generally applicable., GRB 990123 serves as a reminder that multiple imaging of a gamma-ray burst is to be expected eventually in a large enough sample and the analysis of 2 should be generally applicable.613 While we cannot completely rule out the possibility that it has been multiply imaged and strongly magnified. it should be possible to do so soon.," While we cannot completely rule out the possibility that it has been multiply imaged and strongly magnified, it should be possible to do so soon."614 In this case. if we have not observed (or do not observe) an echo of GRB 990123. then the magnification is limited to fr2. except under quite contrived models. leaving CRB 990123 as the most intrinsically luminous cosmic event vet observed in its entirety.," In this case, if we have not observed (or do not observe) an echo of GRB 990123, then the magnification is limited to $\mu\sim2$, except under quite contrived models, leaving GRB 990123 as the most intrinsically luminous cosmic event yet observed in its entirety."615 We thank Martin. Rees for encouragement. the Institute of Astronomy. University of Cambridge for hospitality. and the Beverly and. Raymond Sackler Foundation for support during the preparation of this paper.," We thank Martin Rees for encouragement, the Institute of Astronomy, University of Cambridge for hospitality, and the Beverly and Raymond Sackler Foundation for support during the preparation of this paper."616 Support under NSE evant AST 95-290170 and NASA erant. 5-2837 is also gratefully acknowledgect., Support under NSF grant AST 95-29170 and NASA grant 5-2837 is also gratefully acknowledged.617,.618 and, and.619" where /: aud /. are the radial ancl vertical wavenumbers. respectively. J,,(ha) are Bessel functions of the first kind and ay. ao. 54. bs and ¢ ave functions determined by the initial field distribution and the conditions of continuity on 2=zz."," where $k$ and $k_z$ are the radial and vertical wavenumbers, respectively, $J_m(k\varpi)$ are Bessel functions of the first kind and $a_1$ , $a_2$, $b_1$, $b_2$ and $c$ are functions determined by the initial field distribution and the conditions of continuity on $z=\pm z_0$."620" The decay rate is (he+hr), proporlional to the inverse of the modulus of the vector wavenumber k=fe+/.e."," The decay rate is (k_z^2+k^2), proportional to the inverse of the modulus of the vector wavenumber ${\bf k}=k\hat{\bf e}_\varpi+k_z\hat{\bf e}$."621" The condition of continuity of QP/0z at 2τμ leads to the relation (2h. τι)= Ohh, The limit of an infinitesimally thin disk is recovered under the following ordering: (the disk thickness is much smaller than the vertical wavelength. that in {urnis much smaller than the radial wavelength)."," The condition of continuity of $\partial P/\partial z$ at $z=\pm z_0$ leads to the relation (2k_z z_0)=2 k_z k. The limit of an infinitesimally thin disk is recovered under the following ordering: $z_0 \ll k_z^{-1} \ll k^{-1} \ll \varpi$ (the disk thickness is much smaller than the vertical wavelength, that in turnis much smaller than the radial wavelength)."622" With these approximations. eeuation (5) then gives he/2z, and equation (AT)) becomes 52yh?&ΜΕ τμ. as found in our case."," With these approximations, equation \ref{cont_cond}) ) then gives $k\approx623k_z^2 z_0$ and equation\ref{rate}) ) becomes $\gamma\approx \eta624k_z^2\approx k/z_0$ , as found in our case."625aud ©.,and $\Omega$.626 These measurements were eeucrated assuming that here is a planetary companion with orbital parameters iu Table 1.. and (7.9)(0.0.1.0 rad).," These measurements were generated assuming that there is a planetary companion with orbital parameters in Table \ref{HD 154345 orbit}, , and $(I, \Omega) = (0.0, 1.0$ rad)."627 This simulated data was used together with the real RV measurements oiblished iu Ws to find the Πιο T4 or which the rue nass of the planet could still be measured with the SIM telescope., This simulated data was used together with the real RV measurements published in W08 to find the limiting $T_{A}$ for which the true mass of the planet could still be measured with the SIM telescope.628 The selection £=Oo was made because changing this value would resul in a higher planetary nass and hence ina stronger astrometric VAsignal. making he detection of orbital plane parameters even casicr.," The selection $I=0$ was made because changing this value would result in a higher planetary mass and hence in a stronger astrometric signal, making the detection of orbital plane parameters even easier."629" Reeardless of large error bars. we found that it is possible o detect the orbital plane parameters with 7T,=1.0 vears."," Regardless of large error bars, we found that it is possible to detect the orbital plane parameters with $T_{A} = 1.0$ years."630" With this short timeline. the error bars of the yaralucters were [020, 0.22] aud [0.39. 1.5L) for 7 and ©. respectively, demoustrating that it was indeed possible to determine their values."," With this short timeline, the error bars of the parameters were [-0.30, 0.22] and [0.39, 1.54] for $I$ and $\Omega$, respectively, demonstrating that it was indeed possible to determine their values."631 The time needed to make ai positive detection of an extrasolar planetary companion candidate depends essentially on its orbital period., The time needed to make a positive detection of an extrasolar planetary conpanion candidate depends essentially on its orbital period.632 It is comunonly assumed that. to be able to detect the signature of such companion. an observational timeline longer than the orbital period is required.," It is commonly assumed that, to be able to detect the signature of such companion, an observational timeline longer than the orbital period is required."633 Also. since most of the cxoplanet candidates have been detected using the RV method. only the lower lit of their mass is available.," Also, since most of the exoplanet candidates have been detected using the RV method, only the lower limit of their mass is available."634 With the iid of future space telescopes aud accurate astrometric mcasiurciuicuts. it will be possible to detect the inclination aud thus the true mass of plauctary candidates.," With the aid of future space telescopes and accurate astrometric measurements, it will be possible to detect the inclination and thus the true mass of planetary candidates."635 We have shown that when high-precision RV and accurate astrometric measurements are both available. it is possible to detect the true mass of stellar companions with observational timelines cousiderably shorter than 1ο] orbital periods.," We have shown that when high-precision RV and accurate astrometric measurements are both available, it is possible to detect the true mass of stellar companions with observational timelines considerably shorter than their orbital periods."636 Also. when the RV measurements wve a long time span. astrometric measurements can reveal the true mass of a stellar companion in less time iu one tenth of the orbital period of the syste.," Also, when the RV measurements have a long time span, astrometric measurements can reveal the true mass of a stellar companion in less time than one tenth of the orbital period of the system."637 This bility is also clemonstrated using the BV. measurements f HIID151315 as an example., This ability is also demonstrated using the RV measurements of HD154345 as an example.638 We find that. having jose lüueasuremuients with Fay=10.1 vears idu haud. astrometric observatious with SIM telescope are sufficieu or obtaiuiug the true mass. within a single vear.," We find that, having these measurements with $T_{RV} = 10.4$ years in hand, astrometric observations with SIM telescope are sufficient for obtaining the true mass, within a single year."639 Davesiu iufereunco plavs an portant τοις when extracting information from several sources of neasurelents., Bayesian inference plays an important role when extracting information from several sources of measurements.640 The ability to use BW anc astrometric ueasuremenuts simultancously makes it possible to eiiploy observational timelines below the orbital ones aud stil ο able to make positive exoplanet detections. thus iclpiug to extract the inaxinui amount of information 1X1 nieasurenieuts aud increasing the time efficiencv of observations.," The ability to use RV and astrometric measurements simultaneously makes it possible to employ observational timelines below the orbital ones and still be able to make positive exoplanet detections, thus helping to extract the maximum amount of information from measurements and increasing the time efficiency of observations."641 Tn a forthcoming study. we plan to study the inclusion of additional transit-photometry neasuremoenuts to further tighten the parameter probability ceusities iu transiting scenarios.," In a forthcoming study, we plan to study the inclusion of additional transit-photometry measurements to further tighten the parameter probability densities in transiting scenarios."642 Also. the approach used here should be extended tosvstenis with two or more plauctary COMPaluons.," Also, the approach used here should be extended tosystems with two or more planetary companions."643"Ζι=Zo cannot he mace unless the interior docs not rotate rigidy but instead the observed J, value is influcuced by deep winds (?)..",$Z_1=Z_2$ cannot be made unless the interior does not rotate rigidy but instead the observed $J_4$ value is influenced by deep winds \citep{Militzer+08}.644" Ou the other laud. as reffig: Jup,oncergshouws.Z4Zo is not a favorite option for the DET-MD based Jupiter model. since that would imply Zi«Z. or even zero."," On the other hand, as \\ref{fig:Jup_converg} shows, $Z_1\ll Z_2$ is not a favorite option for the DFT-MD based Jupiter model, since that would imply $Z_1\ll Z_{\odot}$ or even zero."645 This would coutracict heavy. clement abundauce measurements ni Jupiter's atinosphere. which indicate Z4=ὃνZ..," This would contradict heavy element abundance measurements in Jupiter's atmosphere, which indicate $Z_1\geq 2\times Z_{\odot}$."646 Therefore. Z422Za is nota free choice for the DET-ME based model.," Therefore, $Z_1\approx Z_2$ is a free choice for the DFT-MD based model."647 Consequeuth. the very. differeut. Jupiter core Inasses obtained usiug these two ab-initio EOS are not primarily due to different assumptions about the distribution of heavy elements.," Consequently, the very different Jupiter core masses obtained using these two ab-initio EOS are not primarily due to different assumptions about the distribution of heavy elements."648 In order to resolve this problem. a comparison of the II/Ile adiabats is highly desirable.," In order to resolve this problem, a comparison of the H/He adiabats is highly desirable."649" Furthermore. iscutropic compression experiments in the 0.5—[ Mbar regime where J» and J, are most scusitive to metallicty would ereatlv help to discriminate between compoetiug Jupiter models."," Furthermore, isentropic compression experiments in the $0.5-4$ Mbar regime where $J_2$ and $J_4$ are most sensitive to metallicty would greatly help to discriminate between competing Jupiter models."650 For the other EOS considered here. both the assumptions 4=Za or Z4xZo» give acceptable Jupiter models aud hence are a iatter of free choice.," For the other EOS considered here, both the assumptions $Z_1=Z_2$ or $Z_1\not=Z_2$ give acceptable Jupiter models and hence are a matter of free choice."651 As we have seen in refsec:Jupiter... Jupiter models that use oue particular EOS can have various resulting Mu.Z4.Z2} triples.," As we have seen in \\ref{sec:Jupiter}, Jupiter models that use one particular EOS can have various resulting $\{M_{core}, Z_1, Z_2\}$ triples."652" Without the constraint imuposed by Z4, however. the varicty of solutions would be iuunueuse. iucludiug Moore>UsMy and Mz>38AL)."," Without the constraint imposed by $J_4$ however, the variety of solutions would be immense, including $M_{core}>18\ME$ and $M_Z>38\ME$."653" For extrasolar plaucts. curreutly available gravity data are M, aud Fe, only,"," For extrasolar planets, currently available gravity data are $M_p$ and $R_p$ only."654 A potentially observational constraint equivalent to Jy has been sugeested to be the tidal Love umber &» C2)... which measures the ability of a planet to develop an elliptic deformation in response to a tidal perturber such as the close-by parent star.," A potentially observational constraint equivalent to $J_2$ has been suggested to be the tidal Love number $k_2$ \citep{RW09}, which measures the ability of a planet to develop an elliptic deformation in response to a tidal perturber such as the close-by parent star."655 In this section. we present implications of knowing a precise Ay value of the Neptune-sized extrasolar planet CJ 136b.," In this section, we present implications of knowing a precise $k_2$ value of the Neptune-sized extrasolar planet GJ 436b."656" About 30 light vears away from Earth. the Hot Neptune 136b (A,=23.17Mj. RB,=£22 R4) (7) orbits the Mestar 136."," About 30 light years away from Earth, the Hot Neptune $\:$ 436b $M_p=23.17\ME$, $R_p=4.22\RE$ ) \citep{Torres+08} orbits the M-star $\:$ 436."657 Placed ia a imiass-racdius diagram. this planet is located close to theoretical AZ-R relations of wari water planets.," Placed in a mass-radius diagram, this planet is located close to theoretical $M$ $R$ relations of warm water planets."658 Accordingly. interior structure models assmuius au irou-silicate core. a water laver. ind a ΠΠΠο euvelope allow for a composition of water and U/Ue (?).. but also for a water-less composition.," Accordingly, interior structure models assuming an iron-silicate core, a water layer, and a H/He envelope allow for a composition of water and H/He \citep{Figueira+09}, but also for a water-less composition."659" I/We cuvelope models. whether dry or not. are found to have 0.02<hy0,2 (2).."," H/He envelope models, whether dry or not, are found to have $0.02<k_2<0.2$ \citep{N-GJ436b+10}."660 We here hy=0.2 and search for the core mass aud water conteut that satisfy this additional coustraint., We here $k_2=0.2$ and search for the core mass and water content that satisfy this additional constraint.661 We allow water be mixed homogencously iuto the IT/IIe euvelope (two-laver model) or confined to a deep water laver (three-laver models) aud combinations iu between (Neptune-like threc-Iaver models)., We allow water be mixed homogeneously into the H/He envelope (two-layer model) or confined to a deep water layer (three-layer models) and combinations in between (Neptune-like three-layer models).662" Figure 2. shows the result in comparison with LMC-REOS based Jupiter models forced to meet the observed ο value. but uot J,"," Figure \ref{fig:J2k2} shows the result in comparison with LM-REOS based Jupiter models forced to meet the observed $J_2$ value, but not $J_4$."663 Iu both cases. the solutions are located along a straight line (solutions for different A5 or J5 values would span parallel lines).," In both cases, the solutions are located along a straight line (solutions for different $k_2$ or $J_2$ values would span parallel lines)."664 For both planets. aud hence in ecueral. the upper Iit i core mass 1s obtained for homogencous envelope models (compare," For both planets, and hence in general, the upper limit in core mass is obtained for homogeneous envelope models (compare"665ancl processed the data with their iniproved. version of the WD code.,and processed the data with their improved version of the WD code.666 More recently. a reanalysis of the Andersenctal.(1988). RV's was obtained by Ixaranii&Alohehi(2007) witha further improvement of the spectroscopic parameters.," More recently, a reanalysis of the \citet{and88} RV's was obtained by \citet{kar07} with a further improvement of the spectroscopic parameters."667 Llowever. their solution can be considered as disputable since they seem not to have included several uncertainties (of the orbital period. for example) into the total error budget and thus presumably underestimated the final errors.," However, their solution can be considered as disputable since they seem not to have included several uncertainties (of the orbital period, for example) into the total error budget and thus presumably underestimated the final errors."668 Our solution. based. on our RV data ancl ASAS photometry is compared with the ones from Andersenctal.(1088) and Miloneetal.(1992). in Table 4.," Our solution, based on our RV data and ASAS photometry is compared with the ones from \citet{and88} and \citet{mil92} in Table \ref{com_aiphe}."669 In. general our results are in agreement with the previous papers., In general our results are in agreement with the previous papers.670 One should note that having only S RV measurements [ου every component. we were able to improve the spectroscopic results of Andersenetal.(1988). who hac46 datapoints for every component. by a factor of 9 to 4.," One should note that having only 8 RV measurements for every component, we were able to improve the spectroscopic results of \citet{and88}, who had 46 datapoints for every component, by a factor of 2 to 4."671 Unfortunately. having only one light-curve from ASAS we cannot compete with the results of Miloneetal.(1992) who used light curves from 12 bandpasses: most of which were more precise than ours.," Unfortunately, having only one light-curve from ASAS we cannot compete with the results of \citet{mil92} who used light curves from 12 bandpasses; most of which were more precise than ours."672 Still. their phase coverage is not complete and the orbital and physical parameters might. be improved. with high-precision photometry.," Still, their phase coverage is not complete and the orbital and physical parameters might be improved with high-precision photometry."673 Our solution converged to a somewhat different value of the orbital inclination than Ancersen’s and Alillone’s., Our solution converged to a somewhat different value of the orbital inclination than Andersen's and Millone's.674 This is of course the reason for the discrepancy in absolute masses between the solutions., This is of course the reason for the discrepancy in absolute masses between the solutions.675 Our. AZsin’?/ is however Fu more precise., Our $M\sin^3i$ is however far more precise.676 “Phus we may conclude that this systems parameters can be derived with an unprecedented precision (possibly ~0.01 in masses and ~0.1 in radi) if only one had. more iocine RY measurements and millimagnitude photometry., Thus we may conclude that this systems' parameters can be derived with an unprecedented precision (possibly $\sim 0.01$ in masses and $\sim 0.1$ in radii) if only one had more iodine RV measurements and millimagnitude photometry.677 UX Alen. as well as Al Phe. was discovered to be à variable in Bamberg patrol plates and reported by Strohmeier (1966).," UX Men, as well as AI Phe, was discovered to be a variable in Bamberg patrol plates and reported by \citet{str66}."678. The first orbital solution was obtained by Lambert(1974) and the first full physical analysis. based on Imboerts radial velocities and photometry. was done w Clausen&CGronbech.(1976).," The first orbital solution was obtained by \citet{imb74} and the first full physical analysis, based on Imberts' radial velocities and photometry, was done by \citet{cla76}."679. Later. this photometric dataset was reanalised together with the new COILAVEL racial velocities by Andersenetal.(1989). who obtained he most up-to-date solution for UX Alen.," Later, this photometric dataset was reanalised together with the new CORAVEL radial velocities by \citet{and89} who obtained the most up-to-date solution for UX Men."680 Comparison of his solution with our results is shown in Table 5.., Comparison of this solution with our results is shown in Table \ref{com_uxmen}.681 Again. our results are in general in agreement with Andersen's.," Again, our results are in general in agreement with Andersen's."682 As for Al Phe. having 58 radial velocity measurements of UX Alen. we succeeded to reach a better precision in the spectroscopic parameters than Andersen et al.," As for AI Phe, having 8 radial velocity measurements of UX Men, we succeeded to reach a better precision in the spectroscopic parameters than Andersen et al."683 with 29 datapoints for the primary and 31 for the secondary., with 29 datapoints for the primary and 31 for the secondary.684 In our model we fixed the eccentricity to 0., In our model we fixed the eccentricity to 0.685 We found no signillicant improvement in the best-fitting mocel (in terms of rms) when e and o were set as free pramoeters and the resulting e was undistinguishable from0 within the formal errors., We found no signifficant improvement in the best-fitting model (in terms of $rms$ ) when $e$ and $\omega$ were set as free prameters and the resulting $e$ was undistinguishable from 0 within the formal errors.686 The non-zero eccentricity may be however induced by a putative third body. found in NAC'O images by 'l'okovininctal.