A first estimate of the Milky Way dark matter halo spin

The spin, $\lambda$, of dark matter (DM) halos in cosmological simulations follows a log normal distribution and has little correlation with galaxy observables. As such, there is currently no way to infer the $\lambda$ parameter of individual halos hosting observed galaxies. We present here a first attempt to measure $\lambda$ starting from the dynamically distinct stellar components identified in high-resolution cosmological simulations with Galactic Structure Finder. In a subsample of NIHAO galaxies, we find tight correlations between the total angular momentum (AM) of the DM halos, $J_h$, and the azimuthal AM, $J_z$, of the stellar components of the form: log($J_h$)=$\alpha$+$\beta\cdot$log($J_z$). The stellar halos have the tightest relation with $\alpha=9.50\pm0.42$ and $\beta=0.46\pm0.04$. The other tight relation is with the disks: $\alpha=6.15\pm0.92$ and $\beta=0.68\pm0.07$. We used Gaia DR2 and APOGEE to generate a combined kinematics-abundance space, where the Galaxy's thin and thick stellar disks stars can be neatly separated and their rotational velocity profiles, $v_{\phi}(R)$, can be computed. For both disks, $v_{\phi}(R)$ decreases with radius with $\sim$2 km s$^{-1}$ kpc$^{-1}$ for $R\gtrsim5$ kpc, resulting in $v_{\phi,thin}\backsimeq221$ km s$^{-1}$ and $v_{\phi,thick}\backsimeq188$ km s$^{-1}$ at $R_{\odot}$. These velocity profiles together with the Galaxy mass model of Cautun et al. (2020) result in the AM for the two disks: $J_{z,thin}=(3.26\pm0.43)\times10^{13}$ and $J_{z,thick}=(1.20\pm0.30)\times10^{13}$ M$_{\odot}$ kpc km s$^{-1}$, where the DM halo is assumed to have a contracted NFW profile. Adopting the correlation found in simulations, the spin estimate of the Galaxy's DM halo is $\lambda_{MW}=0.061^{+0.022}_{-0.016}$. If the DM halo has a NFW profile instead, the spin becomes $\lambda_{MW}=0.088^{+0.024}_{-0.020}$, making the Galaxy a more extreme outlier.