The Galactic massive black hole ( MBH ) , with a mass of M _ { \bullet } = 3.6 \times 10 ^ { 6 } M _ { \odot } , is the closest known MBH , at a distance of only 8 \mathrm { kpc } .
The proximity of this MBH makes it possible to observe gravitational waves from stars with periapse in the observational frequency window of the Laser Interferometer Space Antenna ( LISA ) .
This is possible even if the orbit of the star is very eccentric , so that the orbital frequency is many orders of magnitude below the LISA frequency window , as suggested by Rubbo et al .
( 48 ) .
Here we give an analytical estimate of the detection rate of such gravitational wave bursts .
The burst rate is critically sensitive to the inner cut-off of the stellar density profile .
Our model accounts for mass-segregation and for the physics determining the inner radius of the cusp , such as stellar collisions , energy dissipation by gravitational wave emission , and consequences of the finite number of stars .
We find that stellar black holes have a burst rate of the order of 1 { yr ^ { -1 } } , while the rate is of order \lesssim 0.1 { yr ^ { -1 } } for main sequence stars and white dwarfs .
These analytical estimates are supported by a series of Monte Carlo samplings of the expected distribution of stars around the Galactic MBH , which yield the full probability distribution for the rates .
We estimate that no burst will be observable from the Virgo cluster .