(2006) about 0.751arcsec from the binary.," The non-zero eccentricity may be however induced by a putative third body, found in NACO images by \citet{tok06} about 0.751arcsec from the binary."687 V415. Aql was first reported as a variable by HLolfmeister (1936)., V415 Aql was first reported as a variable by \citet{hof36}.688. The first ephemeris 2428670.532 | [7 2.4628 d was determined by Guthnick&Schneller(1936, The first ephemeris 2428670.532 + $E \cdot$ 2.4628 d was determined by \citet{gut39}.689) The double-lined character was not. previously reported thus there was no racial velocity curve obtained to date and the only known ight curve analysis was done by Brancewiez&Dworak(1980) who derived. an orbital period. of 2.46273 d. Our UN data. despite having only 3 measurements for. every component. clearly shows that the actual period is (wo times onger.," The double-lined character was not previously reported thus there was no radial velocity curve obtained to date and the only known light curve analysis was done by \citet{bra80} who derived an orbital period of 2.46273 d. Our RV data, despite having only 3 measurements for every component, clearly shows that the actual period is two times longer."690 This is confirmed by the ASAS light curve exhibiting unequal eclipses (see Eig. 12)., This is confirmed by the ASAS light curve exhibiting unequal eclipses (see Fig. \ref{fig_master}) ).691 Η divided by 2. our period is in a good agreement with the value from Brancewiez&Dworak (1980).," If divided by 2, our period is in a good agreement with the value from \citet{bra80}."692. Unfortunately. the uncertainties of their results are unavailable.," Unfortunately, the uncertainties of their results are unavailable."693 In Fable 6 we compare their results with ours., In Table \ref{com_v415aql} we compare their results with ours.694 The improvement in the derived parameters is obvious., The improvement in the derived parameters is obvious.695 Also he distance estimate given by Brancewicz&Dworak(1980 of this should be now treated with caution., Also the distance estimate given by \citet[][see Tab. \ref{tab_info} of this should be now treated with caution.696 Out of the eighteen eclipsing binaries in our sample. 15 are," Out of the eighteen eclipsing binaries in our sample, 15 are"697represents illumination of gas bv the X-ray rotating beams in à region between the accretion column ancl the discs transition region.,represents illumination of gas by the X-ray rotating beams in a region between the accretion column and the disc's transition region.698 Each pulse may then represent reprocessed. gas slightly further out. from. the continuum. region which is supported. by the phase delays of 0.1 spin eveles., Each pulse may then represent reprocessed gas slightly further out from the continuum region which is supported by the phase delay of 0.1 spin cycles.699 For zero phase delay. the continuum and. emission regions would lic in the same axis (racial infall).," For zero phase delay, the continuum and emission regions would lie in the same axis (radial infall)."700 For a yhase delav of 0.25 eveles. the corotation velocity. of the emission region would be perpencicular to the racial infall of he continuum region.," For a phase delay of 0.25 cycles, the corotation velocity of the emission region would be perpendicular to the radial infall of the continuum region."701 Therefore. the emission region ies in a region between corotation and radial infall. aud most likely. tracing the magnetic field lines.," Therefore, the emission region lies in a region between corotation and radial infall, and most likely, tracing the magnetic field lines."702 Such a delay is consistent with the field lines being swept back by the »erturbed Dow of disc matter., Such a delay is consistent with the field lines being swept back by the perturbed flow of disc matter.703 The nearly svmmetrie pulses in the continuum indicate accreting poles of equal brightness at anti-diamoetric ocations., The nearly symmetric pulses in the continuum indicate accreting poles of equal brightness at anti-diametric locations.704 The pulses are very asvmimetric with the irst pulse dominating over the second one (lux is higher by a factor of 2)., The pulses are very asymmetric with the first pulse dominating over the second one (flux is higher by a factor of 2).705 Phe width of the pulses is identical. 318417 xIM n. which. indicates. à common OPLgL.M and sets upper imits for the broadening mechanism in the emission-region. perhaps the scale of turbulence (change from circular motion to quasi-racial) or the sound velocity (2<LO” Ix).," The width of the pulses is identical, $\pm$ 17 km $^{-1}$, which indicates a common origin, and sets upper limits for the broadening mechanism in the emission-region, perhaps the scale of turbulence (change from circular motion to quasi-radial) or the sound velocity $T <70610^{6}$ K)."707" While one pulse is in maximum. blueshift. the other is in maximum recshift (""corkscrew) which is entirely consistent with an accretion curtain."," While one pulse is in maximum blueshift, the other is in maximum redshift (“corkscrew”) which is entirely consistent with an accretion curtain."708 “Phe maximum of the first. pulse is viewed. directly. [rom the (lower) pole whilst the curtain Mocks any visibility of theLL region from the upper »ole. resulting in the minimum of the second pulse (in the average-subtracted line. profiles).," The maximum of the first pulse is viewed directly from the (lower) pole whilst the curtain blocks any visibility of the region from the upper pole, resulting in the minimum of the second pulse (in the average-subtracted line profiles)."709 This varving view of the wo inner parts of the curtain explains the quaclrapole-like xutern of the pulsed. emission in Fig., This varying view of the two inner parts of the curtain explains the quadrapole-like pattern of the pulsed emission in Fig.710 10., 10.711 Partial overlap of the pulses between spin. phases 0.50.7 suggests that the azimuthal extent is large enough so that the two pulse ocations can be viewed simultaneously at times., Partial overlap of the pulses between spin phases 0.5–0.7 suggests that the azimuthal extent is large enough so that the two pulse locations can be viewed simultaneously at times.712 The phase range of the pulses also suggests that the azimuthal extent of the accretion curtain in the continuum is smaller than hat of the emission regions (Lig., The phase range of the pulses also suggests that the azimuthal extent of the accretion curtain in the continuum is smaller than that of the emission regions (Fig.713 7)., 7).714 We associate the emission-line pulsations with material which has lost its Keplerian Dow due to the magnetic fields coupling and is most likely close to radial free-fall along he magnetic field lines (see previous discussion about phase delay)., We associate the emission-line pulsations with material which has lost its Keplerian flow due to the magnetic field's coupling and is most likely close to radial free-fall along the magnetic field lines (see previous discussion about phase delay).715 Then. theLL emission region will be located within he magnetosphere of the white dwarf and will rotate with he spin period of 545 seconds.," Then, the emission region will be located within the magnetosphere of the white dwarf and will rotate with the spin period of 545 seconds."716 Εις gives|l2xdi -—gd./sn;--uAkms where Vie.-=408 km 17. 2?=545 seconds is. the spin. »eriod.," This gives$ V = V_{obs}/~\sin~i = \frac{2~\pi~R}{P} $ km $^{-1}$, where $V_{obs} = 408$ km $^{-1}$, $P =545$ seconds is the spin period."717" ""There is no eclipse in the X-ray and. optical light curves.", There is no eclipse in the X-ray and optical light curves.718" On the other hand. the two accreting poles of the white chvarl (double-peak pulse) can be viewed only in hieh-inclination systenis. (50, 70°) and this is most likely the case for RX JO558|5353."," On the other hand, the two accreting poles of the white dwarf (double-peak pulse) can be viewed only in high-inclination systems $50^{o}-70^{o}$ ) and this is most likely the case for RX J0558+5353."719 Phe pulsations become visible only for favourable orientations of the rotating scarchlight beans to the line-of-sight., The pulsations become visible only for favourable orientations of the rotating searchlight beams to the line-of-sight.720 Truly. this is supported by a correlation xtween inclination andpulse amplitude (Ποτος and Mason 1990).," Truly, this is supported by a correlation between inclination andpulse amplitude (Hellier and Mason 1990)."721" For a free-fall velocity of 408 kim sn60°=471 kms +. the distance is οlot km or RY4.9RewAly? from the white chwarl. assuming an inclination of 60"" and using Bag70.84totAZ,Ob"" lm (Llamacla Salpeter 1901)."," For a free-fall velocity of 408 km $^{-1}$ / $\sin~60^{o} = 471$ km $^{-1}$ , the distance is $ R \sim 4.1 \times 10^{4}$ km or $ R \sim 4.9~R_{wd}~M^{+0.6}_{0.6} $ from the white dwarf, assuming an inclination of $^{o}$ and using $R_{wd} \sim 0.84 \times 10^{4}~M^{-0.6}_{0.6} $ km (Hamada Salpeter 1961)."722 Τμ may well represent the magnetospheric radius where the disc. ds. disrupted. [I—B4. hall the Alfven radius. which gives Hoa~O26Row(ANLapiiy)dsLot km where Ly; is the luminosity in units of 107 eres s.! and pao is the magnetic moment in units of 107 € em? (Ghosh and Lamb LOTS).," This may well represent the magnetospheric radius where the disc is disrupted, $R=R_{mag}$, half the Alfven radius, which gives $ R_{mag} \sim 0.26 ~R_{wd}~ ( M_{0.6}^{0.91}~~L_{33}^{-2/7}~723\mu_{30}^{4/7}) = 4.1 \times 10^{4}$ km where $L_{33}$ is the luminosity in units of $10^{33}$ ergs $^{-1}$ and $\mu_{30}$ is the magnetic moment in units of $10^{30}$ G $^{3}$ (Ghosh and Lamb 1978)."724 The impact of the stream overflow on the discs transition region is slightlv further out at ⋅⋅UST ≼≻⋅↖∖↻∫↘⋟⋯∣⇀∪⊓⊽⊓↾⊽−↿∖↙∫∶≱⋅⋅↱≻⊐⋜⋯∠⇂⊔⋯∙∖⇁↓↥⋜↧∖⇁∢⊾↓∪∖∖⋎∢⊾↓⋅∖⇁⋖⋅⇂⋯∙↓↿⊓⋅≱∖∪⇂ MN ∿∶∫≻⋅↱≻∪↓∡⊔, The impact of the stream overflow on the disc's transition region is slightly further out at $6.86~R_{wd}~M_{0.6}^{-0.27}$ $q=0.5$ ) and may have lower velocities of $\sim$ 350 km $^{-1}$.725↓⊳∖⊥⊳↾∐↥∢⋅≼∙⋖⋟↓⋅∢≱∣⋜↧⇂↕⋖⋟↓↕↓⋅⋯∐⊔⊳∖∫⊐⋟⋯↿∖↓⊲↸↓⋅, The corotation radius $R_{co}$ (Frank et al.726⋜⋯↥⊔⊾↿⋜↧↓⊳↓≤⋗≤⊔⊐⋡ Peo~10RewMUTORF isH larger than the magnetosphere (slow rotator) for accretion to occur.," 1992), $R_{co} \sim 10~R_{wd}~M^{-0.27}_{0.6}$, is larger than the magnetosphere (slow rotator) for accretion to occur."727 αρα et al. (, Haberl et al. (728"1994) derive an observed Iuminosity of 0.18107(—L300y eres + from the N-rav Hlux between 0.1-2.4. keV. Fittingpe the X-ray spectrum with a blackbody of 57 eV. (soft component) and a bremsstrahlung spectrum of 10. keV. (hard component) gives a luminosity of 1.710°ο... eres + for an absorption column density of 6107"" LE em.? (LHaberl et al.",1994) derive an observed luminosity of $0.18~\times~10^{32}~ (\frac{d}{300~{\rm pc}})^{2}$ ergs $^{-1}$ from the X-ray flux between 0.1-2.4 keV. Fitting the X-ray spectrum with a blackbody of 57 eV (soft component) and a bremsstrahlung spectrum of 10 keV (hard component) gives a luminosity of $1.7~\times~10^{33}~(\frac{d}{300~{\rm pc}})^{2}$ ergs $^{-1}$ for an absorption column density of $6~\times~~10^{20}$ H $^{-2}$ (Haberl et al.729 1994)., 1994).730 ‘Phis can be used to estimate the magnetic moment of the white dwarl of 2.407 G em? (or B0.5 MG). assuming a Ao= 1. Ly;= 1. d=300 pe and a negligible softX-ray luminosity compared to the hard. X-ray component.," This can be used to estimate the magnetic moment of the white dwarf of $2.4~\times~10^{32}$ G $^{3}$ (or $B \sim 0.5$ MG), assuming a $M_{0.6} = 1$ , $L_{33}=1$ , $d = 300$ pc and a negligible softX-ray luminosity compared to the hard X-ray component."731 Such a magnetic moment is not inconsistent with the existence of an accretion disc. evidence for which we found. from the periodogram," Such a magnetic moment is not inconsistent with the existence of an accretion disc, evidence for which we found from the periodogram"732is Ἱπαάσσα at 2=0.157 aud hence likely to be the 21-cim absorber.,is indeed at $z = 0.437$ and hence likely to be the 21-cm absorber.733 The quasar field was imaged using the EFOSC? iustrument on the ESO 3.611 telescope at La Silla duriug the night of 29th Jaunary. 2001.," The quasar field was imaged using the EFOSC2 instrument on the ESO 3.6m telescope at La Silla during the night of 29th January, 2001."734 The Bessel BR-buik 1inage was obtained on CCD #110 in the uubinned mode (0.157 aresec/pix. 2060 « 2060 pixels = 5.1 « 5.1 arcmin feld).," The Bessel R-band image was obtained on CCD 40 in the unbinned mode (0.157 arcsec/pix, 2060 $\times$ 2060 pixels $\equiv$ 5.4 $\times$ 5.4 arcmin field)."735 We obtained a total of teu dithex inages of 150s cach., We obtained a total of ten dithered images of 450s each.736 The calibration observations iucluded twilielr sky flats aud observations of the stadia fell RUI52 (Landolt 1992))., The calibration observations included twilight sky flats and observations of the standard field RU152 \cite{landolt92}) ).737 We used the seieuce frames ο construc and subtract the fringe pattern from the frames., We used the science frames to construct and subtract the fringe pattern from the frames.738 The atmospheric extinction and the CCD colour term were calculated using observations of standard fields taken at several airimasscs and in other bands., The atmospheric extinction and the CCD colour term were calculated using observations of standard fields taken at several airmasses and in other bands.739 We expect the photometry to be accurate to about and use a conservative error of 0.1 mae., We expect the photometry to be accurate to about and use a conservative error of 0.1 mag.740 The images were reduced. calibrated. registered aud co-added m a standard mauner using IRAF.," The images were reduced, calibrated, registered and co-added in a standard manner using IRAF."741 The final image obtained had a zero-point of R=32.601 with au RAIS of 10.5 counts/pix., The final image obtained had a zero-point of R=32.601 with an RMS of 10.5 counts/pix.742 Figue 2 shows a grevscale plot of a 15 «15E aresec section of the field around the quasar., Figure \ref{fig:image} shows a greyscale plot of a 45 $\times$ 45 arcsec section of the field around the quasar.743 The quasar (Q) aud a rather bright neiglibour (A). separated by 2.2 arcsec. are visible. close to (aud south of) the centre of the field.," The quasar (Q) and a rather bright neighbour (A), separated by 2.2 arcsec, are visible, close to (and south of) the centre of the field."744 The quasar magnitude was measured to be R=19.55 while that of its neiglibour was found to be R=21.27., The quasar magnitude was measured to be $R = 19.55$ while that of its neighbour was found to be $R = 21.27$.745 We also obtained an miage of the field usine the Aagellan G.51à. telescope at the Las Campanas Observatory., We also obtained an image of the field using the Magellan 6.5m telescope at the Las Campanas Observatory.746 The Πανάς Lbbaud image was obtained ou a direct CCD caluera du the uubiuued mode (0.069 arcsec(pis. 2018 « 2018 pixels = 2.36 < 2.36 arcium field).," The Harris I-band image was obtained on a direct CCD camera in the unbinned mode (0.069 arcsec/pix, 2048 $\times$ 2048 pixels $\equiv$ 2.36 $\times$ 2.36 arcmin field)."747 We obtained lL exposures of 600s cach: the miages were reduced in the same manner as before., We obtained 4 exposures of 600s each; the images were reduced in the same manner as before.748 Towever. it may be noted that. due to technical problems. we could not obtain a skv/domie fiat aud had to use the dark-sky. fat to flat-held the nuaee.," However, it may be noted that, due to technical problems, we could not obtain a sky/dome flat and had to use the dark-sky flat to flat-field the image."749 The finecs on the nuages were hence divided out rather than subtracted which resulted in an additional error of a few per cent iu the photometry across the frames., The fringes on the images were hence divided out rather than subtracted which resulted in an additional error of a few per cent in the photometry across the frames.750 However. the total photometric error is again abou ει nae.," However, the total photometric error is again about 0.1 mag."751 We measure magnitudes of £=19.11 for the quasar and 7=21.27 for the ucighbour., We measured magnitudes of $I = 19.41$ for the quasar and $I = 21.27$ for the neighbour.752 The optical long-slit spectrum was obtained using the EFOSC? instrmucut ou the ESO 3.611 telescope during the night of 19th March. 2001.," The optical long-slit spectrum was obtained using the EFOSC2 instrument on the ESO 3.6m telescope during the night of 19th March, 2001."753 Crisin #111 (300 Tain. 3300 1520A)) was used with CCD £110 (immed. 242 pixel size 0.311 aresec) to obtain a spectrum with a resolution of L1 A//pixcl.," Grism 11 (300 l/mm, 3300 – ) was used with CCD 40 (binned $\times$ 2 pixel size 0.314 arcsec) to obtain a spectrum with a resolution of 4.1 /pixel."754 The standard calibration iucluded Πο-Δι are lap exposures for wavelength, The standard calibration included He-Ar arc lamp exposures for wavelength755"can be observed in the highly saturated forest at z6, where the density fluctuations themselves cause substantial fluctuations7 in 7° (?), is questionable.","can be observed in the highly saturated forest at $z \ga 6$, where the density fluctuations themselves cause substantial fluctuations in $\taueff$ \citep{LOF06}, is questionable."756 We systematically study the expected fluctuations in the hydrogen ionizing background in the epoch following reionization (z~ 6)., We systematically study the expected fluctuations in the hydrogen ionizing background in the epoch following reionization $z\sim$ 5--6).757" Unlike at lower redshifts (z< 4), the UVB can be quite inhomogenous in this regime."," Unlike at lower redshifts $z\lsim4$ ), the UVB can be quite inhomogenous in this regime."758" This is due to the smaller mean free path of ionizing photons, as well as the clustering of increasingly rare ionizing sources."," This is due to the smaller mean free path of ionizing photons, as well as the clustering of increasingly rare ionizing sources."759 We confirm that there is a sizable spread (the widths of the PDFs at half of the maximum likelihoods spanning factors of ~ 2-4) and asymmetry in the distribution of ionizing fluxes in a cosmological volume., We confirm that there is a sizable spread (the widths of the PDFs at half of the maximum likelihoods spanning factors of $\sim$ 2–4) and asymmetry in the distribution of ionizing fluxes in a cosmological volume.760 Expected values of the m.f.p., Expected values of the m.f.p.761" are large enough (Amfp2,20 Mpc), and sources are ubiquitous enough, that the PDF of the ionizing background is asymmetric, with tail extending to higher values."," are large enough $\lmfp\gsim20$ Mpc), and sources are ubiquitous enough, that the PDF of the ionizing background is asymmetric, with a tail extending to higher values."762" This high-value tail is set by clusteringa on small scales, and is insensitive to the contributions of distant sources (ie. Amfp) (?)