Muffled Murmurs: Environmental effects in the LISA stochastic signal from stellar-mass black hole binaries

TL;DR

This work investigates how environmental effects in gas-rich environments alter the LISA-detectable SGWB from stellar-mass black hole binaries. By deriving DF- and accretion-induced modifications to the binary frequency evolution and GW energy spectrum, the authors construct phenomenological templates (RPL and RPLP) and perform Bayesian inference on simulated LISA data, including Galactic foregrounds. They find that dynamical friction with typical AGN-disk densities ($ ho oughly 10^{-10}$–$10^{-9}$ g cm$^{-3}$) yields a measurable suppression of the SGWB and strong Bayes factors against a vacuum model, while gas accretion is generally undetectable within the LISA band. They also show that a sub-population undergoing environmental effects can be identified, and demonstrate agnostic tests of extra energy-loss channels (including a time-varying Newton's constant) with constraints on $| d G/ d t|/G \, aisebox{.3ex}{$ ot hickspace riangleright$}\, 10^{-4}$ yr$^{-1}$. Overall, the paper provides a practical framework to probe sBBH environments and tests of gravity using LISA's SGWB.

Abstract

The population of unresolved stellar-mass black hole binaries (sBBHs) is expected to produce a stochastic gravitational-wave background (SGWB) potentially detectable by the Laser Interferometer Space Antenna (LISA). In this work, we compute the imprint of astrophysical environmental effect--such as gas dynamical friction and accretion--on this background. Using the sBBHs population constraints obtained by the LIGO--Virgo--Kagra collaboration, we compute the expected SGWB and develop a phenomenological parametric model that can accurately capture the effect of dynamical friction and accretion. Using our model, we perform Bayesian inference on simulated signals to assess the detectability of these environmental effects. We find that even for large injected values of the Eddington ratio, the effect of accretion in the SGWB is undetectable by LISA. However, LISA will be able to constrain the effect of dynamical friction with an upper bound on the gas density of $ρ\lesssim 7.6 \times 10^{-10} \mathrm{g \, cm^{-3}}$, thus probing the sBBH environment forming in typical thin accretion disks around Active Galactic Nuclei (AGNs). For injected densities of $ρ\sim 10^{-10}-10^{-9} \mathrm{g} \, \mathrm{cm}^{-3}$, dynamical friction effects can be well measured and clearly distinguished from vacuum, with Bayes factors reaching up to $\sim$ 60, even when the Galactic foreground is included.

Figures (13)

• Figure 1: The SGWB spectra $\Omega_{\mathrm{GW}}(f)$ for various disk densities $\rho$, with the normalization $\rho_0 = 10^{-10}\mathrm{g}\, \mathrm{cm}^{-3}$. The solid lines correspond to different values of $\rho$, with the vacuum case corresponding to $\rho = 0$. The gray dashed (black dotted) curves denotes the LISA power-law sensitivity (PLS) and Bayesian power-law sensitivity (BPLS), assuming a signal-to-noise ratio of 10, a Bayes factor threshold of 10, and 10% noise level uncertainty.
• Figure 2: The SGWB spectra $\Omega_{\mathrm{GW}}(f)$, driven by gas accretion, for a range of Eddington ratios $f_{\mathrm{Edd}}$. The solid lines correspond to different values of $f_{\rm Edd}$, with the vacuum case corresponding to $f_{\rm Edd} = 0$. The gray dashed and black dotted curves indicate the LISA power-law sensitivity (PLS) and Bayesian power-law sensitivity (BPLS) under the same assumptions made in \ref{['subsec:eff_DF']}.
• Figure 3: Marginalized posteriors for the dynamical friction model across various matter density regimes. Solid (dashed) contours and histograms correspond to analyses with (without) the inclusion of the Galactic foreground. Two-dimensional contours correspond to $90\%$ credible regions. Dash-dot represent the true value for $\rho$ and the single asymptotic value for $A_{\rm vac}$ (as listed in \ref{['tab:env_mapping_params']}).
• Figure 4: Cumulative SNR of the best-fit recovered SGWB model as a function of frequency. The solid and dashed lines represent the cases with and without the Galactic foreground respectively, while the different colored lines correspond to different $\rho^{\rm inj}$.
• Figure 5: Marginalized posterior probability for $\log_{10}(\rho / \rho_0)$ shown for the cases with (blue histogram) and without (red dashed histogram) Galactic foreground parameters included. The vertical lines indicate the one-sided $90\%$ credible intervals and the black histogram indicates the uniform prior on $\log_{10}(\rho / \rho_0)$. Observe that the constraint is slightly weaker when including the Galactic parameters.