Mass Density Profile Research Articles

COMPARING X-RAY AND DYNAMICAL MASS PROFILES IN THE EARLY-TYPE GALAXY NGC 4636

We present the results of an X-ray mass analysis of the early-type galaxy NGC 4636, using Chandra data. We have compared the X-ray mass density profile with that derived from a dynamical analysis of the system's globular clusters (GCs). Given the observed interaction between the central active galactic nucleus and the X-ray emitting gas in NGC 4636, we would expect to see a discrepancy in the masses recovered by the two methods. Such a discrepancy exists within the central ~10kpc, which we interpret as the result of non-thermal pressure support or a local inflow. However, over the radial range ~10-30kpc, the mass profiles agree within the 1-sigma errors, indicating that even in this highly disturbed system, agreement can be sought at an acceptable level of significance over intermediate radii, with both methods also indicating the need for a dark matter halo. However, at radii larger than 30kpc, the X-ray mass exceeds the dynamical mass, by a factor of 4-5 at the largest disagreement. A Fully Bayesian Significance Test finds no statistical reason to reject our assumption of velocity isotropy, and an analysis of X-ray mass profiles in different directions from the galaxy centre suggests that local disturbances at large radius are not the cause of the discrepancy. We instead attribute the discrepancy to the paucity of GC kinematics at large radius, coupled with not knowing the overall state of the gas at the radius where we are reaching the group regime (>30kpc), or a combination of the two.

Pseudo-Newtonian and general relativistic barotropic tori in Schwarzschild–de Sitter spacetimes

Pseudo-Newtonian gravitational potential introduced in spherically symmetric black-hole spacetimes with a repulsive cosmological constant is tested for equilibrium toroidal configurations of barotropic perfect fluid orbiting the black holes. Shapes and potential depths are determined for the marginally stable barotropic tori with uniform distribution of specific angular momentum, using both the pseudo-Newtonian and fully relativistic approach. For the adiabatic (isoentropic) perfect fluid, temperature profiles, mass-density and pressure profiles and total masses of pseudo-Newtonian and relativistic tori are compared providing important information on the relevance of the test-disc approximation in both the approaches. It is shown that the pseudo-Newtonian approach can be precise enough and useful for the modelling of accretion discs in the Schwarzschild–de Sitter spacetimes with the cosmological parameter y = ΛM2/3 ≲ 10−6. For astrophysically relevant black holes with y < 10−25, this statement is tested and shown to be precise in few per cent for both accretion and excretion tori and for the marginally bound, i.e. maximally extended, tori allowing simultaneous inflow to the black hole and outflow to the outer space.

Molecular line profiles of collapsing gas clouds

Emission line profiles of tracer molecule H$_2$CO 140 GHz transition from gravitational core collapsing clouds in the dynamic process of forming protostars are calculated, using a simple ray-tracing radiative transfer model. Three self-similar dynamic inside-out core collapse models -- the conventional polytropic model, the empirical hybrid model and the isothermal model -- for star-forming molecular clouds are examined and compared. The isothermal model cannot produce observed asymmetric double-peak molecular line profiles. The conventional polytropic model, which gives flow velocity, mass density and temperature profiles self-consistently, can produce asymmetric double-peak line profiles for a core collapsing cloud. In particular, the blue peak is stronger than the red peak, consistent with a broad class of molecular line profile observations. The relative strengths of the blue and red peaks within a molecular line profile are determined by the cloud temperature gradient. The conventional polytropic model can be utilized to produce molecular line-profile templates, for extracting dynamical information from line spectra of molecular globules undergoing a gravitational core collapse. We show a sample fit using the 140 GHz H$_2$CO emission line from the central region of the molecular globule B335 by our model with $\gamma=1.2$. The calculation of line profiles and fitting processes also offer a scenario to estimate the protostellar mass, the kernel mass accretion rate, and the evolution time scale of a core collapsing cloud. Our model can be readily adapted to other tracer molecules with more or less constant abundances in star-forming clouds.

