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

We examine expected effective spin (⁠|$\chi _{{\rm eff},1{\rm yr}}$|⁠) and orbital eccentricity (⁠|$e_{1\rm yr}$|⁠) correlations for a population of observable equal-mass massive black hole binaries (MBHBs) with total redshifted mass |$M_z\sim [10^{4.5},10^{7.5}]~{{\rm M}_{\odot }}$| embedded in a circumbinary disc (CBD) at redshifts |$z=1$| and |$z=2$|⁠ , 1 yr before merging in the Laser Interferometer Space Antenna (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 mini-discs 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 |$M_z\lesssim 10^{5}~{{\rm M}_{\odot }}$| 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. [ABSTRACT FROM AUTHOR]