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

Abstract

Abstract We examine expected effective spin (χeff, 1yr) and orbital eccentricity ($e_{1\rm yr}$) correlations for a population of observable equal-mass massive black hole binaries (MBHBs) with total redshifted mass Mz ∼ [104.5, 107.5] M⊙ embedded in a circumbinary disc (CBD) at redshifts z = 1 and z = 2, 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 less-well-established formation of retrograde minidiscs coupled with a stable retrograde CBD throughout the binary evolution from the self-gravitating radius. Conversely, prograde accretion channels result in positive $\chi _{{\rm eff},1\rm yr}$ and non-measurable $e_{1\rm yr}$ except for almost unity Eddington ratio and Mz ≲ 105 M⊙ MBHBs at z = 1. 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.