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ABSTRACT We assess the possibility of detecting both eccentricity and gas effects (migration and accretion) in the gravitational wave (GW) signal from LISA massive black hole binaries at redshift z=1. Gas induces a phase correction to the GW signal with an effective amplitude (C ₆) and a semimajor axis dependence (assumed to follow a power-law with slope n ₆). We use a complete model of the LISA response and employ a gas-corrected post-Newtonian inspiral-only waveform model TaylorF2Ecc. By using the Fisher formalism and Bayesian inference, we constrain C ₆ together with the initial eccentricity e₀, the total redshifted mass Mᵦ, the primary-to-secondary mass ratio q, the dimensionless spins ₁, ₂ of both component BHs, and the time of coalescence tc. We find that simultaneously constraining C ₆ and e₀ leads to worse constraints on both parameters with respect to when considered individually. For a standard thin viscous accretion disc around Mᵦ=10⁵~ M, q=8, ₁, ₂=0. 9, and tc=4 years MBHB, we can confidently measure (with a relative error of 50 per cent) an Eddington ratio f ₄₃₃ 0. 1 for a circular binary and f ₄₃₃ 1 for an eccentric system assuming O (10) stronger gas torque near-merger than at the currently explored much-wider binary separations. The minimum measurable eccentricity is e₀ 10^-2. 75 in vacuum and e₀ 10^-2 in gas. A weak environmental perturbation (f ₄₃₃ 1) to a circular binary can be mimicked by an orbital eccentricity during inspiral, implying that an electromagnetic counterpart would be required to confirm the presence of an accretion disc.
Garg et al. (Thu,) studied this question.