Detectability of Wandering Intermediate-Mass Black Holes in the Milky Way Galaxy from Radio to X-rays

Intermediate-mass black holes (IMBHs, $10^{3-6} \, \rm{M_\odot}$), are typically found at the center of dwarf galaxies and might be wandering, thus far undetected, in the Milky Way (MW). We use model spectra for advection-dominated accretion flows to compute the typical fluxes, in a range of frequencies spanning from radio to X-rays, emitted by a putative population of $10^5 \, \rm{M_\odot}$ IMBHs wandering in five realistic, volume-weighted, MW environments. We predict that $\sim 27\%$ of the wandering IMBHs can be detected in the X-ray with Chandra, $\sim 37\%$ in the near-infrared with the Roman Space Telescope, $\sim 49\%$ in the sub-mm with CMB-S4 and $\sim 57\%$ in the radio with ngVLA. We find that the brightest fluxes are emitted by IMBHs passing through molecular clouds or cold neutral medium, where they are always detectable. We propose criteria to facilitate the selection of candidates in multi-wavelength surveys. Specifically, we compute the X-ray to optical ratio ($\alpha_{\rm ox}$) and the optical to sub-mm ratio, as a function of the accretion rate of the IMBH. We show that at low rates the sub-mm emission of IMBHs is significantly higher than the optical, UV and X-ray emission. Finally, we place upper limits on the number $N_\bullet$ of these objects in the MW: $N_\bullet<2000$ and $N_\bullet<100$, based on our detectability expectations and current lack of detections in molecular clouds and cold neutral medium, respectively. These predictions will guide future searches of IMBHs in the MW, which will be instrumental to understanding their demographics and evolution.