The missing dwarf galaxies of the Local Group

We study the Local Group (LG) dwarf galaxy population predicted by the \apostle $\Lambda$CDM cosmological hydrodynamics simulations. These indicate that: (i)~the total mass within $3$ Mpc of the Milky Way-Andromeda midpoint ($M_{\rm 3Mpc}$) typically exceeds $\sim 3$ times the sum of the virial masses ($M_{\rm 200crit}$) of the two primaries and (ii)~the dwarf galaxy formation efficiency per unit mass is uniform throughout the volume. This suggests that the satellite population within the virial radii of the Milky Way and Andromeda should make up fewer than one third of all LG dwarfs within $3$ Mpc. This is consistent with the fraction of observed LG galaxies with stellar mass $M_*>10^7\,M_{\odot}$ that are satellites ($12$ out of $42$; i.e., $28$ per cent). For the \apostle galaxy mass-halo mass relation, the total number of such galaxies further suggests a LG mass of $M_{\rm 3 Mpc}\sim 10^{13} \, M_{\odot}$. At lower galaxy masses, however, the observed satellite fraction is substantially higher ($42$ per cent for $M_*>10^5\,M_{\odot}$). If this is due to incompleteness in the field sample, then $\sim 50$ dwarf galaxies at least as massive as the Draco dwarf spheroidal must be missing from the current LG {\it field} dwarf inventory. The incompleteness interpretation is supported by the pronounced flattening of the LG luminosity function below $M_*\sim 10^7\, M_{\odot}$, and by the scarcity of low-surface brightness LG field galaxies compared to satellites. The simulations indicate that most missing dwarfs should lie near the virial boundaries of the two LG primaries, and predict a trove of nearby dwarfs that await discovery by upcoming wide-field imaging surveys.