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 Gaia space mission places a robust upper limit on the ejection rate of HVSs from the GC of 3 x 10(-2) yr(-1). We improve this constraint in this work by additionally considering the absence of post-main sequence HVSs in Gaia Early Data Release 3 as well as 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) x 10(-4) yr(-1). This preferred ejection rate can be as large as 10(-2) yr(-1) for a very top-light IMF and as low as 10(-4.5) yr(-1) if the IMF is extremely top-heavy. Constraints will improve further with future Gaia data releases, regardless of how many HVS candidates are found therewithin.