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The strong equivalence principle is violated by gravity theories of Milgromian dynamics (MOND) through the action of the external field effect. We test two different Lagrangian theories AQUAL and QUMOND based on their numerical solutions of the external field effect, by comparing two independent estimates of the mean external field strength of the nearby universe: a theory-deduced value from fitting the outer rotation curves of 114 galaxies and an empirical value from the large-scale distribution of cosmic baryons. The AQUAL-deduced external field strength from rotation curves agrees with that from the large-scale cosmic environment, while QUMOND-deduced value is somewhat higher. This suggests that AQUAL is likely to be preferred over QUMOND as an effective non-relativistic limit of a potential relativistic modified gravity theory., Comment: 6 pages, 2 figures, 1 table (results revised, conclusions strengthened)

The missing gravity in galaxies requires dark matter, or alternatively a modification of gravity or inertia. These theoretical possibilities of fundamental importance may be distinguished by the statistical relation between the observed centripetal acceleration of particles in orbital motion and the expected Newtonian acceleration from the observed distribution of baryons in galaxies. Here predictions of cold dark matter halos, modified gravity, and modified inertia are compared and tested by a statistical sample of galaxy rotation curves from the Spitzer Photometry and Accurate Rotation Curves (SPARC) database. Modified gravity under an estimated mean external field correctly predicts the observed statistical relation of accelerations from both the inner and outer parts of rotation curves. Taken at face value there is a $6.9\sigma$ difference between the inner and outer parts on an acceleration plane which would be inconsistent with current proposals of modified inertia. Removing galaxies with possible systematic concerns such as central bulges or special inclinations does not change this trend. Cold dark matter halos predict a systematically deviating relation from the observed one. All aspects of rotation curves are most naturally explained by modified gravity., Comment: ApJ, in press (results revised, conclusions unchanged)

In MOND (modified Newtonian dynamics)-based theories the strong equivalence principle is generically broken in an idiosyncratic manner, manifested in the action of an "external field effect (EFE)". The internal dynamics in a self-gravitating system is affected even by a constant external field. In disk galaxies the EFE can induce warps and modify the rotational speeds. Due to the non-linearity of MOND, it is difficult to derive analytic expressions of this important effect in a disk. Here we study numerically the EFE in two non-relativistic Lagrangian theories of MOND: the `Aquadratic-Lagrangian' theory (AQUAL) and `Quasilinear MOND' (QUMOND). For AQUAL we consider only the axisymmetric field configurations with the external field along the disk axis, or a spherical galaxy with test-particle orbits inclined to the external field. For the more manageable QUMOND we calculate also the three-dimensional field configurations, with the external field inclined to the disk axis. We investigate particularly to what degree an external field modifies the quasi-flat part of rotation curves. While our QUMOND results agree well with published numerical results in QUMOND, we find that AQUAL predicts weaker EFE than published AQUAL results. However, AQUAL still predicts stronger EFE than QUMOND, which demonstrates current theoretical uncertainties. We also illustrate how the MOND prediction on the rising part of the rotation curve, in the inner parts, depends largely on disk thickness but only weakly on a plausible external field for a fixed galaxy model. Finally, we summarize our results for the outer parts as an improved, approximate analytic expression., Comment: Astrophysical Journal, accepted (7 figures, 1 table)

Theories of modified gravity generically violate the strong equivalence principle, so that the internal dynamics of a self-gravitating system in free fall depends on the strength of the external gravitational field (the external field effect). We fit rotation curves (RCs) from the SPARC database with a model inspired by Milgromian dynamics (MOND), which relates the outer shape of a RC to the external Newtonian field from the large-scale baryonic matter distribution through a dimensionless parameter $e_{\rm N}$. We obtain a $>4��$ statistical detection of the external field effect (i.e. $e_{\rm N}>0$ on average), confirming previous results. We then locate the SPARC galaxies in the cosmic web of the nearby Universe and find a striking contrast in the fitted $e_{\rm N}$ {values} for galaxies in underdense versus overdense regions. Galaxies in an underdense region between 22 and 45 Mpc from the celestial axis in the northern sky have RC fits consistent with $e_{\rm N}\simeq0$, while those in overdense regions adjacent to the CfA2 great wall and the Perseus-Pisces supercluster return $e_{\rm N}$ that are a factor of two larger than the median for SPARC galaxies. We also calculate independent estimates of $e_{\rm N}$ from galaxy survey data and find that they agree with the $e_{\rm N}$ inferred from the RCs within the uncertainties, the chief uncertainty being the spatial distribution of baryons not contained in galaxies or clusters., Astrophysical Journal, in press, 13 figures, 3 tables

The strong equivalence principle (SEP) distinguishes General Relativity from other viable theories of gravity. The SEP demands that the internal dynamics of a self-gravitating system under free-fall in an external gravitational field should not depend on the external field strength. We test the SEP by investigating the external field effect (EFE) in Milgromian dynamics (MOND), proposed as an alternative to dark matter in interpreting galactic kinematics. We report a detection of this EFE using galaxies from the Spitzer Photometry and Accurate Rotation Curves (SPARC) sample together with estimates of the large-scale external gravitational field from an all-sky galaxy catalog. Our detection is threefold: (1) the EFE is individually detected at $8\sigma$ to $11\sigma$ in "golden" galaxies subjected to exceptionally strong external fields, while it is not detected in exceptionally isolated galaxies, (2) the EFE is statistically detected at more than $4\sigma$ from a blind test of 153 SPARC rotating galaxies, giving a mean value of the external field consistent with an independent estimate from the galaxies' environments, and (3) we detect a systematic downward trend in the weak gravity part of the radial acceleration relation at the right acceleration predicted by the EFE of the MOND modified gravity. Tidal effects from neighboring galaxies in the $\Lambda$CDM context are not strong enough to explain these phenomena. They are not predicted by existing $\Lambda$CDM models of galaxy formation and evolution, adding a new small-scale challenge to the $\Lambda$CDM paradigm. Our results point to a breakdown of the SEP, supporting modified gravity theories beyond General Relativity., Comment: ApJ (published), 14 figures, 2 tables (several environmental gravitational fields corrected, Table 2 indexing error fixed, and Figs 5 & 6 revised from an Erratum accepted for publication)

