On formation rate of close binaries consisting of a super-massive black hole and a white dwarf

The formation rate of a close binary consisting of a super-massive black hole and a compact object (presumably a white dwarf) in galactic cusps is calculated with help of the so-called loss cone approximation. For a powerlaw cusp of radius ra, the black hole mass M ∼ 106M⊙, and the fraction of the compact objects δ ∼ 0.1 this rate Ṅwd ∼ 4 · 10K(p) √ GM r a ≈ 3 · 10K(p)( M 10M⊙ ) 1/2 ( ra 1pc ) −3/2 yr. The function K(p) depends on parameter p determining the cusp profile, and for the standard cusp profiles with p = 1/4 K(p) ∼ 2. We estimate the probability Pr of finding of a compact object orbiting around a black hole with the period P in one particular galaxy to be Pr ∼ 10( P/10 s M/10M⊙ ) 8/3 ( 6M⊙ ra/1pc ) 3/2 . The object with the period P ∼ 10s emits gravitational waves with amplitude sufficient to be detected by LISA type gravitational wave antenna from the distance ∼ 10Mpc. Based on estimates of masses of super-massive black holes in nearby galaxies, we speculate that LISA would detect several such events during its mission.