."," This high-value tail is set by clustering on small scales, and is insensitive to the contributions of distant sources (i.e. $\lmfp$ ) \citep{MD08}."763" We also find that the PDFs are most sensitive to the m.f.p.,"," We also find that the PDFs are most sensitive to the m.f.p.,"764 with higher values of Amfp increasingly truncating the low-value tails., with higher values of $\lmfp$ increasingly truncating the low-value tails.765" Furthermore, we note that the analytic formalism of ? severely underestimates the width of the flux PDF at this epoch, since it ignores the clustering of sources."," Furthermore, we note that the analytic formalism of \citet{MW04} severely underestimates the width of the flux PDF at this epoch, since it ignores the clustering of sources."766 The power spectra of the ionizing background are even more sensitive to the details of the source model., The power spectra of the ionizing background are even more sensitive to the details of the source model.767" We have shown that an approach analogous to the halo model, in which contributions from the proximity zones of single sources (which dominate fluctuations on small scales and are independent of the large-scale galaxy distribution) and multiple sources (which dominate on large scales, and which depend on the large-scale clustering of the ionizing sources) are separated, provides a good match to the simulated results, although nonlinear clustering provides even more small-scale power than the analytic model predicts."," We have shown that an approach analogous to the halo model, in which contributions from the proximity zones of single sources (which dominate fluctuations on small scales and are independent of the large-scale galaxy distribution) and multiple sources (which dominate on large scales, and which depend on the large-scale clustering of the ionizing sources) are separated, provides a good match to the simulated results, although nonlinear clustering provides even more small-scale power than the analytic model predicts."768" The single-source component is particularly sensitive to the number density of galaxies; unfortunately, these power spectra will be nearly impossible to observe with the fforest."," The single-source component is particularly sensitive to the number density of galaxies; unfortunately, these power spectra will be nearly impossible to observe with the forest."769 We also model the imprint of various UVBs in the fforest at z~ 5-6., We also model the imprint of various UVBs in the forest at $z\sim$ 5–6.770" We find that the fforest spectra are extremely insensitive to the details of the UVB, despite marked differences in the PDFs and power spectra of our various UVBs."," We find that the forest spectra are extremely insensitive to the details of the UVB, despite marked differences in the PDFs and power spectra of our various UVBs."771" This is attributable to the fact that the ooptical depth scales as rcA?/T, and the squared overdensity distribution, f(A?), is much wider than all of our T distributions."," This is attributable to the fact that the optical depth scales as $\tau\propto\Delta^2/\Gamma$, and the squared overdensity distribution, $f(\Delta^2)$, is much wider than all of our $\Gamma$ distributions."772" In fact, even the extreme scenario of a uniform background (i.e. a delta function [ distribution), only underestimates the value of (Γιο) inferred from the fforrest by a few percent."," In fact, even the extreme scenario of a uniform background (i.e. a delta function $\Gamma$ distribution), only underestimates the value of $\langle\Gamma_{12}\rangle$ inferred from the forrest by a few percent."773 Thus our results justify the common assumption of a uniform UVB in fforest analysis., Thus our results justify the common assumption of a uniform UVB in forest analysis.774 We also confirm that accurate modeling of the density field is very important in the 75(Γιο) relation., We also confirm that accurate modeling of the density field is very important in the $\taueff \leftrightarrow \langle\Gamma_{12}\rangle$ relation.775 We find significant differences (factor of ~ 2) in this relation among the numerical and extrapolated ? density distributions (though we stress again that we did not create detailed mock spectra in this work)., We find significant differences (factor of $\sim$ 2) in this relation among the numerical and extrapolated \citet{MHR00} density distributions (though we stress again that we did not create detailed mock spectra in this work).776" At higher redshifts, the 7°"" statistic increasingly depends on a narrower range in the low-value density PDF."," At higher redshifts, the $\taueff$ statistic increasingly depends on a narrower range in the low-value density PDF."777 Large-scale hydrodynamical modeling of the statistics of these rare voids is therefore essential in interpreting the high-redshift fforest., Large-scale hydrodynamical modeling of the statistics of these rare voids is therefore essential in interpreting the high-redshift forest.778" ? have recently studied the IGM density field during reionization, and do find significant differences from the ? fitting formula, although their simulation boxes are much too small to study the rare voids pertinent to these efforts."," \citet{Pawlik09} have recently studied the IGM density field during reionization, and do find significant differences from the \citet{MHR00} fitting formula, although their simulation boxes are much too small to study the rare voids pertinent to these efforts."779 An interesting comparison can be made between our analysis of hydrogen reionization and similar effects during and after helium reionization (Dixon, An interesting comparison can be made between our analysis of hydrogen reionization and similar effects during and after helium reionization (Dixon780absorption.,absorption.781" It is clear, however that the K-[3.6], [3.6]-[4.5] two colour diagram is an excellent diagnostic for low gravity and hence youth."," It is clear, however that the $K$ -[3.6], [3.6]-[4.5] two colour diagram is an excellent diagnostic for low gravity and hence youth."782 The J-[4.5] colour also shows an excess for PLZJ93 over the template field dwarf., The $J$ -[4.5] colour also shows an excess for PLZJ93 over the template field dwarf.783 The reason for this is not obvious., The reason for this is not obvious.784" The [4.5] filter covers the CO band, with the band edge at 4.6 microns."," The [4.5] filter covers the CO band, with the band edge at 4.6 microns."785" No methane in the object should mean more CO (for a fixed amount of C), and therefore more absorption."," No methane in the object should mean more CO (for a fixed amount of C), and therefore more absorption."786 Recently ? have seen evidence of CO and CO» in the [4.5] filter in L dwarfs and it is stronger than predicted by models., Recently \citet*{yamamura10} have seen evidence of CO and $_{\rm 2}$ in the [4.5] filter in L dwarfs and it is stronger than predicted by models.787" In the past the CO has been attributed to vertical mixing in the atmospheres (?),, however, it remains to be seen if low gravity is affecting the CO» and thus removing this source of absorption."," In the past the CO has been attributed to vertical mixing in the atmospheres \citep{oppenheimer98}, however, it remains to be seen if low gravity is affecting the $_{\rm 2}$ and thus removing this source of absorption."788" The H-[4.5] colour of PLZJ93 (T.a21107 KK) is 3.03 which does not fit the ? relation for field stars cooler than 1000 K. This relation was also confirmed by (?) who also noted that it became stronger below 800 K, but used the low scatter in the relationship to determine that it is not gravity sensitive in this temperature regime."," The $H$ -[4.5] colour of PLZJ93 $_{\rm eff}$ K) is 3.03 which does not fit the \citet{warren07} relation for field stars cooler than 1000 K. This relation was also confirmed by \citep{leggett10} who also noted that it became stronger below 800 K, but used the low scatter in the relationship to determine that it is not gravity sensitive in this temperature regime."789" At higher temperatures, such as for PLZJ93, the relation is quite likely to be gravity/age sensitive."," At higher temperatures, such as for PLZJ93, the relation is quite likely to be gravity/age sensitive."790" PLZJ23, PLZJ93 and PLZJ100 are all clearly cooler than field dwarfs with spectral type TO, but none of them have any methane absorption as judged by their methane colour index."," PLZJ23, PLZJ93 and PLZJ100 are all clearly cooler than field dwarfs with spectral type T0, but none of them have any methane absorption as judged by their methane colour index."791" We assume PLZJ23 has a positive methane colour index, but due to its broad band spectral type being estimated at L8, it was not observed in methane filters."," We assume PLZJ23 has a positive methane colour index, but due to its broad band spectral type being estimated at L8, it was not observed in methane filters."792" The definition of the T spectral class is the appearance of methane so strictly, via this definition, PLZJ93 and PLZJ100 cannot be described as T dwarfs."," The definition of the T spectral class is the appearance of methane so strictly, via this definition, PLZJ93 and PLZJ100 cannot be described as T dwarfs."793" The colours of these two objects are, however, not compatible with those of field L dwarfs as presented in ?.."," The colours of these two objects are, however, not compatible with those of field L dwarfs as presented in \citet{leggett02}."794 Our colours for these Pleiades dwarfs also do not appear to be consistent with the colours types presented in ? fora low gravity L dwarf sequence up until L5., Our colours for these Pleiades dwarfs also do not appear to be consistent with the colours types presented in \citet{cruz09} for a low gravity L dwarf sequence up until L5.795" The colours of a low gravity L5 dwarf are given as J—H=1.52+0.04 and J—K,=2.52+0.03.", The colours of a low gravity L5 dwarf are given as $J-H=$ $\pm$ 0.04 and $J-K_s=2.52\pm0.03$.796 Our objects are much bluer that this., Our objects are much bluer that this.797 It may however be the case that low gravity late L dwarfs show notably different colours to high gravity late L dwarfs which may explain this discrepancy., It may however be the case that low gravity late L dwarfs show notably different colours to high gravity late L dwarfs which may explain this discrepancy.798 This may be an additional indication that the L-T transition occurs at a lower temperature in low gravity objects than for high gravity objects., This may be an additional indication that the L-T transition occurs at a lower temperature in low gravity objects than for high gravity objects.799" It does appear however, that until an L dwarf sequence is available for low gravity late L and early T dwarfs we have a classification problem and cannot assign these Pleiads an estimated spectral type based upon their photometry."," It does appear however, that until an L dwarf sequence is available for low gravity late L and early T dwarfs we have a classification problem and cannot assign these Pleiads an estimated spectral type based upon their photometry."800" If spectra could be observed for PLZJ23, PLZJ93 and PLZJ100 it might be possible to classify them as late low gravity L dwarfs, i.e. an extension of the low gravity sequence started in ? for the Pleiades, and ? for field dwarfs."," If spectra could be observed for PLZJ23, PLZJ93 and PLZJ100 it might be possible to classify them as late low gravity L dwarfs, i.e. an extension of the low gravity sequence started in \citet{bihain10} for the Pleiades, and \citet{cruz09} for field dwarfs."801 Using methane and IRAC imaging we have shown that 3 of the 6 L-T dwarf candidates discovered by ? are likely galaxies., Using methane and IRAC imaging we have shown that 3 of the 6 L-T dwarf candidates discovered by \citet{casewell07} are likely galaxies.802" Of the remaining 3, all have photometry that shows that they are likely members of the Pleiades open star cluster and are low gravity L and T dwarfs."," Of the remaining 3, all have photometry that shows that they are likely members of the Pleiades open star cluster and are low gravity L and T dwarfs."803 Our findings are consistent with those of ? ? , Our findings are consistent with those of \citet{burgess09} \citet{bihain10} 804Heating by active galactic nuclei (AGN) is currently regarded as the most likely mechanism preventing excessive cooling of the hot intracluster medium (ICM) in galaxy groups and clusters (e.g.??.andreferences therein)..,"Heating by active galactic nuclei (AGN) is currently regarded as the most likely mechanism preventing excessive cooling of the hot intra–cluster medium (ICM) in galaxy groups and clusters \citep[e.g.,][and references805therein]{McNamaraNulsen07,PetersonFabian06}."806 Cool core clusters typically have a central giant elliptical or cD galaxy. 70-100 per cent.," Cool core clusters typically have a central giant elliptical or cD galaxy, 70-100 per cent."807 of which host radio sources (22)..," of which host radio sources \citep{Burns90,Mittaletal09}."808 Accretion of cooling gas onto the centra supermassive black hole of the central galaxy is believed to fue outbursts which then reheat the cooling material., Accretion of cooling gas onto the central supermassive black hole of the central galaxy is believed to fuel outbursts which then reheat the cooling material.809 Cool core clusters are also known to have strongly centrally peaked abundance profiles (e.g.22). as are many X-ray brigh galaxy groups (e.g..2)..," Cool core clusters are also known to have strongly centrally peaked abundance profiles \citep[e.g.,][]{Bohringeretal04,DeGrandiMolendi04}, as are many X-ray bright galaxy groups \citep[e.g.,][]{RasmussenPonman07}."810 The location of the dominant elliptical a the centre of this peak suggests that it is probably the source of these metals. and observed metal masses are found to be consisten with the quantities expected from supernovae and stellar winds.," The location of the dominant elliptical at the centre of this peak suggests that it is probably the source of these metals, and observed metal masses are found to be consistent with the quantities expected from supernovae and stellar winds."811 In particular. the iron mass profiles of systems across a wide range of mass are consistent with long-term enrichment primarily by SNTa in the central dominant galaxy (222).," In particular, the iron mass profiles of systems across a wide range of mass are consistent with long-term enrichment primarily by SNIa in the central dominant galaxy \citep{Bohringeretal04,RasmussenPonman07,Werneretal08}."812 The iron mass profiles of cool core systems are found to be more extended than the light distribution of the central galaxy. indicating that metals are transported outward from the cluster core (e.g..22).," The iron mass profiles of cool core systems are found to be more extended than the light distribution of the central galaxy, indicating that metals are transported outward from the cluster core \citep[e.g.,][]{DavidNulsen08,RasmussenPonman09}."813 The central AGN is clearly a strong candidate to drive this process. and numerous studies have used metallicity measurements to constrain models of AGN—driven gas motions (e.g..2222)..," The central AGN is clearly a strong candidate to drive this process, and numerous studies have used metallicity measurements to constrain models of AGN–driven gas motions \citep[e.g.,][]{Rebuscoetal05,Rebuscoetal06,DavidNulsen08,Xiangetal09}."814 Evidence of enrichment associated with the radio jets and lobes of central radio galaxies has been found in nearby X-ray bright clusters (e.g..2222). suggesting that AGN-driven outflows or entrainment is a viable mechanism for transporting enriched gus to large radii.," Evidence of enrichment associated with the radio jets and lobes of central radio galaxies has been found in nearby X–ray bright clusters \citep[e.g.,][]{Sandersetal04,Simionescuetal08,Simionescuetal09,Kirkpatricketal09}, suggesting that AGN–driven outflows or entrainment is a viable mechanism for transporting enriched gas to large radii."815 However. with unambiguous examples identitied only in a handful of clusters. it is as yet unclear how common this process is. and the identification and characterisation of outflows in other systems is a necessity.," However, with unambiguous examples identified only in a handful of clusters, it is as yet unclear how common this process is, and the identification and characterisation of outflows in other systems is a necessity."816 In this paper we construct temperature and abundance maps of the poor cluster AWM 4. so as to investigate the effect of an ongoing AGN outburst on the structure of the intracluster medium (ICM) and in particular the metallicity distribution.," In this paper we construct temperature and abundance maps of the poor cluster AWM 4, so as to investigate the effect of an ongoing AGN outburst on the structure of the intracluster medium (ICM) and in particular the metallicity distribution."817 The central dominant elliptical galaxy. NGC 6051. hosts a powerful radio source. 4C424.36. which has been characterised in detail using deep multi-frequency observations from the Giant Metrewave Radio Telescope (2)..," The central dominant elliptical galaxy, NGC 6051, hosts a powerful radio source, 4C+24.36, which has been characterised in detail using deep multi-frequency observations from the Giant Metrewave Radio Telescope \citep{Giacintuccietal08}."818 We have previously examined the temperature and abundance structure of the cluster using, We have previously examined the temperature and abundance structure of the cluster using819To quantify nicrovariation of a DLC. by far the most commonly uscd statistic is the so-called C-statistie (0.8. Jang Miller 1995: Romero et 11999).,"To quantify microvariation of a DLC, by far the most commonly used statistic is the so-called $C$ -statistic (e.g., Jang Miller 1995; Romero et 1999)."820 This technique uses a variability parameter C. which is an average of 6] and C2 with Llere Var(qsl). Var(q52) and Var(sl52) are the variance of observational scatters of the cüllerential instrumental. magnitudes. of. the starl. s2 and star. respectively.," This technique uses a variability parameter $C$, which is an average of $C1$ and $C2$ with Here $Var (q-s1)$, $Var (q-s2)$ and $Var (s1-s2)$ are the variance of observational scatters of the differential instrumental magnitudes of the $-$ star1, $-$ s2 and $-$ star2, respectively."821 “Phe normally adopted criterion to claim that variability is present is Co22.576. which corresponds to a nominal confidence level of 20.99. Despite the very common use of these C-statisties. de Diego (2010) has pointed out it has severe problems.," The normally adopted criterion to claim that variability is present is $C822\geq 2.576$, which corresponds to a nominal confidence level of $\ge8230.99$ Despite the very common use of these $C$ -statistics, de Diego (2010) has pointed out it has severe problems."824 Because it, Because it825To assess the siguilicauce of the light curve it dillerences above. we have examined iu detail the HR—A’ colors of the afterglow Lor tve six 4 data points.,"To assess the significance of the light curve fit differences above, we have examined in detail the $R-K'$ colors of the afterglow for the six $K'$ data points."826 At each epoch. we use selected {4 data points to obtain the most reliable interpolaed or extrapolated Ro flux at the time of the Ih’ measurement.," At each epoch, we use selected R data points to obtain the most reliable interpolated or extrapolated R flux at the time of the K' measurement."827 All measurements are adjusted to he zero point of Heuclen et al (2000)., All measurements are adjusted to the zero point of Henden et al (2000).828 Details lor each epoc follow., Details for each epoch follow.829 larch 3.215: We tuterpolate betwee: the Maeh 3.21 and March 3.25 Nordic Optical Telescope measurements by Jeuseu et al (2000). obaiuiug fP=920.115£0.01.," March 3.215: We interpolate between the March 3.21 and March 3.25 Nordic Optical Telescope measurements by Jensen et al (2000), obtaining $R=20.145 \pm 0.04$."830 Hence. t—A’=2.62+0.07i.," Hence, $R-K' = 2.62 \pm 0.07$."831 lare 3.99: We take a weiglited average olf the three measuwements from March 3.51 (Garnavich et al 2000a: H:ulpern οἱ al 2000a: Veillet et al 200(Ja.b).," March 3.55: We take a weighted average of the three measurements from March 3.51 (Garnavich et al 2000a; Halpern et al 2000a; Veillet et al 2000a,b)."832 Wea ορ’ correctious to place the first two epoc15 Oll he Heiden e al zero pout. aud further add 0.0:21 jagnitucdes to adjust the R flux to the Iv’ epoch. one Iour late C," We apply corrections to place the first two epochs on the Henden et al zero point, and further add $0.02$ magnitudes to adjust the R flux to the $K'$ epoch, one hour later. ("833Ehis corresponds to a local /| decay.),This corresponds to a local $t^{-1}$ decay.)834 We obtain 2=20.32£0.01 aud H—bk’=2.79£0.05.," We obtain $R=20.32 \pm 0.04$ and $R-K' = 2.79835\pm 0.05$."836 larch LOL: We combine four B. measurements from March. Lis to £50 (three from Jensen οἱ al 2000: one from Halpern et al 2000b. adjusted |N 0.05 mag to the Heuden et al zero point) aud interpolate to the March 1.909 point of Bhargavij Cowsik to obtain /?