arXiv:2010.10779v2, Dark matter phenomena in rotationally supported galaxies exhibit a characteristic acceleration scale of g† ≈ 1.2 × 10−10 m s−2. Whether this acceleration is a manifestation of a universal scale, or merely an emergent property with an intrinsic scatter, has been debated in the literature. Here we investigate whether a universal acceleration scale exists in dispersion-supported galaxies using two uniform sets of integral field spectroscopy (IFS) data from SDSS-IV MaNGA and ATLAS3D. We apply the spherical Jeans equation to 15 MaNGA and 4 ATLAS3D slow-rotator E0 (i.e., nearly spherical) galaxies. Velocity dispersion profiles for these galaxies are well determined with observational errors under control. Bayesian inference indicates that all 19 galaxies are consistent with a universal acceleration of g† = 1.5+0.9−0.6 × 10−10 m s−2. Moreover, all 387 data points from the radial bins of the velocity dispersion profiles are consistent with a universal relation between the radial acceleration traced by dynamics and that predicted by the observed distribution of baryons. This universality remains if we include 12 additional non-E0 slow-rotator elliptical galaxies from ATLAS3D. Finally, the universal acceleration from MaNGA and ATLAS3D is consistent with that for rotationally supported galaxies, so our results support the view that dark matter phenomenology in galaxies involves a universal acceleration scale., This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2019R1F1A1062477). M.B. acknowledges support from the NFS grant AST-1816330. H.D.S. acknowledges support from the Centro Superior de Investigaciones Cientificas PIE2018-50E099.

Spatially resolved kinematics of nearby galaxies has shown that the ratio of dynamical- to stellar population-based estimates of the mass of a galaxy ($M_*^{\rm JAM}/M_*$) correlates with $\sigma_e$, if $M_*$ is estimated using the same IMF for all galaxies and the stellar M/L ratio within each galaxy is constant. This correlation may indicate that, in fact, the IMF is more dwarf-rich for galaxies with large $\sigma$. We use this correlation to estimate a dynamical or IMF-corrected stellar mass, $M_*^{\rm \alpha_{JAM}}$, from $M_{*}$ and $\sigma_e$ for a sample of $6 \times 10^5$ SDSS galaxies for which spatially resolved kinematics is not available. We also compute the `virial' mass estimate $k(n,R)\,R_e\,\sigma_R^2/G$, where $n$ is the Sersic index, in the SDSS and ATLAS$^{\rm 3D}$ samples. We show that an $n$-dependent correction must be applied to the $k(n,R)$ values provided by Prugniel & Simien (1997). Our analysis also shows that the shape of the velocity dispersion profile in the ATLAS$^{\rm 3D}$ sample varies weakly with $n$: $(\sigma_R/\sigma_e) = (R/R_e)^{-\gamma(n)}$. The resulting stellar mass functions, based on $M_*^{\rm \alpha_{JAM}}$ and the recalibrated virial mass, are in good agreement. If the $M_*^{\rm \alpha_{JAM}}/M_* - \sigma_e$ correlation is indeed due to the IMF, and stellar M/L gradients can be ignored, then our $\phi(M_*^{\rm \alpha_{JAM}})$ is an estimate of the stellar mass function in which $\sigma_e$-dependent variations in the IMF across the population have been accounted for. Using a Fundamental Plane based observational proxy for $\sigma_e$ produces comparable results. By demonstrating that cheaper proxies are sufficiently accurate, our analysis should enable a more reliable census of the mass in stars for large galaxy samples, at a fraction of the cost. Our results are provided in tabular form., Comment: 17 pages, 19 figures, 4 tables. Accepted for publication by MNRAS. Tables 1, C1 and C2 are provided as ancillary files

We investigate the anisotropy of the stellar velocity dispersions within the effective radius, $R_{\rm e}$, in 24 ATLAS$^{\rm 3D}$ pure-bulge galaxies, 16 of which are kinematic slow rotators (SRs). We allow the spherical anisotropy parameter $\beta$ to be radially varying and allow a radial gradient in the stellar mass-to-light ratio ($M_\star/L$) through the parameter $K$ introduced earlier. The median anisotropy for SRs depends on $K$ as follows: $\langle\beta_{\rm m}\rangle = a + b K$ with $a=0.19\pm 0.05$, $b=-0.13\pm 0.07$ ($\Lambda$CDM) or $a=0.21\pm 0.05$, $b=-0.26\pm 0.08$ (MOND), where $\beta_{\rm m}$ refers to the radially averaged quantity. Under the $\Lambda$CDM paradigm this scaling is tied to a scaling of $\langle f_{\rm DM}\rangle = (0.16\pm 0.03) +(0.31\pm 0.06) K$, where $f_{\rm DM}$ refers to the DM fraction within a sphere of $r=R_{\rm e}$. For $K=0$ (constant $M_\star/L$), we obtain radially biased results with $\langle\beta_{\rm m}\rangle \approx 0.2$ consistent with previous results. However, marginalizing over $0 < K < 1.5$ yields $\langle\beta_{\rm m}\rangle = 0.06 ^{+0.11}_{-0.14}$ with $\langle f_{\rm DM}\rangle = 0.35 \pm 0.08$: isotropy is preferred. This isotropy hides the fact that $\beta_{\rm m}$ is correlated with kinematic features such as counter rotating cores (CRCs), kinematically distinct cores (KDCs), and low-level velocities (LVs): SRs with LVs are likely to be radially biased while SRs with CRCs are likely to be tangentially biased, and SRs with KDCs are intermediate. Existing cosmological simulations allow us to understand these results qualitatively in terms of their dynamical structures and formation histories although there exist quantitative tensions. More realistic cosmological simulations, particularly allowing for $M_\star/L$ gradients, may be required to better understand SRs., Comment: 11 figures, 3 tables, ApJ, accepted for publication

