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

Low-mass ($M_{\star}/M_{\sun} \lesssim 0.45$) white dwarfs, including the so called extremely low-mass white dwarfs (ELM, $M_{\star}/M_{\sun } \lesssim 0.18-0.20$), are being currently discovered in the field of our Galaxy through dedicated photometric surveys. The fact that some of them pulsate opens the unparalleled chance for sounding their interiors. We present a detailed nonadiabatic pulsational analysis of such stars based on a new set of He-core white-dwarf models with masses ranging from $0.1554$ to $0.4352 M_{\sun}$ derived by computing the non-conservative evolution of a binary system consisting of an initially $1 M_{\sun}$ ZAMS star and a $1.4 M_{\sun}$ neutron star. We have computed nonadiabatic radial modes and nonradial 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. 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 which 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 as 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 an excellent agreement.