Pulsating low-mass white dwarfs in the frame of new evolutionary sequences : IV. The secular rate of period change

Context. An increasing number of low-mass (M⋆/M⊙ ≲ 0.45) and extremely low-mass (ELM, M⋆/M⊙ ≲ 0.18−0.20) white-dwarf stars are being discovered in the field of the Milky Way. Some of these stars exhibit long-period g-mode pulsations, and are called ELMV variable stars. Also, some low-mass pre-white dwarf stars show short-period p-mode (and likely radial-mode) photometric variations, and are designated as pre-ELMV variable stars. The existence of these new classes of pulsating white dwarfs and pre-white dwarfs opens the prospect of exploring the binary formation channels of these low-mass white dwarfs through asteroseismology. Aims. We aim to present a theoretical assessment of the expected temporal rates of change of periods () for such stars, based on fully evolutionary low-mass He-core white dwarf and pre-white dwarf models. Methods. Our analysis is based on a large set of adiabatic periods of radial and nonradial pulsation modes computed on a suite of low-mass He-core white dwarf and pre-white dwarf models with masses ranging from 0.1554 to 0.4352 M⊙, which were derived by computing the non-conservative evolution of a binary system consisting of an initially 1 M⊙ ZAMS star and a 1.4 M⊙ neutron star companion. Results. We computed the secular rates of period change of radial (ℓ = 0) and nonradial (ℓ = 1,2) g and p modes for stellar models representative of ELMV and pre-ELMV stars, as well as for stellar objects that are evolving just before the occurrence of CNO flashes at the early cooling branches. We find that the theoretically expected magnitude of of g modes for pre-ELMVs is by far larger than for ELMVs. In turn, of g modes for models evolving before the occurrence of CNO flashes are larger than the maximum values of the rates of period change predicted for pre-ELMV stars. Regarding p and radial modes, we find that the larger absolute values of correspond to pre-ELMV models. Conclusions. We conclude that any eventual measurement of a rate of period change for a given pulsating low-mass pre-white dwarf or white dwarf star could shed light about its evolutionary status. Also, in view of the systematic difficulties in the spectroscopic classification of stars of the ELM Survey, an eventual measurement of could help to confirm that a given pulsating star is an authentic low-mass white dwarf and not a star from another stellar population.Instituto de Astrofísica de La Plat