Radial Velocity Dispersion Profile Research Articles

Self-consistent dynamical models with a finite extent – III. Truncated power-law spheres

ABSTRACT Fully analytical dynamical models usually have an infinite extent, while real star clusters, galaxies, and dark matter haloes have a finite extent. The standard method for generating dynamical models with a finite extent consists of taking a model with an infinite extent and applying a truncation in binding energy. This method, however, cannot be used to generate models with a preset analytical mass density profile. We investigate the self-consistency and dynamical properties of a family of power-law spheres with a general tangential Cuddeford (TC) orbital structure. By varying the density power-law slope γ and the central anisotropy β0, these models cover a wide parameter space in density and anisotropy profiles. We explicitly calculate the phase–space distribution function for various parameter combinations, and interpret our results in terms of the energy distribution of bound orbits. We find that truncated power-law spheres can be supported by a TC orbital structure if, and only if, γ ≥ 2β0, which means that the central density slope–anisotropy inequality is both a sufficient and a necessary condition for this family. We provide closed expressions for structural and dynamical properties such as the radial and tangential velocity dispersion profiles, which can be compared against more complex numerical modelling results. This work significantly adds to the available suite of self-consistent dynamical models with a finite extent and an analytical description.

Fresh Insights on the Kinematics of M49's Globular Cluster System with MMT/Hectospec Spectroscopy

Abstract We present the first results of an MMT/Hectospec campaign to measure the kinematics of globular clusters (GCs) around M49—the brightest galaxy in the Virgo galaxy cluster, which dominates the Virgo B subcluster. The data include kinematic tracers beyond 95 kpc (∼5.2 effective radii) for M49 for the first time, enabling us to achieve three key insights reported here. First, beyond ∼20′–30′ (∼100–150 kpc), the GC kinematics sampled along the minor photometric axis of M49 become increasingly hotter, indicating a transition from GCs related to M49 to those representing the Virgo B intra-cluster medium. Second, there is an anomaly in the line-of-sight radial velocity dispersion (σ r,los) profile in an annulus ∼10–15′ (∼50–90 kpc) from M49 in which the kinematics cool by Δσ r,los ≈ 150 km s−1 relative to those in- or outward. The kinematic fingerprint of a previous accretion event is hinted at in projected phase-space, and we isolate GCs that both give rise to this feature, and are spatially co-located with two prominent stellar shells in the halo of M49. Third, we find a subsample of GCs with velocities representative of the dwarf galaxy VCC 1249 that is currently interacting with M49. The spatial distribution of these GCs closely resembles the morphology of VCC 1249's isophotes, indicating that several of these GCs are likely in the act of being stripped from the dwarf during its passage through M49's halo. Taken together, these results point toward the opportunity of witnessing ongoing giant halo assembly in the depths of a cluster environment.

The galaxy population within the virial radius of the Perseus cluster

Context. The Perseus cluster is one of the most massive nearby galaxy clusters and is fascinating in various respects. Though the galaxies in the central cluster region have been intensively investigated, an analysis of the galaxy population in a larger field is still outstanding. Aims. This paper investigates the galaxies that are brighter than B ≈ 20 within a field corresponding to the Abell radius of the Perseus cluster. Our first aim is to compile a new catalogue in a wide field around the centre of the Perseus cluster. The second aim of this study is to employ this catalogue for a systematic study of the cluster galaxy population with an emphasis on morphology and activity. Methods. We selected the galaxies in a 10 square degrees field of the Perseus cluster on Schmidt CCD images in B and Hα in combination with SDSS images. Morphological information was obtained both from the “eyeball” inspection and the surface brightness profile analysis. We obtained low-resolution spectra for 82 galaxies and exploited the spectra archive of SDSS and redshift data from the literature. Results. We present a catalogue of 1294 galaxies with morphological information for 90% of the galaxies and spectroscopic redshifts for 24% of them. We selected a heterogeneous sample of 313 spectroscopically confirmed cluster members and two different magnitude-limited samples with incomplete redshift data. These galaxy samples were used to derive such properties as the projected radial velocity dispersion profile, projected radial density profile, galaxy luminosity function, supermassive black hole mass function, total stellar mass, virial mass, and virial radius, to search for indications of substructure, to select active galaxies, and to study the relation between morphology, activity, density, and position. In addition, we present brief individual descriptions of 18 cluster galaxies with conspicuous morphological peculiarities.

