Spherical Jeans Research Articles

Galaxy structure from multiple tracers – II. M87 from parsec to megaparsec scales

Following a number of conflicting studies of M87's mass profile, we undertake a dynamical analysis of multiple tracer populations to constrain its mass over a large radius range. We combine stellar kinematics in the central regions with the dynamics of 612 globular clusters out to 200 kpc and satellite galaxies extending to scales comparable with the virial radius. Using a spherical Jeans analysis, we are able to disentangle the mass contributions from the dark and baryonic components and set constraints on the structure of each. Assuming isotropy, we explore four different models for the dark matter halo and find that a centrally-cored dark matter distribution is preferred. We infer a stellar mass-to-light ratio $\Upsilon_{\star,v} = 6.9 \pm 0.1$ -- consistent with a Salpeter-like IMF -- and a core radius $r_c = 67 \pm 20$ kpc. We then introduce anisotropy and find that, while the halo remains clearly cored, the radial stellar anisotropy has a strong impact on both $\Upsilon_{\star,v}$ and the core's radius; here we find $\Upsilon_{\star,v} = 3.50_{-0.36}^{+0.32}$ -- consistent with a Chabrier-like IMF -- and $r_c = 19.00_{-8.34}^{+8.38}$ kpc. Thus the presence of a core at the centre of the dark halo is robust against anisotropy assumptions, while the stellar mass and core size are not. We are able to reconcile previously discrepant studies by showing that modelling the globular cluster data alone leads to the very different inference of a super-NFW cusp, thus highlighting the value of multiple-population modelling, and we point to the possible role of M87's AGN and the cluster environment in forming the central dark matter core.

Comparing Galactic Center MSSM dark matter solutions to the Reticulum II gamma-ray data

Observations with the Fermi Large Area Telescope (LAT) indicate a possible small photon signal originating from the dwarf galaxy Reticulum II that exceeds the expected background between 2 GeV and 10 GeV . We have investigated two specific scenarios for annihilating WIMP dark matter within the phenomenological Minimal Supersymmetric Standard Model (pMSSM) framework as a possible source for these photons. We find that the same parameter ranges in pMSSM as reported by an earlier paper to be consistent with the Galactic Center excess, are also consistent with the excess observed in Reticulum II, resulting in a J-factor of log 10(J(αint=0.5̂)) ≃ (20.3−20.5)+0.2−0.3 GeV2cm−5. This J-factor is consistent with log 10(J(αint=0.5̂)) = 19.6+1.0−0.7 GeV2cm−5, which was derived using an optimized spherical Jeans analysis of kinematic data obtained from the Michigan/Magellan Fiber System (M2FS).

STELLAR VELOCITY DISPERSION AND ANISOTROPY OF THE MILKY WAY INNER HALO

We measure the three components of velocity dispersion, $\sigma_{R},\sigma_{\theta},\sigma_{\phi}$, for stars within 6 < R < 30 kpc of the Milky Way using a new radial velocity sample from the MMT telescope. We combine our measurements with previously published data so that we can more finely sample the stellar halo. We use a maximum likelihood statistical method for estimating mean velocities, dispersions, and covariances assuming only that velocities are normally distributed. The alignment of the velocity ellipsoid is consistent with a spherically symmetric gravitational potential. From the spherical Jeans equation, the mass of the Milky Way is M(<12 kpc) = $1.3\times10^{11}$ M$_{\odot}$ with an uncertainty of 40%. We also find a region of discontinuity, 15 < R < 25 kpc, where the estimated velocity dispersions and anisotropies diverge from their anticipated values, confirming at high significance the break observed by others. We argue that this break in anisotropy is physically explained by coherent stellar velocity structure in the halo, such as the Sgr stream. To significantly improve our understanding of halo kinematics will require combining radial velocities with future Gaia proper motions.