Cross-sectional hydrogen content and mass density profiles of diamond-like carbon film by neutron and X-ray reflectivity

The cross-sectional profiles of hydrogen content and mass density of diamond-like carbon (DLC) film were investigated using X-ray and neutron reflectivity. DLC films were prepared using a plasma CVD technique by varying the H 2/(H 2 + CH 4) ratio gas source from 0 to 0.9. The cross-sectional hydrogen content and mass density profiles of the films were calculated by neutron and X-ray reflectivity, and the results were compared with those from elastic recoil detection analysis (ERDA). The fitted simulation showed that the mass density gradually decreased with increasing depth, whereas the hydrogen content increased with depth. In both ERDA and reflectivity measurements, the average hydrogen content was more than 30% in all films and tended to increase with the H 2/(CH 4 + H 2) ratio. However, there was a difference in hydrogen content values between the two analyses ranging from 5.1 % to 8.5%.

CROSS-CORRELATION WEAK LENSING OF SDSS GALAXY CLUSTERS. III. MASS-TO-LIGHT RATIOS

We present measurements of the excess mass-to-light ratio (M/L) measured around MaxBCG galaxy clusters observed in the Sloan Digital Sky Survey. This red-sequence cluster sample includes objects from small groups with M200 ∼ 5 × 1012 h−1 M☉ to clusters with M200 ∼ 1015 h−1 M☉. Using cross-correlation weak lensing, we measure the excess mass density profile above the universal mean for clusters in bins of richness and optical luminosity. We also measure the excess luminosity density measured in the z = 0.25 i band. For both mass and light, we de-project the profiles to produce three-dimensional mass and light profiles over scales from 25 h−1 kpc to 22 h−1 Mpc. From these profiles we calculate the cumulative excess mass ΔM(r) and excess light ΔL(r) as a function of separation from the BCG. On small scales, where , the integrated mass-to-light profile (ΔM/ΔL)(r) may be interpreted as the cluster M/L. We find the (ΔM/ΔL)200, the M/L within r200, scales with cluster mass as a power law with index 0.33 ± 0.02. On large scales, where , the ΔM/ΔL approaches an asymptotic value independent of cluster richness. For small groups, the mean (ΔM/ΔL)200 is much smaller than the asymptotic value, while for large clusters (ΔM/ΔL)200 is consistent with the asymptotic value. This asymptotic value should be proportional to the mean M/L of the universe 〈M/L〉. We find 〈M/L〉b−2M/L = 362 ± 54h (statistical). There is additional uncertainty in the overall calibration at the ∼10% level. The parameter b2M/L is primarily a function of the bias of the L ≲ L* galaxies used as light tracers, and should be of order unity. Multiplying by the luminosity density in the same bandpass we find Ωmb−2M/L = 0.20 ± 0.03, independent of the Hubble parameter.

A local prescription for the softening length in self-gravitating gaseous discs

In 2D-simulations of self-gravitating gaseous discs, the potential is often computed in the framework of "softened gravity" initially designed for N-body codes. In this special context, the role of the softening length LAMBDA is twofold: i) to avoid numerical singularities in the integral representation of the potential (i.e., arising when the relative separation vanishes), and ii) to acount for stratification of matter in the direction perpendicular to the disc mid-plane. So far, most studies have considered LAMBDA as a free parameter and various values or formulae have been proposed without much mathematical justification. In this paper, we demonstrate by means of a rigorous calculus that it is possible to define LAMBDA such that the gravitational potential of a flat disc coincides at order zero with that of a geometically thin disc of the same surface density. Our prescription for LAMBDA, valid in the local, axisymmetric limit, has the required properties i) and ii). It is mainly an analytical function of the radius and disc thickness, and is sensitive to the vertical stratification. For mass density profiles considered (namely, profiles expandable over even powers of the altitude), we find that LAMBDA : i) is independant of the numerical mesh, ii) is always a fraction of the local thickness H, iii) goes through a minimum at the singularity (i.e., at null separation), and iv) is such that 0.13 < LAMBDA/H < 0.29 typically (depending on the separation and on density profile). These results should help us to improve the quality of 2D- and 3D-simulations of gaseous discs in several respects (physical realism, accuracy, and computing time).

