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Stellar mass compact objects in short period orbits about a$10^{4.5}$--$10^{7.5}$ solar mass massive black hole (MBH) are thought to be asignificant continuous-wave source of gravitational radiation for the ESA/NASALaser Interferometer Space Antenna (LISA) gravitational wave detector. However,these extreme mass-ratio inspiral sources began in long-period, nearlyparabolic orbits that have multiple close encounters with the MBH. Thegravitational radiation emitted during these close encounters may be detectableby LISA as a gravitational wave burst if the characteristic passage timescaleis less than $10^5$ seconds. Scaling a static, spherical model to the size andmass of the Milky Way bulge we estimate an event rate of ~ 15 per year for suchburst signals, detectable by LISA with signal-to-noise greater than five,originating in our galaxy. When extended to include Virgo cluster galaxies ourestimate increases to a gravitational wave burst rate of ~ 18. We conclude thatthese extreme mass-ratio burst sources may be a steady and significant sourceof gravitational radiation in the LISA data streams.Comment: 4 pages, minor revisions. Accepted for ApJ Letter

Event Rate for Extreme Mass Ratio Burst Signals in the LISA Band