=20.59+0.01.," March 4.64: We combine four R measurements from March 4.48 to 4.50 (three from Jensen et al 2000; one from Halpern et al 2000b, adjusted by 0.05 mag to the Henden et al zero point) and interpolate to the March 4.909 point of Bhargavi Cowsik to obtain $R=20.59 \pm 0.04$."837 Hence. εἰ=2.93£0.06.," Hence, $R-K' = 2.93 \pm 0.06$."838 larch 5.61: We extrapolate the Marchi 5.63 R band point from Veillet et al (2000) to the I’ epoch. obtaining 2=20.85£0.01 aud 2—A’=2.81-E0.06.," March 5.61: We extrapolate the March 5.63 R band point from Veillet et al (2000) to the K' epoch, obtaining $R = 20.85 \pm 0.04$ and $R-K'839= 2.84 \pm 0.06$."840 larch 6.595: This epoc Lis during the “plateau” in the R band ligh curve ((Beruabel et al 2000)., March 6.595: This epoch is during the “plateau” in the R band light curve (Bernabei et al 2000).841 Fitting a single power law through the BR ¢lata trom March 6.135 to March T.22. evaluatiug it at March 6.595. aud estimating the [αν error through Monte Carlo sitjiulatious. we find £0.07.," Fitting a single power law through the R data from March 6.135 to March 7.22, evaluating it at March 6.595, and estimating the flux error through Monte Carlo simulations, we find $R=21.57 \pm 0.07$ ."842 The resulting colo ds 2—INT=3.0040.1L., The resulting color is $R-K' = 3.00 \pm 0.14$.843" This color does de»end o1] OUI assessinent that dle ""plateau"" is a real featu'e.", This color does depend on our assessment that the “plateau” is a real feature.844 It we extend the fit to earlier times (starting at March 5.93). the color becomes 0.11 mag blue* though a sinee power law fit does uot descriye the clata well over the full period from March 5.93 to March. 7.22.," If we extend the fit to earlier times (starting at March 5.93), the color becomes $0.14$ mag bluer, though a single power law fit does not describe the data well over the full period from March 5.93 to March 7.22."845 March 8.590: We use the R (ata from March 8.116 through 9.52., March 8.590: We use the R data from March 8.146 through 9.52.846" We again fit a single power law decay through all the R daa. evaluate it at the epoch of the IX, measurement. aud determine the error bar [rom simulations."," We again fit a single power law decay through all the R data, evaluate it at the epoch of the K' measurement, and determine the error bar from simulations."847 The resu tis R=21.950.01. so that /?—N'=2.663- 0.10.," The result is $R = 21.95 \pm 0.04$, so that $R-K' = 2.66 \pm 0.10$ ."848" These values of 2—A"" are plotted as a [uuction of time in figure 2..", These values of $R-K'$ are plotted as a function of time in figure \ref{rkfig}.849 If we assuue a sinele [I—A! color throughout the alterglow. the best fit is 1—A!=2.79.," If we assume a single $R-K'$ color throughout the afterglow, the best fit is $R-K' = 2.79$."850 With 42/d.o.£=2.87 for 5 degrees of [reedoim. this fit is not especially good.," With $\chi^2 / \dof = 2.87$ for $5$ degrees of freedom, this fit is not especially good."851 We cousider three possible explanations for the observed variation of 2—N' with time., We consider three possible explanations for the observed variation of $R-K'$ with time.852 First. it is possible that the color variations are real.," First, it is possible that the color variations are real."853 Second. as suggestedMD by Masetti et al (2000). it may be that there are no true color variations. but that the afterglow exhibits achromatic f[Iuctuations on time scales short compared to the interval betweenobservatious.," Second, as suggested by Masetti et al (2000), it may be that there are no true color variations, but that the afterglow exhibits achromatic fluctuations on time scales short compared to the interval betweenobservations."854 If so. the fIuctuatious need to," If so, the fluctuations need to"855From the study of X-ray transient svstemis. it ds. possible o determine the masses of stellar-mass black-holes. by observing the cool secondary star during quiescence (see e.g. Charles. 1999).,"From the study of X-ray transient systems, it is possible to determine the masses of stellar-mass black-holes, by observing the cool secondary star during quiescence (see e.g. Charles, 1999)."856 In this paper we present new observations of he late-type secondary star in the soft X-ray transient GRO J0422|32 (Nova Per 1992/ V5IS Per)., In this paper we present new observations of the late-type secondary star in the soft X-ray transient GRO J0422+32 (Nova Per 1992/ V518 Per).857" Since the discovery of 0422]32 on August 5th. 1992. whilst in outburst. by he ""Compton. Gamma Rav Observatory’ (Paciesas ct al. 1992). there have been three subsequent mini! outbursts: December 1992 (Llarmon. Fishman DPaciesas. 1992). August 1993 (Filipenko Matheson. 1993) and. December-January 1993/4 (Zhao et al. 1993)."," Since the discovery of J0422+32 on August 5th 1992, whilst in outburst, by the `Compton Gamma Ray Observatory' (Paciesas et al, 1992), there have been three subsequent `mini' outbursts: December 1992 (Harmon, Fishman Paciesas, 1992), August 1993 (Filipenko Matheson, 1993) and December-January 1993/4 (Zhao et al, 1993)."858 The svstem has been observed at. L=20.03 (Orosz&Bailvn1995). ancl L=20.22 (Casaresοἱal1995).. but never. as we show in this paper. in absolute quicscence.," The system has been observed at I=20.03 \cite{Oros95} and I=20.22 \cite{Casa95}, but never, as we show in this paper, in absolute quiescence."859 Therefore. observations in the optical have been dominated bv the [lux emitted. from the accretion disc around. the compact object. making observations of the Al-star difficult.," Therefore, observations in the optical have been dominated by the flux emitted from the accretion disc around the compact object, making observations of the M-star difficult."860 Lere we present results showing that JO422|32 was fainter still in December LOOT. thus observations of the secondary were more accessible. due to less contamination from the disc.," Here we present results showing that J0422+32 was fainter still in December 1997, thus observations of the secondary were more accessible, due to less contamination from the disc."861 Previously. Beckman ct al (1997) have determined a minimum mass of the compact object (black hole) of 15M.. from an IL band Dight-curve.," Previously, Beekman et al (1997) have determined a minimum mass of the compact object (black hole) of $_\odot$, from an I band light-curve."862 From calculations by line. Ixolb Burderi (1996) based on the ‘cise instability model’. where the mass transfer rate must be below a critical level in order for low mass X-ray binary svstenis to. become transient. à minimum. mass of the compact object can be calculated.," From calculations by King, Kolb Burderi (1996) based on the `disc instability model', where the mass transfer rate must be below a critical level in order for low mass X-ray binary systems to become transient, a minimum mass of the compact object can be calculated."863 H£ their assumptions are correct. Beckman et al (1997) calculated: a minimum. mass of the compact object of 28M...," If their assumptions are correct, Beekman et al (1997) calculated a minimum mass of the compact object of $_\odot$."864 This mass is impossibly large for stellar evolution models., This mass is impossibly large for stellar evolution models.865 From studying the ellipsoidal modulation alone. we constrain the black-hole to have a much lower minimum mass. which is consistent with the evolution of massive stars that form black holes.," From studying the ellipsoidal modulation alone, we constrain the black-hole to have a much lower minimum mass, which is consistent with the evolution of massive stars that form black holes."866components in component E was largely an exercise in intuition al the lower frequencies.,components in component E was largely an exercise in intuition at the lower frequencies.867 Therefore. we have fitted (he strongest eniission component in E. calling it E1. but otherwise have not split component E into multiple subcomponents.," Therefore, we have fitted the strongest emission component in E, calling it E1, but otherwise have not split component E into multiple subcomponents."868" El has a steep radio spectrum. with a (wo-point spectral index between 8 and 15 Gllz of ayy,=—1.2Y+0.16 (defining 5S,xv“)."," E1 has a steep radio spectrum, with a two-point spectral index between 8 and 15 GHz of $\alpha_{8,15}=-1.27\pm 0.16$ (defining $S_\nu\propto \nu^{+\alpha}$ )."869" In contrast. D3b. the most powerful component of D3. has ayy,=—0.11£0.23."," In contrast, D3b, the most powerful component of D3, has $\alpha_{8,15}=-0.11\pm 0.23$."870" Component D3c has ayy,=—0.48d:0.30. consistent with either a flat or a steep spectrum. while D3a is not clearly separable from D3b at 8 GlIz. and therefore cannot be fitted."," Component D3c has $\alpha_{8,15}=-0.48\pm 0.30$, consistent with either a flat or a steep spectrum, while D3a is not clearly separable from D3b at 8 GHz, and therefore cannot be fitted."871 The second method of analysis was to produce an image of (he spectral index between 5 and 15 GlIz., The second method of analysis was to produce an image of the spectral index between 8 and 15 GHz.872 This was done by aligning the 8 and 15 GIIz images on the strongest peak of D3. then computing the spectral index at each individual pixel anc generating a new image: (his image was blanked αἱ all points where either of the input images had a [lux clensity less than five (nes (he noise level.," This was done by aligning the 8 and 15 GHz images on the strongest peak of D3, then computing the spectral index at each individual pixel and generating a new spectral-index image; this image was blanked at all points where either of the input images had a flux density less than five times the noise level."873 The spectral indices then. were evaluated along major axis slices through components D3 and E. Figure 4. shows the spectral index along the major axis slice of Component E. There clearly is no flat- or inverted-spectrum component here. so it is unlikely that Component E contains the nucleus of NGC 4151.," The spectral indices then were evaluated along major axis slices through components D3 and E. Figure \ref{fig:sliceE} shows the spectral index along the major axis slice of Component E. There clearly is no flat- or inverted-spectrum component here, so it is unlikely that Component E contains the nucleus of NGC 4151."874 Figure 5 shows the spectral index (top panel) and the 15 GllIz total intensity (bottom panel) along (he major axis (Gin the direction Irom West to East) of Component. D3: the locations of the three sub-components in D3 are indicated in the figure., Figure \ref{fig:sliceD} shows the spectral index (top panel) and the 15 GHz total intensity (bottom panel) along the major axis (in the direction from West to East) of Component D3; the locations of the three sub-components in D3 are indicated in the figure.875 It appears that (here is [Iat-spectirum emission near all three radio components., It appears that there is flat-spectrum emission near all three radio components.876 We note. however (hat the major axis slice does not intersect the peak of D3c. which is considerably north of the major axis defined bx the (wo stronger components.," We note, however that the major axis slice does not intersect the peak of D3c, which is considerably north of the major axis defined by the two stronger components."877 The apparent [at spectrum near D3c appears to be an artifact of the fact that the slice actually intersects (he edge of the radio component. where (he SNI is quite low and the spectrum probably is affected by component registration errors that are a small fraction of a beam in size.," The apparent flat spectrum near D3c appears to be an artifact of the fact that the slice actually intersects the edge of the radio component, where the SNR is quite low and the spectrum probably is affected by component registration errors that are a small fraction of a beam in size."878 We (hen nist assess the spectra of D3a and D3b Irom the spectral slices., We then must assess the spectra of D3a and D3b from the spectral slices.879 The image was produced by aligning the 8 GlIz and 15 Gllz peaks. in D3b. to an accuracy ol about 1 microaresecond.," The spectral-index image was produced by aligning the 8 GHz and 15 GHz peaks, in D3b, to an accuracy of about 1 microarcsecond."880" Assuming that this alignment is correct. the spectral index at the exact location of D3b can be taken [rom the spectral-index slice. and is found to be Axis=£0.16+0.23. consistent with the value of —0.11£0.23 that was found [rom the eaussian fitting,"," Assuming that this alignment is correct, the spectral index at the exact location of D3b can be taken from the spectral-index slice, and is found to be $\alpha_{8,15}=+0.16\pm 0.23$, consistent with the value of $-0.11\pm 0.23$ that was found from the gaussian fitting."881 At D3a. we [ind a similar spectral index of n&445=+0.20+0.24.," At D3a, we find a similar spectral index of $\alpha_{8,15}=+0.20\pm 0.24$."882 This cannot be compared wilh the value [rom a gaussian [it because (he 8-Gllz image has no distinct peak at the location of D3a., This cannot be compared with the value from a gaussian fit because the 8-GHz image has no distinct peak at the location of D3a.883 We note that taking single values [rom a spectral index slice is a perilous endeavor. because this process amounts to assuming both infinite resolution and perfect alignment of the two input images.," We note that taking single values from a spectral index slice is a perilous endeavor, because this process amounts to assuming both infinite resolution and perfect alignment of the two input images."884 The beam size along (he major axis of D3 is 0.5 mas. as plotted in Figure 5.. and the absolute alienment of (he 8 GlIIz aud 15 Gllz images probably is known to no better (han 0.10.2 mas.," The beam size along the major axis of D3 is 0.5 mas, as plotted in Figure \ref{fig:sliceD}, and the absolute alignment of the 8 GHz and 15 GHz images probably is known to no better than 0.1–0.2 mas."885 Therefore. the best conclusions that can," Therefore, the best conclusions that can"886while stars (hat clissipate their disks late. end up as slow rotators Herbst&Mundt| 2005).,"while stars that dissipate their disks late, end up as slow rotators \citep{bouvier94,rebull04,HM05}."887. Most rotational evolution models explore only (he case of a single strs interaction with its disk., Most rotational evolution models explore only the case of a single star's interaction with its disk.888 Comparing the (v;—IN) index with the rotation period of single stars enables us lo compare our results to the theoretical frameworks which use single star + disk scenarios., Comparing the $(K_{s}-N)$ index with the rotation period of single stars enables us to compare our results to the theoretical frameworks which use single star + disk scenarios.889 Furthermore. there is some evidence that the presence of a companion affects the evolution of a disk around a PAIS object (Meyeretal.1997b:Ghez1994).," Furthermore, there is some evidence that the presence of a companion affects the evolution of a disk around a PMS object \citep{meyer97b,ghez94}."890. Jensenοἱal.(1996) and Jensen&Mathieu(1997) present convincing evidence that disks [rom 50-100AU. are allected by the presence of binary companions over this range of separationis., \citet{jensen96} and \citet{JM97} present convincing evidence that disks from 50-100AU are affected by the presence of binary companions over this range of separations.891" In Figure 4 we combine data points from Figure 1 with (A,—V) and period data available for unresolved. binaries (listed in Table 4).", In Figure 4 we combine data points from Figure 1 with $(K_{s}-N)$ and period data available for unresolved binaries (listed in Table 4).892" Performing a linear correlation test similar to the one described in section 3. for (A,—.N) vs. rotation period. resulted in a correlation coefficient of 0.35. for 38 data points (not including upper-limits)."," Performing a linear correlation test similar to the one described in section 3, for $(K_{s}-N)$ vs. rotation period, resulted in a correlation coefficient of 0.35, for 38 data points (not including upper-limits)."893 This means the probability Chat linear correlation is random is <0.05. suggesting that the presence of unresolved. binaries in a sample of voung stars could anv expected correlation.," This means the probability that linear correlation is random is $< 0.05$, suggesting that the presence of unresolved binaries in a sample of young stars could any expected correlation."894 We also conducted a two sided IxX-5 test on the objects in Figure d. separating them into disked and clisk-less stars. as described in section 3.," We also conducted a two sided K-S test on the objects in Figure 4, separating them into disked and disk-less stars, as described in section 3."895 We derived a D-statistic of 0.45. which indicates that the probability the distributions are similar is 7.0%.," We derived a D-statistic of 0.45, which indicates that the probability the distributions are similar is $7.0\%$."896 This is a 1.06 result., This is a $1.0\sigma$ result.897 So we cannot confidently assert that the period distributions were drawn [rom different parent populations., So we cannot confidently assert that the period distributions were drawn from different parent populations.898 Ghezetal.