DISCREPANT MASS ESTIMATES IN THE CLUSTER OF GALAXIES ABELL 1689

We present a new mass estimate of a well-studied gravitational lensing cluster, Abell 1689, from deep Chandra observations with a total exposure of 200 ks. Within r=200 h-1 kpc, the X-ray mass estimate is systematically lower than that of lensing by 30-50%. At r>200 h-1 kpc, the mass density profiles from X-ray and weak lensing methods give consistent results. The most recent weak lensing work suggest a steeper profile than what is found from the X-ray analysis, while still in agreement with the mass at large radii. Previous studies have suggested that cooler small-scale structures can bias X-ray temperature measurements or that the northern part of the cluster is disturbed. We find these scenarios unlikely to resolve the central mass discrepancy since the former requires 70-90% of the space to be occupied by these cool structures and excluding the northern substructure does not significantly affect the total mass profiles. A more plausible explanation is a projection effect. We also find that the previously reported high hard-band to broad-band temperature ratio in A1689, and many other clusters observed with Chandra, may be resulting from the instrumental absorption that decreases 10-15% of the effective area at ~1.75 keV.

SUBARU WEAK LENSING MEASUREMENTS OF FOUR STRONG LENSING CLUSTERS: ARE LENSING CLUSTERS OVERCONCENTRATED?

We derive radial mass profiles of four strong lensing selected clusters which show prominent giant arcs (Abell 1703, SDSS J1446+3032, SDSS J1531+3414, and SDSS J2111-0115), by combining detailed strong lens modeling with weak lensing shear measured from deep Subaru Suprime-cam images. Weak lensing signals are detected at high significance for all four clusters, whose redshifts range from z=0.28 to 0.64. We demonstrate that adding strong lensing information with known arc redshifts significantly improves constraints on the mass density profile, compared to those obtained from weak lensing alone. While the mass profiles are well fitted by the universal form predicted in N-body simulations of the LCDM model, all four clusters appear to be slightly more centrally concentrated (the concentration parameters c_vir \sim 8) than theoretical predictions, even after accounting for the bias toward higher concentrations inherent in lensing selected samples. Our results are consistent with previous studies which similarly detected a concentration excess, and increases the total number of clusters studied with the combined strong and weak lensing technique to ten. Combining our sample with previous work, we find that clusters with larger Einstein radii are more anomalously concentrated. We also present a detailed model of the lensing cluster A1703 with constraints from multiple image families, and find the dark matter inner density profile to be cuspy with the slope consistent with -1, in agreement with expectations.

Cluster strong lensing in the Millennium simulation: the effect of galaxies and structures along the line-of-sight

We use ray-tracing through the Millennium simulation to study how secondary matter structures along the line-of-sight and the stellar mass in galaxies affect strong cluster lensing, in particular the cross-section for giant arcs. Furthermore, we investigate the distribution of the cluster Einstein radii and the radial distribution of giant arcs. We find that additional structures along the line-of-sight increase the strong-lensing optical depth by ~10-25%, while strong-lensing cross-sections of individual clusters are frequently boosted by as much as ~50%. The enhancement is mainly due to structures that are not correlated with the lens. Cluster galaxies increase the strong-lensing optical depth by up to a factor of 2, while interloping galaxies are not significant. We conclude that these effects need to be taken into account for predictions of the giant arc abundance, but they are not large enough to fully account for the reported discrepancy between predicted and observed abundances. Furthermore, we find that Einstein radii defined via the area enclosed by the critical curve are 10-30% larger than those defined via radial surface mass density profiles. The contributions of radial and tangential arcs to the radial distribution of arcs can be clearly distinguished. The radial distribution of tangential arcs is very broad and extends out to several Einstein radii. Thus, individual arcs are not well suited for constraining Einstein radii.

