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We identify Local Group (LG) analogs in the IllustrisTNG cosmological simulation, and use these to study two mass estimators for the LG: one based on the timing argument (TA) and one based on the virial theorem (VT). Including updated measurements of the Milky Way-M31 tangential velocity and the cosmological constant, we show that the TA mass estimator slightly overestimates the true median LG-mass, though the ratio of the TA to the true mass is consistent at the approximate 90% c.l. These are in broad agreement with previous results using dark matter-only simulations. We show that the VT estimator better estimates the true LG-mass, though there is a larger scatter in the virial mass to true mass ratio relative to the corresponding ratio for the TA. We attribute the broader scatter in the VT estimator to several factors, including the predominantly radial orbits for LG satellite galaxies, which differs from the VT assumption of isotropic orbits. With the systematic uncertainties we derive, the updated measurements of the LG mass at 90% c.l. are $4.75_{-2.41}^{+2.22} times 10^{12}$ M$_odot$ from the TA and $2.0_{-1.5}^{+2.1} times 10^{12}$ M$_odot$ from the VT.
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We use a suite of high-resolution cosmological dwarf galaxy simulations to test the accuracy of commonly-used mass estimators from Walker et al.(2009) and Wolf et al.(2010), both of which depend on the observed line-of-sight velocity dispersion and the 2D half-light radius of the galaxy, $Re$. The simulations are part of the the Feedback in Realistic Environments (FIRE) project and include twelve systems with stellar masses spanning $10^{5} - 10^{7} M_{odot}$ that have structural and kinematic properties similar to those of observed dispersion-supported dwarfs. Both estimators are found to be quite accurate: $M_{Wolf}/M_{true} = 0.98^{+0.19}_{-0.12}$ and $M_{Walker}/M_{true} =1.07^{+0.21}_{-0.15}$, with errors reflecting the 68% range over all simulations. The excellent performance of these estimators is remarkable given that they each assume spherical symmetry, a supposition that is broken in our simulated galaxies. Though our dwarfs have negligible rotation support, their 3D stellar distributions are flattened, with short-to-long axis ratios $ c/a simeq 0.4-0.7$. The accuracy of the estimators shows no trend with asphericity. Our simulated galaxies have sphericalized stellar profiles in 3D that follow a nearly universal form, one that transitions from a core at small radius to a steep fall-off $propto r^{-4.2}$ at large $r$, they are well fit by Sersic profiles in projection. We find that the most important empirical quantity affecting mass estimator accuracy is $Re$ . Determining $Re$ by an analytic fit to the surface density profile produces a better estimated mass than if the half-light radius is determined via direct summation.
We make detailed theoretical predictions for the assembly properties of the Local Group (LG) in the standard LambdaCDM cosmological model. We use three cosmological N-body dark matter simulations from the CLUES project, which are designed to reproduce the main dynamical features of the matter distribution down to the scale of a few Mpc around the LG. Additionally, we use the results of an unconstrained simulation with a sixty times larger volume to calibrate the influence of cosmic variance. We characterize the Mass Aggregation History (MAH) for each halo by three characteristic times, the formation, assembly and last major merger times. A major merger is defined by a minimal mass ratio of 10:1. We find that the three LGs share a similar MAH with formation and last major merger epochs placed on average approx 10 - 12 Gyr ago. Between 12% and 17% of the halos in the mass range 5 x 10^11 Msol/h < M_h < 5 x 10^12 Msol/h have a similar MAH. In a set of pairs of halos within the same mass range, a fraction of 1% to 3% share similar formation properties as both halos in the simulated LG. An unsolved question posed by our results is the dynamical origin of the MAH of the LGs. The isolation criteria commonly used to define LG-like halos in unconstrained simulations do not narrow down the halo population into a set with quiet MAHs, nor does a further constraint to reside in a low density environment. The quiet MAH of the LGs provides a favorable environment for the formation of disk galaxies like the Milky Way and M31. The timing for the beginning of the last major merger in the Milky Way dark matter halo matches with the gas rich merger origin for the thick component in the galactic disk. Our results support the view that the specific large and mid scale environment around the Local Group play a critical role in shaping its MAH and hence its baryonic structure at present.
