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 power-law cusp of radius r _ { a } , the black hole mass M \sim 10 ^ { 6 } M _ { \odot } , and the fraction of the compact objects \delta \sim 0.1 this rate \dot { N } _ { wd } \sim 4 \cdot 10 ^ { -5 } K ( p ) \sqrt { { GM \over r _ { a } ^ { 3 } } } \approx 3 \cdot 10 % ^ { -9 } K ( p ) { ( { M \over 10 ^ { 6 } M _ { \odot } } ) } ^ { 1 / 2 } { ( { r _ { a } \over 1 pc } ) } ^ { -3 / 2 } yr ^ { -1 } .
The function K ( p ) depends on parameter p determining the cusp profile , and for the standard cusp profiles with p = 1 / 4 K ( p ) \sim 2 .
We estimate the probability { \it Pr } of finding of a compact object orbiting around a black hole with the period P in one particular galaxy to be { \it Pr } \sim 10 ^ { -7 } { ( { P / 10 ^ { 3 } s \over M / 10 ^ { 6 } M _ { \odot } } ) } ^ { 8 / 3 } { ( { M / 10 ^ { 6 } M _ { % \odot } \over r _ { a } / 1 pc } ) } ^ { 3 / 2 } .
The object with the period P \sim 10 ^ { 3 } s emits gravitational waves with amplitude sufficient to be detected by LISA type gravitational wave antenna from the distance \sim 10 ^ { 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 .