Diffuse X-Ray and Gamma-Ray Limits on Boson Stars that Interact with Nuclei

Light bosonic dark matter can form gravitationally bound states known as boson stars. In this work, we explore a new signature of these objects interacting with the interstellar medium (ISM). We show how small effective couplings between the bosonic dark matter and the nucleon lead to a potential that accelerates ISM baryons as they transit the boson star, making the ISM within radiate at a high rate and energy. The low ISM density, however, implies the majority of Galactic boson stars will be too faint to be observable through this effect. By contrast, the diffuse photon flux, in hard x-rays and soft gamma-rays, produced by boson stars interacting with the ionized ISM phases can be sizable. We compute this diffuse flux and compare it to existing observations from HEAO-1, INTEGRAL and COMPTEL to infer limits on the fraction of these objects. This novel method places constraints on boson star dark matter while avoiding back-action effects from ambient baryons on the boson star configuration, unlike terrestrial searches where it has been noted that back-action can screen light bosonic fields. In addition, this study could be extended to other couplings and structures formed from light dark matter. For dark matter masses $(10^{-14}$, $10^{-8}) \ {\rm eV}$ and boson star masses $(10^{-10}$, $10^{-1}) \ M_{\odot}$, we find the constraints on the fraction can go down to $f_* \lesssim 10^{-9}$ for dark matter in boson stars that is directly coupled to the Standard Model.