Dark matter annihilation and decay in dwarf spheroidal galaxies: the classical and ultrafaint dSphs

Dwarf spheroidal (dSph) galaxies are prime targets for present and future gamma-ray telescopes hunting for indirect signals of particle dark matter. The interpretation of the data requires careful assessment of their dark matter content in order to derive robust constraints on candidate relic particles. Here, we use an optimised spherical Jeans analysis to reconstruct the `astrophysical factor' for both annihilating and decaying dark matter in 21 known dSphs. Improvements with respect to previous works are: (i) the use of more flexible luminosity and anisotropy profiles to minimise biases, (ii) the use of weak priors tailored on extensive sets of contamination-free mock data to improve the confidence intervals, (iii) systematic cross-checks of binned and unbinned analyses on mock and real data, and (iv) the use of mock data including stellar contamination to test the impact on reconstructed signals. Our analysis provides updated values for the dark matter content of 8 `classical' and 13 `ultrafaint' dSphs, with the quoted uncertainties directly linked to the sample size; the more flexible parametrisation we use results in changes compared to previous calculations. This translates into our ranking of potentially-brightest and most robust targets---viz., Ursa Minor, Draco, Sculptor---, and of the more promising, but uncertain targets---viz., Ursa Major 2, Coma---for annihilating dark matter. Our analysis of Segue 1 is extremely sensitive to whether we include or exclude a few marginal member stars, making this target one of the most uncertain. Our analysis illustrates challenges that will need to be addressed when inferring the dark matter content of new `ultrafaint' satellites that are beginning to be discovered in southern sky surveys.

DARK MATTER ANNIHILATION AND DECAY PROFILES FOR THE RETICULUM II DWARF SPHEROIDAL GALAXY

The dwarf spheroidal galaxies (dSph) of the Milky Way are among the most attractive targets for indirect searches of dark matter. In this work, we reconstruct the dark matter annihilation (J-factor) and decay profiles for the newly discovered dSph Reticulum II. Using an optimized spherical Jeans analysis of kinematic data obtained from the Michigan/Magellan Fiber System (M2FS), we find Reticulum II's J-factor to be among the largest of any Milky Way dSph. We have checked the robustness of this result against several ingredients of the analysis. Unless it suffers from tidal disruption or significant inflation of its velocity dispersion from binary stars, Reticulum II may provide a unique window on dark matter particle properties.

Testing modified Newtonian dynamics through statistics of velocity dispersion profiles in the inner regions of elliptical galaxies

Modified Newtonian dynamics (MOND) proposed by Milgrom provides a paradigm alternative to dark matter (DM) 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 spheroidal early-type galaxies, but it remains unclear whether MOND can fit the various empirical properties of early-type galaxies for the whole ranges of mass and radius. As a way of rigorously testing MOND in elliptical galaxies we calculate the MOND-predicted velocity dispersion profiles (VDPs) in the inner regions of ∼2000 nearly round Sloan Digital Sky Survey elliptical galaxies under a variety of assumptions on velocity dispersion (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 parametrized 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.

The SLUGGS survey: multipopulation dynamical modelling of the elliptical galaxy NGC 1407 from stars and globular clusters

We perform in-depth dynamical modelling of the luminous and dark matter (DM) content of the elliptical galaxy NGC 1407. Our strategy consists of solving the spherical Jeans equations for three independent dynamical tracers: stars, blue GCs and red GCs in a self-consistent manner. We adopt a maximum-likelihood Markov-Chain Monte Carlo fitting technique in the attempt to constrain the inner slope of the DM density profile (the cusp/core problem), and the stellar initial mass function (IMF) of the galaxy. We find the inner logarithmic slope of the DM density profiles to be $\gamma = 0.6\pm0.4$, which is consistent with either a DM cusp ($\gamma = 1$) or with a DM core $(\gamma = 0)$. Our findings are consistent with a Salpeter IMF, and marginally consistent with a Kroupa IMF. We infer tangential orbits for the blue GCs, and radial anisotropy for red GCs and stars. The modelling results are consistent with the virial mass--concentration relation predicted by $\Lambda$CDM simulations. The virial mass of NGC 1407 is $\log$ $M_{\rm vir} = 13.3 \pm 0.2 M_{\odot}$, whereas the stellar mass is $\log M_* = 11.8 \pm 0.1 M_{\odot}$. The overall uncertainties on the mass of NGC 1407 are only 5 per cent at the projected stellar effective radius. We attribute the disagreement between our results and previous X-ray results to the gas not being in hydrostatic equilibrium in the central regions of the galaxy. The halo of NGC 1407 is found be DM dominated, with a dynamical mass-to-light ratio of $M/L=260_{-100} ^{+174} M_{\odot}/L_{\odot, B}$. However, this value can be larger up to a factor of 3 depending on the assumed prior on the DM scale radius.

