Gravitational-Wave Background from Extragalactic Double White Dwarfs for LISA

TL;DR

The paper investigates the stochastic gravitational-wave background produced by extragalactic double white dwarfs (DWDs) and its impact on LISA measurements of cosmological backgrounds. Using COSMIC for population synthesis across multiple star-formation histories and metallicities, it computes the SGWB via the standard $\Omega_{\mathrm{GW}}$ formalism, incorporating mass-transfer and tidal effects to assess high-frequency behavior. The authors find that the extragalactic DWD background is detectable by LISA across all models, with the dominant uncertainty stemming from the cosmic star-formation rate density and substantial sensitivity to common-envelope evolution; a knee in the spectrum around $f_b \approx 7\ \mathrm{mHz}$ encodes envelope-ejection physics and could constrain binary evolution models. Anisotropies are predicted to be small, implying the background is effectively isotropic, but the foreground must be explicitly modeled to avoid biasing cosmological SGWB searches. Overall, these results quantify a robust LISA foreground and provide fits and diagnostics to integrate this background into future analyses of gravitational-wave backgrounds.

Abstract

Recent studies have revealed the contribution of extragalactic DWD to the astrophysical SGWB could be detectable in the mHz regime by LISA. Conversely, the presence of this SGWB could hamper the detection of cosmological SGWB, which are one of the key targets of GW astronomy. We aim to confirm the spectrum of the extragalactic DWD SGWB and estimate its detectability with LISA under different assumptions. We also aim at understanding the main uncertainties in the spectrum and estimate if the signal could be anisotropic. We use population synthesis code COSMIC with several assumptions on binary evolution and initial conditions. We incorporate a specific treatment to account for the mass transfer and tidal torques after DWDs formation. Our study is in global agreement with previous studies, although we find a lower contribution at high frequencies, due to a different treatment of mass transfer in stellar binaries. We find that the uncertainties in the amplitude are dominated by the SFR model, and to a lesser degree by the binary evolution model. The inclusion of tidal effects and mass transfer episodes in DWDs can change the amplitude of the estimated SGWB up to a factor 3 at the highest frequencies. For all the models, we find that this SGWB would be detectable observable by LISA after 4 years. Under the hypothesis of an homogeneous Universe beyond 200Mpc, anisotropies associated to the astrophysical population of DWDs will likely not be detectable. We provide fits of this SGWB under different assumptions to be used by the community. We demonstrate variability in SGWB predictions, emphasizing uncertainties due to different astrophysical assumptions. We highlight the importance of determining the position of the knee in the SGWB spectrum, as it provides insights on mass transfer models. The prediction of this SGWB is of critical importance for LISA in the context of observing other SGWB.

Figures (12)

• Figure 1: Spectral energy density of the SGWB from extragalactic DWDs for various population synthesis models (see §\ref{['subsc:Cosmic']}) and various SFRD models (see §\ref{['subsubsc:SFRD']}). The different population synthesis models are indicated with the same markers as in Fig. \ref{['fig:etaDWD']}. Dotted, solid, and dashed lines correspond to the SFR models from strolger04, madau14, and madau17 respectively. The black line represents the LISA sensitivity curve colpi24, while the gray one shows the PI curve thrane13 for four years of observation time and SNR=10. The light blue curve is the confusion noise from Galactic DWDs robson19 and the green shaded band is the 90% credible interval of the SGWB from all compact object binaries estimated from observations of GWs abbott23. As a comparison, the blue shaded band shows the SGWB from extragalactic DWDs estimated in farmer03 and the pink curve indicates the the best-fit model obtained in staelens24. In Appendix \ref{['app:parameters']}, we discuss and summarize the fits of SGWB from extragalactic DWDs of all SFR models and stellar population synthesis models as presented in Table \ref{['tab:appendix_parameters']}.
• Figure 2: Spectral energy density of the SGWB from extragalactic DWDs for the various types of DWDs, with our defaultCOSMIC model and the SFRD from madau14. Different colours indicate the contribution from different type of DWD binaries. We do not show the contribution of ONe-ONe binaries here, as it is several orders of magnitude below due to their rarity. The sum of all the contributions is shown in black. Additional curves represent the LISA sensitivity, the PI curve, and the confusion noise from Galactic DWDs.
• Figure 3: Spectral energy density integrated over frequency for different redshift bins. The total contribution from all redshift bins is shown in black. Different colours indicate the contribution from different types of DWD binaries.
• Figure 4: SGWB from extragalactic DWDs when considering a more realistic treatment of DWD evolution, including episodes of mass transfer and tidal effects. The scatter points indicate the standard case with only GWs, with the defaultCOSMIC model and SFRD from madau14. The shaded area covers predictions from different assumptions about tidal effects. Additional curves represent the LISA sensitivity, the PI curve, and the confusion noise from Galactic DWDs.
• Figure 5: Cumulative contribution of extragalactic DWDs to the SGWB as a function of redshift, using our default population synthesis model and the SFRD from madau14. The black dots represent the integrated contribution over the complete frequency range, and the coloured ones correspond to different specific frequency bands. The redshift marking the limit of the homogeneous isotropic Universe $z=0.05$ is indicated as the gray vertical dashed line, as is $z=0.5$.