Datensatz

Zusammenfassung

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 ($C_{\rm g}$) and a
semi-major axis dependence (assumed to follow a power-law with slope $n_{\rm
g}$). 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 constrain $C_{\rm g}$ together with the
initial eccentricity $e_0$, the total redshifted mass $M_z$, the
primary-to-secondary mass ratio $q$, the dimensionless spins $\chi_{1,2}$ of
both component BHs, and the time of coalescence $t_c$. We find that
simultaneously constraining $C_{\rm g}$ and $e_0$ leads to worse constraints on
both parameters with respect to when considered individually. For a standard
thin viscous accretion disc around $M_z=10^5~{\rm M}_\odot$, $q=8$,
$\chi_{1,2}=0.9$, and $t_c=4$ years MBHB, we can confidently measure (with a
relative error of $<50 $ per cent) an Eddington ratio ${\rm f}_{\rm
Edd}\sim0.1$ for a circular binary and ${\rm f}_{\rm Edd}\sim1$ for an
eccentric system assuming ${O}(10)$ stronger gas torque near-merger than at the
currently explored much-wider binary separations. The minimum measurable
eccentricity is $e_0\gtrsim10^{-2.75}$ in vacuum and $e_0\gtrsim10^{-2}$ in
gas. A weak environmental perturbation (${\rm f}_{\rm Edd}\lesssim1$) 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.