Spherical Jeans analysis for dark matter indirect detection in dwarf spheroidal galaxies - impact of physical parameters and triaxiality

Dwarf spheroidal (dSph) galaxies are among the most promising targets for the indirect detection of dark matter (DM) from annihilation and/or decay products. Empirical estimates of their DM content - and hence the magnitudes of expected signals - rely on inferences from stellar-kinematic data. However, various kinematic analyses can give different results and it is not obvious which are most reliable. Using extensive sets of mock data of various sizes (mimicking 'ultra-faint' and 'classical' dSphs) and an MCMC engine, here we investigate biases, uncertainties, and limitations of analyses based on parametric solutions to the spherical Jeans equation. For a variety of functional forms for the tracer and DM density profiles, as well as the orbital anisotropy profile, we examine reliability of estimates for the astrophysical J- and D-factors for annihilation and decay, respectively. For large (N > 1000) stellar-kinematic samples typical of 'classical' dSphs, errors tend to be dominated by systematics, which can be reduced through the use of sufficiently general and flexible functional forms. For small (N < 100) samples typical of 'ultrafaints', statistical uncertainties tend to dominate systematic errors and flexible models are less necessary. We define an optimal strategy that would mitigate sensitivity to priors and other aspects of analyses based on the spherical Jeans equation. We also find that the assumption of spherical symmetry can bias estimates of J (with the 95% credibility intervals not encompassing the true J-factor) when the object is mildly triaxial (axis ratios b/a = 0.8, c/a = 0.6). A concluding table summarises the typical error budget and biases for the different sample sizes considered.

Resolving the mass–anisotropy degeneracy of the spherically symmetric Jeans equation – II. Optimum smoothing and model validation

The spherical Jeans equation is widely used to estimate the mass content of a stellar systems with apparent spherical symmetry. However, this method suffers from a degeneracy between the assumed mass density and the kinematic anisotropy profile, $\beta(r)$. In a previous work, we laid the theoretical foundations for an algorithm that combines smoothing B-splines with equations from dynamics to remove this degeneracy. Specifically, our method reconstructs a unique kinematic profile of $\sigma_{rr}^2$ and $\sigma_{tt}^2$ for an assumed free functional form of the potential and mass density $(\Phi,\rho)$ and given a set of observed line-of-sight velocity dispersion measurements, $\sigma_{los}^2$. In Paper I (submitted to MNRAS: MN-14-0101-MJ) we demonstrated the efficiency of our algorithm with a very simple example and we commented on the need for optimum smoothing of the B-spline representation; this is in order to avoid unphysical variational behaviour when we have large uncertainty in our data. In the current contribution we present a process of finding the optimum smoothing for a given data set by using information of the behaviour from known ideal theoretical models. Markov Chain Monte Carlo methods are used to explore the degeneracy in the dynamical modelling process. We validate our model through applications to synthetic data for systems with constant or variable mass-to-light ratio $\Upsilon$. In all cases we recover excellent fits of theoretical functions to observables and unique solutions. Our algorithm is a robust method for the removal of the mass-anisotropy degeneracy of the spherically symmetric Jeans equation for an assumed functional form of the mass density.

The central dynamics of M3, M13, and M92: stringent limits on the masses of intermediate-mass black holes

We used the PMAS integral field spectrograph to obtain large sets of radial velocities in the central regions of three northern Galactic globular clusters: M3, M13, and M92. By applying the novel technique of crowded field 3D spectroscopy, we measured radial velocities for about 80 stars within the central ~ 10 arcsec of each cluster. These are by far the largest spectroscopic datasets obtained in the innermost parts of these clusters up to now. To obtain kinematical data across the whole extent of the clusters, we complement our data with measurements available in the literature. We combine our velocity measurements with surface brightness profiles to analyse the internal dynamics of each cluster using spherical Jeans models, and investigate whether our data provide evidence for an intermediate-mass black hole in any of the clusters. The surface brightness profiles reveal that all three clusters are consistent with a core profile, although shallow cusps cannot be excluded. We find that spherical Jeans models with a constant mass-to-light ratio provide a good overall representation of the kinematical data. A massive black hole is required in none of the three clusters to explain the observed kinematics. Our 1sigma (3sigma) upper limits are 5300 M_sun (12000 M_sun) for M3, 8600 M_sun (13000 M_sun) for M13, and 980 M_sun (2700 M_sun) for M92. A puzzling circumstance is the existence of several potential high velocity stars in M3 and M13, as their presence can account for the majority of the discrepancies that we find in our mass limits compared to M92.

