Astronomers using a large sample of halo stars estimated the mass of the Milky Way out to 100 kpc and found that it is 6.31 ± 0.32(stat.) ± 1.26(sys.) × 10¹¹ M
The total mass of the Milky Way has been an historically difficult parameter to pin down. Despite decades of measurements, there remains an undercurrent of elusiveness surrounding “the mass of the Milky Way”. However, the continued eagerness to provide an accurate measure is perhaps unsurprising — the mass of a halo is arguably its most important characteristic. For example, almost every property of a galaxy is dependent on its halo mass, and thus this key property is essential to place our “benchmark” Milky Way galaxy in context within the general galaxy population. In addition, the host halo mass is inherently linked to its subhalo population, so most of the apparent small scale discrepancies with the ΛCDM model are strongly dependent on the Milky Way mass. Moreover, tests of alternative dark matter candidates critically depend on the total mass of the Milky Way, particularly for astrophysical tests.
The uncertainty has stemmed from two major shortcomings:
(1) a lack of luminous tracers with full 6D phase-space information out to the viral radius of the Galaxy, and (2) an underestimated, or unquantified, systematic uncertainty in the mass estimate.
However, there has been significant progress since the first astrometric data release from the Gaia satellite. This game-changing mission for Milky Way science provided the much needed tangential velocity components for significant numbers of halo stars, globular clusters and satellite galaxies. Indeed, there are encouraging signs that we are converging to a total mass of just over 1×10¹²M. However, mass estimates at very large distances (i.e. beyond 50 kpc), are dominated by measures using the kinematics of satellite galaxies, which probe out to the virial radius of the Galaxy. It is well-known that the dwarf satellites of the Milky Way have a peculiar planar alignment, and, without independent measures at these large distances, there remains uncertainty over whether or not the satellites are biased kinematic tracers of the halo.
Arguably the most promising tracers at large radii are the halo stars. They are significantly more numerous than the satellite galaxies and globular clusters, and are predicted to reach out to the virial radius of the Galaxy. There currently exist thousands of halo stars with 6D phase-space measurements, thanks to the exquisite Gaia astrometry and wide-field spectroscopic surveys such as the Sloan Digital Sky Survey (SDSS) and the Large Sky Area Multi-Object Fibre Spectroscopic Telescope (LAMOST) survey. Moreover, with future Gaia data releases and the next generation of wide-field spectroscopic surveys from facilities such as the Dark Energy Spectroscopic Instrument, the WHT Enhanced Area Velocity Explorer, and the 4-metre Multi-Object Spectroscopic Telescope, there will be hundreds of thousands of halo stars with 6D measurements. The magnitude limit of Gaia and the complementary spectroscopic surveys will likely limit the samples of halo stars to within ∼100 kpc, but this is still an appreciable fraction of the virial radius (∼0.5𝑟200c), and will probe relatively unchartered territory beyond 50 kpc.
As we enter a regime of more precise mass measures, and significantly reduced statistical uncertainties, it is vital to be mindful of any systematic influences in our mass estimates. Although many mass-modelling techniques assume dynamical equilibrium, it is well-documented that “realistic” stellar haloes can be a mash-up of several coherent streams and substructures. Thus, comparisons with cosmologically motivated models of stellar haloes are crucial. However, while cosmological simulations can provide much needed context, the unique assembly history of the Milky Way is most relevant for Galactic mass measurements. For example, the influence of the Sagittarius (Sgr) stream, which contributes a significant fraction to the total stellar halo mass, needs to be considered. Furthermore, and perhaps more importantly, it has recently been recognised that the recent infall of the massive Large Magellanic Cloud (LMC) can imprint significant velocity gradients in the Milky Way halo. Indeed, Erkal et al. (2020) showed that these velocity gradients can bias equilibrium based mass modelling, and is thus an effect that can no longer ignore.
In this work, researchers compile a sample of distant (𝑟 > 50 kpc) halo stars from the literature with 6D phase-space measurements, and use a distribution function analysis to measure the total mass within 100 kpc. They pay particular attention to systematic influences, such as the Sagittarius (Sgr) stream and the LMC, and, where possible, correct for these perturbative effects.
They used a rigid Milky Way-LMC model to constrain the systematic reflex motion effect of the massive LMC on their halo mass estimate. And found that, simple velocity offset correction in 𝑣los and 𝑣𝑏 can minimize the overestimate caused by the reflex motion induced by the LMC, and, assuming a rigid LMC mass of 1.5 × 10¹¹ M, they can recover the true mass within 1-𝜎.
Then by applying their method to a sample of Milky Way-mass haloes from the Auriga simulation they found that the halo masses are typically underestimated by 10%. However, this bias is reduced to ∼ 5% if we only consider haloes with relatively quiescent recent accretion histories. The residual bias is due to the presence of long-lived shell-like structures in the outer halo. The halo-to-halo scatter is ∼20% for the quiescent haloes, and represents the dominant source of error in the mass estimate of the Milky Way.
They also found that the mass of milky way within 100 kpc is 6.31 ± 0.32(stat.) ± 1.26(sys.) × 10¹¹ M. A systematic bias correction (+5%), and additional uncertainty (20%), are included based on their results from the Auriga simulations and found that the mass estimates are slightly higher when they do not include a velocity offset to correct for the reflex motion induced by the LMC, or slightly lower when Sgr stars are included in their analysis.
Their mass estimate within 100 kpc is in good agreement with recent, independent measures in the same radial range. If they assume the predicted mass-concentration relation for Navarro-Frenk-White haloes, their measurement favours a total (pre-LMC infall) Milky Way mass of 𝑀200c = 1.05 ± 0.25 × 10¹²M, or (post-LMC infall) mass 𝑀200c = 1.20 ± 0.25 × 10¹²M when a rigid 1.5 × 10¹¹M LMC is included.
References: Alis J. Deason, Denis Erkal, Vasily Belokurov, Azadeh Fattahi, Facundo A. Gómez, Robert J. J. Grand, Rüdiger Pakmor, Xiang-Xiang Xue, Chao Liu, Chengqun Yang, Lan Zhang, Gang Zhao, “The mass of the Milky Way out to 100 kpc using halo stars”, ArXiv, 2020. https://arxiv.org/abs/2010.13801
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