(1993) estimate that 2/3 of the stars in the Tan-Aur region are multiple svstenms., \citet{ghez93} estimate that 2/3 of the stars in the Tau-Aur region are multiple systems.899 Yet. the linear correlation test only includes 13 binary svstems compared to the 25 sinele svstenms (excluding upperlimits).," Yet, the linear correlation test only includes 13 binary systems compared to the 25 single systems (excluding upperlimits)."900 This is because (here is a lack of photometric period data for approx 85'& of the stars surveved to be multiple svstems. compared to 50% for those survved to be single svstems (Ghezetal.1993:LeinertSimon1995:Bouvieral.1993.1995:Osterlohet 1996).," This is because there is a lack of photometric period data for approx $\%$ of the stars surveyed to be multiple systems, compared to $\%$ for those survyed to be single systems \citep{ghez93,leinert93,simon95,bouvier93,bouvier95,osterloh96}."901. This is probably due to the difficulty in interpreting data from binary svstems., This is probably due to the difficulty in interpreting data from binary systems.902 Most. photometric period survevs that include binaries do nol resolve companions and hence it is hard (ο know for certain a) which component's period was determined (if the stars are of comparable brightness) or b) i£ the light. fluctuations were due to orbital motions (eclipsing) or actual rotational motion (spots)., Most photometric period surveys that include binaries do not resolve companions and hence it is hard to know for certain a) which component's period was determined (if the stars are of comparable brightness) or b) if the light fluctuations were due to oribital motions (eclipsing) or actual rotational motion (spots).903 In addition. components in a close binary system are hard to resolve in the infrared.," In addition, components in a close binary system are hard to resolve in the infrared."904 The source of flux rom an unresolved. multiple svstem cannot be easily determined., The source of N-band flux from an unresolved multiple system cannot be easily determined.905 Contributions from each stellar component. the dust disk around each object. or a circumbinary disk could add to the N-band fIux.," Contributions from each stellar component, the dust disk around each object, or a circumbinary disk \citep{ghez94} could add to the N-band flux."906 In investigating star-disk interactions in the PAIS.," In investigating star-disk interactions in the PMS,"907the same as the correction in the A-band )).,the same as the correction in the $K$ -band ).908 In summary. the svstematic errors in our I-band red clump distance to the LAIC are probably of order (photometric calibration) and (population correction). and thus comparable to the statistical error obtained.," In summary, the systematic errors in our $K$ -band red clump distance to the LMC are probably of order (photometric calibration) and (population correction), and thus comparable to the statistical error obtained."909 The A-band red clump distance to (he LAIC is in agreement will previously reported {- results (811)., The $K$ -band red clump distance to the LMC is in agreement with previously reported $I$ -band results 1).910" The only serious cliscrepancy is (ae short cdistauce result of Udalski (2000) based on OGLE II data,", The only serious discrepancy is the short distance result of Udalski (2000) based on OGLE II data.911" Udalski (2000) finds a mean dereddened red. clamp brightness of fy=17.94440.014, for 9 fields in the LMC halo.", Udalski (2000) finds a mean dereddened red clump brightness of $I_0 = 17.944 \pm 0.014_r$ for 9 fields in the LMC halo.912 Those fields are on average 27.12 from the center of the LMC. nearly perpendicular to the line-of-nocles. and on (henear sile of the inclined clisk (wan der Marel et al.," Those fields are on average $2^{\circ}.12$ from the center of the LMC, nearly perpendicular to the line-of-nodes, and on the side of the inclined disk (van der Marel et al."913 2002)., 2002).914 Correcting lor the 0.02 mag zero-point offset between OGLE II and our /WE data. and for geometric projection. the Udalski (2000) red clump brightness becomes fy=18.024 mag (at LAIC center).," Correcting for the 0.02 mag zero-point offset between OGLE II and our /WF data, and for geometric projection, the Udalski (2000) red clump brightness becomes $I_0 = 18.024$ mag (at LMC center)."915 For comparison. our dereddened red clump brightness (Table 1) corrected to the LAIC center is J)=18.019 mag.," For comparison, our dereddened red clump brightness (Table 1) corrected to the LMC center is $I_0 = 18.019$ mag."916 The results ol this work. Udalski (2000). ancl Romaniello et al. (," The results of this work, Udalski (2000), and Romaniello et al. ("9172000) therefore all agree. which lends strong support to the accuracy of the A-band red clamp distance to the LMC.,"2000) therefore all agree, which lends strong support to the accuracy of the $K$ -band red clump distance to the LMC."918 Bretthorst(1998) describes the Bayesian theory of modelling data using a sinusoid plus white noise., \cite{bre98} describes the Bayesian theory of modelling data using a sinusoid plus white noise.919" In this formalism, our metric can be shown to be is the squared magnitude of the discrete Fourier transform of the data."," In this formalism, our metric can be shown to be is the squared magnitude of the discrete Fourier transform of the data."920" N is the number of data points in the light curve, R(w)=Σιcos(wt;), Ι(ω)=Σιsin(wt;) and στπις is the rms scatter of the data."," $N$ is the number of data points in the light curve, $R(\omega) = \sum_{i=1}^{N}\cos(\omega t_i)$, $I(\omega) = \sum_{i=1}^{N}\sin(\omega t_i)$ and $\sigma_{\mbox{rms}}$ is the rms scatter of the data."921 We have assumed the data is mean-subtracted., We have assumed the data is mean-subtracted.922" As discussed in B11, the choice of a threshold for periodicity detection is best made empirically."," As discussed in B11, the choice of a threshold for periodicity detection is best made empirically."923 We selected S=0.3 as an appropriate threshold between clear-cut periodic variability and non-periodic or ambiguous cases., We selected $S = 0.3$ as an appropriate threshold between clear-cut periodic variability and non-periodic or ambiguous cases.924" This threshold is slightly lower than the value of S=0.4 used in the Monitor project (seee.g.Irwinetal.2006),, which is reasonable given the vastly superior time-sampling of the data."," This threshold is slightly lower than the value of $S=0.4$ used in the Monitor project \citep[see e.g.][]{irw06}, which is reasonable given the vastly superior time-sampling of the data."925" This threshold can be compared to a power spectrum cut, since the power spectrum is given by PS(w)=4C(w)/N where, following Kjeldsen&Bedding(1995) we have normalised the power spectra such that a sinusoidal oscillation of amplitude A gives rise to a peak of height A? in the power spectrum."," This threshold can be compared to a power spectrum cut, since the power spectrum is given by $\mbox{PS}(\omega) = 4C(\omega) / N$ where, following \cite{kje95} we have normalised the power spectra such that a sinusoidal oscillation of amplitude $A$ gives rise to a peak of height $A^2$ in the power spectrum."926 Our threshold is then equivalent to a power spectrum threshold of Sps= 0.6775., Our threshold is then equivalent to a power spectrum threshold of $S_{\mbox{PS}} = 0.6\sigma^2_{\mbox{rms}}$ .927 By comparison Kjeldsen&Bedding(1995) give an expression for the noise level in the power spectrum of OCPS=4orms/N., By comparison \cite{kje95} give an expression for the noise level in the power spectrum of $\sigma_{\mbox{PS}} = 4 \sigma_{\mbox{rms}} / N$.928" In our data, N>1, so our threshold is conservative when comparing to white noise."," In our data, $N \gg 1$, so our threshold is conservative when comparing to white noise."929" However, white noise is not the dominant factor defining our ability to detect periodicities."," However, white noise is not the dominant factor defining our ability to detect periodicities."930" To test the appropriateness of our periodicity threshold on data with realistic noise properties, we ran a set of simulations where we injected periodic signals into actual light curves."," To test the appropriateness of our periodicity threshold on data with realistic noise properties, we ran a set of simulations where we injected periodic signals into actual light curves."931" We randomly selected 1000 Q1 light curves with low variability (Ryar< Rvarsun) and no significant period (S« 0.25), and injected sinusoidal signals into them, with random periods uniformly distributed between 2 and 16 days,and random amplitudes ranging from 0.1 to 10 times the"," We randomly selected 1000 Q1 light curves with low variability $R_{\rm var} < R_{\rm var,Sun}$ ) and no significant period $S < 0.25$ ), and injected sinusoidal signals into them, with random periods uniformly distributed between 2 and 16 days,and random amplitudes ranging from 0.1 to 10 times the"932"where W(E) is the relative velocity distribution and O,; accounts for reactions of like particles.",where $\psi(E)$ is the relative velocity distribution and $\delta_{\alpha\beta}$ accounts for reactions of like particles.933" Because we will be dealing with the correction due to dynamic sereening (a ratio between the unscreened and screened reaction rates), we can ignore the density factor and focus on the reaction rate per pair ofparticles. where jis the reduced mass of the pair. and the Maxwell- distribution is used for (E)."," Because we will be dealing with the correction due to dynamic screening (a ratio between the unscreened and screened reaction rates), we can ignore the density factor and focus on the reaction rate per pair ofparticles, where $\mu$ is the reduced mass of the pair, and the Maxwell--Boltzmann distribution is used for $\psi(E)$."934" The cross section o(E) can be defined as a product of three separate energy-dependent factors where b=31282,Z;A!?keV!7, with Z, and Z,; being the charges of the interacting ions and A is the reduced atomic weight."," The cross section $\sigma(E)$ can be defined as a product of three separate energy-dependent factors where $b= 31.28 Z_{\alpha}Z_{\beta}A^{1/2} \;\rm{keV}^{1/2}$, with $Z_{\alpha}$ and $Z_{\beta}$ being the charges of the interacting ions and $A$ is the reduced atomic weight."935 The exponential factor in this expression comes from the barrier penetratior probability. the inverse energy dependence comes from the quantum-mechanical interaction betwee the two particles. and SCE) contains the intrinsically nuclear parts of the probability for a nuclear reactior to occur.," The exponential factor in this expression comes from the barrier penetration probability, the inverse energy dependence comes from the quantum–mechanical interaction between the two particles, and $S(E)$ contains the intrinsically nuclear parts of the probability for a nuclear reaction to occur."936 With this substitution for c&(E). Equation 2 can be re-written as In the non-resonant reaction case. S(E) is slowly varying with £. so we can treat if as a constant So evaluated at the energy where exp(-E/kpT—b/E) is maximum.," With this substitution for $\sigma(E)$, Equation \ref{eq:lambda1} can be re-written as In the non-resonant reaction case, $S(E)$ is slowly varying with $E$, so we can treat it as a constant $S_0$ evaluated at the energy where ${\rm{exp}}(-E/k_BT -b/E^{1/2})$ is maximum."937 Then the reaction rate per pair of particles (without screening) can be computed as Salpeter(1954) developed a treatment to include the effect of static. electron. screening. on. nuclear reaction rates., Then the reaction rate per pair of particles (without screening) can be computed as \citet{Salpeter_1954} developed a treatment to include the effect of static electron screening on nuclear reaction rates.938 Here we summarize his method which we will use in Section 2 as the inspiration for our calculation of the dynamic sereening correction., Here we summarize his method which we will use in Section \ref{sect:method} as the inspiration for our calculation of the dynamic screening correction.939" We begin by writing the total interaction energy as a combination of the bare Coulomb potential and a contribution from the plasma: consider a case in which the classical impact parameter r. 1s very small compared with the charge cloud radius Ry and the nuclear radius 75, 1s much smaller than r,.", We begin by writing the total interaction energy as a combination of the bare Coulomb potential and a contribution from the plasma: Then consider a case in which the classical impact parameter $r_{\rm{c}}$ is very small compared with the charge cloud radius $R_D$ and the nuclear radius $r_{\rm{n}}$ is much smaller than $r_{\rm{c}}$.940" Then the barrier penetration factor for ry <¢<r.depends only on the expression For distances larger than r,. the barrier penetration factor hardly depends on the potential."," Then the barrier penetration factor for $r_{\rm{n}}<r<r_{\rm{c}}$ depends only on the expression For distances larger than $r_{\rm{c}}$, the barrier penetration factor hardly depends on the potential."941" OG"") must be small for distances greater than Αρ and approach a constant value C, of the order of magnitude of ZiZose[/Rp for small r.", $U(r)$ must be small for distances greater than $R_D$ and approach a constant value $U_0$ of the order of magnitude of $Z_1Z_2e^2/R_D$ for small $r$.942" Then. where £i, i5 the relative kinetic energy for which the integrand in Equation 2. reaches à sharp maximum."," Then, where $E_{\rm{max}}$ is the relative kinetic energy for which the integrand in Equation \ref{eq:lambda1} reaches a sharp maximum."943 If this inequality ts satisfied. U(r) can be replaced by the potential at the origin Uy.," If this inequality is satisfied, $U(r)$ can be replaced by the potential at the origin $U_0$."944 By examining expression 8.. we can see that the screening potential has effectively increased. the kinetic energy by a magnitude of Up. so the cross section factors for Uia=Uca+Vo are equivalent to the unscreened factors with energy E—Uo.," By examining expression \ref{eq:Edep}, we can see that the screening potential has effectively increased the kinetic energy by a magnitude of $U_0$, so the cross section factors for $U_{\rm{total}}=U_{\rm{Coulomb}}+U_0$ are equivalent to the unscreened factors with energy $E-U_0$."945 Equation 2. can then be replaced by With the change of variables E’=E—Uy and the approximation (E+Ug)= E'. the reaction rate per pair of particles becomes the penetration factor for E! =—Ugis so small. the lower limit of the integral can be set to zero without significantly changing the value of the integral.," Equation \ref{eq:lambda1} can then be replaced by With the change of variables $E'=E-U_0$ and the approximation $(E'+U_0) \approx E'$ , the reaction rate per pair of particles becomes Because the penetration factor for $E'=-U_0$ is so small, the lower limit of the integral can be set to zero without significantly changing the value of the integral."946 We then see that, We then see that947is additionally contaminated by the [uctuations due to the background subtraction procedure whose inlluence can only be predicted in a statistic way.,is additionally contaminated by the fluctuations due to the background subtraction procedure whose influence can only be predicted in a statistic way.948 To evaluate such effect. we have generated for cach convolved linc à set of hypothetical observations where random. background. fluctuations have been added to the source signal.," To evaluate such effect, we have generated for each convolved line a set of hypothetical observations where random background fluctuations have been added to the source signal."949 These Uuetuations are generated with a Monte Carlo procedure that takes into account the background properties. predicted. for SPI., These fluctuations are generated with a Monte Carlo procedure that takes into account the background properties predicted for SPI.950 A eaussian has been [fitted to every “observation” by using the X7 technique as it would be actually done in a real observation and finally a line width has been obtained.," A gaussian has been fitted to every ""observation"" by using the $\chi^{2}$ technique as it would be actually done in a real observation and finally a line width has been obtained."951 In each set more than 300 observations have been simulated., In each set more than 300 observations have been simulated.952 With this procedure it is possible to determine the clistribution of errors associated to the measurement of the width for any line. for anv model and explosion distance.," With this procedure it is possible to determine the distribution of errors associated to the measurement of the width for any line, for any model and explosion distance."953 Calculations have only been performed for the S47 keV line. since it has the maximum chance of being detected.," Calculations have only been performed for the 847 keV line, since it has the maximum chance of being detected."954 The observations were taken 120 days after the explosion., The observations were taken 120 days after the explosion.955 The results obtained are summarized in Figure 6.., The results obtained are summarized in Figure \ref{fig5}.956 where for each model a pair of curves is displaved., where for each model a pair of curves is displayed.957 At every explosion distance the pair defines an interval of possible measured widths which contains the values that would. be obtained by 90% of observers measuring the same line at the same distance (90 dispersion. bar)., At every explosion distance the pair defines an interval of possible measured widths which contains the values that would be obtained by 90 of observers measuring the same line at the same distance (90 dispersion bar).958 In the figure it can be appreciated that the dispersion. of the measures is 0 [or an explosion at distance O but it steeply grows with the explosion distance. being Larger for lines with low [luxga," In the figure it can be appreciated that the dispersion of the measures is 0 for an explosion at distance 0 but it steeply grows with the explosion distance, being larger for lines with low fluxes."959 This is particularly important for the SUB and DEF mockLg since they have the lowest luminosities.," This is particularly important for the SUB and DEF models, since they have the lowest luminosities."960 For all mocdels the distribution of hypothetical measures is skewed., For all models the distribution of hypothetical measures is skewed.961 That is. he observations are not svmumetrically spread: around. the original line width but there is a tendency to measure widths arger than the original values which are indicated in the igure.," That is, the observations are not symmetrically spread around the original line width but there is a tendency to measure widths larger than the original values which are indicated in the figure."962 As the possible errors become more important the significance of à measure decreases., As the possible errors become more important the significance of a measure decreases.963 Hence. it is necessary o adopt a quantitative criterium which establishes the maximum clistance at which a measurement of a line width jas physical meaning.," Hence, it is necessary to adopt a quantitative criterium which establishes the maximum distance at which a measurement of a line width has physical meaning."964 We take this distance at the point at which the width of the dispersion bar for a line equals its original width., We take this distance at the point at which the width of the dispersion bar for a line equals its original width.965 Assuming this definition the distances are: ~ 5.5 Alpe. ~ 8 Alpe ~ 7.5 Alpe and ~ 6 Alpe for DEF. DEL. DET and SUB respectively.," Assuming this definition the distances are: $\sim$ 5.5 Mpc, $\sim$ 8 Mpc $\sim$ 7.5 Mpc and $\sim$ 6 Mpc for DEF, DEL, DET and SUB respectively."966 jut more important than determining when the width of a line can be measured. is to know when this measure will be useful to discriminate among the dillerent models.," But more important than determining when the width of a line can be measured, is to know when this measure will be useful to discriminate among the different models."967 ligure 6 provides the information necessary to reject. or identify models from. observations using measured. widths., Figure \ref{fig5} provides the information necessary to reject or identify models from observations using measured widths.968 Taking the measured. width and the explosion distance for a given observation an observer can reject all the models whose associated pair of curves in the figure do not contain the measure., Taking the measured width and the explosion distance for a given observation an observer can reject all the models whose associated pair of curves in the figure do not contain the measure.969 By doing this we ensure a probability > 90% of correct model rejection., By doing this we ensure a probability $>$ 90 of correct model rejection.970 In the same wav. if the pair of curves corresponding to only one of the models contains the given measure. the observer can identify this model as observed.," In the same way, if the pair of curves corresponding to only one of the models contains the given measure, the observer can identify this model as observed."971 This would leac to a correct. model identification in. more than 90 of cases., This would lead to a correct model identification in more than 90 of cases.972 However. the confidence of the method decreases when we consider distances where the 90 dispersion bars of two or more mocels overlap.," However, the confidence of the method decreases when we consider distances where the 90 dispersion bars of two or more models overlap."973 For any pair of models. the point of intersection between the respective pairs of curves places the distance below of which it can be assured that mocel discrimination with the use of witdh measurcments will be correctly performed in more than 90 of observations.," For any pair of models, the point of intersection between the respective pairs of curves places the distance below of which it can be assured that model