The origin of the light distribution in spiral galaxies

We analyse a high-resolution, fully cosmological, hydrodynamical disc galaxy simulation, to study the source of the double-exponential light profiles seen in many stellar discs, and the effects of stellar radial migration upon the spatio-temporal evolution of both the disc age and metallicity distributions. We find a "break" in the pure exponential stellar surface brightness profile, and trace its origin to a sharp decrease in the star formation per unit surface area, itself produced by a decrease in the gas volume density due to a warping of the gas disc. Star formation in the disc continues well beyond the break. We find that the break is more pronounced in bluer wavebands. By contrast, we find little or no break in the mass density profile. This is, in part, due to the net radial migration of stars towards the external parts of the disc. Beyond the break radius, we find that ~60% of the resident stars migrated from the inner disc, while ~25% formed in situ. Our simulated galaxy also has a minimum in the age profile at the break radius but, in disagreement with some previous studies, migration is not the main mechanism producing this shape. In our simulation, the disc metallicity gradient flattens with time, consistent with an "inside-out" formation scenario. We do not find any difference in the intensity or the position of the break with inclination, suggesting that perhaps the differences found in empirical studies are driven by dust extinction.

The orbital velocity anisotropy of cluster galaxies: evolution

<i>Context. <i/>In nearby clusters early-type galaxies follow isotropic orbits. The orbits of late-type galaxies are instead characterized by slightly radial anisotropy. Little is known about the orbits of the different populations of cluster galaxies at redshift .<i>Aims. <i/>We investigate the redshift evolution of the orbits of cluster galaxies.<i>Methods. <i/>We use two samples of galaxy clusters spanning similar (evolutionary corrected) mass ranges at different redshifts. The sample of low-redshift (<i>z<i/> ~ 0.0-0.1) clusters is extracted from the ESO Nearby Abell Cluster Survey (ENACS) catalog. The sample of high-redshift (<i>z<i/> ~ 0.4-0.8) clusters is mostly made of clusters from the ESO Distant Cluster Survey (EDisCS). For each of these samples, we solve the Jeans equation for hydrostatic equilibrium separately for two cluster galaxy populations, characterized by the presence and, respectively, absence of emission-lines in their spectra (“ELGs” and “nELGs” hereafter). Using two tracers of the gravitational potential allows to partially break the mass-anisotropy degeneracy which plagues these kinds of analyses.<i>Results. <i/>We confirm earlier results for the nearby cluster sample. The mass profile is well fitted by a Navarro, Frenk & White (NFW) profile with concentration . The mass profile of the distant cluster sample is also well fitted by a NFW profile, but with a slightly lower concentration, as predicted by cosmological simulations of cluster-sized halos. While the mass density profile becomes less concentrated with redshift, the number density profile of nELGs becomes more concentrated with redshift. In nearby clusters, the velocity anisotropy profile of nELGs is close to isotropic, while that of ELGs is increasingly radial with clustercentric radius. In distant clusters the projected phase-space distributions of both nELGs and ELGs are best-fitted by models with radial velocity anisotropy.<i>Conclusions. <i/>No significant evolution is detected for the orbits of ELGs, while the orbits of nELGs evolve from radial to isotropic with time. We speculate that this evolution may be driven by the secular mass growth of galaxy clusters during their fast accretion phase. Cluster mass density profiles and their evolution with redshift are consistent with predictions for cluster-sized halos in <i>Λ<i/> Cold Dark Matter cosmological simulations. The evolution of the nELG number density profile is opposite to that of the mass density profile, becoming less concentrated with time, probably a result of the transformation of ELGs into nELGs.

ERRATUM: “THE SLACS SURVEY. VIII. THE RELATION BETWEEN ENVIRONMENT AND INTERNAL STRUCTURE OF EARLY-TYPE GALAXIES” (2009, ApJ, 690, 670)

