The mass of our Milky Way

We perform an extensive review of the numerous studies and methods used to determine the total mass of the Milky Way. We group the various methods into seven broad classes, including: i) estimating Galactic escape velocity using high velocity objects; ii) measuring the rotation curve through terminal and circular velocities; iii) modeling halo stars, globular clusters and satellite galaxies with the Spherical Jeans equation and iv) with phase-space distribution functions; v) simulating and modeling the dynamics of stellar streams and their progenitors; vi) modeling the motion of the Milky Way, M31 and other distant satellites under the framework of Local Group timing argument; and vii) measurements made by linking the brightest Galactic satellites to their counterparts in simulations. For each class of methods, we introduce their theoretical and observational background, the method itself, the sample of available tracer objects, model assumptions, uncertainties, limits and the corresponding measurements that have been achieved in the past. Both the measured total masses within the radial range probed by tracer objects and the extrapolated virial masses are discussed and quoted. We also discuss the role of modern numerical simulations in terms of helping to validate model assumptions, understanding systematic uncertainties and calibrating the measurements. While measurements in the last two decades show a factor of two scatters, recent measurements using \textit{Gaia} DR2 data are approaching a higher precision. We end with a detailed discussion of future developments, especially as the size and quality of the observational data will increase tremendously with current and future surveys. In such cases, the systematic uncertainties will be dominant and thus will necessitate a much more rigorous testing and characterization of the various mass determination methods.Comment: invited review published by Science China Physics, Mechanics & Astronom

Efficient Formation of Massive Galaxies at Cosmic Dawn by Feedback-Free Starbursts

JWST observations indicate a surprising excess of luminous galaxies at $z\sim 10$ and above, consistent with efficient conversion of the accreted gas into stars, unlike the suppression of star formation by feedback at later times. We show that the high densities and low metallicities at this epoch {\it guarantee} a high star-formation efficiency (SFE) in the most massive dark-matter haloes. Feedback-free starbursts (FFBs) occur when the free-fall time is shorter than $\sim 1$ Myr, below the time for low-metallicity massive stars to develop winds and supernovae. This corresponds to a characteristic density of $\sim 3\times 10^3$cm$^{-3}$. A comparable threshold density permits a starburst by allowing cooling to star-forming temperatures in a free-fall time. The galaxies within $\sim 10^{11} M_\odot$ haloes at $z \sim 10$ are expected to have FFB densities. The halo masses allow efficient gas supply by cold streams in a halo crossing time $\sim 80$ Myr. The FFBs gradually turn all the accreted gas into stars in clusters of $\sim 10^{4-7} M_\odot$ within galaxies that are rotating discs or shells. The starbursting clouds are insensitive to radiative feedback and are shielded against feedback from earlier stars. We predict high SFE above thresholds in redshift and halo mass, where the density is $10^{3-4}$cm$^{-3}$. The $z\sim 10$ haloes of $\sim 10^{10.8} M_\odot$ are predicted to host galaxies of $\sim 10^{10} M_\odot$ with SFR $\sim 65 M_\odot$ yr$^{-1}$ and sub-kpc sizes. The metallicity is $\leq 0.1 Z_\odot$ with little gas, dust, outflows and hot circumgalactic gas, allowing a top-heavy IMF but not requiring it. The compact galaxies with thousands of young FFB clusters may have implications on reionization, black-hole growth and globular clusters.Comment: 20 pages, 7 figure

Physical evolution of dark matter halo around the depletion boundary

We investigate the build-up of the halo profile out to large scale in a cosmological simulation, focusing on the roles played by the recently proposed depletion radii. We explicitly show that halo growth is accompanied by the depletion of the environment, with the inner depletion radius demarcating the two. This evolution process is also observed via the formation of a trough in the bias profile, with the two depletion radii identifying key scales in the evolution. The ratio between the inner depletion radius and the virial radius is approximately a constant factor of 2 across redshifts and halo masses. The ratio between their enclosed densities is also close to a constant of 0.18. These simple scaling relations reflect the largely universal scaled mass profile on these scales, which only evolves weakly with redshift. The overall picture of the boundary evolution can be broadly divided into three stages according to the maturity of the depletion process, with cluster halos lagging behind low mass ones in the evolution. We also show that the traditional slow and fast accretion dichotomy of halo growth can be identified as accelerated and decelerated depletion phases respectively.Comment: 14 pages, 10 figures, accepted by Ap

