Constraints on the Galactic Centre environment from Gaia hypervelocity stars

Following a dynamical encounter with Sgr A*, binaries in the Galactic Centre (GC) can be tidally separated and one member star ejected as a hyper-velocity star (HVS) with a velocity beyond the escape speed of the Milky Way. As GC-born objects located in more observationally accessible regions of the sky, HVSs offer insight into the stellar population in the inner parsecs of the Milky Way. We perform a suite of simulations ejecting HVSs from the GC, exploring how detectable HVS populations depend on assumptions concerning the GC stellar population, focusing on those that are both gravitationally unbound from the Galaxy and which would appear in current and/or future data releases from the \textit{Gaia} space mission with precise astrometry and measured radial velocities. We show that predictions are sensitive to two parameters in particular: the shape of the stellar initial mass function (IMF) in the GC and the ejection rate of HVSs. The absence of confident HVS candidates in \textit{Gaia} Data Release 2 excludes scenarios in which the HVS ejection rate is $\gtrsim3\times10^{-2} \, \mathrm{yr^{-1}}$. Stricter constraints will be placed on these parameters when more HVS candidates are unearthed in future \textit{Gaia} data releases -- assuming recent determinations of the GC IMF shape, one confident HVS \textit{at minimum} is expected in \textit{Gaia} DR3 and DR4 as long as the HVS ejection rate is greater than $\sim 10^{-3} \, \mathrm{yr^{-1}}$ and $\sim10^{-5} \, \mathrm{yr^{-1}}$, respectively.