Limits of vacuum-template subtraction for LISA massive black hole binary sources in realistic environments

TL;DR

This work addresses whether vacuum GW templates suffice for subtracting MBH binaries in LISA when environments with gas induce dephasing. It combines MBH population models with gas-driven dephasing to simulate 4 years of LISA data and compute the resulting residual background, deriving a simple fit for the residual amplitude. The study finds a median residual SNR of ${{\rm SNR} = 3.2^{+5.4}_{-1.9}} \times \sqrt{\frac{f_{\rm Edd}\, \langle \dot n \rangle}{20\, {\rm yr}^{-1}}}$, with a PSD resembling a stochastic foreground and a low-frequency residual approaching the quadrature sum of all MBH signals; for merger rates $\langle \dot n \rangle \gtrsim 15\ \, \text{yr}^{-1}$ the residual can exceed LISA sensitivity. The residual’s shape is well described by $h_c^{\rm res} \approx C \exp\left[ -\left(\frac{f}{f_c}\right)^{1/2}\right]$, with parameters $C$ and $f_c$ given in the text. These results imply that environmental effects must be incorporated in population-level analyses and motivate developing mitigation strategies, potentially via environment-aware waveforms or time-domain data handling, to preserve LISA’s scientific potential.

Abstract

We investigate the impact of gravitational wave (GW) dephasing due to gas accretion on the subtraction of massive black hole (MBH) binary signals over 4 yr of LISA data in the context of the global-fit. Based on state of the art predictions for the population of merging MBHs, we show that imperfect subtraction with vacuum waveform templates leaves a GW residual with an SNR of $3.2^{+5.4}_{-1.9}\times \sqrt{f_{\rm Edd} \langle \dot n \rangle/(20\, {\rm yr}^{-1})}$, where $f_{\rm Edd}$ is the typical Eddington ratio and $\langle \dot n \rangle$ the mean merger rate of LISA MBH binaries. We characterize the dependence of the residual on key population hyper-parameters, provide a simple fitting function and discuss detection and mitigation strategies.

Figures (4)

• Figure 1: Normalised differential merger rates from the ASTRID simulation 2025wang, L-Galaxies 2024izquierdo and 2020barausse (green). We employ a lognormal parametrization (black) with representative uncertainties (grey) to broadly reproduce the results of and the variation between different predictions. The distribution in mass ratio $q$ is truncated between 0.01 and 1.
• Figure 2: Realisation of the MBH binary signals observed over 4 years in LISA. Here we consider $\sim100$ sources (thin black lines). Their total power results from the addition of individual GWs with differing phases (shown are the actual sum and the sum in quadrature, blue lines). The residual (ochre, here for $f_{\rm Edd}=1$) caused by subtracting vacuum waveforms from the signals with gas effects resembles a stochastic background. Its properties are characterized in section \ref{['sec:Results']}.
• Figure 3: Residuals calculated from $10^3$ draws from the representative population distributions discussed in section \ref{['sec:Methods:pop']}. The medians (solid) are bracketed by the 68th and 90th percentiles (shaded). They can be fit by the simple function shown in Eq. \ref{['eq:fit1']} (dashed line, here for $\langle \dot n \rangle=10$ yr$^{-1}$).
• Figure 4: SNR of the residual background as a function of the population hyper-parameters. The median (solid) and percentiles (shaded) are calculated from 300 draws for each value of the mean merger rate $\langle \dot n \rangle$ (blue), mean redshift $\langle z \rangle$ (green) and mean primary mass $\langle M_1 \rangle$ (red). Shown are also the hyper-parameter ranges discussed in section \ref{['sec:Methods:pop']} (grey areas).