Testing the Kerr nature of intermediate-mass and supermassive black hole binaries using spin-induced multipole moment measurements

The gravitational wave measurements of spin-induced multipole moment coefficients of a binary black hole system can be used to distinguish black holes from other compact objects [N. V. Krishnendu et al., PRL 119, 091101 (2017)]. Here, we apply the idea proposed in [N. V. Krishnendu et al., PRL 119, 091101 (2017)] to binary systems composed of intermediate-mass and supermassive black holes and derive the expected bounds on their Kerr nature using future space-based gravitational wave detectors. Using astrophysical models of binary black hole population, we study the measurability of the spin-induced quadrupole and octupole moment coefficients using LISA and DECIGO. The errors on spin-induced quadrupole moment parameter of the binary system are found to be { $leq 0.1$ for almost $3%$ of the total supermassive binary black hole population which is detectable by LISA whereas it is $sim 46%$ for the intermediate-mass black hole binaries observable by DECIGO at its design sensitivity.} We find that { errors on} {it both} the quadrupole and octupole moment parameters can be estimated to { be} $leq 1$ for $sim 2%$ and $sim 50%$ {of the population} respectively for LISA and DECIGO detectors. { Our findings suggest that a subpopulation of binary black hole events, with the signal to noise ratio thresholds greater than 200 and 100 respectively for LISA and DECIGO detectors, would permit tests of black hole nature to 10% precision.}