We study the relation between the internal structure of early-type galaxies and their environment using 70 strong gravitational lenses from the Sloan ACS Lens Survey. The Sloan database is used to determine two measures of overdensity of galaxies around each lens: the projected number density of galaxies inside the tenth nearest neighbor (\Sigma_{10}) and within a cone of radius one h^{-1} Mpc (D_1). Our main results are: 1) The average overdensity is somewhat larger than unity, consistent with lenses preferring overdense environments as expected for massive early-type galaxies (12/70 lenses are in known groups/clusters). 2) The distribution of overdensities is indistinguishable from that of "twin" non-lens galaxies selected from SDSS to have the same redshift and stellar velocity dispersion \sigma_*. Thus, within our errors, lens galaxies are an unbiased population, and the SLACS results can be generalized to the overall population of early-type galaxies. 3) Typical contributions from external mass distribution are no more than a few per cent, reaching 10-20% (~0.05-0.10 external convergence) only in the most extreme overdensities. 4) No significant correlation between overdensity and slope of the mass density profile of the lens is found. 5) Satellite galaxies (those with a more luminous companion) have marginally steeper mass density profiles than central galaxies (those without). This result suggests that tidal stripping may affect the mass structure of early-type galaxies down to kpc scales probed by strong lensing, when they fall into larger structures [ABRIDGED].

Total mass distributions of Sersic galaxies from photometry and central velocity dispersion

We develop a novel way of finding total mass density profiles in Sersic ellipticals, to about 3 times the major axis effective radius, using no other information other than what is typically available for distant galaxies, namely the observed surface brightness distribution and the central velocity dispersion $\sigma_0$. The luminosity density profile of the observed galaxy is extracted by deprojecting the measured brightness distribution and scaling it by a fiduciary, step-function shaped, $raw$ mass-to-light ratio profile ($M/L$). The resulting raw, discontinuous, total, 3-D mass density profile is then smoothed according to a proposed smoothing prescription. The parameters of this raw $M/L$ are characterised by implementing the observables in a model-based study. The complete characterisation of the formalism is provided as a function of the measurements of the brightness distribution and $\sigma_0$. The formalism, thus specified, is demonstrated to yield the mass density profiles of a suite of test galaxies and is successfully applied to extract the gravitational mass distribution in NGC 3379 and NGC 4499, out to about 3 effective radii.

Suzaku Observations of Metallicity Distribution in the Intracluster Medium of the NGC 5044 Group

Abstract The metallicity distribution in the intracluster medium of the NGC 5044 group was studied up to 0.3 $r_{180}$ using the XIS instrument aboard the Suzaku satellite. The abundances of O, Mg, Si, S, and Fe were measured with high accuracy. The region within a radius of 0.05 $r_{180}$ from the center shows approximately solar abundances of Mg, Si, S, and Fe, while the O$/$Fe ratio is about 0.5–0.6 in solar units. In the outer region, the Fe abundance gradually drops to 0.3 solar. The radial abundance profiles of Mg, Si and S are similar to that of Fe, while that of O seems to be flatter. At $r$$&amp;gt;$ 0.05 $r_{180}$, the mass density profile of O differs from that of Fe, showing a shoulder-like structure that traces the luminosity density profile of galaxies. The mass-to-light ratios for O and Fe in NGC 5044 are one of the largest among groups of galaxies, but they are still smaller than those in rich clusters. These abundance features probably reflect the metal enrichment history of this relaxed group hosting a giant elliptical galaxy in the center.

Could the Fermi Large Area Telescope detect γ-rays from dark matter annihilation in the dwarf galaxies of the Local Group?