Fossil group origins

Aims. We aim to study how the velocity segregation and the radial profile of the velocity dispersion depend on the prominence of the brightest cluster galaxies (BCGs). Methods. We divided a sample of 102 clusters and groups of galaxies into four bins of magnitude gap between the two brightest cluster members. We then computed the velocity segregation in bins of absolute and relative magnitude. Moreover, for each bin of magnitude gap we computed the radial profile of the velocity dispersion. Results. When using absolute magnitudes, the segregation in velocity is limited to the two brightest bins and no significant difference is found for different magnitude gaps. However, when we use relative magnitudes, a trend appears in the brightest bin: the larger the magnitude gap, the larger the velocity segregation. We also show that this trend is mainly due to the presence, in the brightest bin, of satellite galaxies in systems with small magnitude gaps: in fact, if we study central galaxies and satellites separately, this trend is mitigated and central galaxies are more segregated than satellites for any magnitude gap. A similar result is found in the radial velocity dispersion profiles: a trend is visible in central regions (where the BCGs dominate) but, if we analyse the profile using satellites alone, the trend disappears. In the latter case, the shape of the velocity dispersion profile in the centre of the systems with different magnitude gaps shows three types of behaviour: systems with the smallest magnitude gaps have an almost flat profile from the centre to the external regions; systems with the largest magnitude gaps show a monothonical growth from the low values of the central part to the flat ones in the external regions; and finally, systems with 1.0 < Δm12 ≤ 1.5 show a profile that peaks in the centre and then decreases towards the external regions. Conclusions. We suggest that two mechanisms could be responsible for the observed differences in the velocity segregation of the BCGs: an earlier formation of systems with a larger magnitude gap or a more centrally concentrated halo. However, the radial profiles of the velocity dispersion confirm that central galaxies are more relaxed, but that the satellite galaxies do not seem to be affected by the magnitude gap.

Gaia unveils the kinematics of multiple stellar populations in 47 Tucanae

The series of events, which occurred at high redshift and originated multiple stellar populations in Globular Clusters (GCs) are still poorly understood. Theoretical work suggests that the present-day dynamics of stars in nearby GCs, including the rotation and velocity dispersion, may retain important clues on the formation of multiple populations. So far, the dynamics of multiple populations have been investigated either from radial velocities of a relatively-small sample of stars, or from relative proper motions of stars in the small field of view provided by the Hubble Space Telescope. In this context, Gaia provides the unique opportunity to investigate the dynamics of thousands GC stars over a wide field of view. For the first time, we combine Gaia DR2 proper motions and multi-band photometry to study the internal motions of the two main stellar populations of 47 Tucanae in a wide field of view. We confirm that this cluster exhibits high rotation on the plane of the sky and find that both stellar generations share similar rotation patters. Second-generation stars show stronger anisotropies and smaller tangential-velocity dispersion than the first generation, while there is no significant difference between their radial-velocity dispersion profiles. We discuss the impact of these results in the context of the formation scenarios for multiple stellar populations in GCs.

The Density Profile and Kinematics of the Milky Way with RR Lyrae Stars

Abstract Most of the known RR Lyraes are type ab RR Lyraes (RRLab), and they are an excellent tool to map the Milky Way and its substructures. We find that 1148 RRLab stars determined by Drake et al. have been observed by spectroscopic surveys of SDSS and LAMOST. We derived the radial velocity dispersion, circular velocity, and mass profile from 860 halo tracers in Paper I. Here we present the stellar densities and radial velocity distributions of the thick disk and halo of the Milky Way. The 288 RRLab stars located in the thick disk have the mean metallicity of [Fe/H] = −1.02. Three thick disk tracers have a radial velocity lower than 215 km s−1. With 860 halo tracers, which have a mean metallicity of [Fe/H] = −1.33, we find a double power law of n(r) ∝ r −2.8 and n(r) ∝ r −4.8 with a break distance of 21 kpc to express the halo stellar density profile. The radial velocity dispersion at 50 kpc is around 78 km s−1.

