Numerical investigation of plasma-driven superradiant instabilities

Photons propagating in a plasma acquire an effective mass μ, which is given by the plasma frequency and which scales with the square root of the plasma density. As noted previously in the literature, for electron number densities n _e ∼ 10⁻³ cm⁻³ (such as those measured in the interstellar medium) the effective mass induced by the plasma is μ ∼ 10⁻¹² eV. This would cause superradiant instabilities for spinning black holes of a few tens of solar masses. An obvious problem with this picture is that densities in the vicinity of black holes are much higher than in the interstellar medium because of accretion, and possibly also pair production. We have conducted numerical simulations of the superradiant instability in spinning black holes surrounded by a plasma with density increasing closer to the black hole, in order to mimic the effect of accretion. While we confirm that superradiant instabilities appear for plasma densities that are sufficiently low near the black hole, we find that astrophysically realistic accretion disks are unlikely to trigger such instabilities. (paper)