We derive an accurate mass estimator for dispersion-supported stellar systems and demonstrate its validity by analyzing resolved line-of-sight velocity data for globular clusters, dwarf galaxies, and elliptical galaxies. Specifically, by manipulating the spherical Jeans equation we show that the dynamical mass enclosed within the 3D deprojected half-light radius r_1/2 can be determined with only mild assumptions about the spatial variation of the stellar velocity dispersion anisotropy. We find M_1/2 = 3 σ_los^2 r_1/2 / G ~ 4 σ_los^2 R_eff / G, where σ_los^2 is the luminosity-weighted square of the line-of-sight velocity dispersion and R_eff is the 2D projected half-light radius. While deceptively familiar in form, this formula is not the virial theorem, which cannot be used to determine accurate masses unless the radial profile of the total mass is known a priori. We utilize this finding to show that all of the Milky Way dwarf spheroidal galaxies (MW dSphs) are consistent with having formed within a halo of mass approximately 3 x 10^9 M_sun in Lambda CDM cosmology. The faintest MW dSphs seem to have formed in dark matter halos that are at least as massive as those of the brightest MW dSphs, despite the almost five orders of magnitude spread in luminosity. We expand our analysis to the full range of observed dispersion-supported stellar systems and examine their I-band mass-to-light ratios (M/L). The M/L vs. M_1/2 relation for dispersion-supported galaxies follows a U-shape, with a broad minimum near M/L ~ 3 that spans dwarf elliptical galaxies to normal ellipticals, a steep rise to M/L ~ 3,200 for ultra-faint dSphs, and a more shallow rise to M/L ~ 800 for galaxy cluster spheroids.
We investigate the reliability of mass estimators based on the observable velocity dispersion and half-light radius $R_\mathrm{h}$ for dispersion-supported galaxies. We show how to extend them to flattened systems and provide simple formulae for the mass within an ellipsoid under the assumption the dark matter density and the stellar density are stratified on the same self-similar ellipsoids. We demonstrate explicitly that the spherical mass estimators (Walker et al. 2009, Wolf et al. 2010) give accurate values for the mass within the half-light ellipsoid, provided $R_\mathrm{h}$ is replaced b…
An improved transformation of the full width at half maxima (FWHM) of the [O III] 5007 line in AGNs to the stellar velocity dispersion, sigma, of the host galaxy is given. This significantly reduces the systematic errors in using the [O III] FWHM as a proxy for sigma. AGN black hole masses, M, estimated using the Dibai single epoch spectrum method, are combined with the new estimates of sigma to give a revised AGN M-sigma relationship extending up to high masses. This shows that the masses of the most massive black holes are systematically higher than predicted by extrapolation of M \propto si…
The observed stellar kinematics of dispersion-supported galaxies are often used to measure dynamical masses. Recently, several analytical relationships between the stellar line-of-sight velocity dispersion, the projected (2D) or deprojected (3D) half-light radius, and the total mass enclosed within the half-light radius, relying on the spherical Jeans equation, have been proposed. Here, we make use of the APOSTLE cosmological hydrodynamical simulations of the Local Group to test the validity and accuracy of such mass estimators for both dispersion and rotation-supported galaxies, for field and…
We examine scaling relations of dispersion-supported galaxies over more than eight orders of magnitude in luminosity by transforming standard fundamental plane parameters into a space of mass (M1/2), radius (r1/2), and luminosity (L1/2). We find that from ultra-faint dwarf spheroidals to giant cluster spheroids, dispersion-supported galaxies scatter about a one-dimensional "fundamental curve" through this MRL space. The weakness of the M1/2-L1/2 slope on the faint end may imply that potential well depth limits galaxy formation in small galaxies, while the stronger dependence on L1/2 on the bri…
Using a set of 73 numerically simulated galaxy clusters, we have characterised the statistical and physical biases for three velocity dispersion and mass estimators, namely biweight, gapper and standard deviation, in the small number of galaxies regime ($N_{gal} \leq 75$), both for the determination of the velocity dispersion and the dynamical mass of the clusters via the $σ-M$ relation. These results are used to define a new set of unbiased estimators, that are able to correct for those statistical biases. By applying these new estimators to a subset of simulated observations, we show that th…
We study the use of red sequence selected galaxy spectroscopy for unbiased estimation of galaxy cluster masses. We use the publicly available galaxy catalog produced using the semi-analytic model of De Lucia & Blaizot (2007) on the Millenium Simulation (Springel et al. 2005). We explore the impacts on selection using galaxy color, projected separation from the cluster center, and galaxy luminosity. We study the relationship between cluster mass and velocity dispersion and identify and characterize the following sources of bias and scatter: halo triaxiality, dynamical friction of red luminous g…
