Eccentricity without Measuring Eccentricity: Discriminating among Stellar Mass Black Hole Binary Formation Channels

We show how the observable number of binaries in LISA is affected by eccentricity through its influence on the peak gravitational-wave frequency, enhanced binary number density required to produce the LIGO observed rate, and the reduced signal-to-noise ratio (S/N) for an eccentric event. We also demonstrate how these effects should make it possible to learn about the eccentricity distribution and formation channels by counting the number of binaries as a function of frequency, even with no explicit detection of eccentricity. We also provide a simplified calculation for S/N of eccentric binaries.