On the 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 the help of the so-called loss cone approximation. For a power-law cusp of radius r(a) , the black hole mass Msimilar to 10(6) M-., and the fraction of the compact objects deltasimilar to 0.1, this rate. The function K(p) depends on parameter p determining the cusp profile, and for the standard cusp profiles with p = 1/4, K (p) similar to 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 Prsimilar to 10(-7) [(P /10(3) s)/(M/10 (6) M-. )](8/3)[(M/10(6) M-.)/(r(a)/1 pc)](3/2). The object with the period Psimilar to 10(3) s emits gravitational waves with amplitude sufficient to be detected by the LISA-type gravitational wave antenna from the distance similar to10(3) Mpc. 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.