We present a measurement of average histograms of line-of-sight velocities over pairs of galaxies and galaxy clusters. Since the histogram can be measured at different galaxy-cluster separations, this observable is commonly referred to as the stacked phase-space density. We formulate the stacked phase-space density based on a halo-model approach so that the model can be applied to real samples of galaxies and clusters. We examine our model by using an actual sample of massive clusters with known weak-lensing masses and spectroscopic observations of galaxies around the clusters. A likelihood an…
We present Keck LRIS spectroscopy for a sample of 103 massive galaxies with redshifts 0.9 < z < 1.6. Of these, 56 are quiescent with high signal-to-noise absorption line spectra, enabling us to determine robust stellar velocity dispersions for the largest sample yet available beyond a redshift of 1. Together with effective radii measured from deep Hubble Space Telescope images, we calculate dynamical masses and address key questions relating to the puzzling size growth of quiescent galaxies over 0 < z < 2. We examine the relationship between stellar and dynamical masses at high redshift, findi…
We present the stellar velocity dispersion measurements for 5 Luminous Compact Galaxies (LCGs) at z=0.5-0.7. These galaxies are vigorously forming stars with average SFR $\sim$ 40 M$_{\odot}$/yr. We find that their velocity dispersions range from $\sim137\ \rm{km/s}$ to $260\ \rm{km/s}$, while their stellar masses range between $4\times 10^{9}$ and $10^{11}$ M$_{\odot}$. If these LCGs evolve passively after this major burst of star formation, their masses and velocity dispersions, as well as their evolved colours and luminosities are most consistent with the values characteristic of early-type…
The kinematic dispersions of disc stars can be used to measure the dynamic contributions of baryons to the rotation curves of spiral galaxies and hence to trace the amount and distribution of the remaining dark matter. However, the simple single-component infinite disc model traditionally used to convert stellar dispersions to mass-densities is no longer adequate. The dark matter halo has a significant effect upon the stellar dispersions for any non-maximal disc. The correction for cuspy dark matter halos is particularly large, suggesting that such models are not consistent with the observed s…
We extend the comparison between the set of local galaxies having dynamically measured black holes with galaxies in the Sloan Digital Sky Survey (SDSS). We first show that the most up-to-date local black hole samples of early-type galaxies with measurements of effective radii, luminosities, and Sérsic indices of the bulges of their host galaxies, have dynamical mass and Sérsic index distributions consistent with those of SDSS early-type galaxies of similar bulge stellar mass. The host galaxies of local black hole samples thus do not appear structurally different from SDSS galaxies, sharing sim…
It is shown that, if the tracer population is supported by a spherical dark halo with a core or a cusp diverging more slowly than that of a singular isothermal sphere, the logarithmic cusp slope 'g' of the tracers must be given exactly by g=2b where b is their velocity anisotropy parameter at the center unless the same tracers are dynamically cold at the center. If the halo cusp diverges faster than that of the singular isothermal sphere, the velocity dispersion of the tracers must diverge at the center too. In particular, if the logarithmic halo cusp slope is larger than two, the diverging ve…
We present Gran-Telescopio-Canarias/OSIRIS optical spectra of 4 of the most compact and massive early-type galaxies in the Groth Strip Survey at redshift z~1, with effective radii Reff=0.5-2.4 kpc and photometric stellar masses Mstar=1.2-4x10^11 Msun. We find these galaxies have velocity dispersions sigma=156-236 km/s. The spectra are well fitted by single stellar population models with approximately 1 Gyr of age and solar metallicity. We find that: i) the dynamical masses of these galaxies are systematically smaller by a factor of ~6 than the published stellar masses using BRIJK photometry; i…
We investigate how accurately the total mass of neutrinos is constrained from the magnitude dispersion of SNe Ia due to the effects of gravitational lensing. For this purpose, we use the propagation equation of light bundles in a realistic inhomogeneous universe and propose a sample selection for supernovae to avoid difficulties associated with small-scale effects such as strong lensing or shear effects. With a fitting formula for the nonlinear matter power spectrum taking account of the effects of massive neutrinos, we find that in our model it is possible to obtain the upper limit $Σm_ν \sim…
