Mass-ratio distribution of extremely low-mass white dwarf binaries

Knowing the masses of the components of binary systems is very useful for constraining the possible scenarios that could lead to their existence. While it is sometimes possible to determine the mass of the primary star, it is challenging to obtain good mass estimates of the secondary of a single-line spectroscopic binary. If the sample of such binaries is large enough, however, it is possible to use statistical methods to determine the mass-ratio distribution, and thus, the mass distribution of the secondary. Recently, the mass distribution of companions to extremely low-mass white dwarfs was studied using a sample of binaries from the ELM WD Survey. I reanalyse the same sample with two different methods: in the first one, I assume some functional form for the mass distribution, while in the second, I apply an inversion method. I show that the resulting companion-mass distribution can be as well approximated by either a uniform or a Gaussian distribution. The mass-ratio distribution derived from the inversion method without assuming any a priori functional form shows some additional fine-grain structure, although, given the small sample, it is difficult to claim that this structure is statistically significant. I conclude that it is not yet possible to fully constrain the distribution of the mass of the companions to extremely low-mass white dwarfs, although it appears that the probability to have a neutron star in one of the systems is indeed very low.