Wandering intermediate-mass black holes in Milky Way-mass galaxies in cosmological simulations: myth or reality?

In this work, we address the following question: ``can we use the current cosmological simulations to identify intermediate-mass black holes (IMBHs) and quantify a putative population of wandering IMBHs?''. We compare wandering-IMBH counts in different simulations with different sub-grid methods and post-processing recipes, the ultimate goal being to aid future wandering-IMBH detection efforts. In particular, we examine simulations in which IMBHs are identified as BH seeds forming at high redshift and those in which they are identified using star clusters as proxies, which implicitly appeals to a stellar dynamical formation channel. In addition, we employ the extremely high-resolution cosmological hydrodynamical ``zoom-in'' simulation GigaEris with the star cluster proxies method to identify IMBHs. We find consistent counts of wandering high-redshift IMBHs across most of the different cosmological simulations employed so far in the literature, despite the different identification approaches, resulting in 5 to 18 wandering IMBHs per Milky Way-sized galaxy at $z \geq 3$. Nevertheless, we argue this is only coincidental, as a significant discrepancy arises when examining the formation sites and the mass ranges of the wandering IMBHs. Furthermore, we cannot determine how many of the IMBHs identified at high redshift in GigaEris will be wandering IMBHs at $z = 0$ as opposed to how many will accrete to the central supermassive BH, promoting its growth. All of this casts doubts on the ability of current cosmological simulations to inform observational searches for wandering IMBHs.