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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 mightbe formed is after the merger of a helium-core white dwarf with a main-sequencestar that produces a red giant branch star and fails to ignite helium. We use astellar-evolution code to compute models of the remnants of these mergers andfind a relation between the pre-merger masses and the final white dwarf mass.Combining our results with a model population, we predict that the massdistribution of single low-mass white dwarfs formed through this channel spansthe range 0.37 to 0.5Msolar and peaks between 0.45 and 0.46Msolar. Helium whitedwarf--main-sequence star mergers can also lead to the formation of singlehelium white dwarfs with masses up to 0.51Msolar. In our model the Galacticformation rate of single low-mass white dwarfs through this channel is about8.7X10^-3yr^-1. Comparing our models with observations, we find that themajority of single low-mass white dwarfs (<0.5Msolar) are formed from heliumwhite dwarf--main-sequence star mergers, at a rate which is about $2$ per centof the total white dwarf formation rate.

Evolution models of helium white dwarf--main-sequence star merger remnants: the mass distribution of single low-mass white dwarfs