We use recent proper motion measurements of the tangential velocity of M31, along with its radial velocity and distance, to derive the likelihood of the sum of halo masses of the Milky Way and M31. This is done using a sample halo pairs in the Bolshoi cosmological simulation of $Lambda$CDM cosmology selected to match properties and environment of the Local Group. The resulting likelihood gives estimate of the sum of masses of $M_{rm MW,200}+M_{rm M31,200}=$ $2.40_{-1.05}^{+1.95}times10^{12},M_{odot}$ ($90%$ confidence interval). This estimate is consistent with individual mass estimates for the Milky Way and M31 and is consistent, albeit somewhat on the low side, with the mass estimated using the timing argument. We show that although the timing argument is unbiased on average for all pairs, for pairs constrained to have radial and tangential velocities similar to that of the Local Group the argument overestimates the sum of masses by a factor of $1.6$. Using similar technique we estimate the total dark matter mass enclosed within $1$ Mpc from the Local Group barycenter to be $M_{rm LG}(r<1, {rm Mpc})=4.2_{-2.0}^{+3.4}times10^{12},M_{odot}$ ($90%$ confidence interval).
We contend that a single power law halo mass distribution is appropriate for direct matching to the stellar masses of observed Local Group dwarf galaxies, allowing the determination of the slope of the stellar mass-halo mass relation for low mass galaxies. Errors in halo masses are well defined as the Poisson noise of simulated local group realisations, which we determine using constrained local universe simulations (CLUES). For the stellar mass range 10$^7$<M*<10$^8$M$_odot$, for which we likely have a complete census of observed galaxies, we find that the stellar mass-halo mass relation follows a power law with slope of 3.1, significantly steeper than most values in the literature. The steep relation between stellar and halo masses indicates that Local Group dwarf galaxies are hosted by dark matter halos with a small range of mass. Our methodology is robust down to the stellar mass to which the census of observed Local Group galaxies is complete, but the significant uncertainty in the currently measured slope of the stellar-to halo mass relation will decrease dramatically if the Local Group completeness limit was $10^{6.5}$M$odot$ or below, highlighting the importance of pushing such limit to lower masses and larger volumes.
Studies of cluster mass and velocity anisotropy profiles are useful tests of dark matter models, and of the assembly history of clusters of galaxies. These studies might be affected by unknown systematics caused by projection effects. We aim at testing observational methods for the determination of mass and velocity anisotropy profiles of clusters of galaxies. Particularly, we focus on the MAMPOSSt technique (Mamon et al. 2013). We use results from two semi-analytic models of galaxy formation coupled with high-resolution N-body cosmological simulations, the catalog of De Lucia & Blaizot (2007) and the FIRE catalog based on the new GAlaxy Evolution and Assembly model. We test the reliability of the Jeans equation in recovering the true mass profile when full projected phase-space information is available. We examine the reliability of the MAMPOSSt method in estimating the true mass and velocity anisotropy profiles of the simulated halos when only projected phase-space information is available, as in observations. The spherical Jeans equation provides a reliable tool for the determination of cluster mass profiles, also for subsamples of tracers separated by galaxy color. Results are equally good for prolate and oblate clusters. Using only projected phase-space information, MAMPOSSt provides estimates of the mass profile with a standard deviation of 35-69 %, and a negative bias of 7-17 %, nearly independent of radius, and that we attribute to the presence of interlopers in the projected samples. The bias changes sign, that is, the mass is over-estimated, for prolate clusters with their major axis aligned along the line-of-sight. MAMPOSSt measures the velocity anisotropy profiles accurately in the inner cluster regions, with a slight overestimate in the outer regions, both for the whole sample of observationally-identified cluster members and separately for red and blue galaxies.
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