On the uncertainty of the White Dwarf Astrophysical Gravitational Wave Background

The astrophysical gravitational wave background (AGWB) is a stochastic GW signal that is emitted by different populations of inspiralling binary systems containing compact objects. In the frequency range between 10^-4 and 10^-1 Hz it will be detected by future space-based gravitational wave detectors like the Laser Interferometer Space Antenna (LISA). Recently, Staelens & Nelemans 2024 (SN24) concluded that the white dwarf (WD) contribution to the AGWB dominates over that of black holes (BHs). We aim to investigate the uncertainties of the WD AGWB that arise from the use of different stellar metallicities, different star formation rate density (SFRD) models, and different binary evolution models. We use the code developed by SN24 to determine the WD component of the AGWB. We use a metallicity dependent SFRD based on Chruslinska et al (2019, 2020, 2021) to construct five different SFRD models. We use four different population models that use different common-envelope treatment and six different metallicities for each model. For all possible combinations, the WD component of the AGWB is dominant over other populations of compact objects. The effects of metallicity and population model are smaller than the effect of a (metallicity dependent) SFRD model. We find a range of about a factor of 5 in the level of the WD AGWB around a mid value of OmegaWD = 4 10^-12 at 1 mHz and a shape that depends weakly on the model. We find an uncertainty for the WD component of the AGWB of about a factor 5. We note that there exist other uncertainties that have an effect on this signal as well. We discuss whether the turnover of the WD AGWB at 10 mHz will be detectable by LISA, and find that this is likely. We confirm the previous finding that the WD component of the AGWB dominates over other populations, in particular BHs.