We determine the Milky Way (MW) mass profile inferred from fitting physically motivated models to the Gaia DR2 Galactic rotation curve and other data. Using various hydrodynamical simulations of MW-mass haloes, we show that the presence of baryons induces a contraction of the dark matter (DM) distribution in the inner regions, r ≲ 20 kpc. We provide an analytic expression that relates the baryonic distribution to the change in the DM halo profile. For our galaxy, the contraction increases the enclosed DM halo mass by factors of roughly 1.3, 2, and 4 at radial distances of 20, 8, and 1 kpc, respectively compared to an uncontracted halo. Ignoring this contraction results in systematic biases in the inferred halo mass and concentration. We provide a best-fitting contracted NFW halo model to the MW rotation curve that matches the data very well.1 The best-fit has a DM halo mass, $M_{200}^{\rm DM}=0.97_{-0.19}^{+0.24}\times 10^{12}\,\mathrm{M}_\odot$, and concentration before baryon contraction of $9.4_{-2.6}^{+1.9}$, which lie close to the median halo mass–concentration relation predicted in ΛCDM. The inferred total mass, $M_{200}^{\rm total}=1.08_{-0.14}^{+0.20} \times 10^{12}\,\mathrm{M}_\odot$, is in good agreement with recent measurements. The model gives an MW stellar mass of $5.04_{-0.52}^{+0.43}\times 10^{10}\,\mathrm{M}_\odot$ and infers that the DM density at the Solar position is $\rho _{\odot }^{\rm DM}=8.8_{-0.5}^{+0.5}\times 10^{-3}\,\mathrm{M}_\odot \,\mathrm{pc}^{-3}\equiv 0.33_{-0.02}^{+0.02}\,\rm {GeV}\,\rm {cm}^{-3}$. The rotation curve data can also be fitted with an uncontracted NFW halo model, but with very different DM and stellar parameters. The observations prefer the physically motivated contracted NFW halo, but the measurement uncertainties are too large to rule out the uncontracted NFW halo.

Dark matter subhalos are the remnants of (incomplete) halo mergers. Identifying them and establishing their evolutionary links in the form of merger trees is one of the most important applications of cosmological simulations. The hbt (Hierachical Bound-Tracing) code identifies haloes as they form and tracks their evolution as they merge, simultaneously detecting subhaloes and building their merger trees. Here we present a new implementation of this approach, hbt+ , that is much faster, more user friendly, and more physically complete than the original code. Applying hbt+ to cosmological simulations, we show that both the subhalo mass function and the peak-mass function are well fitted by similar double-Schechter functions. The ratio between the two is highest at the high-mass end, reflecting the resilience of massive subhaloes that experience substantial dynamical friction but limited tidal stripping. The radial distribution of the most-massive subhaloes is more concentrated than the universal radial distribution of lower mass subhaloes. Subhalo finders that work in configuration space tend to underestimate the masses of massive subhaloes, an effect that is stronger in the host centre. This may explain, at least in part, the excess of massive subhaloes in galaxy cluster centres inferred from recent lensing observations. We demonstrate that the peak-mass function is a powerful diagnostic of merger tree defects, and the merger trees constructed using hbt+ do not suffer from the missing or switched links that tend to afflict merger trees constructed from more conventional halo finders. We make the hbt+ code publicly available.

We present a model for the formation of the first galaxies before and after the reionization of hydrogen in the early universe. In this model, galaxy formation can only take place in dark matter haloes whose mass exceeds a redshift-dependent critical value, which, before reionization, is equal (in the simplest case) to the mass at which atomic hydrogen cooling becomes effective and, after reionization, is equal to the mass above which gas cannot remain in hydrostatic equilibrium. We define the Halo Occupation Fraction (HOF) as the fraction of haloes that host a luminous galaxy as a function of halo mass. The HOF is established by the interplay between the evolution of the critical mass and the assembly history of haloes and depends on three factors: the minimum halo mass for galaxy formation before reionization, the redshift of reionization, and the intensity of the (evolving) external photoheating rate. Our fiducial model predicts a cutoff in the galaxy mass function at a present-day halo mass, |$M_{200} \sim 3\times 10^{8} \, \mathrm{M}_{\odot }$|⁠; 100 per cent occupation at |$M_{200} \gt 5\times 10^9 \, \mathrm{M}_{\odot }$|⁠; and a population of starless gaseous haloes of present-day mass in the range 10⁶ ≲ M₂₀₀/M_⊙ ≲ 5 × 10⁹, in which the gas is in thermal equilibrium with the ultraviolet background radiation and in hydrostatic equilibrium in the gravitational potential of the halo. The transition between HOF = 0 and HOF = 1 reflects the stochastic nature of halo mass growth. We explore how these characteristic masses vary with model assumptions and parameter values. The results of our model are in excellent agreement with cosmological hydrodynamic simulations of galaxy formation.

We use a compilation of disc galaxy rotation curves to assess the role of the luminous component (‘baryons’) in the rotation curve diversity problem. As in earlier work, we find that rotation curve shape correlates with baryonic surface density: high surface density galaxies have rapidly rising rotation curves consistent with cuspy cold dark matter haloes; slowly rising rotation curves (characteristic of galaxies with inner mass deficits or ‘cores’) occur only in low surface density galaxies. The correlation, however, seems too weak to be the main driver of the diversity. In addition, dwarf galaxies exhibit a clear trend, from ‘cuspy’ systems where baryons are unimportant in the inner mass budget to ‘cored’ galaxies where baryons actually dominate. This trend constrains the various scenarios proposed to explain the diversity, such as (i) baryonic inflows and outflows during galaxy formation; (ii) dark matter self-interactions; (iii) variations in the baryonic mass structure coupled to rotation velocities through the ‘mass discrepancy–acceleration relation’ (MDAR); or (iv) non-circular motions in gaseous discs. Together with analytical modelling and cosmological hydrodynamical simulations, our analysis shows that each of these scenarios has promising features, but none seems to fully account for the observed diversity. The MDAR, in particular, is inconsistent with the observed trend between rotation curve shape and baryonic importance; either the trend is caused by systematic errors in the data or the MDAR does not apply. The origin of the dwarf galaxy rotation curve diversity and its relation to the structure of cold dark matter haloes remains an open issue.