The application of Bayesian techniques to astronomical data is generally non-trivial because the fitting parameters can be strongly degenerated and the formal uncertainties are themselves uncertain. An example is provided by the contradictory claims over the presence or absence of a universal acceleration scale (g$_\dagger$) in galaxies based on Bayesian fits to rotation curves. To illustrate the situation, we present an analysis in which the Newtonian gravitational constant $G_N$ is allowed to vary from galaxy to galaxy when fitting rotation curves from the SPARC database, in analogy to $g_{\dagger}$ in the recently debated Bayesian analyses. When imposing flat priors on $G_N$, we obtain a wide distribution of $G_N$ which, taken at face value, would rule out $G_N$ as a universal constant with high statistical confidence. However, imposing an empirically motivated log-normal prior returns a virtually constant $G_N$ with no sacrifice in fit quality. This implies that the inference of a variable $G_N$ (or g$_{\dagger}$) is the result of the combined effect of parameter degeneracies and unavoidable uncertainties in the error model. When these effects are taken into account, the SPARC data are consistent with a constant $G_{\rm N}$ (and constant $g_\dagger$)., Accepted for publication in A&A Letters

We carry out spherical Jeans modeling of nearly round pure-bulge galaxies selected from the ATLAS$^{\rm 3D}$ sample. Our modeling allows for gradients in the stellar mass-to-light ratio ($M_\star/L$) through analytic prescriptions parameterized with a `gradient strength' $K$ introduced to accommodate any viable gradient. We use a generalized Osipkov-Merritt model for the velocity dispersion (VD) anisotropy. We produce Monte Carlo sets of models based on the stellar VD profiles under both the $\Lambda$CDM and MOND paradigms. Here, we describe the galaxy data, the empirical inputs, and the modeling procedures of obtaining the Monte Carlo sets. We then present the projected dynamical stellar mass, $M_{\rm \star e}$, within the effective radius $R_{\rm e}$, and the fundamental mass plane (FMP) as a function of $K$. We find the scaling of the $K$-dependent mass with respect to the ATLAS$^{\rm 3D}$ reported mass as: $\log_{10} \left[M_{\star{\rm e}}(K)/M_{\star{\rm e}}^{\rm A3D} \right] = a' + b' K$ with $a'=-0.019\pm 0.012$ and $b'=-0.18\pm 0.02$ ($\Lambda$CDM), or $a'=-0.023\pm 0.014$ and $b'=-0.23\pm 0.03$ (MOND), for $0\le K < 1.5$. The FMP has coefficients consistent with the virial expectation and only the zero-point scales with $K$. The median value of $K$ for the ATLAS$^{\rm 3D}$ galaxies is $\langle K\rangle =0.53^{+0.05}_{-0.04}$. We perform a similar analysis of the much larger SDSS DR7 spectroscopic sample. In this case, only the VD within a single aperture is available, so we impose the additional requirement that the VD slope be similar to that in the ATLAS$^{\rm 3D}$ galaxies. Our analysis of the SDSS galaxies suggests a positive correlation of $K$ with stellar mass., Comment: ApJ, in press (32 pages in preprint style including 22 figures; Fig 21 corrected)

We carry out a systematic investigation of the total mass density profile of massive (Mstar~3e11 Msun) early-type galaxies and its dependence on redshift, specifically in the range 0, Comment: 14 pages, 8 figures. MNRAS, accepted. Main result of the paper in Figure 2

Within a galaxy the stellar mass-to-light ratio $\Upsilon_*$ is not constant. Spatially resolved kinematics of nearby early-type galaxies suggest that allowing for a variable initial mass function (IMF) returns significantly larger $\Upsilon_*$ gradients than if the IMF is held fixed. If $\Upsilon_*$ is greater in the central regions, then ignoring the IMF-driven gradient can overestimate $M_*^{\rm dyn}$ by as much as a factor of two for the most massive galaxies, though stellar population estimates $M_*^{\rm SP}$ are also affected. Large $\Upsilon_*$-gradients have four main consequences: First, $M_*^{\rm dyn}$ cannot be estimated independently of stellar population synthesis models. Second, if there is a lower limit to $\Upsilon_*$ and gradients are unknown, then requiring $M_*^{\rm dyn}=M_*^{\rm SP}$ constrains them. Third, if gradients are stronger in more massive galaxies, then $M_*^{\rm dyn}$ and $M_*^{\rm SP}$ can be brought into agreement, not by shifting $M_*^{\rm SP}$ upwards by invoking constant bottom-heavy IMFs, as advocated by a number of recent studies, but by revising $M_*^{\rm dyn}$ estimates in the literature downwards. Fourth, accounting for $\Upsilon_*$ gradients changes the high-mass slope of the stellar mass function $\phi(M_*^{\rm dyn})$, and reduces the associated stellar mass density. These conclusions potentially impact estimates of the need for feedback and adiabatic contraction, so our results highlight the importance of measuring $\Upsilon_*$ gradients in larger samples., Comment: 13 pages, 7 figures, MNRAS in press