discrimination with the use of witdh measurements will be correctly performed in more than 90 of observations."974 We take this distance as the maximum distance reasonable for model discrimination by means of width measurements., We take this distance as the maximum distance reasonable for model discrimination by means of width measurements.975 In. Table ο we summarize. these maximum distances for the different combinations of models., In Table \ref{Tab6} we summarize these maximum distances for the different combinations of models.976 Line widths for SUD and DIZL mocels are indistinguishable for distances larger than 1 Alpe., Line widths for SUB and DEL models are indistinguishable for distances larger than 1 Mpc.977 However. in the remaining cases the differences between cach model pair are noticeable ancl it is possible to discriminate among them up to distances of the order of 4 to 7 Alpe.," However, in the remaining cases the differences between each model pair are noticeable and it is possible to discriminate among them up to distances of the order of 4 to 7 Mpc."978 Particularly interesting are the dilferences between DEL and DEP models which otherwise have very similar line intensities (Table 2))., Particularly interesting are the differences between DEL and DET models which otherwise have very similar line intensities (Table \ref{Tab2}) ).979 If we had adopted a level of confidence lower than 90 aM would have been possible to celine longer distances for model discrimination., If we had adopted a level of confidence lower than 90 it would have been possible to define longer distances for model discrimination.980 However. due to the steep Increase of the dispersion at the distances the limits obatined would not be appreciably longer.," However, due to the steep increase of the dispersion at the distances the limits obatined would not be appreciably longer."981 Raclioactivity is not the only source of 5-rav emission. in SNla explosions., Radioactivity is not the only source of $\gamma$ -ray emission in SNIa explosions.982 The interaction of the high velocity ejecta with the surroundings can induce emission of 5-ravs due to, The interaction of the high velocity ejecta with the surroundings can induce emission of $\gamma$ -rays due to983calculate the kinetic and potential energies as well as the angular momentum from the particles.,calculate the kinetic and potential energies as well as the angular momentum from the particles.984" The kinetic energy, Ex for a halo is the sum of the kinetic energy (3m-v) of each particle assigned to the halo."," The kinetic energy, $E_{\rm{K}}$ for a halo is the sum of the kinetic energy $\:m\: \vec{v}\cdot\vec{v}$ ) of each particle assigned to the halo."985" A halo's angular momentum, J, is calculated similarly as the sum of each particle's angular momentum (m7x 4)."," A halo's angular momentum, $\vec{J}$, is calculated similarly as the sum of each particle's angular momentum $m\;\vec{r}\times\vec{v}$ )."986" The potential energy, Ec, of a halo is calculated using a direct summation: where G is Newton’s gravitational constant, Np the number of particles in the halo, and 7;; is the distance between particles { and j."," The potential energy, $E_{\rm{G}}$, of a halo is calculated using a direct summation: where $G$ is Newton's gravitational constant, $N_h$ the number of particles in the halo, and $\vec{r}_{ij}$ is the distance between particles $i$ and $j$."987" In all of these definitions, the velocities are with respect to the halo's mean velocity, and the positions are with respect to the centre of the halo."," In all of these definitions, the velocities are with respect to the halo's mean velocity, and the positions are with respect to the centre of the halo."988" Throughout this paper, the centre of the halo refers to the location of the densest particle, which we use as a proxy for the location of the minimum of the halo’s potential well."," Throughout this paper, the centre of the halo refers to the location of the densest particle, which we use as a proxy for the location of the minimum of the halo's potential well."989" The only exception will be in section 4,, in which we use the centre of mass to cross reference halos in simulations of different resolution."," The only exception will be in section \ref{sec:CT}, in which we use the centre of mass to cross reference halos in simulations of different resolution."990" Having now calculated Ex and Eq for our haloes, we can measure how virialized the haloes are at these early epochs."," Having now calculated $E_{\rm{K}}$ and $E_{\rm{G}}$ for our haloes, we can measure how virialized the haloes are at these early epochs."991" The scalar virial theorem states that for an isolated, collisionless system in a steady state, the total kinetic energy should be equal to half the total potential energy: 2Ex+Eq=0."," The scalar virial theorem states that for an isolated, collisionless system in a steady state, the total kinetic energy should be equal to half the total potential energy: $2E_{\rm{K}} + E_{\rm{G}} = 0$."992" Thus, measuring the total kinetic and potential energies gives us insight into the dynamical state of these dark matter haloes."," Thus, measuring the total kinetic and potential energies gives us insight into the dynamical state of these dark matter haloes."993" However, we note that the two key assumptions of the virial theorem (an isolated halo and steady state) are not strictly valid for these halos at these epochs."," However, we note that the two key assumptions of the virial theorem (an isolated halo and steady state) are not strictly valid for these halos at these epochs."994" First, these haloes are still actively merging and"," First, these haloes are still actively merging and"995 , 996as in Fig.,as in Fig.997 1. confirm that the MS broadening is a result of the superposition of two narrower but offset distributions.," 1, confirm that the MS broadening is a result of the superposition of two narrower but offset distributions."998 Two Κον points should be emphasized., Two key points should be emphasized.999 First. for stars fainter than the vertical TO. the color offset disappears and the unevolved. MSs are indistinguishable.," First, for stars fainter than the vertical TO, the color offset disappears and the unevolved MSs are indistinguishable."1000 Second. while we have used the V.B—I diagram to illustrate the separation to optimal effect. the color separation is apparent wilh either the V.5—V CAD or the V.—7 CAD. with the D—/ trend being the sum of the two offsets.," Second, while we have used the $V, B-I$ diagram to illustrate the separation to optimal effect, the color separation is apparent with either the $V, B-V$ CMD or the $V, V-I$ CMD, with the $B-I$ trend being the sum of the two offsets."1001 Given these constraints. we can now evaluate the likelihood that the offsets are caused by photometric errors. reddening. aud/or age.," Given these constraints, we can now evaluate the likelihood that the offsets are caused by photometric errors, reddening, and/or age."1002 The internal precision of the ST03 photometry is exceptional but this doesn't preclude the possibility of radiallv-dependent. svstematic shifts in color.," The internal precision of the ST03 photometry is exceptional but this doesn't preclude the possibility of radially-dependent, systematic shifts in color."1003 To test this. we compared the BY photometry of STO3 with that of Ixaluzuv&Rucinski(1995).. the next most accurate photometric database covering approximately (he same area. derived using a reduction and calibration procedure independent of STO3.," To test this, we compared the $BV$ photometry of ST03 with that of \citet{KR95}, the next most accurate photometric database covering approximately the same area, derived using a reduction and calibration procedure independent of ST03."1004 D—V. was adopted as the color index due the lack of £ photometry in the Ixaluziuv&Rucinski(1995). survey., $B-V$ was adopted as the color index due the lack of $I$ photometry in the \citet{KR95} survey.1005 Fig., Fig.1006 3 shows the residuals in 2—V. in the sense (ST03 - IKXR95). for all stars brighter than V. — 20.0 as a function of radial position in pixels on (he coordinate scale of STO3.," 3 shows the residuals in $B-V$, in the sense (ST03 - KR95), for all stars brighter than $V$ = 20.0 as a function of radial position in pixels on the coordinate scale of ST03."1007 Stars with absolute residuals larger than 0.15 mag have been excluded [rom the analvsis., Stars with absolute residuals larger than 0.15 mag have been excluded from the analysis.1008 The vertical bar illustrates the breakpoint defining inner versus outer region in Fig., The vertical bar illustrates the breakpoint defining inner versus outer region in Fig.1009 2., 2.1010 The filled circles show the mean residuals wilh standard deviations in annuli LOO pixels wide., The filled circles show the mean residuals with standard deviations in annuli 100 pixels wide.1011 While there is evidence that the P—V. photometry of STO3 for the inner region is slightly redder (han (the outer. compared to the svstem of Ikaluzny&Rucinski(1995).. the difference (40.0070 + 0.0015 mag) is too small to produce the color shift as defined bv the WB—V CMD.," While there is evidence that the $B-V$ photometry of ST03 for the inner region is slightly redder than the outer, compared to the system of \citet{KR95}, the difference (+0.0070 $\pm$ 0.0015 mag) is too small to produce the color shift as defined by the $V, B-V$ CMD."1012 Even more important. because the magnitudes are independently calibrated in each filter. a color gradient. would only arise if there is a radiallv-dependent olfset in each of the individual calibrations which coincidentally combined to produce color," Even more important, because the magnitudes are independently calibrated in each filter, a color gradient would only arise if there is a radially-dependent offset in each of the individual calibrations which coincidentally combined to produce color"1013Robust variance using the trimming algorithm (8) ts applied while calculating (15): outliers are marked by the indicator function /nd(i).,Robust variance using the trimming algorithm (8) is applied while calculating (15): outliers are marked by the indicator function $ind(i)$.1014 The results of computer simulation for 2048 and m-100 are shown in Fig., The results of computer simulation for $n=2048$ and $m=100$ are shown in Fig.1015 7. 8 and 9.," 7, 8 and 9."1016 Fig., Fig.1017 7 shows the ;) outputs of the Pearson's correlator. upper panel. and the robust correlator (15). lower panel. for the correlation coefficient of the input signals p.=0. re.. for the uncorrelated inputs. except RFI. which are 100% correlated.," 7 shows the $m$ outputs of the Pearson's correlator, upper panel, and the robust correlator (15), lower panel, for the correlation coefficient of the input signals $\rho=0$, i.e., for the uncorrelated inputs, except RFI, which are $100\%$ correlated."1018 The upper panel shows considerable bias. while the fluctuations of correlator output in the lower panel vary around zero.," The upper panel shows considerable bias, while the fluctuations of correlator output in the lower panel vary around zero."1019 Fig., Fig.1020 8 gives the same situation but for o.=0.1 and Fig., 8 gives the same situation but for $\rho=0.1$ and Fig.1021 9 - for p=0.2., 9 - for $\rho=0.2$.1022" In all these examples a considerable bias 1s visible for the Pearson's correlator and there is an absence of bias for the ""sum-difference"" correlator.", In all these examples a considerable bias is visible for the Pearson's correlator and there is an absence of bias for the “sum-difference” correlator.1023 Of course. other post-correlation methods can be used in the case of narrow-band persistent RFI with a stable spatial orientation. for example. (Cornwell et al.2004)).," Of course, other post-correlation methods can be used in the case of narrow-band persistent RFI with a stable spatial orientation, for example, (Cornwell et \cite{corn}) )."1024 But in the case of sporadic burst-like RFI. the proposed pre-correlation statistical analysis is more appropriate: only n=2000 samples were used for each correlator input. which corresponds toa microsecond time scale for typical bandwidths.," But in the case of sporadic burst-like RFI, the proposed pre-correlation statistical analysis is more appropriate: only $n\approx2000$ samples were used for each correlator input, which corresponds to a microsecond time scale for typical bandwidths."1025 Several examples of applications of the aforementioned algorithms are presented The auto-spectrum in Fig., Several examples of applications of the aforementioned algorithms are presented The auto-spectrum in Fig.1026 10 is calculated using the “raw” data recorded at LOFAR CSI for three hours., 10 is calculated using the “raw” data recorded at LOFAR CS1 for three hours.1027 Data consisting, Data consisting1028in steps of 1 dex.,in steps of 1 dex.1029 These luminosities correspond to mass-loss rates in the range 1071?—10-8Moyr~' and are similar to values calculated by Alexander et al. (, These luminosities correspond to mass-loss rates in the range $10^{-10}-10^{-8}$ $_\odot$ $^{-1}$ and are similar to values calculated by Alexander et al. (10302004).,2004).1031" In order to calculate images we compute scattered light images at 1.6, 2.1 3.8um with band passes corresponding to the H, Kk’ L’ bands."," In order to calculate images we compute scattered light images at 1.6, 2.1 $\mu1032 $ m with band passes corresponding to the H, K' L' bands."1033 In order to consider the relative contributions of crystaline to amorphous dust we take the calculated crystallinity fractions in the disc of Dullemond et al. (, In order to consider the relative contributions of crystalline to amorphous dust we take the calculated crystallinity fractions in the disc of Dullemond et al. (10342006) for an evolved Herbig Ae/Be star.,2006) for an evolved Herbig Ae/Be star.1035" We assume that this disc crystallinity fraction is the same at the base of our photoevaporative wind, such that the crystallinity fraction along the streamline can be calculated by following the thermal evolution of the dust entrained on that streamline."," We assume that this disc crystallinity fraction is the same at the base of our photoevaporative wind, such that the crystallinity fraction along the streamline can be calculated by following the thermal evolution of the dust entrained on that streamline."1036" A photoevaporative disc wind is a thermally driven hydrodynamic wind occuring when the disc's surface is heated to temperatures of order the escape temperature, allowing it to launch a freely expanding wind."," A photoevaporative disc wind is a thermally driven hydrodynamic wind occuring when the disc's surface is heated to temperatures of order the escape temperature, allowing it to launch a freely expanding wind."1037 While the wind driving source for lower mass (T-Tauri) stars is likely to be X-rays (Owen et al., While the wind driving source for lower mass (T-Tauri) stars is likely to be X-rays (Owen et al.1038" 2010a, Ercolano Owen 2010, Ercolano Clarke 2010, Owen et al."," 2010a, Ercolano Owen 2010, Ercolano Clarke 2010, Owen et al."1039 2010b) the wind driving source around intermediate mass stars has not yet been thouroughly investigated., 2010b) the wind driving source around intermediate mass stars has not yet been thouroughly investigated.1040" X-ray photoevaporation may still occur to some degree; however, the lower Lx/Luo; ratio of Herbig Ae/Be compared to T-Tauri stars and their higher EUV fluxes, may reduce the role of X-rays in driving the wind."," X-ray photoevaporation may still occur to some degree; however, the lower $L_X/L_{bol}$ ratio of Herbig Ae/Be compared to T-Tauri stars and their higher EUV fluxes, may reduce the role of X-rays in driving the wind."1041 We adopt here the EUV driven wind of Hollenbach et al (1994) and hydrodynamic solution of Font et al. (, We adopt here the EUV driven wind of Hollenbach et al (1994) and hydrodynamic solution of Font et al. (1042"2004), which is asimple andscalable hydrodynamic solution, allowing us to consider a wide range of parameter space, something not possible with more complicated FUV models (Gorti Hollenbach 2009) or X-ray models (Owen et al.","2004), which is a and hydrodynamic solution, allowing us to consider a wide range of parameter space, something not possible with more complicated FUV models (Gorti Hollenbach 2009) or X-ray models (Owen et al."1043 2010a)., 2010a).1044 'The simplified EUV treatment is suitable for the purpose of this work which aims at being the first approach in studying the qualitative aspects of scattered light emission from a disc wind., The simplified EUV treatment is suitable for the purpose of this work which aims at being the first approach in studying the qualitative aspects of scattered light emission from a disc wind.1045 We have repeated the calculation of Font et al. (, We have repeated the calculation of Font et al. (1046"2004) and Alexander (2008) and we refer the reader to these papers for a detailed description of the model setup, while the basics are summarised below.","2004) and Alexander (2008) and we refer the reader to these papers for a detailed description of the model setup, while the basics are summarised below."1047 In order to determine an accurate kinematic structure of the wind we must compute a numerical solution to the problem., In order to determine an accurate kinematic structure of the wind we must compute a numerical solution to the problem.1048" We use the code (Stone Norman 1992); we employ a spherical grid with 0=[0,7/2], the radial grid cells are logarithmically spaced, such that we have adequate resolution at small radius to resolve the onset of the flow."," We use the code (Stone Norman 1992); we employ a spherical grid with $\theta=[0,\pi/2]$, the radial grid cells are logarithmically spaced, such that we have adequate resolution at small radius to resolve the onset of the flow."1049" 'The calculation is an isothermal wind calculation with the sound speed set to c,= 10km s! and the radius scaled to the length scale ry=GM./c2 ie. the radius at which the internal energy of the gas is enough to unbind the gas from the star.", The calculation is an isothermal wind calculation with the sound speed set to $c_s=10$ km $^{-1}$ and the radius scaled to the length scale $r_g=GM_*/c_s^2$ i.e. the radius at which the internal energy of the gas is enough to unbind the gas from the star.1050" We use a radial range of r=[0.05,40]rg with N,=240 and Ne=50."," We use a radial range of $r=[0.05,40]r_g$ with $N_r=240$ and $N_{\theta}=50$."1051 The number density at the base (i.e. the density along the 6=7/2 axis) of the wind was calculated semi-analytically by Hollenbach et al. (, The number density at the base (i.e. the density along the $\theta=\pi/2$ axis) of the wind was calculated semi-analytically by Hollenbach et al. (1052"1994) and scales as R~°/? for R<Ry and as R~*/? outside Ry, as in Font et al. (","1994) and scales as $R^{-3/2}$ for $R<R_g$ and as $R^{-5/2}$ outside $R_g$, as in Font et al. ("10532004) and Alexander et al. (,2004) and Alexander et al. (1054"2008) we adopt the smooth density profile suggested by that varies between the two power laws: where n, is the density at R, which was determined through the numerical calculations of Hollenbachetal.(1994) to be: where 6 is the ionizing luminosity.",2008) we adopt the smooth density profile suggested by \citet{font04} that varies between the two power laws: where $n_g$ is the density at $R_g$ which was determined through the numerical calculations of \citet{hollenbach94} to be: where $\Phi$ is the ionizing luminosity.1055" We note that this hydrodynamic calculation does not include a cold bound ‘disc’ component, since as discussed above the base density structure of the wind is known a priori."," We note that this hydrodynamic calculation does not include a cold bound `disc' component, since as discussed above the base density structure of the wind is known a priori."1056" This base density, along with Keplerian rotation is reset at every time-step and the model is allowed to evolve to a steady state launching a wind from the grid's mid-plane (representing the disc's surface)."," This base density, along with Keplerian rotation is reset at every time-step and the model is allowed to evolve to a steady state launching a wind from the grid's mid-plane (representing the disc's surface)."1057" As expected, we find excellent agreement with the results of the Fontetal.