Abstract
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.
Highlights
White dwarf (WD) stars constitute the last stage in the life of the majority (∼97%) of stars populating the Universe, including our Sun (Winget & Kepler 2008; Fontaine & Brassard 2008; Althaus et al 2010)
The dependence of the blue edges of instability on the convective efficiency adopted in the equilibrium models is documented in Fig. 8, where we show the Teff− log g diagrams displaying our low-mass He-core WD evolutionary tracks, along with the blue edge of the ELMV instability strip for radial ( = 0) and nonradial ( = 1, 2) p and g modes, which correspond to different versions of the mixing length theory (MLT) theory of convection: ML1, ML2, and ML3
Having shown that our theoretical predictions are in good agreement with the position of the ELMVs in the diagram Teff −log g – provided that the stellar models are computed with the ML2 version of the MLT theory of convection – we want to compare the theoretical ranges of periods associated to unstable modes with the pulsation periods exhibited by the observed stars
Summary
White dwarf (WD) stars constitute the last stage in the life of the majority (∼97%) of stars populating the Universe, including our Sun (Winget & Kepler 2008; Fontaine & Brassard 2008; Althaus et al 2010). That so many constant (non variable) low-mass WDs coexist with ELMV WDs in the same domain of Teff and log g2 may be indicating substantially different internal structures, and so have quite distinct evolutionary origins This contrasts with the welldocumented purity of the ZZ Ceti instability strip, which indicates that all the DA WDs crossing the effective temperature interval 12 500 K >∼ Teff >∼ 10 700 K do pulsate. Nonadiabatic studies (Córsico et al 2012; Van Grootel et al 2013) predict that many unstable g and p modes are excited by the same partial ionization mechanism at work in ZZ Ceti stars, roughly at the right effective temperatures and the correct range of the periods observed in ELMVs. In this paper, our second work of the series on this topic, we perform a thorough stability analysis on the set of state-of-the-art evolutionary models of Althaus et al (2013).
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