Extreme mass-ratio inspirals into Newtonian Proca stars

Abstract

Massive bosonic fields can form self-gravitating solitonic structures, which for vector fields are known as Proca stars. For ultralight fields, these structures can describe the cores of dark matter haloes surrounding the supermassive black holes at the center of galaxies. It has been argued that future gravitational-wave detectors might be able to probe the properties of dark matter structures. However, most of the analyses considering ultralight dark matter have focused on massive scalar fields. In this work, we study how Proca stars respond to a perturbing small object inspiralling in their interior, in the Newtonian limit. We consider both Newtonian spherically symmetric Proca stars and the non-spherically symmetric ground-state solutions. We compute the total energy lost by the orbiting object and compare it to the case where the bosonic star is composed of a scalar field. Our results show that, at the Newtonian level, the energy lost by the object in a Proca star ground state is similar to that in its scalar field counterpart, with relative differences of at most $\sim 20\%$, while the maximum orbital energy loss rate in the ground-state configuration can be one to two orders of magnitude larger than in the spherically symmetric Proca star, when a central parasitic black hole is present. Our work motivates the need to study extreme mass-ratio inspirals into Proca stars using a fully relativistic setup, where differences between the Proca and scalar boson star ground states are expected to become more significant.