We carry out a systematic investigation of the total mass density profile of massive (Mstar>2e11 Msun) early-type galaxies and its dependence on galactic properties and host halo mass with the aid of a variety of lensing/dynamical data and large mock galaxy catalogs. The latter are produced via semi-empirical models that, by design, are based on just a few basic input assumptions. Galaxies, with measured stellar masses, effective radii and S��rsic indices, are assigned, via abundance matching relations, host dark matter halos characterized by a typical LCDM profile. Our main results are as follows: (i) In line with observational evidence, our semi-empirical models naturally predict that the total, mass-weighted density slope at the effective radius gamma' is not universal, steepening for more compact and/or massive galaxies, but flattening with increasing host halo mass. (ii) Models characterized by a Salpeter or variable initial mass function and uncontracted dark matter profiles are in good agreement with the data, while a Chabrier initial mass function and/or adiabatic contractions/expansions of the dark matter halos are highly disfavored. (iii) Currently available data on the mass density profiles of very massive galaxies (Mstar>1e12 Msun), with Mhalo>3e14 Msun, favor instead models with a stellar profile flatter than a S��rsic one in the very inner regions (r, 23 pages, 10 figures, 3 Appendices (with an extra 7 figures). ApJ, accepted. Main results in Figures 3, 5, 6, 8

The central regions of nearby elliptical galaxies are dominated by baryons (stars) and provide interesting laboratories for studying the radial acceleration relation (RAR). We carry out exploratory analyses and discuss the possibility of constraining the RAR in the super-critical acceleration range $(10^{-9.5},\hspace{1ex}10^{-8})$~${\rm m}~{\rm s}^{-2}$ using a sample of nearly round pure-bulge (spheroidal, dispersion-dominated) galaxies including 24 ATLAS$^{\rm 3D}$ galaxies and 4201 SDSS galaxies covering a wide range of masses, sizes and luminosity density profiles. We consider a range of current possibilities for the stellar mass-to-light ratio ($M_\star/L$), its gradient and dark or phantom matter (DM/PM) halo profiles. We obtain the probability density functions (PDFs) of the parameters of the considered models via Bayesian inference based on spherical Jeans Monte Carlo modeling of the observed velocity dispersions. We then constrain the DM/PM-to-baryon acceleration ratio $a_{\rm X}/a_{\rm B}$ from the PDFs. Unless we ignore observed radial gradients in $M_\star/L$, or assume unreasonably strong gradients, marginalization over nuisance factors suggests $a_{\rm X}/a_{\rm B} = 10^{p} (a_{\rm B}/a_{+1})^q$ with $p = -1.00 \pm 0.03$ (stat) $^{+0.11}_{-0.06}$ (sys) and $q=-1.02 \pm 0.09$ (stat) $^{+0.16}_{-0.00}$ (sys) around a super-critical acceleration $a_{+1}\equiv 1.2\times 10^{-9}~{\rm m}~{\rm s}^{-2}$. In the context of the $\Lambda$CDM paradigm, this RAR suggests that the NFW DM halo profile is a reasonable description of galactic halos even after the processes of galaxy formation and evolution. In the context of the MOND paradigm, this RAR favors the Simple interpolating function but is inconsistent with the vast majority of other theoretical proposals and fitting functions motivated mainly from sub-critical acceleration data., Comment: ApJ, accepted (22 pages including 19 figures)

We assemble a statistical set of global mass models for ~2,000 nearly spherical SDSS galaxies at a mean redshift of 0.12 based on their aperture velocity dispersions and newly derived luminosity profiles in conjunction with published velocity dispersion profiles and empirical properties and relations of galaxy and halo parameters. When two-component (i.e. stellar plus dark) mass models are fitted to the SDSS aperture velocity dispersions, the predicted velocity dispersion profile (VP) slopes within the effective radius R_eff match well the distribution in observed elliptical galaxies. In contrast, the single-component models cannot reproduce the VP slope distribution. From a number of input variations the models exhibit for the radial range 0.1 R_eff < r < R_eff a tight correlation =(1.865+/-0.008)+(-4.93+/-0.15) where is the mean slope absolute value of the total mass density and is the mean slope of the velocity dispersion profile, which leads to a super-isothermal = 2.15+/-0.04 for =-0.058+/-0.008 in observed elliptical galaxies. Furthermore, the successful two-component models appear to imply a typical slope curvature pattern in the total mass profile because for the observed steep luminosity (stellar mass) profile and the weak lensing inferred halo profile at large radii a total mass profile with monotonically varying slope would require too high DM density in the optical region giving rise to too large aperture velocity dispersion and too shallow VP., Comment: 21 pages, 19 figures, 2 tables, MNRAS, in press

We employ a bias-corrected abundance matching technique to investigate the coevolution of the LCDM dark halo mass function (HMF), the observationally derived velocity dispersion and stellar mass functions (VDF, SMF) of galaxies between z=1 and 0. We use for the first time the evolution of the VDF constrained through strong lensing statistics by Chae (2010) for galaxy-halo abundance matching studies. As a local benchmark we use a couple of z ~ 0 VDFs (a Monte-Carlo realised VDF based on SDSS DR5 and a directly measured VDF based on SDSS DR6). We then focus on connecting the VDF evolution to the HMF evolution predicted by N-body simulations and the SMF evolution constrained by galaxy surveys. On the VDF-HMF connection, we find that the local dark halo virial mass-central stellar velocity dispersion (Mvir-sigma) relation is in good agreement with the individual properties of well-studied low-redshift dark haloes, and the VDF evolution closely parallels the HMF evolution meaning little evolution in the Mvir-sigma relation. On the VDF-SMF connection, it is also likely that the stellar mass-stellar velocity dispersion (Mstar-sigma) relation evolves little taking the abundance matching results together with other independent observational results and hydrodynamic simulation results. Our results support the simple picture that as the halo grows hierarchically, the stellar mass and the central stellar velocity dispersion grow in parallel. We discuss possible implications of this parallel coevolution for galaxy formation and evolution under the LCDM paradigm.

