Accurate masses for dispersion-supported galaxies

By Joe Wolf, G. Martinez, James S. Bullock, M. Kaplinghat, M. Geha, R. Muñoz, J. Simon, Frank F. Avedo. 2009

583 citations recorded by the source corpus.

We derive an accurate mass estimator for dispersion-supported stellar systems and demonstrate its validity by analysing 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 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 as long as the projected velocity dispersion profile is fairly flat near the half-light radius, as is typically observed. We find M 1/2 = 3G -1 (σ 2 los )r 1/2 ≃ 4G -1 (σ 2 los )R e , where (σ 2 los ) is the luminosity-weighted square of the line-of-sight velocity dispersion and R e 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 a mass of approximately 3 x 10 9 M ⊙ . assuming a A cold dark matter cosmology. The faintest MW dSphs seem to have formed in dark matter haloes that are at least as massive as those of the brightest MW dSphs, despite the almost five orders of magnitude spread in luminosity between them. We expand our analysis to the full range of observed dispersion-supported stellar systems and examine their dynamical I-band mass-to-light ratios Υ I 1/2 . The Υ I 1/2 versus M 1/2 relation for dispersion-supported galaxies follows a U shape, with a broad minimum near Υ I 1/2 ≃ 3 that spans dwarf elliptical galaxies to normal ellipticals, a steep rise to Υ I 1/2 ≃ 3200 for ultra-faint dSphs and a more shallow rise to Υ I 1/2 ≃ 800 for galaxy cluster spheroids.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/79ef142dabbd610a5c83d4558d6dc4d7d3ca428b

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Citations in the corpus

The impact of baryonic physics on the structure of dark matter haloes: the view from the FIRE cosmological simulations (2015, methodology): “For comparison we also include the observational data from Milky Way satellite galaxies (Strigari et al. 2007; Walker et al. 2009; Wolf et al. 2010) and Local Group field galaxies (Kirby et al. 2014).”
SEARCH FOR GAMMA-RAY EMISSION FROM DES DWARF SPHEROIDAL GALAXY CANDIDATES WITH FERMI-LAT DATA (2015, background): “…half-light radius of a dSph and the mass within the half-light radius have been found to obey a simple scaling relation, assuming that the velocity dispersions are nearly constant in radius and the anisotropy of the stars is not strongly radially dependent (Walker et al. 2009; Wolf et al. 2010).”
A METHOD FOR MEASURING (SLOPES OF) THE MASS PROFILES OF DWARF SPHEROIDAL GALAXIES (2011, background): “First, for a spherically symmetric dSph in dynamic equilibrium, the product of halflight radius and (squared) velocity dispersion provides an estimate of the mass enclosed within the halflight radius (Walker et al. 2009a; Wolf et al. 2010).”
MAMPOSSt: Modelling Anisotropy and Mass Profiles of Observed Spherical Systems – I. Gaussian 3D velocities (2012, methodology): “A common method to extract the mass profile is to assume that the line-of-sight (hereafter, LOS) velocity distribution, at given projected radius, is Gaussian (Strigari et al. 2008; Battagliaet al. 2008; Wolf et al. 2010).”
Subhaloes in self-interacting galactic dark matter haloes (2012, background): “In particular, Wolf et al. (2010) found that the value of the mass enclosed within the 3-dimensional deprojected half-light radius r1/2 is accurately given by M1/2 ≈ 3G−1 〈 σ2los 〉 r1/2 (or equivalently V 2circ(r1/2) ≈ 3 〈 σ2los 〉 ), where〈 σ2los 〉 is the luminosity-weighted square of the…”
Dark matter cores all the way down (2015, background): “…exquisite detail, providing detailed star formation histories (e.g. Weisz et al. 2014); orbits (e.g. Lux et al. 2010); masses (e.g. Walker et al. 2009; Wolf et al. 2010); and dark matter mass profiles (e.g. Kleyna et al. 2003; Goerdt et al. 2006; Cole et al. 2012; Battaglia et al. 2008; Walker &…”
Can feedback solve the too-big-to-fail problem? (2013, methodology): “…along with observed values of the mass enclosed within the deprojected half-light radius of each of the bright dSphs around the Milky Way (computed by Wolf et al. 2010, who used data from Walker et al. 2009 in addition to data from Muñoz et al. 2005; Koch et al. 2007; Simon & Geha 2007 and Mateo…”
THE BARYON CONTENT OF COSMIC STRUCTURES (2009, background): “We assume isotropic internal orbits to relate the observed line-of sight velocity dispersion σ to the circular velocity: Vc = √ 3σ (Wolf et al. 2009).”
SEARCH FOR DARK MATTER SATELLITES USING FERMI-LAT (2012, background): “The central mass of Draco is well known from stellar kinematics (Strigari et al. 2008; Walker et al. 2009; Wolf et al. 2010); however, the total dark matter mass for Draco is less certain due to the lack of kinematic measurements in the outer regions of the halo.”
On the correlations between galaxy properties and supermassive black hole mass (2011, background): “Wolf et al. (2010) found a different coefficient (α = 4) for their derivation of a mass estimator for stellar systems supported by velocity dispersion.”
The ATLAS3D project XV: benchmark for early-type galaxies scaling relations from 260 dynamical models: mass-to-light ratio, dark matter, fundamental plane and mass plane (2012, methodology): “The remaining 10 per cent difference from Wolf et al. (2010) is easily explained by the small increase of 〈σ 2los〉∞ due to the inclusion of a dark halo.”
ETHOS - an effective theory of structure formation: dark matter physics as a possible explanation of the small-scale CDM problems (2015, background): “The right panel also contains observational data from nine of the classical MW dSphs taken from Wolf et al. (2010).”
The Local Group on FIRE: dwarf galaxy populations across a suite of hydrodynamic simulations (2018, methodology): “We calculate V1/2 = Vcirc(R1/2), the implied circular velocity at the 3D (deprojected) half-light radius, for the majority of our galaxies with the Wolf et al. (2010) formula, i.e. based on the velocity dispersion of the stars.”
One Law to Rule Them All: The Radial Acceleration Relation of Galaxies (2016, background): “Following Wolf et al. (2010), we have gobs(r1/2) = −∇Φtot(r1/2) = 3 σ2? r1/2 , (6) where r1/2 is the deprojected 3D half-light radius.”