Accretion mediated spin-eccentricity correlations in LISA massive black hole binaries

Abstract

We examine expected effective spin ($\ddot{I}{‡}_{\mathrm{eff},1\mathrm{yr}}$) and orbital eccentricity ($e_{1\mathrm{yr}}$) correlations for a population of observable equal-mass massive black hole binaries (MBHBs) with total redshifted mass $M_z\sim [10^{4.5},10^{7.5}]{\mathrm{M}}_{\odot }$ embedded in a circumbinary disc (CBD), one-year before merging in the LISA band. We find a strong correlation between measurable eccentricity and negative effective spin for MBHBs that are carried to merger by retrograde accretion. This is due to the well-established eccentricity pumping of retrograde accretion and the formation of retrograde CBD-aligned mini-discs, as observed in hydrodynamical simulations. Conversely, prograde accretion channels result in positive $\ddot{I}{‡}_{\mathrm{eff},1\mathrm{yr}}$ and non-measurable $e_{1\mathrm{yr}}$. This clear contrast between the two CBD orientations - and particularly the unique signature of retrograde configurations - provides a promising way to unlock the mysteries of MBHB formation channels in the LISA era.

Accepted by MNRAS. 8 pages and 5 figures