We study galaxy evolution from z=1 to z=0 as a function of velocity dispersion sigma for galaxies with sigma > 95 km/s based on the measured and Monte Carlo realised local velocity dispersion functions (VDFs) of galaxies and the revised statistical properties of 30 strongly-lensed sources. We assume that the total (luminous plus dark) mass profile of a galaxy is isothermal in the optical region for 0 < z < 1 as suggested by mass modelling of lensing galaxies. For the evolutionary behaviours of the VDFs we find that: (1) the number density of massive (mostly early-type) galaxies with sigma > 200 km/s evolves differentially in the way that the number density evolution is greater at a higher velocity dispersion; (2) the number density of intermediate and low mass early-type galaxies (95 km/s < sigma < 200 km/s) is nearly constant; (3) the late-type VDF transformed from the Monte Carlo realised circular velocity function is consistent with no evolution in its shape or integrated number density consistent with galaxy survey results. These evolutionary behaviours of the VDFs are strikingly similar to those of the dark halo mass function (DMF) from N-body simulations and the stellar mass function (SMF) predicted by recent semi-analytic models of galaxy formation under the current LambdaCDM hierarchical structure formation paradigm. Interestingly, the VDF evolutions appear to be qualitatively different from ``stellar mass-downsizing'' evolutions obtained by many galaxy surveys. The coevolution of the DMF, the VDF and the SMF is investigated in quantitative detail in a following paper. We consider several possible systematic errors for the lensing analysis and find that they are not likely to alter the conclusions.(abridged), MNRAS, accepted (20 pages, 12 figures), parts of section 6 of v2 moved to a following work

Modified Newtonian dynamics (MOND) provides a paradigm alternative to dark matter that has been successful in fitting and predicting the rich phenomenology of rotating disc galaxies. There have also been attempts to test MOND in dispersion-supported early-type galaxies, but it remains unclear whether MOND can fit the various empirical properties of early-type galaxies. As a way of rigorously testing MOND in elliptical galaxies we calculate the MOND-predicted velocity dispersion profiles (VDPs) in the inner regions of $\sim 2000$ nearly round SDSS elliptical galaxies under a variety of assumptions on VD anisotropy, and then compare the predicted distribution of VDP slopes with the observed distribution in 11 ATLAS3d galaxies selected with essentially the same criteria. We find that the MOND model parameterised with an interpolating function that works well for rotating galaxies can also reproduce the observed distribution of VDP slopes based only on the observed stellar mass distribution without DM or any other galaxy-to-galaxy varying factor. This is remarkable in view that Newtonian dynamics with DM requires a specific amount and/or profile of DM for each galaxy in order to reproduce the observed distribution of VDP slopes. When we analyse non-round galaxy samples using the MOND-based spherical Jeans equation, we do not find any systematic difference in the mean property of the VDP slope distribution compared with the nearly round sample. However, in line with previous studies of MOND through individual analyses of elliptical galaxies, varying MOND interpolating function or VD anisotropy can lead to systematic change in the VDP slope distribution, indicating that a statistical analysis of VDPs can be used to constrain specific MOND models with an accurate measurement of VDP slopes or a prior constraint on VD anisotropy., Comment: 10 pages, 8 figures, MNRAS, accepted

Extensive analyses of statistical strong gravitational lensing are performed based on the final Cosmic Lens All Sky Survey (CLASS) well-defined statistical sample of flat spectrum radio sources and current estimates of galaxy luminosity functions per morphological type. The analyses are done under the assumption that galactic lenses are well-approximated by singular isothermal ellipsoids and early-type galaxies evolved passively since redshift $z \sim 1$. Depending on how the late-type galaxy population is treated (i.e., whether its characteristic velocity dispersion is constrained or not), we find for a flat universe with a cosmological constant that the present matter fraction of the present critical density $\Omega_{\rm m} = 0.31^{+0.27}_{-0.14}$ (68%) for the unconstrained case or $0.40^{+0.28}_{-0.16}$ (68%) for the constrained case, with an additional systematic uncertainty of $\approx 0.11$ arising from the present uncertainty in the distribution of CLASS sources in redshift and flux density. For a flat universe with a constant equation of state for dark energy w = $p_x$(pressure)/$\rho_x$(energy density), we find that $w < -0.55^{+0.18}_{-0.11}$ (68%) for the unconstrained case or $w < -0.41^{+0.28}_{-0.16}$ (68%) for the constrained case. For the equal frequencies of oblates and prolates, we find that $\sigma_{*}^{(e)} = 198^{+22}_{-18}$ km s$^{-1}$ (68%) for a `steep' $\alpha^{(e)}=-1$ or $\sigma_{*}^{(e)} = 181^{+18}_{-15}$ km s$^{-1}$ (68%) for a `shallow' $\alpha^{(e)}=-0.54$. Finally, from the relative frequencies of doubly-imaged sources and quadruply-imaged sources, we find that a mean projected mass ellipticity of early-type galaxies $\bar{\epsilon}_{\rm mass} = 0.42$ with a 68% lower limit of 0.28. (Abridged), Comment: 31 pages, 12figures, 6 tables, to appear in MNRAS (referee comments incorporated, a section on future prospects added)

