Helium core white dwarf evolution - including white dwarf companions to neutron stars

We present a detailed calculation of the evolution of low-mass helium white dwarfs. These white dwarfs are formed via long-term, low-mass binary evolution. After detachment from the Roche lobe, the hot helium cores have a rather thick hydrogen layer with masses between 0.001 to 0.06 M⊙. We found that the majority of our computed models experience one or two hydrogen shell flashes. The duration of the flashes is between a few ×106 y to a few ×107 y. In several flashes the white dwarf radius will increase so much that it forces the model to fill its Roche lobe again. Our calculations show that the cooling history of the helium white dwarf depends dramatically on the thickness of the hydrogen layer. The presence of low-mass helium white dwarf secondaries in millisecond pulsar binaries allows to determine the age of the systems independently of the rotational history of the pulsars. The same method may be applied to double degenerate systems. We discuss the cooling history of the low-mass, helium core white dwarfs in short orbital period millisecond pulsars.