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Register a new userBayesian Mass Estimates of the Milky Way: including measurement uncertainties with hierarchical Bayes
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We present a hierarchical Bayesian method for estimating the total mass and mass profile of the Milky Way Galaxy. The new hierarchical Bayesian approach further improves the framework presented by Eadie, Harris, & Widrow (2015) and Eadie & Harris (2016) and builds upon the preliminary reports by Eadie et al (2015a,c). The method uses a distribution function $f(mathcal{E},L)$ to model the galaxy and kinematic data from satellite objects such as globular clusters (GCs) to trace the Galaxys gravitational potential. A major advantage of the method is that it not only includes complete and incomplete data simultaneously in the analysis, but also incorporates measurement uncertainties in a coherent and meaningful way. We first test the hierarchical Bayesian framework, which includes measurement uncertainties, using the same data and power-law model assumed in Eadie & Harris (2016), and find the results are similar but more strongly constrained. Next, we take advantage of the new statistical framework and incorporate all possible GC data, finding a cumulative mass profile with Bayesian credible regions. This profile implies a mass within $125$kpc of $4.8times10^{11}M_{odot}$ with a 95% Bayesian credible region of $(4.0-5.8)times10^{11}M_{odot}$. Our results also provide estimates of the true specific energies of all the GCs. By comparing these estimated energies to the measured energies of GCs with complete velocity measurements, we observe that (the few) remote tracers with complete measurements may play a large role in determining a total mass estimate of the Galaxy. Thus, our study stresses the need for more remote tracers with complete velocity measurements.
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We present mass and mass profile estimates for the Milky Way Galaxy using the Bayesian analysis developed by Eadie et al (2015b) and using globular clusters (GCs) as tracers of the Galactic potential. The dark matter and GCs are assumed to follow different spatial distributions; we assume power-law model profiles and use the model distribution functions described in Evans et al. (1997); Deason et al (2011, 2012a). We explore the relationships between assumptions about model parameters and how these assumptions affect mass profile estimates. We also explore how using subsamples of the GC population beyond certain radii affect mass estimates. After exploring the posterior distributions of different parameter assumption scenarios, we conclude that a conservative estimate of the Galaxys mass within 125kpc is $5.22times10^{11} M_{odot}$, with a $50%$ probability region of $(4.79, 5.63) times10^{11} M_{odot}$. Extrapolating out to the virial radius, we obtain a virial mass for the Milky Way of $6.82times10^{11} M_{odot}$ with $50%$ credible region of $(6.06, 7.53) times 10^{11} M_{odot}$ ($r_{vir}=185^{+7}_{-7}$kpc). If we consider only the GCs beyond 10kpc, then the virial mass is $9.02~(5.69, 10.86) times 10^{11} M_{odot}$ ($r_{vir}=198^{+19}_{-24}$kpc). We also arrive at an estimate of the velocity anisotropy parameter $beta$ of the GC population, which is $beta=0.28$ with a $50%$ credible region (0.21, 0.35). Interestingly, the mass estimates are sensitive to both the dark matter halo potential and visible matter tracer parameters, but are not very sensitive to the anisotropy parameter.
In a series of three papers, Eadie et al. developed a hierarchical Bayesian method to estimate the Milky Way Galaxys mass given a physical model for the potential, a measurement model, and kinematic data of test particles such as globular clusters (GCs) or halo stars in the Galaxys halo. The Galaxys virial mass was found to have a 95% Bayesian credible region (c.r.) of $(0.67, 1.09) times 10^{12} M_{odot}$. In the present study, we test the hierarchical Bayesian method against simulated galaxies created in the McMaster Unbiased Galaxy Simulations 2 (MUGS2), for which the true mass is known. We estimate the masses of MUGS2 galaxies using GC analogs from the simulations as tracers. The analysis, completed as a blind test, recovers the true $M_{200}$ of the MUGS2 galaxies within 95% Bayesian c.r. in 8 out of 18 cases. Of the 10 galaxy masses that were not recovered within the 95% c.r., a large subset have posterior distributions that occupy extreme ends of the parameter space allowed by the priors. A few incorrect mass estimates are explained by the exceptional evolution history of the galaxies. We also find evidence that the model cannot describe both the galaxies inner and outer structure simultaneously in some cases. After removing the GC analogs associated with the galactic disks, the true masses were found more reliably (13 out of 18 were predicted within the c.r.). Finally, we discuss how representative the GC analogs are of the real GC population in the Milky Way.