We report the final results of the search for gravitationally lensed flat-spectrum radio sources found in the combination of CLASS (Cosmic Lens All Sky Survey) and JVAS (Jodrell-Bank VLA Astrometric Survey). VLA observations of 16,503 sources have been made, resulting in the largest sample of arcsec-scale lens systems available. Contained within the 16,503 sources is a complete sample of 11,685 sources having two-point spectral indices between 1.4 and 5 GHz flatter than -0.5 and 5 GHz flux densities $\geq$30 mJy. A subset of 8,958 sources form a well-defined statistical sample suitable for analysis of the lens statistics. We describe the systematic process by which 149 candidate lensed sources were picked from the statistical sample on the basis of possessing multiple compact components in the 0.2 arcsec-resolution VLA maps. Candidates were followed up with 0.05 arcsec resolution MERLIN and 0.003 arcsec VLBA observations at 5 GHz and rejected as lens systems if they failed well-defined surface brightness and/or morphological tests. Maps for all the candidates can be found on the World Wide Web at http://www.jb.man.ac.uk/research/gravlens/index.html We summarize the properties of each of the 22 gravitational lens systems in JVAS/CLASS. Twelve are double-image systems, nine are four-image systems and one is a six-image system. Thirteen constitute a statistically well-defined sample giving a point-source lensing rate of 1:690$\pm$190. The interpretation of the results in terms of the properties of the lensing galaxy population and cosmological parameters will be published elsewhere. (Abridged), v2: web link in the abstract fixed; some corrections made in section 6.1

A new two-image gravitational lens system has been discovered as a result of the Cosmic Lens All-Sky Survey (CLASS). Radio observations with the VLA, MERLIN and the VLBA at increasingly higher resolutions all show two components with a flux density ratio of ~7:1 and a separation of 1.34". Both components are compact and have the same spectral index. Followup observations made with the VLA at 8.4 GHz show evidence of a feature to the south-east of the brighter component and a corresponding extension of the weaker component to the north-west. Optical observations with the WHT show ~1.7" extended emission aligned in approximately the same direction as the separation between the radio components with an R-band magnitude of 21.8 +/- 0.4., 6 pages, 5 figures, accepted by MNRAS

We report the results of HST WFPC2 broadband F555W and F702W photometric and F555W polarimetric observations of the "Cloverleaf" QSO H1413+1143. This is a four-component gravitationally-lensed broad absorption line (BAL) QSO. Observations were obtained at two epochs in March 1999 and June 1999 separated by about 100 days. The goal of our program was to detect any relative changes among the components and between the two epochs. Over this time baseline we detected an approximately 0.07 mag dimming in component D of the lensed image, which we interpret as evidence for microlensing. In March 1999 we find significant evidence for a difference in the relative linear polarization of component D in comparison to the other three components; in June 1999 the combined polarization of the Cloverleaf components was lower. In March 1999 the apparently microlensed component D has a rotated polarization position angle and a somewhat higher degree of polarization than the other three components. We suggest that this difference in polarization is due to microlensing magnification of part of a scattered-light (i.e. polarized) continuum-producing region. The results indicate that in the Cloverleaf the size-scale of the polarized scattered-light region exceeds about 10^{16} cm but lies interior to the region producing the broad emission lines (< 10^{18} cm)., 21 pages, accepted for publication in ApJ

We study profiles of mass density, velocity dispersion (VD), and their combination using $\sim 2000$ nearly spherical and rotation-free SDSS galaxies. For observational stellar mass density $\rho_{\star}(r)$ we consider a range of dark matter (DM) distribution $\rho_{\rm{DM}}(r)$ and VD anisotropy $\beta(r)$ to investigate radial stellar VD $\sigma_{\rm\star r}(r)$ using the spherical Jeans equation. While mass and VD profiles vary appreciably depending on DM distribution and anisotropy, the pseudo-phase-space density-like combination $\rho(r)/\sigma_{\rm\star r}^3(r)$ with total density $\rho(r)= \rho_{\star}(r)+\rho_{\rm{DM}}(r)$ is nearly universal. In the optical region the minus of its logarithmic slope has a mean value of $\langle\chi\rangle\approx 1.86$--$1.90$ with a galaxy-to-galaxy rms scatter of $\approx 0.04$--$0.06$, which is a few times smaller than that of $\rho(r)$ profiles. The scatter of $\chi$ can be increased by invoking wildly varying anisotropies that are, however, less likely because they would produce too large a scatter of line-of-sight VD profiles. As an independent check of this universality we analyze stellar orbit-based dynamical models of 15 ETGs of Coma cluster provided by J. Thomas. Coma ETGs, with $\sigma_{\star\rm{r}}(r)$ replaced by the rms velocity of stars $v_{\star\rm{rms}}(r)$ including net rotation, exhibit a similar universality with a slope of $\chi= 1.93\pm 0.06$. Remarkably, the inferred values of $\chi$ for ETGs match well the slope $\approx 1.9$ predicted by N-body simulations of DM halos. We argue that the inferred universal nature of $\rho(r)/\sigma_{\rm\star r}^3(r)$ cannot be fully explained by equilibrium alone, implying that some astrophysical factors conspire and/or it reflects a fundamental principle in collisionless formation processes., Comment: ApJL, revised and accepted for publication

The gravitational lens 0957+561 is modeled utilizing recent observations of the galaxy and the cluster as well as previous VLBI radio data which have been re-analyzed recently. The galaxy is modeled by a power-law elliptical mass density with a small core while the cluster is modeled by a non-singular power-law sphere as indicated by recent observations. Using all of the current available data, the best-fit model has a reduced chi-squared of approximately 6 where the chi-squared value is dominated by a small portion of the observational constraints used; this value of the reduced chi-squared is similar to that of the recent FGSE best-fit model by Barkana et al. However, the derived value of the Hubble constant is significantly different from the value derived from the FGSE model. We find that the value of the Hubble constant is given by H_0 = 69 +18/-12 (1-K) and 74 +18/-17 (1-K) km/s/Mpc with and without a constraint on the cluster's mass, respectively, where K is the convergence of the cluster at the position of the galaxy and the range for each value is defined by Delta chi-squared = reduced chi-squared. Presently, the best achievable fit for this system is not as good as for PG 1115+080, which also has recently been used to constrain the Hubble constant, and the degeneracy is large. Possibilities for improving the fit and reducing the degeneracy are discussed., 22 pages in aaspp style including 6 tables and 5 figures, ApJ in press (Nov. 1st issue)

