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ABSTRACT 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 at redshift $z=1$. Gas induces a phase correction to the GW signal with an effective amplitude ($$C_{\rm g}$$) and a semimajor 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 inspiral-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 $$\lt 50$$ per cent) an Eddington ratio $${\rm f}_{\rm Edd}\sim 0.1$$ for a circular binary and $${\rm f}_{\rm Edd}\sim 1$$ for an eccentric system assuming $$\mathcal {O}(10)$$ stronger gas torque near-merger than at the currently explored much-wider binary separations. The minimum measurable eccentricity is $$e_0\gtrsim 10^{-2.75}$$ in vacuum and $$e_0\gtrsim 10^{-2}$$ in gas. A weak environmental perturbation ($${\rm f}_{\rm Edd}\lesssim 1$$) to a circular binary can be mimicked by an orbital eccentricity during inspiral, implying that an electromagnetic counterpart would be required to confirm the presence of an accretion disc. 

ABSTRACT We explore the eccentricity measurement threshold of Laser Interferometer Space Antenna (LISA) for gravitational waves radiated by massive black hole binaries (MBHBs) with redshifted BH masses Mz in the range 104.5–107.5 M⊙ at redshift z = 1. The eccentricity can be an important tracer of the environment where MBHBs evolve to reach the merger phase. To consider LISA’s motion and apply the time delay interferometry, we employ the lisabeta software and produce year-long eccentric waveforms using the inspiral-only post-Newtonian model taylorf2ecc. We study the minimum measurable eccentricity (emin, defined one year before the merger) analytically by computing matches and Fisher matrices, and numerically via Bayesian inference by varying both intrinsic and extrinsic parameters. We find that emin strongly depends on Mz and weakly on mass ratio and extrinsic parameters. Match-based signal-to-noise ratio criterion suggest that LISA will be able to detect emin ∼ 10−2.5 for lighter systems (Mz ≲ 105.5 M⊙) and ∼10−1.5 for heavier MBHBs with a 90 per cent confidence. Bayesian inference with Fisher initialization and a zero noise realization pushes this limit to emin ∼ 10−2.75 for lower-mass binaries, assuming a <50 per cent relative error. Bayesian inference can recover injected eccentricities of 0.1 and 10−2.75 for a 105 M⊙ system with an ∼10−2 per cent and an ∼10 per cent relative errors, respectively. Stringent Bayesian odds criterion ($$\ln {\mathcal {B}}\gt 8$$) provides nearly the same inference. Both analytical and numerical methodologies provide almost consistent results for our systems of interest. LISA will launch in a decade, making this study valuable and timely for unlocking the mysteries of the MBHB evolution. 

GW190521, the most massive binary black hole merger confidently detected by the LIGO-Virgo- KAGRA Collaboration, is the first gravitational-wave observation of an intermediate-mass black hole. The signal was followed approximately 34 days later by flare ZTF19abanrhr, detected in AGN J124942.3 þ 344929 by the Zwicky Transient Facility at the 78% spatial contour for GW190521’s sky localization. Using the GWTC-2.1 data release, we find that the association between GW190521 and flare ZTF19abanrhr as its electromagnetic counterpart is preferred over a random coincidence of the two transients with a log Bayes’ factor of 8.6, corresponding to an odds ratio of ∼5400∶1 for equal prior odds and ∼400∶1 assuming an astrophysical prior odds of 1=13. Given the association, the multimessenger signal allows for an estimation of the Hubble constant, finding H0 ¼ 102þ27 −25 km s−1 Mpc−1 when solely analyzing GW190521 and 79.2þ17.6 −9.6 km s−1 Mpc−1 assuming prior information from the binary neutron star merger GW170817, both consistent with the existing literature. 

Abstract The Laser Interferometer Space Antenna (LISA) will be a transformative experiment for gravitational wave astronomy, and, as such, it will offer unique opportunities to address many key astrophysical questions in a completely novel way. The synergy with ground-based and space-born instruments in the electromagnetic domain, by enabling multi-messenger observations, will add further to the discovery potential of LISA. The next decade is crucial to prepare the astrophysical community for LISA’s first observations. This review outlines the extensive landscape of astrophysical theory, numerical simulations, and astronomical observations that are instrumental for modeling and interpreting the upcoming LISA datastream. To this aim, the current knowledge in three main source classes for LISA is reviewed; ultra-compact stellar-mass binaries, massive black hole binaries, and extreme or interme-diate mass ratio inspirals. The relevant astrophysical processes and the established modeling techniques are summarized. Likewise, open issues and gaps in our understanding of these sources are highlighted, along with an indication of how LISA could help making progress in the different areas. New research avenues that LISA itself, or its joint exploitation with upcoming studies in the electromagnetic domain, will enable, are also illustrated. Improvements in modeling and analysis approaches, such as the combination of numerical simulations and modern data science techniques, are discussed. This review is intended to be a starting point for using LISA as a new discovery tool for understanding our Universe.