Key points are not available for this paper at this time.
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 (MBHBs) at redshift z=1. Gas induces a phase correction to the GW signal with an effective amplitude (C ₆) and a semi-major 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 in-spiral-only waveform model TaylorF2Ecc. By using the Fisher formalism and Bayesian inference, we explore LISA's ability to 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. Assuming a standard thin viscous accretion disc, for Mᵦ=10⁶~ M_, q=8, ₁, ₂=0. 9, and tc=4 years, we can confidently measure (with a relative error of <50 per cent) an Eddington ratio as small as f ₄₃₃0. 1 for a circular binary while for an eccentric system only f ₄₃₃1 can be inferred. The minimum measurable eccentricity is e₀10^-2. 75 in vacuum and e₀10^-2 in the presence of a circumbinary disc. A weak environmental perturbation (f ₄₃₃1) to a circular binary can be mimicked by an orbital eccentricity during in-spiral, implying that an electromagnetic counterpart would be required to confirm the presence of an accretion disc.
Garg et al. (Wed,) studied this question.