Tailored mass estimators for Milky Way dwarf Spheroidals

TL;DR

This work shows that dynamical mass estimates for Milky Way dwarf spheroidal galaxies are highly sensitive to the shape of the stellar density profile. By fitting flexible 2βγ stellar profiles and applying the projected virial theorem, the authors construct tailored mass estimators whose μ coefficients vary with radius and halo type, revealing systematic uncertainties up to factors of ~10. Incorporating these tailored masses into scaling relations, such as the enclosed mass vs. stellar mass and the Radial Acceleration Relation, significantly broadens the expected scatter and challenges the universality of simple estimators. The results highlight the need for population-level modeling of stellar-density shapes and halo structure to robustly interpret dSph dynamics and their implications for dark matter physics.

Abstract

Assuming spherical symmetry and dynamical equilibrium within a given gravitational potential, a dwarf spheroidal (dSph) galaxy's globally averaged stellar velocity dispersion depends entirely on the shape of its stellar density profile. Thus, the dynamical inference of a dSph's gravitational potential is necessarily sensitive to assumptions about that shape. Relaxing standard assumptions, we fit flexible stellar density models to observations of the Milky Way's known dSph satellites. Considering various choices for the density profile shape and spatial extent of a host dark matter halo, we use the virial theorem to propagate observational uncertainties about the shapes of the inferred dSph stellar density profiles to uncertainties in the inferred dynamical masses. We find that the observed structural diversity of the Milky Way dSph population implies a large range of potential systematic errors (up to factors of 10) associated with standard dynamical mass estimators. We show that accounting for these observational and systematic uncertainties can significantly alter the appearance and behavior of dSph dynamical scaling relations, including enclosed dynamical mass vs. stellar mass and the Radial Acceleration Relation.

Figures (8)

• Figure 1: The stellar density profiles of Milky Way satellites display a remarkable diversity in shapes, which can be accurately fitted by the flexible $2\beta\gamma$ 3D stellar density distribution of Equation \ref{['eq:2bg']}. Shown are binned stellar surface number density profiles $\Sigma$ as a function of the 2D radius $R$ for the three Milky Way satellites Sculptor, Ursa Major II, and Bootes I, normalized by the average number of stars within the half-light radius. Black points with error bars shown binned projected stellar number density profiles (see Section \ref{['sec data']} for details). A black horizontal line indicates a the central value of the gradient-fitted foreground and colored bands indicate the 1-sigma uncertainty region of projected $2\beta\gamma$ profiles.
• Figure 2: For mass follows light models, the dynamical coefficient $\mu$ (see Equation \ref{['mu 1']}) depends on the radius $r$ used when defining the enclosed mass $M({<}r)$. Shown is the variation in $\mu$ vs. enclosing radius between the three galaxies shown in Figure \ref{['SB fig']}. $\mu$ is plotted for the best fit parameters (solid lines) with 1-sigma shading from uncertainties on $R_{\mathrm{h}}$, distance, $\beta$, and $\gamma$. Black symbols show simple mass estimators taken from the literature.
• Figure 3: Like Figure \ref{['MFL fig']}, but showing $\mu$ as a function of the ratio of projected stellar half-light radius to the characteristic size of the dark matter halo ($R_{\mathrm h} /r_{\mathrm{max}}$). Here, $\mu$ depends on $R_{\mathrm h} /r_{\mathrm{max}}$ as well as the shapes of the stellar and dark matter profiles. There is a significant variation in $\mu(R_{\mathrm h} /r_{\mathrm{max}})$ between different $2\beta\gamma$ profiles. The left (right) hand panel shows $\mu$ calculated under the assumption of a cuspy (cored) dark matter halo (see Equations \ref{['cusp density']} and \ref{['core density']}) . Solid lines show the best fit parameters, shading shows 1-sigma observational uncertainties on $\beta$ and $\gamma$. The two dotted grey lines show the mass estimators of walker2009universal and wolf2010accurate as labeled. Note that for this figure we treat stars as massless tracers.
• Figure 4: The half-light radii obtained from the fits to the $2\beta\gamma$ model described in Section \ref{['sec data']} are in most cases consistent with published values in the Local Volume Database (LVD) of Pace2024arXiv241107424P. The left-hand panel compares the half-light radii from the LVD against our fits, revealing four outliers: Hercules (yellow), Ursa Major I (light blue), Carina II (pink), and Leo VI (dark blue) obtained by fitting $2\beta\gamma$ models with half-light radii $5-10$ times larger than previously published values from the LVD. The center and right-hand panels show the ratio of the two half-light radii as a function of the fitted value of $\beta$ and $\gamma$, respectively. Sculptor, Bootes I, and Ursa Major II are plotted in the same colors as in Figures \ref{['SB fig']}-\ref{['cusp/core']}, and Crater II is shown in teal. The dashed line on the leftmost panel shows $R_{\mathrm h, 2\beta\gamma} = R_{\mathrm{h,LVD}}$.
• Figure 5: The dependence of $\mu$ on the inner and outer slopes $\beta$ and $\gamma$ of the $2\beta\gamma$ stellar density profile, for cuspy (upper row) and cored (lower row) dark matter halos. We show in blue and red the values of $\mu$ from the best-fit $2\beta\gamma$ model for each dSph for a fixed segregation of $R_{\mathrm{h}}/r_{\mathrm{max}} = 0.01$ and $1.0$, respectively. Error bars show propagated observational uncertainties. Black curves are computed directly from Equation \ref{['mu 1']}, with different line styles corresponding to different fixed values of $\beta$ and $\gamma$ (left and right, respectively). The range of $\beta$ and $\gamma$ shown by the black curves is the same as the prior range on those parameters in the fits described in Section \ref{['sec data']}. The two dotted grey lines show the mass estimators of walker2009universal and wolf2010accurate as labeled.