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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)

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

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

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

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

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 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)

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)