Unraveling the Complexity of Dwarf Galaxy Dynamics: A Study of Binary Orbital Motions

We investigate the impact of binary orbital motions on the dynamical modeling of dwarf galaxies with intrinsic line-of-sight velocity dispersions ( σvr ) of 1–9 km s−1. Using dwarf galaxies from the auriga level-2 and level-3 simulations, we apply the Jeans Anisotropic Multi-Gaussian Expansion modeling to tracer stars before and after including binaries to recover the dynamical masses. The recovered total masses within the half-mass radius of tracers, M(< r half), are always inflated due to binary motions, with greater inflations occurring for smaller σvr . However, many dwarf galaxies experience central density deflated due to binary motions, with little dependence on σvr . This is due to the negative radial gradients in the velocity dispersion profiles, with the fractional inflation in σvr due to binaries more significant in outskirts. An extreme binary fraction of 70% can lead to central density deflation of up to 10%–20% at 3 km s−1 < σvr < 8 km s−1, with M( < r half) inflated by 4% at 9 km s−1 and up to 15% at 3 km s−1. A lower binary fraction of 36% leads to similar deflations, with the inflations decreasing to approximately 10% at 3 km s−1 and becoming statistically insignificant. The choice of binary orbit distribution models does not result in significant differences, and observational errors tend to slightly weaken the deflations in the recovered central density. Two observations separated by 1 yr to exclude binaries lead to almost zero inflations/deflations for a binary fraction of 36% over 3 km s−1 < σvr<9 km s−1. For σvr∼1 km s−1 to 3 km s−1, a binary fraction of 70% (36%) still results in 60% (30%) to 10% (1%) of inflations in M( < r half), even with two-epoch observation

Unraveling the Complexity of Dwarf Galaxy Dynamics: A study of Binary Orbital Motions

We investigate the impact of binary orbital motions on the dynamical modeling of dwarf galaxies with intrinsic line-of-sight velocity dispersions ($\sigma_{v_r}$) of 1 to 9 km/s. Using dwarf galaxies from the Auriga level-2 and level-3 simulations, we apply the Jeans Anisotropic Multi-Gaussian Expansion modelling to tracer stars before and after including binaries to recover the dynamical masses. The recovered total masses within the half-mass radius of tracers, $M(<r_\mathrm{half})$, are always inflated due to binary motions, with greater inflations occurring for smaller $\sigma_{v_r}$. However, many dwarf galaxies experience central density deflated due to binary motions, with little dependences on $\sigma_{v_r}$. This is due to the negative radial gradients in the velocity dispersion profiles, with the fractional inflation in $\sigma_{v_r}$ due to binaries more significant in outskirts. An extreme binary fraction of 70% can lead to central density deflation of up to 10-20% at 3 km/s$<\sigma_{v_r}<$8 km/s, with $M(<r_\mathrm{half})$ inflated by 4% at 9 km/s and up to 15% at 3 km/s. A lower binary fraction of 36% leads to similar deflations, with the inflations decreasing to approximately 10% at 3 km/s and becoming statistically insignificant. The choice of binary orbit distribution models does not result in significant differences, and observational errors tend to slightly weaken the deflations in the recovered central density. Two observations separated by one year to exclude binaries lead to almost zero inflations/deflations for a binary fraction of 36% over 3 km/s$<\sigma_{v_r}<$9 km/s. For $\sigma_{v_r}\sim$1 km/s to 3 km/s, a binary fraction of 70% (36%) still results in 60% (30%) to 10% (1%) of inflations in $M(<r_\mathrm{half})$, even with two-epoch observation.Comment: accepted by ApJ, comments welcom