Gravitational-wave background from extragalactic double white dwarfs for LISA

Context. Recent studies have revealed that the contribution of extragalactic double white dwarfs (DWDs) to the astrophysical gravitational-wave background could be detectable in the millihertz regime by the LISA space mission. Conversely, the presence of this background could hamper the detection of cosmological backgrounds, which are among the key targets of gravitational-wave astronomy. Aims. We aim to confirm the amplitude and spectrum of the extragalactic DWD background and estimate its detectability with LISA under different assumptions. We also aim to understand the main uncertainties in the amplitude and frequency spectrum and estimate whether the signal could be anisotropic. Methods. We used the population synthesis code COSMIC with several assumptions about binary evolution and initial conditions. We also incorporated a specific treatment to account for the episodes of mass transfer and tidal torques after the formation of the DWDs. Results. 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 star formation 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 background up to a factor of 3 at the highest frequencies. For all the models we consider, we find that this background would be easily detectable, with signal-to-noise-ratio values from 100 to more than 1000 by LISA after 4 years of observations. Under the hypothesis of an homogeneous Universe beyond 200 Mpc, anisotropies associated with the astrophysical population of DWDs will likely not be detectable. We provide phenomenogical fits of the background produced by extragalactic DWDs under different assumptions to be used by the community. Conclusions. We demonstrate significant variability in gravitational-wave background predictions, emphasizing uncertainties due to different astrophysical assumptions. We highlight the importance of determining the position of the knee in the gravitational-wave background spectrum, as it provides insights into mass transfer models. The prediction of this background is of critical importance for LISA in the context of observing other backgrounds.