A combined photometric and kinematic recipe for evaluating the nature of bulges using the CALIFA sample

Understanding the nature of bulges in disc galaxies can provide important insights into the formation and evolution of galaxies. For instance, the presence of a classical bulge suggests a relatively violent history, in contrast, the presence of simply an inner disc (also referred to as a "pseudobulge") indicates the occurrence of secular evolution processes in the main disc. However, we still lack criteria to effectively categorise bulges, limiting our ability to study their impact on the evolution of the host galaxies. Here we present a recipe to separate inner discs from classical bulges by combining four different parameters from photometric and kinematic analyses: The bulge S\'ersic index $n_\mathrm{b}$, the concentration index $C_{20,50}$, the Kormendy (1977) relation and the inner slope of the radial velocity dispersion profile $\nabla\sigma$. With that recipe we provide a detailed bulge classification for a sample of 45 galaxies from the integral-field spectroscopic survey CALIFA. To aid in categorising bulges within these galaxies, we perform 2D image decomposition to determine bulge S\'ersic index, bulge-to-total light ratio, surface brightness and effective radius of the bulge and use growth curve analysis to derive a new concentration index, $C_{20,50}$. We further extract the stellar kinematics from CALIFA data cubes and analyse the radial velocity dispersion profile. The results of the different approaches are in good agreement and allow a safe classification for approximately $95\%$ of the galaxies. In particular, we show that our new "inner" concentration index performs considerably better than the traditionally used $C_{50,90}$ when yielding the nature of bulges. We also found that a combined use of this index and the Kormendy (1977) relation gives a very robust indication of the physical nature of the bulge.

A novel JEAnS analysis of the Fornax dwarf using evolutionary algorithms: mass follows light with signs of an off-centre merger

Dwarf galaxies, among the most dark matter dominated structures of our universe, are excellent test-beds for dark matter theories. Unfortunately, mass modelling of these systems suffers from the well documented mass-velocity anisotropy degeneracy. For the case of spherically symmetric systems, we describe a method for non-parametric modelling of the radial and tangential velocity moments. The method is a numerical velocity anisotropy "inversion", with parametric mass models, where the radial velocity dispersion profile, $\sigma_{\mathrm{rr}}^2$ is modeled as a B-spline, and the optimization is a three step process that consists of: (i) an Evolutionary modelling to determine the mass model form and the best B-spline basis to represent $\sigma_{\mathrm{rr}}^2$; (ii) an optimization of the smoothing parameters; (iii) a Markov chain Monte Carlo analysis to determine the physical parameters. The mass-anisotropy degeneracy is reduced into mass model inference, irrespective of kinematics. We test our method using synthetic data. Our algorithm constructs the best kinematic profile and discriminates between competing dark matter models. We apply our method to the Fornax dwarf spheroidal galaxy. Using a King brightness profile and testing various dark matter mass models, our model inference favours a simple mass-follows-light system. We find that the anisotropy profile of Fornax is tangential ($\beta(r) < 0$) and we estimate a total mass of $M_{\text{tot}} = 1.613 ^{+0.050}_{-0.075} \times 10^8 \, \text{M}_{\odot}$, and a mass-to-light ratio of $\Upsilon_V = 8.93 ^{+0.32}_{-0.47} \, (\text{M}_{\odot}/\text{L}_{\odot})$. The algorithm we present is a robust and computationally inexpensive method for non-parametric modelling of spherical clusters independent of the mass-anisotropy degeneracy.

Detection of Supermassive Black Holes in Two Virgo Ultracompact Dwarf Galaxies

Abstract We present the detection of supermassive black holes (BHs) in two Virgo ultracompact dwarf galaxies (UCDs), VUCD3 and M59cO. We use adaptive optics assisted data from the Gemini/NIFS instrument to derive radial velocity dispersion profiles for both objects. Mass models for the two UCDs are created using multi-band Hubble Space Telescope imaging, including the modeling of mild color gradients seen in both objects. We then find a best-fit stellar mass-to-light ratio (M/L) and BH mass by combining the kinematic data and the deprojected stellar mass profile using Jeans Anisotropic Models. Assuming axisymmetric isotropic Jeans models, we detect BHs in both objects with masses of 4.4 − 3.0 + 2.5 × 10 6 M ⊙ in VUCD3 and 5.8 − 2.8 + 2.5 × 10 6 M ⊙ in M59cO (3σ uncertainties). The BH mass is degenerate with the anisotropy parameter, β z ; for the data to be consistent with no BH requires β z = 0.4 and β z = 0.6 for VUCD3 and M59cO, respectively. Comparing these values with nuclear star clusters shows that, while it is possible that these UCDs are highly radially anisotropic, it seems unlikely. These detections constitute the second and third UCDs known to host supermassive BHs. They both have a high fraction of their total mass in their BH; ∼13% for VUCD3 and ∼18% for M59cO. They also have low best-fit stellar M/Ls, supporting the proposed scenario that most massive UCDs host high-mass fraction BHs. The properties of the BHs and UCDs are consistent with both objects being the tidally stripped remnants of ∼ 10 9 M ⊙ galaxies.

