Determining the full satellite population of a Milky Way-mass halo in a highly resolved cosmological hydrodynamic simulation

We investigate the formation of the satellite galaxy population of a Milky Way-mass halo in a very highly resolved magneto-hydrodynamic cosmological zoom-in simulation (baryonic mass resolution $m_b =$ 800 $\rm M_{\odot}$). We show that the properties of the central star-forming galaxy, such as the radial stellar surface density profile and star formation history, are: i) robust to stochastic variations associated with the so-called ``Butterfly Effect''; and ii) well converged over 3.5 orders of magnitude in mass resolution. We find that there are approximately five times as many satellite galaxies at this high resolution compared to a standard ($m_b\sim 10^{4-5}\, \rm M_{\odot}$) resolution simulation of the same system. This is primarily because 2/3rds of the high resolution satellites do not form at standard resolution. A smaller fraction (1/6th) of the satellites present at high resolution form and disrupt at standard resolution; these objects are preferentially low-mass satellites on intermediate- to low-eccentricity orbits with impact parameters $\lesssim 30$ kpc. As a result, the radial distribution of satellites becomes substantially more centrally concentrated at higher resolution, in better agreement with recent observations of satellites around Milky Way-mass haloes. Finally, we show that our galaxy formation model successfully forms ultra-faint galaxies and reproduces the stellar velocity dispersion, half-light radii, and $V$-band luminosities of observed Milky Way and Local Group dwarf galaxies across 6 orders of magnitude in luminosity ($10^3$-$10^{9}$ $\rm L_{\odot}$).