  It is not known how single white dwarfs with masses less than 0.5Msolar --
low-mass white dwarfs -- are formed. One way in which such a white dwarf might
be formed is after the merger of a helium-core white dwarf with a main-sequence
star that produces a red giant branch star and fails to ignite helium. We use a
stellar-evolution code to compute models of the remnants of these mergers and
find a relation between the pre-merger masses and the final white dwarf mass.
Combining our results with a model population, we predict that the mass
distribution of single low-mass white dwarfs formed through this channel spans
the range 0.37 to 0.5Msolar and peaks between 0.45 and 0.46Msolar. Helium white
dwarf--main-sequence star mergers can also lead to the formation of single
helium white dwarfs with masses up to 0.51Msolar. In our model the Galactic
formation rate of single low-mass white dwarfs through this channel is about
8.7X10^-3yr^-1. Comparing our models with observations, we find that the
majority of single low-mass white dwarfs (<0.5Msolar) are formed from helium
white dwarf--main-sequence star mergers, at a rate which is about $2$ per cent
of the total white dwarf formation rate.

Solar and Stellar Astrophysics