(2004) and Alexander(2008) calculations."," As expected, we find excellent agreement with the results of the \citet{font04} and \citet{alexander08} calculations."1058" In Figure 1 we show a plot of the converged wind structure showing that the wind is approximately spherical once it has reached several scale heights, in agreement with our earlier discussion in Section ??.."," In Figure \ref{fig:structure} we show a plot of the converged wind structure showing that the wind is approximately spherical once it has reached several scale heights, in agreement with our earlier discussion in Section \ref{model}."1059" In order to calculate the dust distribution in the wind, we must make some assumptions about the underlying dust distribution in the disc."," In order to calculate the dust distribution in the wind, we must make some assumptions about the underlying dust distribution in the disc."1060" We adopt a dust to gas mass ratio of 0.01, and a power law grain size distribution of index -3.5 (Mathis, Rumpl Nordsiek, 1977, MRN), with grain sizes ranging from Qmin=5X1073 um to @maz=l1mm, we assume spherical grains with a density of 1g οπι?."," We adopt a dust to gas mass ratio of 0.01, and a power law grain size distribution of index -3.5 (Mathis, Rumpl Nordsiek, 1977, MRN), with grain sizes ranging from $a_{min}$ $\times10^{-3}\mu$ m to $a_{max}$ =1mm, we assume spherical grains with a density of 1g $^{-3}$."1061 We also assume that the dust is fully mixed within the disc up to the transition between the bound cold disc and the hot EUV heated flow., We also assume that the dust is fully mixed within the disc up to the transition between the bound cold disc and the hot EUV heated flow.1062" We then calculate streamlines from the base of the flow to the edge of the grid, then along each streamline, compute the force balance between the drag force (calculated from Equation 1), gravity and the centrifugal force."," We then calculate streamlines from the base of the flow to the edge of the grid, then along each streamline, compute the force balance between the drag force (calculated from Equation 1), gravity and the centrifugal force."1063 We take the dust grain as entrained if the net force along the streamline is >0., We take the dust grain as entrained if the net force along the streamline is $>0$.1064 We then obtain the maximum grain size entrained along the entire streamline, We then obtain the maximum grain size entrained along the entire streamline1065wavelength. or frequency. of the radiation. its location on the sky. and the polarization of (he radiation.,"wavelength, or frequency, of the radiation, its location on the sky, and the polarization of the radiation."1066 Measurements of the latter (vo. location and polarization. follow the statistics of direction.," Measurements of the latter two, location and polarization, follow the statistics of direction."1067 The association ol directional statistics with the measurement of location is obvious. but the application of directional statistics {ο polarization measurements is nol immediately apparent until one recalls that the Stokes parameters ο. U. and. V describe (he orientation of a polarization vector within the Poincaré sphere.," The association of directional statistics with the measurement of location is obvious, but the application of directional statistics to polarization measurements is not immediately apparent until one recalls that the Stokes parameters Q, U, and V describe the orientation of a polarization vector within the Poincaré sphere."1068 The Stokes parameter V defines (he circular polarization of the radiation ancl establishes the z-coordinate of the polarization vector in the Poincaré sphere.," The Stokes parameter V defines the circular polarization of the radiation and establishes the z-coordinate"" of the polarization vector in the Poincaré sphere."1069" The Stokes parameters Q and U describe the radiations linear polarization and establish the vectors x- and ν- respectively,"," The Stokes parameters Q and U describe the radiation's linear polarization and establish the vector's x- and y-coordinates, respectively."1070 Here. polarization measurements are shown to follow directional statistics. and (hese statistics are applied to polarization observations of radio pulsars.," Here, polarization measurements are shown to follow directional statistics, and these statistics are applied to polarization observations of radio pulsars."1071 Pulsars are rapidly rotating. highly magnetized neutron stars.," Pulsars are rapidly rotating, highly magnetized neutron stars."1072 Their rotation periods range between about. Ims and 108. and the strength of the magnetic field at their surfaces ranges from LOS G [or the oldest pulsars to over 101 G [or the voungest.," Their rotation periods range between about 1ms and 10s, and the strength of the magnetic field at their surfaces ranges from $10^8$ G for the oldest pulsars to over $10^{12}$ G for the youngest."1073 A beam of radio emission is emitted from each of the stars magnetic poles., A beam of radio emission is emitted from each of the star's magnetic poles.1074 A pulse of radio emission is observed as (he stars rotation causes the beam (o sweep across an observers line of sight., A pulse of radio emission is observed as the star's rotation causes the beam to sweep across an observer's line of sight.1075 Pulsar radio emission is generally thought to originate from charged particles streaming along open magnetic fields lines above the stars magnetic pole. bul unlike other astrophysical raciative processes (e.g. svnchrotron radiation. maser emission. ancl thermal radiation). it is poorly understood.," Pulsar radio emission is generally thought to originate from charged particles streaming along open magnetic fields lines above the star's magnetic pole, but unlike other astrophysical radiative processes (e.g. synchrotron radiation, maser emission, and thermal radiation), it is poorly understood."1076 Polarization observations of the individiual pulses Irom pulsars are niacde inan attempt to understand the radio emission mechanism and (o study the propagation of radio waves in ultra-strong magnetic fields., Polarization observations of the individiual pulses from pulsars are made in an attempt to understand the radio emission mechanism and to study the propagation of radio waves in ultra-strong magnetic fields.1077 Polarization observations of individual pulses (Lyne et al., Polarization observations of individual pulses (Lyne et al.1078 1971: Manchester et al., 1971; Manchester et al.1079 1975: Backer Rankin 1980: Stinebring et al., 1975; Backer Rankin 1980; Stinebring et al.1080 1984) show that the radiation can be highlv elliplically polarized and hiehlv variable. if not stochastic.," 1984) show that the radiation can be highly elliptically polarized and highly variable, if not stochastic."1081 In many cases. the mean of the polarization position angle varies in an S-shaped pattern across the pulse.," In many cases, the mean of the polarization position angle varies in an S-shaped pattern across the pulse."1082 But histograms of position angle created from the single pulse observations show (the angles follow the pattern in (wo parallel paths separated by about 90 degrees (Stinebring et al., But histograms of position angle created from the single pulse observations show the angles follow the pattern in two parallel paths separated by about 90 degrees (Stinebring et al.1083 1984)., 1984).1084 Furthermore. histograms of fractional linear polarization show that the radiation is significantly depolarized al pulse locations where these orthogonally polarized (OPMSs) modes occur.," Furthermore, histograms of fractional linear polarization show that the radiation is significantly depolarized at pulse locations where these orthogonally polarized (OPMs) modes occur."1085 The OPMS are thought to be the natural modes of wave propagation in pulsar magnetospheres (Allen Melrose 1982: Barnard Arons 1986)., The OPMs are thought to be the natural modes of wave propagation in pulsar magnetospheres (Allen Melrose 1982; Barnard Arons 1986).1086 The narrow bandwidths and short sampling intervals used in single pulse observations cause the instrumental noise in these observations to be large., The narrow bandwidths and short sampling intervals used in single pulse observations cause the instrumental noise in these observations to be large.1087 The narrow bandwidths are used (to overcome pulse smearing effects caused by the dispersion. measure of. and mulüpath scattering in. the interstellar medium.," The narrow bandwidths are used to overcome pulse smearing effects caused by the dispersion measure of, and multipath scattering in, the interstellar medium."1088 The short sampling intervals. (vpically of order LOQus. are needed to adecquatelv resolve the short duration radio pulse.," The short sampling intervals, typically of order 100us, are needed to adequately resolve the short duration radio pulse."1089 The combination of the stochastic nature of the intrinsic. emission, The combination of the stochastic nature of the intrinsic emission1090"The IR LFs of the three different regions were determined as described in Sect. 3.1,,","The IR LFs of the three different regions were determined as described in Sect. \ref{s:corr},"1091" using completeness and purity corrections that are appropriate for each considered region, and multiplying the counts by the fractions of non-AGN galaxies in each Lig--bin and each region to remove the AGN contribution from the IR LFs."," using completeness and purity corrections that are appropriate for each considered region, and multiplying the counts by the fractions of non-AGN galaxies in each -bin and each region to remove the AGN contribution from the IR LFs."1092 Error bars were determined via a bootstrap sampling procedure., Error bars were determined via a bootstrap re-sampling procedure.1093" The three IR LFs are displayed in the panels of Fig. 12,,"," The three IR LFs are displayed in the left-hand panels of Fig. \ref{f:3irlf},"1094 for both the zUΖρ (top panel) and the z sample (bottom panel)., for both the $\rm{z} \cup \rm{z}_p$ (top panel) and the z sample (bottom panel).1095" Power-law function fits to the three IR LFs are shown as dashed lines, and the best-fitting values of the slope parameter are given in Table 1.."," Power-law function fits to the three IR LFs are shown as dashed lines, and the best-fitting values of the slope parameter are given in Table \ref{t:fits}."1096" The slopes of the three region IR LFs do not differ significantly, but taken at face value they suggest that the filament has a flatter IR LF than both the outskirts and (for the zUzy sample) the core."," The slopes of the three region IR LFs do not differ significantly, but taken at face value they suggest that the filament has a flatter IR LF than both the outskirts and (for the $\rm{z} \cup \rm{z}_p$ sample) the core."1097 The IR LF of the filament region is flatter because of an excess of LIRGs relative to the other regions., The IR LF of the filament region is flatter because of an excess of LIRGs relative to the other regions.1098 This is also apparent from a visual inspection of Fig., This is also apparent from a visual inspection of Fig.1099" 12 and also of Fig. 11,,"," \ref{f:3irlf} and also of Fig. \ref{f:regions},"1100 where we show the spatial positions of all supercluster members in the zUzy sample and indicate the LIRGs with pink symbols (square symbols for LIRGs of the z sample)., where we show the spatial positions of all supercluster members in the $\rm{z} \cup \rm{z}_p$ sample and indicate the LIRGs with pink symbols (square symbols for LIRGs of the z sample).1101 Fig., Fig.1102" 12 (left panels) also shows that at lowerLip,, the number densities of IR-emitting galaxies are similar in the core and in the filament regions, and lowest in the outskirts region."," \ref{f:3irlf} (left panels) also shows that at lower, the number densities of IR-emitting galaxies are similar in the core and in the filament regions, and lowest in the outskirts region."1103" When considering the implications of this comparison, one must take into account that the three selected regions are characterized by different densities of normal galaxies, highest in the core, lowest in the outskirts."," When considering the implications of this comparison, one must take into account that the three selected regions are characterized by different densities of normal galaxies, highest in the core, lowest in the outskirts."1104 Similarities in the IR LFs of different regions could be caused by a combination of different densities of normal galaxies and different fractions of IR-emitting galaxies among the total., Similarities in the IR LFs of different regions could be caused by a combination of different densities of normal galaxies and different fractions of IR-emitting galaxies among the total.1105" Viceversa, different IR LFs could simply reflect differences in the densities of normal galaxies combined with similar IR-emitting galaxy fractions among the total."," Viceversa, different IR LFs could simply reflect differences in the densities of normal galaxies combined with similar IR-emitting galaxy fractions among the total."1106 It is therefore also important to compare the relative fractions of IR-emitting galaxies in the different regions., It is therefore also important to compare the relative fractions of IR-emitting galaxies in the different regions.1107" For this, we must determine the densities of normal galaxies in the three different regions."," For this, we must determine the densities of normal galaxies in the three different regions."1108" By adopting the same methodology used for a derivation of the IR LF (see Sect. 3.1)),"," By adopting the same methodology used for a derivation of the IR LF (see Sect. \ref{s:corr}) ),"1109 we determine the r-band LFs in the three regions., we determine the $r$ -band LFs in the three regions.1110" These LFs are well fitted by Schechter functions, and their shapes are not statistically different according to a y? test (?)."," These LFs are well fitted by Schechter functions, and their shapes are not statistically different according to a $\chi^2$ test ."1111". We then integrate these LFs to derive the number densities of r-band selected galaxies with r-band L,>710?Lo."," We then integrate these LFs to derive the number densities of $r$ -band selected galaxies with $r$ -band $\rm{L}_r \geq 7 \, 10^9 \, \rm{L}_{\odot}$."1112" This luminosity represents the lower limit above which our determinations of the r-band LFs appear to be robust, i.e. independent ofsample choice (the zUzy sample or the z sample)."," This luminosity represents the lower limit above which our determinations of the $r$ -band LFs appear to be robust, i.e. independent ofsample choice (the $\rm{z} \cup \rm{z}_p$ sample or the z sample)."1113 It corresponds to a stellar, It corresponds to a stellar1114square fit of the data with the general relation I4). by considering in each case a value of (m less than the number of available data points.,"square fit of the data with the general relation \ref{velr2n}) ), by considering in each case a value of $m$ less than the number of available data points."1115 In Figure |. we show the adjusted rotation curves for the four galaxies considered., In Figure \ref{rotcurv} we show the adjusted rotation curves for the four galaxies considered.1116" The points with error bars are the observations. as reported in Verheijen&Sancici(9001)... while the solid line is the rotation curve determined from (14)) with the values for the fs, given by the numerical fit."," The points with error bars are the observations, as reported in \cite{VS}, while the solid line is the rotation curve determined from \ref{velr2n}) ) with the values for the $A_{2n}$ given by the numerical fit."1117 As we can see. the relation (14) fit quite accurately to the observed data of the four galaxies considered.," As we can see, the relation \ref{velr2n}) ) fit quite accurately to the observed data of the four galaxies considered."1118" Then. from the obtained values for του. the corresponding values of the C's, are determined by using (159) and (17))."," Then, from the obtained values for $A_{2n}$, the corresponding values of the $C_{2n}$ are determined by using \ref{relation}) ) and \ref{constant0}) )."1119" In Table | we present the values ofC, for the four galaxies as well as the corresponding value of à used in CI).", In Table \ref{tab:c2n} we present the values of $C_{2n}$ for the four galaxies as well as the corresponding value of $m$ used in \ref{velr2n}) ).1120 In Table 2 we indicate. for each galaxy. the morphological type according to he Hubble's elassitication of galaxies. the radius e in kpc and the otal mass 4. both in ke and in solar mass units (ME. ).," In Table \ref{tab:mass} we indicate, for each galaxy, the morphological type according to the Hubble's classification of galaxies, the radius $a$ in ${\rm kpc}$ and the total mass $\mathcal{M}$, both in ${\rm kg}$ and in solar mass units $\mathcal{M_{\odot}}$ )."1121" Now. as the set of constants C, it defines completely each particular thin dise model. we can easily compute all the shysical quantities characterizing each galaxy."," Now, as the set of constants $C_{2n}$ it defines completely each particular thin disc model, we can easily compute all the physical quantities characterizing each galaxy."1122" However. as explicit expressions for the gravitational potential (/?.2) and the surface mass density X(/7) can be easily obtained by using the values of he C's, at expressions (1019) and (123). we will not present them rere."," However, as explicit expressions for the gravitational potential $\Phi (R,z)$ and the surface mass density $\Sigma (R)$ can be easily obtained by using the values of the $C_{2n}$ at expressions \ref{eq:poten}) ) and \ref{density}) ), we will not present them here."1123 Insteed. we plot in Figure 2. the surface densities for the four galaxies. as functions of the dimensionless radial coordinate Ifa.," Insteed, we plot in Figure \ref{densit} the surface densities for the four galaxies, as functions of the dimensionless radial coordinate ${\widetilde R} = R/a$ ."1124 For the four galaxies we obtain a well behaved surface mass density.having a maximum at the dise center and then decreasing until vanish at the disc edge.," For the four galaxies we obtain a well behaved surface mass density,having a maximum at the disc center and then decreasing until vanish at the disc edge."1125" In a similar way. we can compute the epiciclic and vertical frequencies by using (22). (24)) and the values of the constants eto, obtained from the numerical fit."," In a similar way, we can compute the epiciclic and vertical frequencies by using \ref{kapr2n}) ), \ref{nur2n}) ) and the values of the constants $A_{2n}$ obtained from the numerical fit."1126 However. as with the surface mass densities. we will not present the explicit expressions here and. instead. we only show the corresponding plots.," However, as with the surface mass densities, we will not present the explicit expressions here and, instead, we only show the corresponding plots."1127 So. in Figure 3. we show the plots of the epiciclic frequencies for the four galaxies considered and. in Figure 4.. the corresponding plots of the vertical frequencies.," So, in Figure \ref{epicic}, we show the plots of the epiciclic frequencies for the four galaxies considered and, in Figure \ref{vertic}, the corresponding plots of the vertical frequencies."1128 From the plots at Figure 3 we can see that only the galaxy NGC4Ol0 presents a small region of radial instability near the disc edge., From the plots at Figure \ref{epicic} we can see that only the galaxy NGC4010 presents a small region of radial instability near the disc edge.1129 On the other hand. as it is shown at Figure 4.. the four galaxies are instable against vertical perturbations.," On the other hand, as it is