Accurate mass estimates from the proper motions of dispersion-supported galaxies
ABSTRACT We derive a new mass estimator that relies on internal proper motion measurements of dispersion-supported stellar systems, one that is distinct and complementary to existing estimators for line-of-sight velocities. Starting with the spherical Jeans equation, we show that there exists a radius where the mass enclosed depends only on the projected tangential velocity dispersion, assuming that the anisotropy profile slowly varies. This is well-approximated at the radius where the log-slope of the stellar tracer profile is −2: r−2. The associated mass is $M(r_{-2}) = 2 G^{-1} \langle \sigma _{\mathcal {T}}^{2}\rangle ^{*} r_{-2}$ and the circular velocity is $V^{2}({r_{-2}}) = 2\langle \sigma _{\mathcal {T}}^{2}\rangle ^{*}$. For a Plummer profile r−2 ≃ 4Re/5. Importantly, r−2 is smaller than the characteristic radius for line-of-sight velocities derived by Wolf et al. Together, the two estimators can constrain the mass profiles of dispersion-supported galaxies. We illustrate its applicability using published proper motion measurements of dwarf galaxies Draco and Sculptor, and find that they are consistent with inhabiting cuspy NFW subhaloes of the kind predicted in CDM but we cannot rule out a core. We test our combined mass estimators against previously published, non-spherical cosmological dwarf galaxy simulations done in both cold dark matter (CDM; naturally more »
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Publication Date:
NSF-PAR ID:
10292852
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
493
Issue:
4
Page Range or eLocation-ID:
5825 to 5837
ISSN:
0035-8711
1. ABSTRACT We present a Bayesian method to identify multiple (chemodynamic) stellar populations in dwarf spheroidal galaxies (dSphs) using velocity, metallicity, and positional stellar data without the assumption of spherical symmetry. We apply this method to a new Keck/Deep Imaging Multi-Object Spectrograph (DEIMOS) spectroscopic survey of the Ursa Minor (UMi) dSph. We identify 892 likely members, making this the largest UMi sample with line-of-sight velocity and metallicity measurements. Our Bayesian method detects two distinct chemodynamic populations with high significance (in logarithmic Bayes factor, ln B ∼ 33). The metal-rich ([Fe/H] = −2.05 ± 0.03) population is kinematically colder (radial velocity dispersion of $\sigma _v=4.9_{-1.0}^{+0.8} \, \mathrm{km} \, \mathrm{s}^{-1}$) and more centrally concentrated than the metal-poor ($[{\rm Fe/H}]=-2.29_{-0.06}^{+0.05}$) and kinematically hotter population ($\sigma _v =11.5_{-0.8}^{+0.9}\, \mathrm{km} \, \mathrm{s}^{-1}$). Furthermore, we apply the same analysis to an independent Multiple Mirror Telescope (MMT)/Hectochelle data set and confirm the existence of two chemodynamic populations in UMi. In both data sets, the metal-rich population is significantly flattened (ϵ = 0.75 ± 0.03) and the metal-poor population is closer to spherical ($\epsilon =0.33_{-0.09}^{+0.12}$). Despite the presence of two populations, we are able to robustly estimate the slope of the dynamical mass profile. We found hints for prolate rotation of order ${\sim}2 \, \mathrm{km} \, \mathrm{s}^{-1}$more »
2. ABSTRACT Core formation and runaway core collapse in models with self-interacting dark matter (SIDM) significantly alter the central density profiles of collapsed haloes. Using a forward modelling inference framework with simulated data-sets, we demonstrate that flux ratios in quadruple image strong gravitational lenses can detect the unique structural properties of SIDM haloes, and statistically constrain the amplitude and velocity dependence of the interaction cross-section in haloes with masses between 106 and 1010 M⊙. Measurements on these scales probe self-interactions at velocities below $30 \ \rm {km} \ \rm {s^{-1}}$, a relatively unexplored regime of parameter space, complimenting constraints at higher velocities from galaxies and clusters. We cast constraints on the amplitude and velocity dependence of the interaction cross-section in terms of σ20, the cross-section amplitude at $20 \ \rm {km} \ \rm {s^{-1}}$. With 50 lenses, a sample size available in the near future, and flux ratios measured from spatially compact mid-IR emission around the background quasar, we forecast $\sigma _{20} \lt 11\rm {\small {--}}23 \ \rm {cm^2} \rm {g^{-1}}$ at $95 {{\ \rm per\ cent}}$ CI, depending on the amplitude of the subhalo mass function, and assuming cold dark matter (CDM). Alternatively, if $\sigma _{20} = 19.2 \ \rmmore » 3. ABSTRACT We perform cosmological zoom-in simulations of 19 relaxed cluster-mass haloes with the inclusion of adiabatic gas in the cold dark matter (CDM) and self-interacting dark matter (SIDM) models. These clusters are selected as dynamically relaxed clusters from a parent simulation with$M_{\rm 200} \simeq (1\!