The dynamics ofz~ 1 clusters of galaxies from the GCLASS survey

We constrain the internal dynamics of a stack of 10 clusters from the GCLASS survey at 0.87<z<1.34. We determine the stack cluster mass profile M(r) using the MAMPOSSt algorithm of Mamon et al., the velocity anisotropy profile beta(r) from the inversion of the Jeans equation, and the pseudo-phase-space density profiles Q(r) and Qr(r), obtained from the ratio between the mass density profile and the third power of the (total and, respectively, radial) velocity dispersion profiles of cluster galaxies. Several M(r) models are statistically acceptable for the stack cluster (Burkert, Einasto, Hernquist, NFW). The total mass distribution has a concentration c=r200/r-2=4.0-0.6+1.0, in agreement with theoretical expectations, and is less concentrated than the cluster stellar-mass distribution. The stack cluster beta(r) is similar for passive and star-forming galaxies and indicates isotropic galaxy orbits near the cluster center and increasingly radially elongated with increasing cluster-centric distance. Q(r) and Qr(r) are almost power-law relations with slopes similar to those predicted from numerical simulations of dark matter halos. Combined with results obtained for lower-z clusters we determine the dynamical evolution of galaxy clusters, and compare it with theoretical predictions. We discuss possible physical mechanisms responsible for the differential evolution of total and stellar mass concentrations, and of passive and star-forming galaxy orbits [abridged].

The σ-bump in elliptical galaxies – a signature of major mergers?

AbstractThe stellar radial velocity dispersion profiles of elliptical galaxies can be well described by a power-law σ(r)∝r−β. We analyze a set of elliptical galaxies formed by major mergers of isolated disk galaxies with mass ratios of 1:1 and 3:1 for several orbital configurations (Johansson et al. 2009). The galaxies in our sample show a deviation from the power-law at 1 − 3Reff, which we term the σ-bump (Schauer et al. 2014). This feature is most prominent in remnants of 1:1 mergers and weakens for remnants of mergers with smaller mass ratios, indicating that the σ-bump is a signature of an equal mass merger. The σ-bump does not vanish with time but stays constant once it has formed, in contrast to shells. It can be seen under all projections, making it an observable feature in the outskirts of elliptical galaxies. We indeed identify three possible σ-bump candidates in the sample of 12 SLUGGS-survey ellipticals studied by Pota et al. (2013), who use globular clusters as tracers for the outer stellar halos (see Schauer et al. 2014, for more details). For further comparisons, we here provide for the first time a two dimensional map of the velocity dispersion of one simulated σ-bump galaxy, to identify the σ-bump in observations of kinematic maps out to several Reff. The σ-bump appears as a global ring-like feature if seen face-on and as an extended box-like feature in its edge-on projection.

Motion of halo tracer objects in the gravitational potential of a low-mass model of the Galaxy

Recently, we determined a lower bound for the Milky Way mass in a point mass approximation. This result was obtained for most general spherically symmetric phase-space distribution functions consistent with a measured radial velocity dispersion. As a stability test of these predictions against a perturbation of the point mass potential, in this paper we make use of a representative of these functions to set the initial conditions for a simulation in a more realistic potential of similar mass and accounting for other observations. The predicted radial velocity dispersion profile evolves to forms still consistent with the measured profile, proving structural stability of the point mass approximation and the reliability of the resulting mass estimate of $2.1\times10^{11}\mathrm{M}_{\odot}$ within $150\,\mathrm{kpc}$. We also find an interesting coincidence with the recent estimates based on the kinematics of the extended Orphan Stream. As a byproduct, we obtain the equations of motion in axial symmetry from a nonstandard Hamiltonian, and derive a formula in the spherical symmetry relating the radial velocity dispersion profile to a directly measured kinematical observable.

Violent relaxation of ellipsoidal clouds

An isolated, initially cold and ellipsoidal cloud of self-gravitating particles represents a relatively simple system to study the effects of the deviations from spherical symmetry in the mechanism of violent relaxation. Initial deviations from spherical symmetry are shown to play a dynamical role that is equivalent to that of density fluctuations in the case of an initially spherical cloud. Indeed, these deviations control the amount of particles energy change and thus determine the properties of the final energy distribution, particularly the appearance of two species of particles: bound and free. Ejection of mass and energy from the system together with the formation of a density profile decaying as $\rho(r) \sim r^{-4}$ and a Keplerian radial velocity dispersion profile, are the prominent features similar to those observed after the violent relaxation of spherical clouds. In addition, we find that ejected particles are characterized by highly non-spherical shapes, whose features can be traced in the initial deviations from spherical symmetry that are amplified during the dynamical evolution: particles can indeed form anisotropic configurations, like bars and/or disks, even though the initial cloud was very close to spherical.

