Eccentricity Without Measuring Eccentricity: Discriminating Among Stellar Mass Black Hole Binary Formation Channels

TL;DR

This paper proposes a method to infer the eccentricity distribution and formation channels of stellar mass black hole binaries using LISA observations, without directly measuring eccentricity, by analyzing the impact on gravitational wave signals.

Contribution

It introduces a novel approach to distinguish black hole binary formation channels through frequency-based counting, bypassing the need for explicit eccentricity detection.

Findings

Eccentricity affects the peak gravitational wave frequency and binary number density.

Counting binaries by frequency can reveal formation channels.

A simplified SNR calculation for eccentric binaries is provided.

Abstract

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 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 signal-to-noise ratio of eccentric binaries.