A UNIVERSAL POWER-LAW PROFILE OF PSEUDO-PHASE-SPACE DENSITY-LIKE QUANTITIES IN ELLIPTICAL GALAXIES

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.

THREE-DIMENSIONAL STELLAR KINEMATICS AT THE GALACTIC CENTER: MEASURING THE NUCLEAR STAR CLUSTER SPATIAL DENSITY PROFILE, BLACK HOLE MASS, AND DISTANCE

We present 3D kinematic observations of stars within the central 0.5 pc of the Milky Way nuclear star cluster using adaptive optics imaging and spectroscopy from the Keck telescopes. Recent observations have shown that the cluster has a shallower surface density profile than expected for a dynamically relaxed cusp, leading to important implications for its formation and evolution. However, the true three dimensional profile of the cluster is unknown due to the difficulty in de-projecting the stellar number counts. Here, we use spherical Jeans modeling of individual proper motions and radial velocities to constrain for the first time, the de-projected spatial density profile, cluster velocity anisotropy, black hole mass ($M_\mathrm{BH}$), and distance to the Galactic center ($R_0$) simultaneously. We find that the inner stellar density profile of the late-type stars, $\rho(r)\propto r^{-\gamma}$ to have a power law slope $\gamma=0.05_{-0.60}^{+0.29}$, much more shallow than the frequently assumed Bahcall $\&$ Wolf slope of $\gamma=7/4$. The measured slope will significantly affect dynamical predictions involving the cluster, such as the dynamical friction time scale. The cluster core must be larger than 0.5 pc, which disfavors some scenarios for its origin. Our measurement of $M_\mathrm{BH}=5.76_{-1.26}^{+1.76}\times10^6$ $M_\odot$ and $R_0=8.92_{-0.55}^{+0.58}$ kpc is consistent with that derived from stellar orbits within 1$^{\prime\prime}$ of Sgr A*. When combined with the orbit of S0-2, the uncertainty on $R_0$ is reduced by 30% ($8.46_{-0.38}^{+0.42}$ kpc). We suggest that the MW NSC can be used in the future in combination with stellar orbits to significantly improve constraints on $R_0$.

The nuclear cluster of the Milky Way: total mass and luminosity

AbstractHere we present the fundamental properties of the nuclear cluster of the Milky Way. First, we derive its structural properties by constructing a density map of the central 1000″ using extinction-corrected star counts. We can describe the data with a two-component model built from Sersic profiles. The inner nearly spherical component is the nuclear cluster. The outer, strongly flattened component can be identified with the stellar component of the circumnuclear zone. Second, we enlarge the radius inside which detailed dynamics are available from 1 pc to 4 pc. We use more than 10000 individual proper motions and more than 2700 radial velocities. We determine the cluster mass by means of isotropic spherical Jeans modeling. We get a nuclear cluster mass within 100″ of M100″=(6.11 ± 0.52|fix R0±0.97|R0) × 106 M⊙, which corresponds to a total cluster mass of MNC=(13.08 ± 2.51|fix R0± 2.08|R0) × 106 M⊙. By combination of our mass with the flux we calculate M/L=0.50 ± 0.12 M⊙/L⊙,Ks for the central 100″. That is broadly consistent with a Chabrier IMF. With its mass and a luminosity of MKs=−15.30±0.26 the nuclear cluster is a bright and massive specimen with a typical size.

High-fidelity view of the structure and fragmentation of the high-mass, filamentary IRDC G11.11-0.12

