On the point mass approximation to calculate the gravitational wave signal from white dwarf binaries

Double white dwarf binaries in the Galaxy dominate the gravitational wave sky and would be detectable for an instrument such as LISA. Most studies have calculated the expected gravitational wave signal under the assumption that the binary white dwarf system can be represented by two point masses in orbit. We discuss the accuracy of this approximation for real astrophysical systems. For non-relativistic binaries in circular orbit the gravitational wave signal can easily be calculated. We show that for these systems the point mass approximation is completely justified when the individual stars are axisymmetric irrespective of their size. We find that the signal obtained from Smoothed-Particle Hydrodynamics simulations of tidally deformed, Roche-lobe filling white dwarfs, including one case when an accretion disc is present, is consistent with the point mass approximation. The difference is typically at the level of one per cent or less in realistic cases, yielding small errors in the inferred parameters of the binaries.