Tidal stirring of Milky Way satellites: a simple picture with the integrated tidal force

Most of dwarf spheroidal galaxies in the Local Group were probably formed via environmental processes like the tidal interaction with the Milky Way. We study this process via N-body simulations of dwarf galaxies evolving on seven different orbits around the Galaxy. The dwarf galaxy is initially composed of a rotating stellar disk and a dark matter halo. Due to the action of tidal forces it loses mass and the disk gradually transforms into a spheroid while stellar motions become increasingly random. We measure the characteristic scale-length of the dwarf, its maximum circular velocity, mass, shape and kinematics as a function of the integrated tidal force along the orbit. The final properties of the evolved dwarfs are remarkably similar if the total tidal force they experienced was the same, independently of the actual size and eccentricity of the orbit.Comment: 5 pages, 2 figures, contribution to the proceedings of JENAM 2010 in Lisbon, Symposium 2 "Environment and the formation of galaxies: 30 years later", comments welcom

Does the Fornax dwarf spheroidal have a central cusp or core?

The dark matter dominated Fornax dwarf spheroidal has five globular clusters orbiting at ~1 kpc from its centre. In a cuspy CDM halo the globulars would sink to the centre from their current positions within a few Gyrs, presenting a puzzle as to why they survive undigested at the present epoch. We show that a solution to this timing problem is to adopt a cored dark matter halo. We use numerical simulations and analytic calculations to show that, under these conditions, the sinking time becomes many Hubble times; the globulars effectively stall at the dark matter core radius. We conclude that the Fornax dwarf spheroidal has a shallow inner density profile with a core radius constrained by the observed positions of its globular clusters. If the phase space density of the core is primordial then it implies a warm dark matter particle and gives an upper limit to its mass of ~0.5 keV, consistent with that required to significantly alleviate the substructure problem.Comment: 6 pages, 5 figures, accepted for publication in MNRAS, high resolution simulations include

On the physical origin of dark matter density profiles

The radial mass distribution of dark matter haloes is investigated within the framework of the spherical infall model. We present a new formulation of spherical collapse including non-radial motions, and compare the analytical profiles with a set of high-resolution N-body simulations ranging from galactic to cluster scales. We argue that the dark matter density profile is entirely determined by the initial conditions, which are described by only two parameters: the height of the primordial peak and the smoothing scale. These are physically meaningful quantities in our model, related to the mass and formation time of the halo. Angular momentum is dominated by velocity dispersion, and it is responsible for the shape of the density profile near the centre. The phase-space density of our simulated haloes is well described by a power-law profile, rho/sigma^3 = 10^{1.46\pm0.04} (rho_c/Vvir^3) (r/Rvir)^{-1.90\pm0.05}. Setting the eccentricity of particle orbits according to the numerical results, our model is able to reproduce the mass distribution of individual haloes.Comment: 12 pages, 13 figures, submitted to MNRA

A Method for Measuring (Slopes of) the Mass Profiles of Dwarf Spheroidal Galaxies

We introduce a method for measuring the slopes of mass profiles within dwarf spheroidal (dSph) galaxies directly from stellar spectroscopic data and without adopting a dark matter halo model. Our method combines two recent results: 1) spherically symmetric, equilibrium Jeans models imply that the product of halflight radius and (squared) stellar velocity dispersion provides an estimate of the mass enclosed within the halflight radius of a dSph stellar component, and 2) some dSphs have chemo-dynamically distinct stellar \textit{sub}components that independently trace the same gravitational potential. We devise a statistical method that uses measurements of stellar positions, velocities and spectral indices to distinguish two dSph stellar subcomponents and to estimate their individual halflight radii and velocity dispersions. For a dSph with two detected stellar subcomponents, we obtain estimates of masses enclosed at two discrete points in the same mass profile, immediately defining a slope. Applied to published spectroscopic data, our method distinguishes stellar subcomponents in the Fornax and Sculptor dSphs, for which we measure slopes $\Gamma\equiv \Delta \log M / \Delta \log r=2.61_{-0.37}^{+0.43}$ and $\Gamma=2.95_{-0.39}^{+0.51}$, respectively. These values are consistent with 'cores' of constant density within the central few-hundred parsecs of each galaxy and rule out `cuspy' Navarro-Frenk-White (NFW) profiles ($d\log M/d\log r \leq 2$ at all radii) with significance \ga 96% and \ga 99%, respectively. Tests with synthetic data indicate that our method tends systematically to overestimate the mass of the inner stellar subcomponent to a greater degree than that of the outer stellar subcomponent, and therefore to underestimate the slope $\Gamma$ (implying that the stated NFW exclusion levels are conservative).Comment: Accepted for publication in The Astrophysical Journal (added references

Unbiased constraints on ultralight axion mass from dwarf spheroidal galaxies

It has been suggested that the internal dynamics of dwarf spheroidal galaxies (dSphs) can be used to test whether or not ultralight axions with $m_a\sim 10^{-22}\text{eV}$ are a preferred dark matter candidate. However, comparisons to theoretical predictions tend to be inconclusive for the simple reason that while most cosmological models consider only dark matter, one observes only baryons. Here we use realistic kinematic mock data catalogs of Milky Way dSph's to show that the "mass-anisotropy degeneracy" in the Jeans equations leads to biased bounds on the axion mass in galaxies with unknown dark matter halo profiles. In galaxies with multiple chemodynamical components this bias can be partly removed by modelling the mass enclosed within each subpopulation. However, analysis of the mock data reveals that the least-biased constraints on the axion mass result from fitting the luminosity-averaged velocity dispersion of the individual chemodynamical components directly. Applying our analysis to two dSph's with reported stellar subcomponents, Fornax and Sculptor, and assuming that the halo profile has not been acted on by baryons, yields core radii $r_{c}>1.5$ kpc and $r_c> 1.2$ kpc respectively, and $m_a<0.4\times 10^{-22}\text{eV}$ at 97.5\% confidence. These bounds are in tension with the number of observed satellites derived from simple (but conservative) estimates of the subhalo mass function in Milky Way-like galaxies. We discuss how baryonic feedback might affect our results, and the impact of such a small axion mass on the growth of structures in the Universe.Comment: 17 pages, 12 figures. Version to match MNRAS. Analysis extended to anisotropic mocks. Main conclusions unchange

Dark Matter in the Milky Way's Dwarf Spheroidal Satellites

The Milky Way's dwarf spheroidal satellites include the nearest, smallest and least luminous galaxies known. They also exhibit the largest discrepancies between dynamical and luminous masses. This article reviews the development of empirical constraints on the structure and kinematics of dSph stellar populations and discusses how this phenomenology translates into constraints on the amount and distribution of dark matter within dSphs. Some implications for cosmology and the particle nature of dark matter are discussed, and some topics/questions for future study are identified.Comment: A version with full-resolution figures is available at http://www.cfa.harvard.edu/~mwalker/mwdsph_review.pdf; 70 pages, 22 figures; invited review article to be published in Vol. 5 of the book "Planets, Stars, and Stellar Systems", published by Springe