Pulsating low-mass white dwarfs in the frame of new evolutionary sequences II. Nonadiabatic analysis

Context. Low-mass (M-star/M-circle dot less than or similar to 0.45) white dwarfs, including the so-called extremely low-mass white dwarfs (ELM, M-star/M-circle dot less than or similar to 0.18-0.20), are being currently discovered in the field of our Galaxy through dedicated photometric surveys. That some of them pulsate raises the unparalleled chance to investigate their interiors. Aims. We present a detailed nonadiabatic pulsational analysis of such stars, employing full evolutionary sequences of low-mass He-core white dwarf models derived from binary star evolution computations. The main aim of this study is to provide a detailed description of the pulsation stability properties of variable low-mass white dwarfs during the terminal cooling branch. Methods. Our nonadiabatic pulsation analysis is based on a new set of He-core white-dwarf models with masses ranging from 0.1554 to 0.4352 M-circle dot, which were derived by computing the nonconservative evolution of a binary system consisting of an initially 1 M-circle dot ZAMS star and a 1.4 M-circle dot neutron star. We computed nonadiabatic radial (l = 0) and nonradial (l = 1, 2) g and p modes to assess the dependence of the pulsational stability properties of these objects with stellar parameters such as the stellar mass, the effective temperature, and the convective efficiency. Results. We found that a dense spectrum of unstable radial modes and nonradial g and p modes are driven by the kappa-gamma mechanism due to the partial ionization of H in the stellar envelope, in addition to low-order unstable g modes characterized by short pulsation periods that are significantly excited by H burning via the epsilon mechanism of mode driving. In all the cases, the characteristic times required for the modes to reach amplitudes large enough to be observable (the e-folding times) are always shorter than cooling timescales. We explore the dependence of the ranges of unstable mode periods (the longest and shortest excited periods) with the effective temperature, the stellar mass, the convective efficiency, and the harmonic degree of the modes. We also compare our theoretical predictions with the excited modes observed in the seven known variable low-mass white dwarfs (ELMVs) and found excellent agreement.