We present the measurements of gas and stellar velocity dispersions in 17 circumnuclear star-forming regions (CNSFRs) and the nuclei of three barred spiral galaxies: NGC2903, NGC3310 and NGC3351 from high dispersion spectra. The stellar dispersions have been obtained from the CaII triplet (CaT) lines at 8494, 8542, 8662A, while the gas velocity dispersions have been measured by Gaussian fits to the Hbeta and to the [OIII]5007A\ lines. The CNSFRs, with sizes of about 100 to 150pc in diameter, are seen to be composed of several individual star clusters with sizes between 1.5 and 6.2pc on HST ima…
We measure black hole masses for 71 BL Lac objects from the Sloan Digital Sky Survey with redshifts out to z~0.4. We perform spectral decompositions of their nuclei from their host galaxies and measure their stellar velocity dispersions. Black hole masses are then derived from the black hole mass - stellar velocity dispersion relation. We find BL Lac objects host black holes of similar masses, ~10^{8.5} M_sun, with a dispersion of 0.4 dex, similar to the uncertainties on each black hole measurement. Therefore, all BL Lac objects in our sample have the same indistinguishable black hole mass. Th…
We present galaxy velocity dispersions and dynamical mass estimates for 44 galaxy clusters selected via the Sunyaev-Zel'dovich (SZ) effect by the Atacama Cosmology Telescope. Dynamical masses for 18 clusters are reported here for the first time. Using \Nbody\ simulations, we model the different observing strategies used to measure the velocity dispersions and account for systematic effects resulting from these strategies. We find that the galaxy velocity distributions may be treated as isotropic, and that an aperture correction of up to 7 per cent in the velocity dispersion is required if the …
Several authors have reported that the dynamical masses of massive compact galaxies ($M_\star \gtrsim 10^{11} \ \mathrm{M_\odot}$, $r_\mathrm{e} \sim 1 \ \mathrm{kpc}$), computed as $M_\mathrm{dyn} = 5.0 \ σ_\mathrm{e}^2 r_\mathrm{e} / G$, are lower than their stellar masses $M_\star$. In a previous study from our group, the discrepancy is interpreted as a breakdown of the assumption of homology that underlie the $M_\mathrm{dyn}$ determinations. Here, we present new spectroscopy of six redshift $z \approx 1.0$ massive compact ellipticals from the Extended Groth Strip, obtained with the 10.4 m …
The evolution of galaxy cluster counts is a powerful probe of several fundamental cosmological parameters. A number of recent studies using this probe have claimed tension with the cosmology preferred by the analysis of the Planck primary CMB data, in the sense that there are fewer clusters observed than predicted based on the primary CMB cosmology. One possible resolution to this problem is systematic errors in the absolute halo mass calibration in cluster studies, which is required to convert the standard theoretical prediction (the halo mass function) into counts as a function of the observ…
This work aims to study the distribution of luminous and dark matter in Coma early-type galaxies. Dynamical masses obtained under the assumption that mass follows light do not match with the masses of strong gravitational lens systems of similar velocity dispersions. Instead, dynamical fits with dark matter halos are in good agreement with lensing results. We derive mass-to-light ratios of the stellar populations from Lick absorption line indices, reproducing well the observed galaxy colours. Even in dynamical models with dark matter halos the amount of mass that follows the light increases mo…
We provide fits to the distribution of galaxy luminosity, size, velocity dispersion and stellar mass as a function of concentration index C_r and morphological type in the SDSS. We also quantify how estimates of the fraction of `early' or `late' type galaxies depend on whether the samples were cut in color, concentration or light profile shape, and compare with similar estimates based on morphology. Our fits show that Es account for about 20% of the r-band luminosity density, rho_Lr, and 25% of the stellar mass density, rho_*; including S0s and Sas increases these numbers to 33% and 40%, and 5…
Dark matter phenomena in rotationally supported galaxies exhibit a characteristic acceleration scale of $g_\dagger \approx 1.2\times 10^{-10}$ m s$^{-2}$. Whether this acceleration is a manifestation of a universal scale, or merely an emergent property with an intrinsic scatter, has been debated in the literature. Here we investigate whether a universal acceleration scale exists in dispersion-supported galaxies using two uniform sets of integral field spectroscopy (IFS) data from SDSS-IV MaNGA and ATLAS$^{\rm 3D}$. We apply the spherical Jeans equation to 15 MaNGA and 4 ATLAS$^{\rm 3D}$ slow-r…
In the warm dark matter scenario, the Press-Schechter formalism is valid only for galaxy masses greater than the "velocity dispersion cut-off". In this work we extend the predictions to masses below the velocity dispersion cut-off, and thereby address the "Missing Satellites Problem", and the rest-frame ultra-violet luminosity cut-off required to not exceed the measured reionization optical depth. We find agreement between predictions and observations of these two phenomena. As a by-product, we obtain the empirical Tully-Fisher relation from first principles.
