Uncertainty of the white dwarf astrophysical gravitational wave background

Context. The astrophysical gravitational wave background (AGWB) is a stochastic gravitational wave (GW) signal emitted by different populations of in-spiralling binary systems containing compact objects throughout the Universe. In the frequency range between 10-4 and 10-1 hertz (Hz), it will be detected by future space-based gravitational wave detectors, such as Laser Interferometer Space Antenna (LISA). In a recent work, we concluded that the white dwarf (WD) contribution to the AGWB dominates that of black holes (BHs) and neutron stars (NSs). Aims. We aim to investigate the uncertainties of the WD AGWB that arise from the use of different stellar metallicities, star formation rate density (SFRD) models, and binary evolution models. Methods. We used the code we previously developed to determine the WD component of the AGWB. We used a metallicity-dependent SFRD based on an earlier work to construct five different SFRD models. We used four different population models based on a range of common-envelope treatments and six different metallicities for each model. Results. 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 less significant 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 value of Omega(WD) = 4 x 10(-12) at 1 mHz and a shape that is weakly dependent on the model. Conclusions. We find the uncertainty for the WD component of the AGWB to be about a factor of 5. We note that there are 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 it to be likely. We confirm our previous findings asserting that the WD component of the AGWB dominates over other populations, in particular, BHs.