Intermediate-mass black holes and contribution to extragalactic background light from Population III stars in Milky Way-like galaxies

The mass range of observed black holes extends from stellar-mass to supermassive scales, yet the existence of objects in the intermediate-mass range of $10^{2} - 10^{5} \text{M}_{\odot}$ remains unconfirmed. Black holes are suspected to compress the surrounding dark matter distribution, forming a ``spike''. If dark matter is self-annihilating, the spike could produce gamma-ray emission sufficiently luminous to be detected. This work aims to estimate the number of expected unmerged intermediate-mass black holes in a Milky Way-like galaxy that could form such spikes. These intermediate-mass black holes are assumed to have formed from the collapse of high-mass Population III stars, such that the resulting merger rate is constrained by observations of gravitational wave emission. It is furthermore estimated to what extent the progenitor Population III stars contribute to the extragalactic background light. The Population III stars are simulated and tracked using the A-SLOTH semi-analytical simulation code and the resulting number of intermediate-mass black holes is constrained by applying the Population III binary black hole merger rate to an effective volume determined from the Population III star formation rate. In this framework, $\sim 130$ unmerged IMBHs from Population III stars are expected to reside in a Milky Way-like galaxy. The contribution of their progenitors to the EBL in the near-infrared is less than $10^{-3} \text{nW} \text{m}^{-2} \text{sr}^{-1}$, well below previous estimates.