The Population of Eccentric Binary Black Holes: Implications for mHz Gravitational Wave Experiments

The observed binary black hole (BBH) mergers indicate a large Galactic progenitor population continuously evolving from large orbital separations and low gravitational wave (GW) frequencies to the final merger phase. We investigate the equilibrium distribution of binary black holes in the Galaxy. Given the observed BBH merger rate, we contrast the expected number of systems radiating in the low-frequency $0.1-10\,$mHz GW band under two assumptions: (1) that all merging systems originate from near-circular orbits, as may be indicative of isolated binary evolution, and (2) that all merging systems originate at very high eccentricity, as predicted by models of dynamically-formed BBHs and triple and quadruple systems undergoing Lidov-Kozai eccentricity oscillations. We show that the equilibrium number of systems expected at every frequency is higher in the eccentric case (2) than in the circular case (1) by a factor of $\simeq 2-15$. This follows from the fact that eccentric systems spend more time than circular systems radiating in the low-frequency GW bands. The GW emission comes in pulses at periastron separated by the orbital period, which may be days to years. For a LISA-like sensitivity curve, we show that if eccentric systems contribute significantly to the observed merger rate, then $\simeq 10$ eccentric systems should be seen in the Galaxy.