Star formation in molecular clouds is intimately linked to their internal mass distribution. We present an unprecedentedly detailed analysis of the column density structure of a high-mass, filamentary molecular cloud, namely IRDC G11.11-0.12 (G11). We use two novel column density mapping techniques: high-resolution (FWHM=2", or ~0.035 pc) dust extinction mapping in near- and mid-infrared, and dust emission mapping with the Herschel satellite. These two completely independent techniques yield a strikingly good agreement, highlighting their complementarity and robustness. We first analyze the dense gas mass fraction and linear mass density of G11. We show that G11 has a top heavy mass distribution and has a linear mass density (M_l ~ 600 Msun pc^{-1}) that greatly exceeds the critical value of a self-gravitating, non-turbulent cylinder. These properties make G11 analogous to the Orion A cloud, despite its low star-forming activity. This suggests that the amount of dense gas in molecular clouds is more closely connected to environmental parameters or global processes than to the star-forming efficiency of the cloud. We then examine hierarchical fragmentation in G11 over a wide range of size-scales and densities. We show that at scales 0.5 pc > l > 8 pc, the fragmentation of G11 is in agreement with that of a self-gravitating cylinder. At scales smaller than l < 0.5 pc, the results agree better with spherical Jeans' fragmentation. One possible explanation for the change in fragmentation characteristics is the size-scale-dependent collapse time-scale that results from the finite size of real molecular clouds: at scales l < 0.5 pc, fragmentation becomes sufficiently rapid to be unaffected by global instabilities.

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.

Indication for an intermediate-mass black hole in the globular cluster NGC 5286 from kinematics

Intermediate-mass black holes (IMBHs, 10^2-10^5 M_sun) fill the gap between stellar-mass black holes and supermassive black holes (SMBHs). Simulations have shown that IMBHs may form in dense star clusters, and therefore may still be present in these smaller stellar systems. We investigate the Galactic globular cluster NGC 5286 for indications of a central IMBH using spectroscopic data from VLT/FLAMES, velocity measurements from the Rutgers Fabry Perot at CTIO, and photometric data from HST. We run analytic spherical and axisymmetric Jeans models with different central black-hole masses, anisotropy, mass-to-light ratio, and inclination. Further, we compare the data to a grid of N-body simulations without tidal field. Additionally, we use one N-body simulation to check the results of the spherical Jeans models for the total cluster mass. Both the Jeans models and the N-body simulations favor the presence of a central black hole in NGC 5286 and our detection is at the 1- to 1.5-sigma level. From the spherical Jeans models we obtain a best fit with black-hole mass M_BH=(1.5+-1.0)x10^3 M_sun. The error is the 68% confidence limit from Monte Carlo simulations. Axisymmetric models give a consistent result. The best fitting N-body model is found with a black hole of 0.9% of the total cluster mass (4.38+-0.18)x10^5 M_sun, which results in an IMBH mass of M_BH=(3.9+-2.0)x10^3 M_sun. Jeans models give lower values for the total cluster mass. Our test of the Jeans models with N-body simulation data shows that this discrepancy has two reasons: The influence of a radially varying M/L profile, and underestimation of the velocity dispersion as the measurements are limited to bright stars. We conclude that detection of IMBHs in Galactic globular clusters remains a challenging task unless their mass fractions are above those found for SMBHs in nearby galaxies. [abridged]

Universal IMF versus dark halo response in early-type galaxies: breaking the degeneracy with the Fundamental Plane

We use the relations between aperture stellar velocity dispersion (\sigma_ap), stellar mass (M_sps), and galaxy size (R_e) for a sample of \sim 150,000 early-type galaxies from SDSS/DR7 to place constraints on the stellar initial mass function (IMF) and dark halo response to galaxy formation. We build LCDM based mass models that reproduce, by construction, the relations between galaxy size, light concentration and stellar mass, and use the spherical Jeans equations to predict \sigma_ap. Given our model assumptions (including those in the stellar population synthesis models), we find that reproducing the median \sigma_ap vs M_sps relation is not possible with {\it both} a universal IMF and a universal dark halo response. Significant departures from a universal IMF and/or dark halo response are required, but there is a degeneracy between these two solutions. We show that this degeneracy can be broken using the strength of the correlation between residuals of the velocity-mass (\Delta log \sigma_ap) and size-mass (\Delta log R_e) relations. The slope of this correlation, d_vr \equiv \Delta log \sigma_ap/\Delta log R_e, varies systematically with galaxy mass from d_vr \simeq -0.45 at M_sps \sim 10^{10}M_sun, to d_vr \simeq -0.15 at M_sps \sim 10^{11.6} M_sun. The virial fundamental plane (FP) has d_vr=-1/2, and thus we find the tilt of the observed FP is mass dependent. Reproducing this tilt requires {\it both} a non-universal IMF and a non-universal halo response. Our best model has mass-follows-light at low masses (Msps < 10^{11.2}M_sun) and unmodified NFW haloes at M_sps \sim 10^{11.5} M_sun. The stellar masses imply a mass dependent IMF which is "lighter" than Salpeter at low masses and "heavier" than Salpeter at high masses.

