Spin-induced quadrupole moment test for eccentric compact binaries

Abstract Spin-induced deformations of individual components of a binary can be quantified using the gravitational wave signal the binary emits. Such deformations are characterised by a parameter, κ , which takes a value of 1 for a black hole and thus its measurement can be used to test the black hole nature. However, in practice, only a symmetric combination of this parameter for a binary ( κ s ) can be measured, thus enabling a test for the black hole nature as studied previously in literature. While previous studies have focused on circular binaries, our work extends the proposal to test the black hole nature of compact objects to eccentric systems, and we forecast the expected measurement precision using a Fisher matrix analysis. We find that, the error in the measurement of the parameter κ s reduces from a value of ∼18% (for the circular case) to close to 8%(4%) for a 10 Μ ⊙ system with dimensionless component spins > 0.8 and with a reference initial eccentricity (e 0 ) of 0.2(0.5) evaluated at 5Hz for Cosmic Explorer(CE). Compared to the estimates obtained by using advanced LIGO design sensitivity, eccentricity and overall improved sensitivity of CE detectors together seem to improve these estimates almost by an order of magnitude.