Constraints on the Galactic Centre environment from Gaia hypervelocity stars II: The evolved population

A dynamical encounter between a stellar binary and Sgr A* in the Galactic Centre (GC) can tidally separate the binary and eject one member with a velocity beyond the escape speed of the Milky Way. These hypervelocity stars (HVSs) can offer insight into the stellar populations in the GC environment. In a previous work, our simulations showed that the lack of main sequence HVS candidates with precise astrometric uncertainties and radial velocities in current data releases from the \textit{Gaia} space mission places a robust upper limit on the ejection rate of HVSs from the GC of $3\times10^{-2} \, \mathrm{yr^{-1}}$. We improve this constraint in this work by additionally considering the absence of post main sequence HVSs in \textit{Gaia} Early Data Release 3 as well the existence of the HVS candidate S5-HVS1. This evidence offers degenerate joint constraints on the HVS ejection rate and the stellar initial mass function (IMF) in the GC. For a top-heavy GC IMF as suggested by recent works, our modelling motivates an HVS ejection rate of $\eta=0.7_{-0.5}^{+1.5} \times10^{-4} \, \mathrm{yr^{-1}}$. This preferred ejection rate can be as large as $10^{-2} \, \mathrm{yr^{-1}}$ for a very top-light IMF and as low as 10$^{-4.5} \, \mathrm{yr^{-1}}$ if the IMF is extremely top-heavy. Constraints will improve further with future \textit{Gaia} data releases, regardless of how many HVS candidates are found therewithin.