Reanalysis of the MACHO constraints on PBH in the light of Gaia DR3 data

The recent astrometric data of hundreds of millions of stars from Gaia DR3 has allowed a precise determination of the Milky Way rotation curve up to $28$~kpc. The data suggests a rapid decline in the density of dark matter beyond $19$~kpc. We fit the whole rotation curve with four components (gas, disk, bulge and halo) and compute the microlensing optical depth to the Large Magellanic Cloud. With this model of the galaxy we reanalyse the microlensing events of the MACHO and EROS-2 Collaborations. Using the published MACHO efficiency function for the duration of their survey, together with the rate of expected events according to the new density profile, we find that the Dark Matter halo could be composed up to $100\%$ of massive compact halo objects for any mass between $10^{-4}$ to $100~M_\odot$, except a broad range around $0.01~M_\odot$, where it cannot be larger than $\sim20~\%$. For the EROS-2 survey, using a modified efficiency curve for consistency with the MACHO analysis, we also find compatibility with a 100\% MACHO halo, but with a tighter constraint around $0.001~M_\odot$ where the halo fraction cannot be larger than $\sim12~\%$. This result assumes that MACHOs all have the same mass. If these were distributed in an extended mass function like that of the Thermal History Model, the constraints are weakened, allowing $100\%$ of all DM in the form of Primordial Black Holes.