What Fraction of Extreme Mass Ratio Inspirals That Merge After the LISA Mission Ends Are Detectable?

Abstract

Stellar-mass compact objects spiraling into massive black holes in galactic nuclei (referred to as "extreme-mass-ratio inspirals", or EMRIs) will be an important class of sources for the Laser Interferometer Space Antenna (LISA). A stellar-mass compact object can radiate in the millihertz band for years to decades before it plunges into its massive black hole, so a substantial fraction of the EMRIs that LISA can detect will still be inspiraling when the mission ends. We calculate what fraction of detectable EMRIs will plunge after the mission ends, and for those we calculate how they are distributed as a function of various parameters, such as their post-mission lifetime. To do this, we draw from astrophysically motivated populations, backward-integrate fully relativistic Kerr FastEMRIWaveforms trajectories for a given time to plunge, and compute the full LISA response over both the four-year nominal and ten-year extended observing windows. We calculate the detectable fraction as an explicit function of time to plunge at signal-to-noise ratio (SNR) thresholds of $ρ=10$, 20, and 30. We find that post-mission EMRIs are roughly one in four of the LISA-detectable population at $ρ>20$ over the four-year mission, and roughly one in six over the ten-year extended mission. The in-window detectable fraction varies by nearly a factor of six at $ρ>20$ across the massive black hole spins and secondary masses we ran, while the share stays between 25% and 33% for the four-year mission and between 13% and 20% for the ten-year one across all of them. The search for EMRIs that plunge more than $\sim 1$ year after the mission ends may require a different algorithm than the one used for EMRIs that plunge during the mission, and the fact that post-mission detections are a substantial fraction of all detections gives some urgency to developing a detection pipeline suitable for them.