We investigate gravitational lens models for the quadruply-lensed Cloverleaf BAL QSO H1413+1143 based on the HST WFPC/WFPC2 astrometric and photometric data of the system by Turnshek et al. and the HST NICMOS-2 data by Falco et al. The accurate image positions and the dust-extinction-corrected relative amplifications, along with a possible detection of the lensing galaxy in the infrared, permit more accurate lens models than were previously possible. While more recent models are qualitatively consistent with the HST data, none of the previous models considered the dust-extinction-corrected relative amplifications of the image components. We use the power-law elliptical mass model to fit the HST data. We find that a single elliptical galaxy perturbed by an external shear can fit the image positions within the observational uncertainties; however, the predicted relative magnifications are only roughly consistent with the observational relative amplifications. We find that a primary galaxy combined with a secondary galaxy in the vicinity of the Cloverleaf or a cluster centered (south-)west of the Cloverleaf can fit both the image positions and relative amplifications within the observational uncertainties. We discuss future observations which could be used to test and/or further constrain lens models of the Cloverleaf.

A detailed study of a power-law lens model is presented for the gravitational lens system Q2237+0305, also known as the Einstein Cross. The adopted three-dimensional distribution for the mass of the lens is more realistic than in previous models and is described by ρ(X, Y, Z) = ρ0[1 + (X/a)2 + (Y/b)2 + (Z/c)2]-ν/2. Hubble Space Telescope (HST) optical positions of the image components and the center of the galactic bulge (Crane et al.) along with radio flux density ratios of the image components (Falco et al.) are used to constrain the model [8 (four relative optical positions) + 3 (relative magnifications) = 11 constraints]. The goodness of fit χ2 is defined using these constraints. The best model has χ2 ≈ 14, which is a better fit than all previous models. We investigate the characteristics of models within the 99% confidence region of parameter space around the best model. We find that the lensing properties (i.e., total image magnification, relative image magnifications, and time delays between image pairs) of models are well described by the ellipticity of the projected mass of the lens, and we calculate a grid of models that illustrates how the lensing properties depend on the ellipticity. We discuss how future observations, such as placing tighter constraints on the brightness of any fifth image, can be used to further constrain the grid of models presented here. The possibility of using the grid of models to place constraints on the Hubble constant is also discussed.

With SDSS galaxy data and halo data from up-to-date N-body simulations we construct a semi-empirical catalog (SEC) of early-type systems by making a self-consistent bivariate statistical match of stellar mass (M_star) and velocity dispersion (sigma) with halo virial mass (M_vir). We then assign stellar mass profile and velocity dispersion profile parameters to each system in the SEC using their observed correlations with M_star and sigma. Simultaneously, we solve for dark matter density profile of each halo using the spherical Jeans equation. The resulting dark matter density profiles deviate in general from the dissipationless profile of NFW or Einasto and their mean inner density slope and concentration vary systematically with M_vir. Statistical tests of the distribution of profiles at fixed M_vir rule out the null hypothesis that it follows the distribution predicted by N-body simulations for M_vir ~< 10^{13.5-14.5} M_solar. These dark matter profiles imply that dark matter density is, on average, enhanced significantly in the inner region of halos with M_vir ~< 10^{13.5-14.5} M_solar supporting halo contraction. The main characteristics of halo contraction are: (1) the mean dark matter density within the effective radius has increased by a factor varying systematically up to ~ 3-4 at M_vir = 10^{12} M_solar, and (2) the inner density slope has a mean of ~ 1.3 with rho(r) ~ r^{-alpha} and a halo-to-halo rms scatter of rms(alpha) ~ 0.4-0.5 for 10^{12} M_solar ~< M_vir ~< 10^{13-14} M_solar steeper than the NFW profile (alpha=1). Based on our results we predict that halos of nearby elliptical and lenticular galaxies can, in principle, be promising targets for gamma-ray emission from dark matter annihilation., 43 pages, 20 figures, JCAP, revised and accepted version

Semi-analytical models of galaxy formation can be used to predict the evolution of the number density of early-type galaxies as a function of the circular velocity at the virial radius, v_{c,vir}. Gravitational lensing probability and separation distribution on the other hand are sensitive to the velocity dispersion (or circular velocity) at about the effective radius. We adopt the singular isothermal ellipsoid (SIE) lens model to estimate the velocity dispersion at the effective radius. We use radio lenses from the Cosmic Lens All-Sky Survey and the PMN-NVSS Extragalactic Lens Survey to study how the velocity dispersions, \sigma_SIE, are related to v_{c,vir}. When we include both the lensing probability and separation distribution as our lensing constraints, we find \sigma_SIE /(200\kms) = [(1.17_{-0.26}^{+0.40}) v_{c,vir}/ (200\kms)]^{0.22^{+0.05}_{-0.04}} for 200\kms \la \sigma_SIE \la 260\kms; at \sigma_SIE = 200\kms, the ratio \sqrt{2} \sigma_SIE / v_{c,vir} is about 1.65^{+0.57}_{-0.37} (68% CL) but decreases to 0.65_{-0.12}^{+0.15} (68% CL) for \sigma_SIE = 260\kms. These results are consistent with those of Seljak (2002) obtained from galaxy-galaxy weak lensing for galaxies of around L_*. However, our results clearly suggest that the ratio must vary significantly as \sigma_SIE is varied and are marginally discrepant with the Seljak results at \sigma_SIE = 260\kms. The scaling \sigma_SIE \propto v_{c,vir}^{0.22\pm 0.05} is broadly consistent with those from galaxy occupation statistics studies and the most recent galaxy-galaxy weak lensing study. (Abridged), Comment: Matches the MNRAS on-line published version