The role of feedback in shaping the structure of the interstellar medium

We present an analysis of the role of feedback in shaping the neutral hydrogen (HI) content of simulated disc galaxies. For our analysis, we have used two realisations of two separate Milky Way-like (~L*) discs - one employing a conservative feedback scheme (MUGS), the other significantly more energetic (MaGICC). To quantify the impact of these schemes, we generate zeroth moment (surface density) maps of the inferred HI distribution; construct power spectra associated with the underlying structure of the simulated cold ISM, in addition to their radial surface density and velocity dispersion profiles. Our results are compared with a parallel, self-consistent, analysis of empirical data from THINGS (The HI Nearby Galaxy Survey). Single power-law fits (P~k^gamma) to the power spectra of the stronger-feedback (MaGICC) runs (over spatial scales corresponding to 0.5 kpc to 20 kpc) result in slopes consistent with those seen in the THINGS sample (gamma = -2.5). The weaker-feedback (MUGS) runs exhibit shallower power law slopes (gamma = -1.2). The power spectra of the MaGICC simulations are more consistent though with a two-component fit, with a flatter distribution of power on larger scales (i.e., gamma = -1.4 for scales in excess of 2 kpc) and a steeper slope on scales below 1 kpc (gamma = -5), qualitatively consistent with empirical claims, as well as our earlier work on dwarf discs. The radial HI surface density profiles of the MaGICC discs show a clear exponential behaviour, while those of the MUGS suite are essentially flat; both behaviours are encountered in nature, although the THINGS sample is more consistent with our stronger (MaGICC) feedback runs.

A “LIGHT,” CENTRALLY CONCENTRATED MILKY WAY HALO?

We discuss a novel approach to "weighing" the Milky Way dark matter halo, one that combines the latest samples of halo stars selected from the Sloan Digital Sky Survey (SDSS) with state-of-the-art numerical simulations of Milky Way analogs. The fully cosmological runs employed in the present study include "Eris", one of the highest-resolution hydrodynamical simulations of the formation of a M_vir=8e11 M_sun late-type spiral, and the dark-matter only M_vir=1.7e12 M_sun "Via Lactea II" simulation. Eris provides an excellent laboratory for creating mock SDSS samples of tracer halo stars, and we successfully compare their density, velocity anisotropy, and radial velocity dispersion profiles with the observational data. Most mock SDSS realizations show the same "cold veil" recently observed in the distant stellar halo of the Milky Way, with tracers as cold as sigma_los ~ 50 km/s between 100-150 kpc. Controlled experiments based on the integration of the spherical Jeans equation as well as a particle tagging technique applied to Via Lactea II show that a "heavy" M_vir 2e12 M_sun realistic host produces a poor fit to the kinematic SDSS data. We argue that these results offer added evidence for a "light," centrally-concentrated Milky Way halo.

Universal properties of violently relaxed gravitational structures

We study the collapse and virialization of an isolated spherical cloud of self-gravitating particles initially at rest and characterised by a power-law density profile, with exponent 0<= \alpha < 3, or by a Plummer, an Hernquist, a NFW, a Gaussian profile. We find that in all cases the virialized structure formed after the collapse has a density profile decaying, at large enough radii, as ~ r^{-4}, and a radial velocity dispersion profile decaying as ~r^{-1}. We show that these profiles originate from the physical mechanism responsible of the ejection of a fraction of cloud's mass and energy during the collapse and that this same mechanism washes out the dependence on the initial conditions. When a large enough initial velocity dispersion is given to the cloud particles, ejection does not occur anymore and consequently the virialized halo density and velocity profiles display features which reflect the initial conditions.

