Direct gravitational imaging of intermediate mass black holes in extragalactic haloes

A galaxy halo may contain a large number of intermediate mass black holes (IMBHs) with masses in the range of 102M⊙{less-than or approximate} MBH {less-than or approximate} 106M⊙. We propose to directly detect these IMBHs by observing multiply imaged QSO-galaxy or galaxy-galaxy strong lens systems in the submillimetre bands with high angular resolution. The silhouette of an IMBH in the lensing galaxy halo would appear as either a monopole-like or a dipole-like variation at the scale of the Einstein radius against the Einstein ring of the dust-emitting region surrounding the QSO.We use a particle tagging technique to dynamically populate a Milky Way-sized dark matter halo with black holes (BHs), and show that the surface mass density andnumber density of IMBHs have power-law dependences on the distance from the centreof the host halo if smoothed on a scale of ~1 kpc. Most of the BHs orbiting close to the centre are freely roaming as they have lost their dark matter hosts during infall due to tidal stripping. Next generation submillimetre telescopes withhigh angular resolution ({less-than or approximate}0.3 mas) will be capable of directly mapping such off-nuclear freely roaming BHs with a mass of ⊙106M{less-than or approximate} in a lensing galaxy that harbours an O(109)M⊙ supermassive black hole in its nucleus.