We improve strong lensing constraints on cosmological parameters in light of the new measurement of the velocity dispersion function of early-type galaxies based on the SDSS DR5 data and recent semi-analytical modeling of galaxy formation. Using both the number statistics of the CLASS statistical sample and the image separation distribution of the CLASS and the PANELS radio-selected lenses, we find the cosmological matter density $\Om = 0.25^{+0.12}_{-0.08}$ (68% CL) assuming evolutions of galaxies predicted by a semi-analytical model of galaxy formation and $\Om = 0.26^{+0.12}_{-0.08}$ assuming no evolution of galaxies for a flat cosmology with an Einstein cosmological constant. For a flat cosmology with a generalized dark energy, we find the non-evolving dark energy equation of state $w_x < -1.2$ ($w_x < -0.5$) at the 68% CL (95% CL)., ApJL, accepted (results and presentations revised; conclusions unchanged)

We use the distribution of gravitationally-lensed image separations observed in the Cosmic Lens All-Sky Survey (CLASS) and the PMN-NVSS Extragalactic Lens Survey (PANELS), which are (nearly) complete for the image separation range $0''.3 \le \Delta \theta \le 6''$, to constrain a model velocity dispersion function (VF) of early-type galaxies. Assuming a current concordance cosmological model and adopting a singular isothermal ellipsoid (SIE) model for galactic potentials, we consider constraining both a characteristic velocity dispersion (parameter $\sigma_*$) and the shape of the function (parameters $\alpha$ and $\beta$; Sheth et al. 2003) for $0.3 \la z \la 1 $. If all three parameters are allowed to vary, then none of the parameters can be tightly constrained by the lensing data because of the small size of the sample. If we fix the shape of the function by either the SDSS local stellar VF or an inferred local stellar VF based on the SSRS2 galaxy sample, then the constrained values of $\sigma_*$ are nearly equal to the corresponding stellar values; we have $f_{\rm SIE/center} (\equiv \sigma_{*{\rm SIE}}/\sigma_{*{\rm center}})= 0.90\pm 0.18 {\rm (SDSS)}$ or $1.04 \pm 0.19 {\rm (SSRS2)}$ assuming non-evolution of the function between the present epoch and $z \sim 0.6$. Finally, using only the CLASS statistical sample (Browne et al. 2003) and thus including an absolute multiple-imaging probability, we find that the SDSS stellar VF may have significantly underestimated the abundance of morphologically early-type galaxies., Comment: 18 pages, 3 figures, accepted version for ApJ (referee comments incorporated)

We use gravitational lenses from the Cosmic Lens All-Sky Survey (CLASS) to constrain the evolution of galaxies since redshift $z \sim 1$ in the current $\LCDM$ cosmology. This constraint is unique as it is based on a mass-selected lens sample of galaxies. Our method of statistical analysis is the same as in Chae (2003). We parametrise the early-type number density evolution in the form of $(1+z)^{\nu_n}$ and the velocity dispersion as $(1+z)^{\nu_v}$. We find that $\nu_n=-0.11^{+0.82}_{-0.89}$ ($1\sigma$) if we assume $\nu_v =0$, implying that the number density of early-type galaxies is within 50% to 164% of the present-day value at redshift $z=1$. Allowing the velocity dispersion to evolve, we find that $\nu_v=-0.4^{+0.5}_{-0.4}$ ($1\sigma$), indicating that the velocity dispersion must be within 57% and 107% of the present-day value at $z=1$. These results are consistent with the early formation and passive evolution of early-type galaxies. More stringent limits from lensing can be obtained from future large lens surveys and by using very high-redshift quasars ($z \ga 5$) such as those found from the Sloan Digital Sky Survey., Comment: 10 pages (preprint format), 2 figures, ApJL in press (December 20th issue)

Fourier series solutions to the deflection and magnification by a family of three-dimensional cusped two power-law ellipsoidal mass distributions are presented. The cusped two power-law ellipsoidal mass distributions are characterized by inner and outer power-law radial indices and a break (or, transition) radius. The model family includes mass models mimicking Jaffe, Hernquist, and $��$ models and dark matter halo profiles from numerical simulations. The Fourier series solutions for the cusped two power-law mass distributions are relatively simple, and allow a very fast calculation even for a chosen small fractional calculational error (e.g. $10^{-5}$). These results will be particularly useful for studying lensed systems which provide a number of accurate lensing constraints and for systematic analyses of large numbers of lenses. Subroutines employing these results for the two power-law model and the results by Chae, Khersonsky, & Turnshek for the generalized single power-law mass model are made publicly available., 20 pages (preprint style), ApJ, in press. Also, available at http://www.jb.man.ac.uk/~chae

We present an analytical formulation of gravitational lensing using familiar triaxial power-law mass distributions, where the 3-dimensional mass density is given by $\rho(X,Y,Z) = \rho_0 [1 + (\frac{X}{a})^2 + (\frac{Y}{b})^2 + (\frac{Z}{c})^2]^{-\nu/2}$. The deflection angle and magnification factor are obtained analytically as Fourier series. We give the exact expressions for the deflection angle and magnification factor. The formulae for the deflection angle and magnification factor given in this paper will be useful for numerical studies of observed lens systems. An application of our results to the Einstein Cross can be found in Chae, Turnshek, & Khersonsky (1998). Our series approach can be viewed as a user-friendly and efficient method to calculate lensing properties that is better than the more conventional approaches, e.g., numerical integrations, multipole expansions., Comment: 24 pages, 3 Postscript figures, ApJ in press (October 10th)