Mass-to-light versus colour relations (MLCRs), derived from stellar population synthesis models, are widely used to estimate galaxy stellar masses (M$_*$) yet a detailed investigation of their inherent biases and limitations is still lacking. We quantify several potential sources of uncertainty, using optical and near-infrared (NIR) photometry for a representative sample of nearby galaxies from the Virgo cluster. Our method for combining multi-band photometry with MLCRs yields robust stellar masses, while errors in M$_*$ decrease as more bands are simultaneously considered. The prior assumptions in ones stellar population modelling dominate the error budget, creating a colour-dependent bias of up to 0.6 dex if NIR fluxes are used (0.3 dex otherwise). This matches the systematic errors associated with the method of spectral energy distribution (SED) fitting, indicating that MLCRs do not suffer from much additional bias. Moreover, MLCRs and SED fitting yield similar degrees of random error ($sim$0.1-0.14 dex) when applied to mock galaxies and, on average, equivalent masses for real galaxies with M$_* sim$ 10$^{8-11}$ M$_{odot}$. The use of integrated photometry introduces additional uncertainty in M$_*$ measurements, at the level of 0.05-0.07 dex. We argue that using MLCRs, instead of time-consuming SED fits, is justified in cases with complex model parameter spaces (involving, for instance, multi-parameter star formation histories) and/or for large datasets. Spatially-resolved methods for measuring M$_*$ should be applied for small sample sizes and/or when accuracies less than 0.1 dex are required. An Appendix provides our MLCR transformations for ten colour permutations of the $grizH$ filter set.
We study methods for reconstructing Bayesian uncertainties on dynamical mass estimates of galaxy clusters using convolutional neural networks (CNNs). We discuss the statistical background of approximate Bayesian neural networks and demonstrate how variational inference techniques can be used to perform computationally tractable posterior estimation for a variety of deep neural architectures. We explore how various model designs and statistical assumptions impact prediction accuracy and uncertainty reconstruction in the context of cluster mass estimation. We measure the quality of our model posterior recovery using a mock cluster observation catalog derived from the MultiDark simulation and UniverseMachine catalog. We show that approximate Bayesian CNNs produce highly accurate dynamical cluster mass posteriors. These model posteriors are log-normal in cluster mass and recover $68%$ and $90%$ confidence intervals to within $1%$ of their measured value. We note how this rigorous modeling of dynamical mass posteriors is necessary for using cluster abundance measurements to constrain cosmological parameters.
We propose a novel method to constrain the Milky Way (MW) mass $M_{rm vir}$ with its corona temperature observations. For a given corona density profile, one can derive its temperature distribution assuming a generalized equilibrium model with non-thermal pressure support. While the derived temperature profile decreases substantially with radius, the X-ray-emission-weighted average temperature, which depends most sensitively on $M_{rm vir}$, is quite uniform toward different sight lines, consistent with X-ray observations. For an Navarro-Frenk-White (NFW) total matter distribution, the corona density profile should be cored, and we constrain $M_{rm vir}=(1.19$ - $2.95) times 10^{12} M_{rm sun}$. For a total matter distribution contributed by an NFW dark matter profile and central baryons, the corona density profile should be cuspy and $M_{rm vir,dm}=(1.34$ - $5.44) times 10^{12} M_{rm sun}$. Non-thermal pressure support leads to even higher values of $M_{rm vir}$, while a lower MW mass may be possible if the corona is accelerating outward. This method is independent of the total corona mass, its metallicity, and temperature at very large radii.
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