KINEMATICS OF THE STELLAR HALO AND THE MASS DISTRIBUTION OF THE MILKY WAY USING BLUE HORIZONTAL BRANCH STARS

Here we present a kinematic study of the Galactic halo out to a radius of $\sim$ 60 kpc, using 4664 blue horizontal branch (BHB) stars selected from the SDSS/SEGUE survey, to determine key dynamical properties. Using a maximum likelihood analysis, we determine the velocity dispersion profiles in spherical coordinates ($\sigma_{r}$, $\sigma_{\theta}$, $\sigma_{\phi}$) and the anisotropy profile ($\beta$). The radial velocity dispersion profile ($\sigma_{r}$) is measured out to a galactocentric radius of $r \sim 60$ kpc, but due to the lack of proper-motion information, $\sigma_{\theta}$, $\sigma_{\phi}$ and $\beta$ could only be derived directly out to $r \sim25$ kpc. From a starting value of $\beta\approx 0.5$ in the inner parts ($9<r/\kpc<12$), the profile falls sharply in the range $r \approx 13-18$ kpc, with a minimum value of $\beta=-1.2$ at $r=17$ kpc, rising sharply at larger radius. In the outer parts, in the range $25<r/\kpc<56$, we predict the profile to be roughly constant with a value of $\beta\approx 0.5$. The newly discovered kinematic anomalies are shown not to arise from halo substructures. We also studied the anisotropy profile of simulated stellar halos formed purely by accretion and found that they cannot reproduce the sharp dip seen in the data. From the Jeans equation, we compute the stellar rotation curve ($v_{\rm circ}$) of the Galaxy out to $r \sim 25$ kpc. The mass of the Galaxy within $r \lesssim 25$ kpc is determined to be $2.1 \times 10^{11}$ $M_{\sun}$, and with a 3-component fit to $v_{\rm circ}(r)$, we determine the virial mass of the Milky Way dark matter halo to be $M_{\rm vir} = 0.9 ^{+0.4}_{-0.3} \times 10^{12}$ $M_{\sun}$ ($R_{\rm vir} = 249^{+34}_{-31}$ kpc).

Global gravitationally organized spiral waves and the structure of NGC 5247

Using observational data, we build numerical N-body, hydrodynamical and combined equilibrium models for the spiral galaxy NGC 5247. The models turn out to be unstable as regards spiral structure formation. We simulate scenarios of spiral structure formation for different sets of equilibrium rotation curves, radial velocity-dispersion profiles and disc thicknesses and demonstrate that in all cases the simulated spiral pattern agrees qualitatively with the observed morphology of NGC 5247. We also demonstrate that an admixture of a gaseous component with a mass of about a few per cent of the total mass of the disc increases the lifetime of a spiral pattern by approximately 30 per cent. The simulated spiral pattern in this case lasts for about 3 Gyr from the beginning of the growth of perturbations.

Flattened velocity dispersion profiles in globular clusters: Newtonian tides or modified gravity?

Over the past couple of years, a number of observational studies have confirmed the flattening of the radial velocity dispersion profiles for stars in various nearby globular clusters. As the projected radial coordinate is increased, a radius appears beyond which, the measured velocity dispersion ceases to drop and settles at a fixed value, $\sigma_{\infty}$. Under Newtonian gravity, this is explained by invoking tidal heating from the overall Milky Way potential on the outer, more loosely bound stars, of the globular clusters in question. From the point of view of modified gravity theories, such an outer flattening is expected on crossing the critical acceleration threshold $a_{0}$, beyond which, a transition to MONDian dynamics is expected, were equilibrium velocities cease to be a function of distance. In this paper we attempt to sort out between the above competing explanations, by looking at their plausibility in terms of an strictly empirical approach. We determine Newtonian tidal radii using masses accurately calculated through stellar population modelling, and hence independent of any dynamical assumptions, distances, size and orbital determinations for a sample of 16 globular clusters. We show that their Newtonian tidal radii at perigalacticon are generally larger that the radii at which the flattening in the velocity dispersion profiles occurs, by large factors of 4, on average. While this point makes the Newtonian tidal explanation suspect, it is found that the radii at which the flattening is observed on average correlate with the radii where the $a_{0}$ threshold is crossed, and that $\sigma_{\infty}$ values scale with the fourth root of the total masses, all features predicted under modified gravity theories.

Virial mass in warped DGP-inspired $\mathcal{L}(R)$ gravity

A version of the virial theorem is derived in a brane-world scenario in the framework of a warped DGP model where the action on the brane is an arbitrary function of the Ricci scalar, \(\mathcal{L}(R)\). The extra terms in the modified Einstein equations generate an equivalent mass term (geometrical mass), which give an effective contribution to the gravitational energy and offer viable explanation to account for the virial mass discrepancy in clusters of galaxies. We also obtain the radial velocity dispersion of galaxy clusters and show that it is compatible with the radial velocity dispersion profile of such clusters. Finally, we compare the result of the model with \(\mathcal{L}(R)\) gravity theories.