Time-frequency Imprints of Extreme Mass-Ratio Inspirals in Confusion Gravitational Wave Background

Detecting individual extreme-mass-ratio inspirals (EMRIs) is a major science goal of future space-based gravitational wave observatories such as Laser Interferometer Space Antenna (LISA) and TianQin. However, matched-filtering can be challenging as waveform templates are required to be accurate over tens of thousands of orbits. We introduce the time-frequency spectrum as an alternative observable that can be exploited to reveal the chirping of EMRIs at the population level. We analytically calculate this spectrum and its correlators for parameterized populations of slowly chirping sources on quasi-circular orbits, assuming a simplified model of the antenna response for a proof of concept. We then exploit this observable to distinguish between Galactic white dwarf binaries and a possible EMRI population, and quantify the precision at which EMRI population parameters can be determined through a Fisher analysis. We explore several scenarios of EMRI populations and find that this new method may allow us to determine EMRI population parameters at an accuracy level of several percent. Since white dwarf binaries have much longer chirping timescales than the EMRIs do, EMRI population properties can still be determined even if their stochastic gravitational wave background has a power spectrum two orders of magnitude weaker than that of the Galactic white dwarf binaries.