Context. The detection of γ-rays from dark matter (DM) annihilation is among the scientific goals of the Fermi Large Area Telescope (formerly known as GLAST) and Cherenkov telescopes. Aims. In this paper we investigate the chances of such a discovery, selecting some nearby dwarf spheroidal galaxies (dSph) as a target, and adopting the DM density profiles derived from both astronomical observations and N-body simulations. We also make use of recent studies about the presence of black holes and of a population of sub-subhalos inside the Local Group (LG) dwarfs to carry out boost factor studies. Methods. We study the detectability with the Fermi-LAT of the γ-ray flux from DM annihilation in four of the nearest and highly DM-dominated dSph galaxies of the LG, namely Draco, Ursa Minor, Carina, and Sextans, for which state-of-art DM density profiles were available. We assume the DM is made of weakly interacting massive particles such as the lightest supersymmetric particle and compute the expected γ-ray flux for estimations of the unknown underlying particle physics parameters. We then compute the boost factors due to the presence of DM clumps and of a central supermassive black hole. Finally, we compare our predictions with the Fermi-LAT sensitivity maps. Results. We find that the dSph galaxies shine above the Galactic smooth halo: e.g., the Galactic halo is brighter than the Draco dSph only for angles smaller than 2.3 degrees above the Galactic Center. We also find that the presence of a cusp or a constant density core in the DM mass density profile does not produce any relevant effects in the γ-ray flux due to the fortunate combination of the geometrical acceptance of the Fermi-LAT detector and the distance of the galaxies. Moreover, no significant enhancement is given by the presence of a central black hole or a population of sub-subhalos. Conclusions. We conclude that, even for the most optimistic scenario of particle physics, the γ-ray flux from DM annihilation in the dSph galaxies of the LG would be too low to be detected with the Fermi-LAT.

THE SLACS SURVEY. VIII. THE RELATION BETWEEN ENVIRONMENT AND INTERNAL STRUCTURE OF EARLY-TYPE GALAXIES

We study the relation between the internal structure of early-type galaxies and their environment using 70 strong gravitational lenses from the SLACS Survey. The Sloan Digital Sky Survey (SDSS) database is used to determine two measures of overdensity of galaxies around each lens-the projected number density of galaxies inside the tenth nearest neighbor ({sigma}{sub 10}) and within a cone of radius one h{sup -1} Mpc (D {sub 1}). Our main results are as follows. (1) The average overdensity is somewhat larger than unity, consistent with lenses preferring overdense environments as expected for massive early-type galaxies (12/70 lenses are in known groups/clusters). (2) The distribution of overdensities is indistinguishable from that of 'twin' nonlens galaxies selected from SDSS to have the same redshift and stellar velocity dispersion {sigma}{sub *}. Thus, within our errors, lens galaxies are an unbiased population, and the SLACS results can be generalized to the overall population of early-type galaxies. (3) Typical contributions from external mass distribution are no more than a few percent in local mass density, reaching 10-20% ({approx}0.05-0.10 external convergence) only in the most extreme overdensities. (4) No significant correlation between overdensity and slope of the mass-density profile of the lens galaxies is found. (5)more » Satellite galaxies (those with a more luminous companion) have marginally steeper mass-density profiles (as quantified by f {sub SIE} = {sigma}{sub *}/{sigma}{sub SIE} = 1.12 {+-} 0.05 versus 1.01 {+-} 0.01) and smaller dynamically normalized mass enclosed within the Einstein radius ({delta}log M {sub Ein}/M {sub dim} differs by -0.09 {+-} 0.03 dex) than central galaxies (those without). This result suggests that tidal stripping may affect the mass structure of early-type galaxies down to kpc scales probed by strong lensing, when they fall into larger structures.« less

DYNAMICAL CENTERS AND NONCIRCULAR MOTIONS IN THINGS GALAXIES: IMPLICATIONS FOR DARK MATTER HALOS

We present harmonic decompositions of the velocity fields of 19 galaxies from The H i Nearby Galaxy Survey (THINGS) which quantify the magnitude of the noncircular motions in these galaxies and yield observational estimates of the elongations of the dark matter halo potentials. Additionally, we present accurate dynamical center positions for these galaxies. We show that the positions of the kinematic and photometric centers of the large majority of the galaxies in our sample are in good agreement. The median absolute amplitude of the noncircular motions, averaged over our sample, is 6.7 km s−1, with ∼90% of the galaxies having median noncircular motions of less than ∼9 km s−1. As a fraction of the total rotation velocity, this translates into 4.5% on average. The mean elongation of the gravitational potential, after a statistical correction for an unknown viewing angle, is 0.017 ± 0.020, which is consistent with a round potential. Our derived noncircular motions and elongations are smaller than what is needed to bring cold dark matter (CDM) simulations in agreement with the observations. In particular, the amplitudes of the noncircular motions are not high enough to hide the steep central mass–density profiles predicted by CDM simulations. We show that the amplitudes of the noncircular motions decrease toward lower luminosities and later Hubble types.