shown at Figure \ref{vertic}, the four galaxies are instable against vertical perturbations."1130(DeLuciaetal.200).. it does not coutribute to the existing stellar mass;,"\citep{DeLucia04}, it does not contribute to the existing stellar mass."1131 When accounting for this. we find that the contribution from simaller central galaxies is considerably reduced (the dot-dashed lines in top panels of Fig. 8))," When accounting for this, we find that the contribution from smaller central galaxies is considerably reduced (the dot-dashed lines in top panels of Fig. \ref{fig:contTest}) )"1132 aud is in better agreement with the SAM predictions (particularly for the Durham model)., and is in better agreement with the SAMs predictions (particularly for the Durham model).1133 This approximated coutribution. however. still appears to be somewhat overestimated. especially in the MPÀ 120del. where the measured coutribution of znaller ceutrals is tiny.," This approximated contribution, however, still appears to be somewhat overestimated, especially in the MPA model, where the measured contribution of smaller centrals is tiny."1134 As ineutioned already. the simplified estimate also inplicitlv assumes a coustaut SEE for the mereime halos. which in reality does vary with halo mass (sce. e... Fie.," As mentioned already, the simplified estimate also implicitly assumes a constant SFE for the merging halos, which in reality does vary with halo mass (see, e.g., Fig."1135 b. in this work and Fig., \ref{fig:Fig10mill50b} in this work and Fig.1136 10 iu ZCZO7)., 10 in ZCZ07).1137 This cau affect the contribution from snaller ceutral galaxies im two wavs: for a halo whose mass is around the peak of SPE or sinaller. this assiuuptiou might overestimate the contribution. while for larger mass halos if can result in an underestimation (which will result iu a stronger downsizing behavior).," This can affect the contribution from smaller central galaxies in two ways: for a halo whose mass is around the peak of SFE or smaller, this assumption might overestimate the contribution, while for larger mass halos it can result in an underestimation (which will result in a stronger downsizing behavior)."1138 The bottom panels of Figure & compare the rough estimation of the merger contribution from satellites to, The bottom panels of Figure \ref{fig:contTest} compare the rough estimation of the merger contribution from satellites to1139The distribution reaches as eacly stae after ~3x101)& or 1000yes.,"The distribution reaches a steady state after $\about3\times10^{10}\unit{s}$, or $\about1000\unit{yrs}$."1140 This is a small fraction of the time speut in pliase 2. sugvesting tiat the iitial conditions are unimportant.," This is a small fraction of the time spent in phase 2, suggesting that the initial conditions are unimportant."1141 Also shown iu he figure are the opacity and otical deyh alter 10!s. but the curve falls exactly on the curve or 3x10!s aud cannot be disiuguisled in the igure.," Also shown in the figure are the opacity and optical depth after $10^{11}\unit{s}$, but the curve falls exactly on the curve for $3\times10^{10}\unit{s}$, and cannot be distinguished in the figure."1142 We see that while the opaciy is quite hie first. it drops quickly wheu erains are allowed O grow. aud the steady state op:€icity througho uost of the atmosphere is very much lower than 2iο>| the order of maguitde of interste eral opacity at these temperatures.," We see that while the opacity is quite high at first, it drops quickly when grains are allowed to grow, and the steady state opacity throughout most of the atmosphere is very much lower than $2\unit{cm^2~g^{-1}}$, the order of magnitude of interstellar grain opacity at these temperatures."1143" Ouly the ower third of the atinosphere (but ~90% of tl lass} is"" consistent. with. the low opacity. of ?.. but the optical depth of tLe radiative zo is slightly lower than it would be with their low opacity."," Only the lower third of the atmosphere (but $\about90\%$ of the mass) is consistent with the low opacity of \citeauthor{hubickyj}, but the optical depth of the radiative zone is slightly lower than it would be with their low opacity."1144 Figure E shows tlie steady sale size distritition of graius in several layers of the atinosphliere. a 0.5Myr. or roughly the middle of phase 2.," Figure \ref{fig:5291nd} shows the steady state size distribution of grains in several layers of the atmosphere, at $0.8\unit{Myr}$, or roughly the middle of phase 2."1145 Because sinall [wegrains are continuotsly being deposited iu all layers. we expect a large population of small graius everywhere.," Because small grains are continuously being deposited in all layers, we expect a large population of small grains everywhere."1146 As we move deeper into the atmosphere we fiud more aud more large [n]€alus., As we move deeper into the atmosphere we find more and more large grains.1147 These are grains that had time to grow while settling from higher up., These are grains that had time to grow while settling from higher up.1148 Iu the lower layers a sienificaut fraction of the total mass of solid eraius is in the form of eraius as large as 0.1.cm., In the lower layers a significant fraction of the total mass of solid grains is in the form of grains as large as $0.1\unit{cm}$.1149 Π is instructive to look at the integrated »operties of the size cdistributiou as a fuuction of height in the envelope. Fig. 5..," It is instructive to look at the integrated properties of the size distribution as a function of height in the envelope, Fig. \ref{fig:5291moments}."1150 Figure 5. shows tlie averages of tlie two quaitities that determine the opacity in each layer: the inass of solid matter present as οalis. and the elficieucy of these gralus as scatterers. shown here by the average cross-section.," Figure \ref{fig:5291moments} shows the averages of the two quantities that determine the opacity in each layer: the mass of solid matter present as grains, and the efficiency of these grains as scatterers, shown here by the average cross-section."1151 Note however that o correctly determine tlie opacity we ueed to kuow the actualsrape of the clistributio Laud not just he averages., Note however that to correctly determine the opacity we need to know the actual shape of the distribution and not just the averages.1152 The mean geometric cross-section. lor exatuple. is uearly identical very |ie and very low in the atmosphere. but the distrituitions (Fig. L))," The mean geometric cross-section, for example, is nearly identical very high and very low in the atmosphere, but the distributions (Fig. \ref{fig:5291nd}) )"1153 are very cliferent., are very different.1154 Figure 5 also slows how the grains’ elliciency as scatterers. the extinction cal be ve'v dilfereut. [ro1 their simple geometric cross-section.," Figure \ref{fig:5291moments} also shows how the grains' efficiency as scatterers, the extinction cross-section, can be very different from their simple geometric cross-section."1155 As the teperature rises. the waveleteth of the peak in tle Plauck spectrum decreases. aud even similar size distributions can have qiite clierent opacities.," As the temperature rises, the wavelength of the peak in the Planck spectrum decreases, and even similar size distributions can have quite different opacities."1156 Figures 6. anc L7 show the oj»acities at roughly the beginniug. 0.ji»Myr. aud the eud. 1.3Myr. oL phase 2 respecively.," Figures \ref{fig:2321base} and \ref{fig:8651base} show the opacities at roughly the beginning, $0.35\unit{Myr}$, and the end, $1.3\unit{Myr}$, of phase 2 respectively."1157 The euvelope auc core of the protoplauet grow iore massive with titje. but the structure of the atinospliere. ve (2.T.p) relation. is not radically different.," The envelope and core of the protoplanet grow more massive with time, but the structure of the atmosphere, the $(z,T,\rho)$ relation, is not radically different."1158 The correspoudiug opacities show the same behavior that was observed in Fig., The corresponding opacities show the same behavior that was observed in Fig.1159 κ)+) — the steady state opacity is highest at the top of the atmosphere. where it is similar to the interstellar opacity. and decreases gradually bringiug the lower third of the atzuosphliere to less than two per cent of the interstellar value.," \ref{fig:5291base} – the steady state opacity is highest at the top of the atmosphere, where it is similar to the interstellar opacity, and decreases gradually bringing the lower third of the atmosphere to less than two per cent of the interstellar value."11601.,.1161 a) The eiipirical influence function as a function of RFT amplitude. ¢=1.1107. the estimates are iade with initial data.," a) The empirical influence function as a function of RFI amplitude, $\sigma=1,n=10^{5}$, the estimates are made with initial data."1162 The curves here and clsewhere are paraimcterized by the fraction of REI iu the total volue of data: e=0.01:0.025:0.5: bj estimates niade usingteamed data: ο) estimates made usingwinsorized d) estimates made as thesquares: e) estimates iade using theestunete aleorithuu: f) estimates made using the algoritlin: ©) estimates made using the algoritliu: h) estimates made using the algorithin of 1) estimates made using the algorithm ofrange., The curves here and elsewhere are parameterized by the fraction of RFI in the total volume of data: $\epsilon=0.01;0.025;0.5$ b) estimates made using data; c) estimates made using d) estimates made as the; e) estimates made using the algorithm; f) estimates made using the algorithm; g) estimates made using the algorithm; h) estimates made using the algorithm of i) estimates made using the algorithm of.11632. Block diagram of computer simulations: winsorization is used for RET mitigation when the total power detector is the backend output as in section L., Block diagram of computer simulations: winsorization is used for RFI mitigation when the total power detector is the backend output as in section 4.1164 1., 1.1165 Results of computer simulations with the algorithin shown in Fig., Results of computer simulations with the algorithm shown in Fig.1166" a) noise with the normal distribution. p=0.0.0=0.5. no b) total power detector output. each poit in this figure corresponds to squaring aud averaging of 10! saluples iu figure a). there are two steps. ""up at point 42100 and “down” at poiut £200 corresponding to the increase of σ froin value 0.5 to the value a|Ao.Ao=0.05. c) interference is added to the noise a): random impulses with the Poisson distibutiou (A= 0.01) aud the lognormal disrtibution of amplitudes (100211—10. standard d) total power detector output with input signal ο) total power detector output with input signal c) aud preliminary wiusorization (equation (9)). note the difference of scale in d) and e)."," a) noise with the normal distribution, $\mu=0.0, \sigma=0.5$, no b) total power detector output, each point in this figure corresponds to squaring and averaging of $10^4$ samples in figure a), there are two steps, “up” at point $\#100$ and “down” at point $\#200$ corresponding to the increase of $\sigma$ from value 0.5 to the value $\sigma+\Delta \sigma, \Delta \sigma=0.05$ c) interference is added to the noise a): random impulses with the Poisson distibution $\lambda=0.04$ ) and the lognormal disrtibution of amplitudes (mean=10, standard d) total power detector output with input signal e) total power detector output with input signal c) and preliminary winsorization (equation (9)), note the difference of scale in d) and e)."11674. Block diagram of computer simulatious: exponential weighting is used for RET mitigation in the frequency domain when the total power detector is the backend output as iu section [., Block diagram of computer simulations: exponential weighting is used for RFI mitigation in the frequency domain when the total power detector is the backend output as in section 4.1168 2 (pulsar or the correlator as in section [., 2 (pulsar or the correlator as in section 4.1169 3. (, 3. (1170vadiointerferometric observations).,radiointerferometric observations).1171 Results of computer simulations of exponcutial weighting with the algorithm shown in Fig., Results of computer simulations of exponential weighting with the algorithm shown in Fig.1172 a) time-frequency prescutation of power spectrum consisting of svsteni noise. enussion and absorption lines and RET (randomly binary-phase manipulated signals). L-50 time sections of spectrum divided ou 256 channels. cach spectrmu is the mean of AZ=100 instantaneous spectra:," a) time-frequency presentation of power spectrum consisting of system noise, emission and absorption lines and RFI (randomly binary-phase manipulated signals), L=50 time sections of spectrum divided on 256 channels, each spectrum is the mean of $M=100$ instantaneous spectra;"1173fraction.,fraction.1174 Εις interpretation is highly simplified in light of the fact that the results have been obtained with data taken in dillerent. restframe bands., This interpretation is highly simplified in light of the fact that the results have been obtained with data taken in different restframe bands.1175 In order to investigate further and better constrain the mass growth and evolution in the number of satellite galaxies per halo over a larger redshift range. one needs to have samples from the same survey at low redshifts.," In order to investigate further and better constrain the mass growth and evolution in the number of satellite galaxies per halo over a larger redshift range, one needs to have samples from the same survey at low redshifts."1176 This can be done with samples from deeper ancl wider redshift surveys., This can be done with samples from deeper and wider redshift surveys.1177 Llere we have concentrated on Iuminosity-threshold samples Icacding to a link between the luminosity of galaxies and the uncerlsing dark matter distribution., Here we have concentrated on luminosity-threshold samples leading to a link between the luminosity of galaxies and the underlying dark matter distribution.1178 The present paper can be seen às à precursor to many studies that can be carried out with larger samples than the VVDS. including CLI - conclitional luminosity function studies (e.g. van den Bosch et al.," The present paper can be seen as a precursor to many studies that can be carried out with larger samples than the VVDS, including CLF - conditional luminosity function studies (e.g. van den Bosch et al."1179 2003. etc).," 2003, etc.),"1180 analyses with galaxy samples of cillerent stellar masses (Zheng ct al., analyses with galaxy samples of different stellar masses (Zheng et al.1181 2007). ete... Phev will certainly: ade to the understanding of the vast pool of underlving clark matter properties anc hopefully obtain tighter constraints on models of galaxy. formation.," 2007), etc.. They will certainly add to the understanding of the vast pool of underlying dark matter properties and hopefully obtain tighter constraints on models of galaxy formation."1182 UA would like to acknowledge funding from the Marie Curie training network supported by the European Communitys Sixth Framework. Programme (FPG)., UA would like to acknowledge funding from the Marie Curie training network supported by the European Community's Sixth Framework Programme (FP6).1183 UA also. thanks Alessandro Sozzetti and Martin. Wilbineer for helpful discussions., UA also thanks Alessandro Sozzetti and Martin Kilbinger for helpful discussions.1184 “Phe authors thank the anonymous referee. [or very useful comments and suggestions that helped improve he paper., The authors thank the anonymous referee for very useful comments and suggestions that helped improve the paper.1185 This research program has been developed within he framework of the VVD$S consortium., This research program has been developed within the framework of the VVDS consortium.1186 This work has »en Funded in part by the ANI program ANR-05-BLAN-1283 and partially supported. by the CNRS-INSU and its Programme National de Cosmologic (France). and by the Italian Ministry (MIUIU) erants COLIN2000 (AIAIO2037133) and COFIN2003 (No.," This work has been funded in part by the ANR program ANR-05-BLAN-0283 and partially supported by the CNRS-INSU and its Programme National de Cosmologie (France), and by the Italian Ministry (MIUR) grants COFIN2000 (MM02037133) and COFIN2003 (No."1187 2003020150) and by ΝΑΙ erants (PRIN-INAF 2005) and the grant. of Polish Ministry. of Science and Higher. Eclueation PDZ/MNISW/07/2006/34., 2003020150) and by INAF grants (PRIN-INAF 2005) and the grant of Polish Ministry of Science and Higher Education PBZ/MNiSW/07/2006/34.1188 The VLT-VIIUMOS observations have been carried. out. on euaranteed time (CLO) allocated by the European Southern Observatory (ESO) to the VIRALOS consortium. under a contractual agreement between the Centre National cle la Recherche Scientifique of France. heading a consortium of Freneh and dBtalian institutes. and ESO. to clesign. manufacture and test the VIAIOS instrument.," The VLT-VIRMOS observations have been carried out on guaranteed time (GTO) allocated by the European Southern Observatory (ESO) to the VIRMOS consortium, under a contractual agreement between the Centre National de la Recherche Scientifique of France, heading a consortium of French and Italian institutes, and ESO, to design, manufacture and test the VIMOS instrument."1189kinematics.,kinematics.1190 The larger uncertainty in modelling them could be due to the limitations of the templates used here., The larger uncertainty in modelling them could be due to the limitations of the templates used here.1191 We classify them as possible mergers or merger remnants in the following., We classify them as possible mergers or merger remnants in the following.1192 In summary. we find that among 33 distant galaxies. 17 are robustly and 9 are possibly reproduced by models of major mergers.," In summary, we find that among 33 distant galaxies, 17 are robustly and 9 are possibly reproduced by models of major mergers."1193 In our simplified model. our goal is just to identify which configuration (phase. orbit. mass ratio. pericenter. see Table 3) is able to reproduce both morphology and kinematics.," In our simplified model, our goal is just to identify which configuration (phase, orbit, mass ratio, pericenter, see Table 3) is able to reproduce both morphology and kinematics."1194 There are several possible biases in such an exercise and several of them have been discussed above., There are several possible biases in such an exercise and several of them have been discussed above.1195 It is however interesting to examine the overall distribution of the configurations parameters that could reproduce the distant starbursts as mergers., It is however interesting to examine the overall distribution of the configurations parameters that could reproduce the distant starbursts as mergers.1196 First. we may consider the mass ratio between the two interlopers.," First, we may consider the mass ratio between the two interlopers."1197 For each configuration in which the two interlopers can be identified. we have used z-band photometry to calculate the mass ratio (see Table 2).," For each configuration in which the two interlopers can be identified, we have used z-band photometry to calculate the mass ratio (see Table 2)."1198 However many starbursts have been identified with merger remnants for which we derive the mass ratio from the modelling., However many starbursts have been identified with merger remnants for which we derive the mass ratio from the modelling.1199 Figure 3 (top) shows a distribution with two peaks at 1:1 and 3:1 dog(W2/M))=0 and -0.48. respectively). which are obviously related to the adoptec methodology.," Figure 3 (top) shows a distribution with two peaks at 1:1 and 3:1 $M_{2}$ $M_{1}$ )=0 and -0.48, respectively), which are obviously related to the adopted methodology."1200 Photometric estimates of the mass ratio can be done for mergers before the second passage (see Figures 1 and 2) when the two components can be separated., Photometric estimates of the mass ratio can be done for mergers before the second passage (see Figures 1 and 2) when the two components can be separated.

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