A simple refinement is proposed to the Dibai method for determining black hole masses in type-1 thermal AGNs. Comparisons with reverberation mapping black hole masses and host galaxy bulge properties suggest that the method is accurate to +/- 0.15 dex. Contrary to what was thought when the black hole mass - stellar velocity dispersion ("M - sigma") relationship was first discovered, it does not have a lower dispersion than the black hole mass - bulge luminosity ("M - L") relationship. The dispersion in the M - L relationship for AGNs decreases strongly with increasing black hole mass or bulge …
[Abridged] We present an analysis of the relation between the masses of cluster- and group-sized halos, extracted from $Λ$CDM cosmological N-body and hydrodynamic simulations, and their velocity dispersions, at different redshifts from $z=2$ to $z=0$. The main aim of this analysis is to understand how the implementation of baryonic physics in simulations affects such relation, i.e. to what extent the use of the velocity dispersion as a proxy for cluster mass determination is hampered by the imperfect knowledge of the baryonic physics. In our analysis we use several sets of simulations with dif…
The second catalogue of Planck Sunyaev-Zeldovich (SZ) sources, hereafter PSZ2, represents the largest galaxy cluster sample selected by means of their SZ signature in a full-sky survey. Using telescopes at the Canary Island observatories, we conducted the long-term observational program 128- MULTIPLE-16/15B (hereafter LP15), a large and complete optical follow-up campaign of all the unidentified PSZ2 sources in the northern sky, with declinations above $-15^\circ$ and no correspondence in the first Planck catalogue PSZ1. This paper is the third and last in the series of LP15 results, after Str…
We assess evolution in the black hole mass - stellar velocity dispersion relationship (M-sigma relationship) for quasars in the Sloan Digital Sky Survey Data Release 7 for the redshift range 0.1 < z < 1.2. We estimate the black hole mass using the "photoionization method," with the broad Hbeta or Mg II emission line and the quasar continuum luminosity. For the stellar velocity dispersion, we use the narrow [O III] or [O II] emission line as a surrogate. This study is a follow-up to an earlier study in which we investigated evolution in the M-sigma relationship in quasars from Data Release 3. T…
Many young extra-galactic clusters have a measured velocity dispersion that is too high for the mass derived from their age and total luminosity, which has led to the suggestion that they are not in virial equilibrium. Most of these clusters are confined to a narrow age range centred around 10 Myr because of observational constraints. At this age the cluster light is dominated by luminous evolved stars, such as red supergiants, with initial masses of ~13-22 Msun for which (primordial) binarity is high. In this study we investigate to what extent the observed excess velocity dispersion is the r…
We investigate effects of baryon dissipation on the dark matter virial scaling relation between total mass and velocity dispersion and the velocity bias of galaxies in groups and clusters using self-consistent cosmological simulations. We show that the baryon dissipation increases the velocity dispersion of dark matter within the virial radius by 5% - 10%. The effect is mainly driven by the change in density and gravitational potential in inner regions of cluster, and it is larger in lower mass systems where gas cooling and star formation are more efficient. We also show that the galaxy veloci…
We present deep Keck/LRIS spectroscopy and HST/WFC3 imaging in the rest-frame optical for a sample of eight galaxies at z~1.5 with high photometrically-determined stellar masses. The data are combined with VLT/XShooter spectra of five galaxies from van de Sande et al. (2011, 2012 to be submitted). We find that these thirteen galaxies have high velocity dispersions, with a median of sigma=301 km s^{-1}. This high value is consistent with their relatively high stellar masses and compact sizes. We study their stellar populations using the strength of Balmer absorption lines, which are not sensiti…
We use a sample of 53 galaxy clusters at 0.03 < z < 0.1 with available masses derived from the caustic technique and with velocity dispersions computed using 208 galaxies on average per cluster, in order to investigate the scaling between richness, mass and velocity dispersion. A tight scaling between richness and mass is found, with an intrinsic scatter of only 0.19 dex in mass and with a slope one, i.e. clusters which have twice as many galaxies are twice as massive. When richness is measured without any knowledge of the cluster mass or linked parameters (such as r200), it can predict mass w…