-\!3)\times 10^{15}{\, \rm M_\odot }$. Both the dark matter and the intracluster gas distributions in SIDM appear more spherical than their CDM counterparts. Mock X-ray images are generated based on the simulations and are compared to the real X-ray images of 84 relaxed clusters selected from the Chandra and ROSAT archives. We perform ellipse fitting for the isophotes of mock and real X-ray images and obtain the ellipticities at cluster-centric radii of$r\simeq 0.1\!-\!0.2R_{\rm 200}$. The X-ray isophotes in SIDM models with increasing cross-sections are rounder than their CDM counterparts, which manifests as a systematic shift in the distribution function of ellipticities. Unexpectedly, the X-ray morphology of the observed non-cool-core clusters agrees better with SIDM models with cross-section$(\sigma /m)= 0.5\!-\!1\, {\rm cm}^2\, {\rm g}^{-1}$than CDM and SIDM with$(\sigma /m)=0.1\, {\rm cm}^2\, {\rm g}^{-1}$. Our statistical analysis indicates that the latter two models are disfavoured at the$68{{\ \rm per\ cent}}$confidence level (as conservativemore » 4. ABSTRACT Galaxy sizes correlate closely with the sizes of their parent dark matter haloes, suggesting a link between halo formation and galaxy growth. However, the precise nature of this relation and its scatter remains to be understood fully, especially for low-mass galaxies. We analyse the galaxy–halo size relation (GHSR) for low-mass ($M_\star \sim 10^{7-9}\, {\rm M}_\odot$) central galaxies over the past 12.5 billion years with the help of cosmological volume simulations (FIREbox) from the Feedback in Realistic Environments (FIRE) project. We find a nearly linear relationship between the half-stellar mass galaxy size R1/2 and the parent dark matter halo virial radius Rvir. This relation evolves only weakly since redshift z = 5:$R_{1/2}\, [{\rm kpc}] = (0.053\pm 0.002)(R_{\rm vir}/35\, {\rm kpc})^{0.934\pm 0.054}$, with a nearly constant scatter$\langle \sigma \rangle = 0.084\, [{\rm dex}]$. While this ratio is similar to what is expected from models where galaxy disc sizes are set by halo angular momentum, the low-mass galaxies in our sample are not angular momentum supported, with stellar rotational to circular velocity ratios vrot/vcirc ∼ 0.15. Introducing redshift as another parameter to the GHSR does not decrease the scatter. Furthermore, this scatter does not correlate with any of the halo propertiesmore » 5. ABSTRACT Globular clusters (GCs) are often used to estimate the dark matter content of galaxies, especially dwarf galaxies, where other kinematic tracers are lacking. These estimates typically assume spherical symmetry and dynamical equilibrium, assumptions that may not hold for the sparse GC population of dwarfs in galaxy clusters. We use a catalogue of GCs tagged on to the Illustris simulation to study the accuracy of GC-based mass estimates. We focus on galaxies in the stellar mass range 108–1011.8 M⊙ identified in nine simulated Virgo-like clusters. Our results indicate that mass estimates are, on average, accurate in systems with GC numbers NGC ≥ 10 and where the uncertainty of individual GC line-of-sight velocities is smaller than the inferred velocity dispersion, σGC. In cases where NGC ≤ 10, however, biases may result, depending on how σGC is computed. We provide calibrations that may help alleviate these biases in methods widely used in the literature. As an application, we find a number of dwarfs with$M_{*} \sim 10^{8.5}\, \mathrm{M}_{\odot }$– comparable with the ultra-diffuse galaxy NGC 1052-DF2 (DF2), notable for the low σGC of its 10 GCs – that have$\sigma _{\rm GC} \sim 7\!-\!15\, {\rm km \,s}^{-1}\$. These DF2 analogues correspond tomore »