Mass estimates from stellar proper motions: the mass of ω Centauri

We lay out and apply methods to use proper motions of individual kinematic tracers for estimating the dynamical mass of star clusters. We first describe a simple projected mass estimator and then develop an approach that evaluates directly the likelihood of the discrete kinematic data given the model predictions. Those predictions may come from any dynamical modelling approach, and we implement an analytic King model, a spherical isotropic Jeans equation model and an axisymmetric, anisotropic Jeans equation model.We apply these approaches to the enigmatic globular cluster omega Centauri, combining the proper motion from van Leeuwen et al (2000) with improved photometric cluster membership probabilities. We show that all mass estimates based on spherical isotropic models yield $(4.55\pm 0.1) \times 10^6 M_{\odot} [D/5.5 \pm 0.2 kpc]^3$, where our modelling allows us to show how the statistical precision of this estimate improves as more proper motion data of lower signal-to-noise are included. MLM predictions, based on an anisotropic axisymmetric Jeans model, indicate for $\omega$ Cen that the inclusion of anisotropies is not important for the mass estimates, but that accounting for the flattening is: flattened models imply $(4.05\pm 0.1) \times 10^6 M_{\odot} [D/5.5 \pm 0.2 kpc]^3$, 10% lower than when restricting the analysis to a spherical model. The best current distance estimates imply an additional uncertainty in the mass estimate of 12%.

Do globular clusters possess dark matter haloes? A case study in NGC 2419

We use recently published measurements of the kinematics, surface brightness and stellar mass-to-light ratio of the globular cluster NGC 2419 to examine the possibility that this Galactic halo satellite is embedded in a low-mass dark matter halo. NGC 2419 is a promising target for such a study, since its extreme Galactocentric distance and large mass would have greatly facilitated the retention of dark matter. A Markov-Chain Monte Carlo approach is used to investigate composite dynamical models containing a stellar and a dark matter component. We find that it is unlikely that a significant amount of dark matter (less than approx. 6% of the luminous mass inside the tidal limit of the cluster) can be present if the stars follow an anisotropic Michie model and the dark matter a double power law model. However, we find that more general models, derived using a new technique we have developed to compute non-parametric solutions to the spherical Jeans equation, suggest the presence of a significant dark matter fraction (approximately twice the stellar mass). Thus the presence of a dark matter halo around NGC 2419 cannot be fully ruled out at present, yet any dark matter within the 10 arcmin visible extent of the cluster must be highly concentrated and cannot exceed 1.1x10^6 Solar masses (99% confidence), in stark contrast to expectations for a plausible progenitor halo of this structure.

Semi-empirical catalog of early-type galaxy-halo systems: dark matter density profiles, halo contraction and dark matter annihilation strength

With Sloan Digital Sky Survey galaxy data and halo data from up-to-date N-body simulations within the ΛCDM framework we construct a semi-empirical catalog (SEC) of early-type galaxy-halo systems by making a self-consistent bivariate statistical match of stellar mass (M⋆) and velocity dispersion (σ) with halo virial mass (Mvir) as demonstrated here for the first time. We then assign stellar mass profile and velocity dispersion profile parameters to each system in the SEC using their observed correlations with M⋆ and σ. 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 Navarro-Frenk-White or Einasto and their mean inner density slope and concentration vary systematically with Mvir. Statistical tests of the distribution of profiles at fixed Mvir rule out the null hypothesis that it follows the distribution predicted by dissipationless N-body simulations for Mvir≲1013.5 – 14.5 M⊙. These dark matter profiles imply that dark matter density is, on average, enhanced significantly in the inner region of halos with Mvir≲1013.5 – 14.5 M⊙ 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 Mvir = 1012 M⊙, and (2) the inner density slope has a mean of ⟨α⟩ ≈ 1.3 with ρdm(r)∝r−α and a halo-to-halo rms scatter of rms(α) ∼ 0.4–0.5 for 1012 M⊙≲Mvir≲1013 – 14 M⊙ steeper than the NFW profile (α = 1). Based on our results we predict that halos of nearby elliptical and lenticular galaxies can, in principle, be promising targets for γ-ray emission from dark matter annihilation.