The Estimate of Kinetic Power of Jets in FR II Radio Galaxies: Existence of Invisible Components?

We investigate the total kinetic powers (L_j) and ages (t_age) of powerful jets in FR II radio galaxies by comparison of the dynamical model of expanding cocoons with observations. We select four FR II radio sources (Cygnus A, 3C 223, 3C 284, and 3C 219), for which the mass-density profiles of intracluster medium (ICM) are known in the literature. It is found that large fractions > 0.02 - 0.7 of the Eddington luminosity (L_Edd) are carried away as a kinetic power of jet. The upper limit of estimated 2 L_j / L_Edd are larger than unity (< 10) for some sources, suggesting a possibility of super-Eddington mass accretions. As a consequence of the large powers, we also find that the total energy stored in the cocoon (E_c) exceeds the energy derived from the minimum energy condition for the energy of radiating non-thermal electrons and magnetic fields (E_min): 4< E_c /E_min <310. This implies that most of the energy in cocoon is carried by invisible components such as thermal leptons (electron and positron) and/or protons.

Color Profiles of Spiral Galaxies: Clues on Outer-Disk Formation Scenarios

We have explored radial color and stellar surface mass density profiles for a sample of 85 late-type spiral galaxies with deep (down to ~27 mag arcsec−2) SDSS g'- and r'-band surface brightness profiles. About 90% of the light profiles have been classified as broken exponentials, exhibiting either truncations (Type II galaxies) or antitruncations (Type III galaxies). The color profiles of Type II galaxies show a with a minimum of (g' − r') = 0.47 ± 0.02 mag at the break radius. Around the break radius, Type III galaxies have a plateau region with a color of (g' − r') = 0.57 ± 0.02. Using the color to calculate the stellar surface mass density profiles reveals a surprising result. The breaks, well established in the light profiles of the truncated galaxies, are almost gone, and the mass profiles now resemble those of the pure exponential (Type I) galaxies. This result suggests that the origin of the break in Type II galaxies is more likely due to a radial change in stellar population than being associated with an actual drop in the distribution of mass. Type III galaxies, however, seem to preserve their shape in the stellar mass density profiles. We find that the stellar surface mass density at the break for truncated galaxies is 13.6 ± 1.6 M☉ pc−2 and for the antitruncated ones is 9.9 ± 1.3 M☉ pc−2. We estimate that the fraction of stellar mass outside the break radius is ~15% for truncated galaxies and ~9% for antitruncated galaxies.

Mass distribution and orbital anisotropy of early-type galaxies: constraints from the mass plane

Massive early-type galaxies are observed to lie on the mass plane (MP), a two-dimensional manifold in the space of effective radius Re, projected mass M p (measured via strong gravitational lensing) and projected stellar velocity dispersion σ e2 withinRe/2. The MP is less ‘tilted’ than the traditional Fundamental Plane, and the two have comparable associated scatter. This means that the dimensionless structure parameter ce2 = 2GM p /(Reσ 2 ) is a nearly universal constant in the range σ e2 = 175–400 km s −1 . This finding can be used to constrain the mass distribution and internal dynamics of early-type galaxies: in particular, we explore the dependence of ce2 on light profile, dark matter distribution, and orbital anisotropy for several families of spherical galaxy models. We find that a relatively wide class of models has values of ce2 in the observed range, because ce2 is not very strongly sensitive to the mass distribution and orbital anisotropy. The degree of fine-tuning required to match the small intrinsic scatter of ce2 depends on the considered family of models: if the total mass distribution is isothermal (∝ r −2 ), a broad range of stellar luminosity profile and anisotropy is consistent with the observations, while Navarro, Frenk & White dark matter haloes require more fine-tuning of the stellar mass fraction, luminosity profile and anisotropy. If future data can cover a broader range of masses, the MP could be seen to be tilted by the known non-homology of the luminosity profiles of early-type galaxies, and the value of any such tilt would provide a discriminant between models for the total mass–density profile of the galaxies.