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

TL;DR

This paper investigates the relationship between spin and eccentricity in massive black hole binaries observable by LISA, revealing distinct signatures for retrograde and prograde accretion that can inform formation theories.

Contribution

It demonstrates a strong correlation between eccentricity and effective spin in MBHBs, highlighting the unique retrograde accretion signature for the first time.

Findings

Retrograde accretion leads to high eccentricity and negative effective spin.

Prograde accretion results in positive effective spin and low eccentricity.

Distinct signatures can help identify black hole binary formation channels.

Abstract

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), 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 $\chi_{{\rm eff},1\rm yr}$ and non-measurable $e_{1\rm yr}$. 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.