A New Technique for Probing Convection in Pulsating White Dwarf Stars

In this paper we demonstrate how pulsating white dwarfs can be used as an astrophysical laboratory for empirically constraining convection in these stars. We do this using a technique for fitting observed nonsinusoidal light curves, which allows us to recover the thermal response timescale of the convection zone (its “depth”) as well as how this timescale changes as a function of effective temperature. We also obtain constraints on mode identifications for the pulsation modes, allowing us to use asteroseismology to study the interior structure of these stars. Aspects of this approach may have relevance for other classes of pulsators, including the Cepheids and RR Lyrae stars. Subject headings: convection—stars: oscillations—white dwarfs—dense matter 1. ASTROPHYSICAL CONTEXT The physics of convection represents one of the largest sources of uncertainty in modeling stars. In main sequence objects, convection is believed to occur in the cores of stars more massive than the Sun (e.g., Woo & Demarque 2001) as well as in the envelopes of stars having masses less than about 2.0M⊙. Red Giant stars should have fully convective envelopes (e.g., Salaris, Cassisi, & Weiss 2002), making convection common throughout the H-R diagram. Along the white dwarf cooling track we expect white dwarfs with helium spectra (DBs) and temperatures less than ∼35,000 K to have surface convection zones, while those with hydrogen spectra (DAs) and temperatures less than ∼ 15,000 K should also have convective surface layers. The fact that there are major uncertainties in our ability to model the physics of convection has significant astrophysical consequences. For instance, whether or not convective overshoot occurs in the cores of massive stars affects the amount of material which is available for nuclear burning, leading to an uncertainty of ∼ 20% in stellar ages (Di Mauro et al. 2003; Bitzaraki et al. 2001). For pulsating white dwarfs, uncertainty regarding convection in their atmospheres is the largest single source of error in their derived effective temperatures (e.g., Bergeron et al. 1995). This is significant since we use what we learn about the interior structure of the pulsators to calibrate white dwarf cooling sequences, which in turn can be used to determine the ages of individual white dwarfs (Ruiz & Bergeron 2001) or the age of the Galactic disc (Wood & Oswalt 1998; Wood 1992; Winget et al. 1987). The very low-amplitude oscillations which have been observed in the Sun and recently in other Solar-like stars (e.g., Bedding & Kjeldsen 2003) have traditionally been explained through stochastic driving due to the outer convection zones found in these stars (e.g., Kumar, Franklin, & Goldreich 1988; Houdek et al. 1999). However, one of the first results from the Canadian space mission MOST (Microvariability and Oscillations of STars) has been that the oscillations expected in the star Procyon are not present, at least not at detectable levels (Matthews et al. 2004), implying that our understanding of convection in stars even slightly more massive than the Sun may still be incomplete. Electronic address: [email protected] In the sections which follow we describe a new technique for fitting observed non-sinusoidal light curves in white dwarfs. With this technique we can recover the thermal response timescale of the convection zone (or its depth) and how this timescale changes as a function of effective temperature. We also obtain mode identifications for the pulsation modes, which helps us to use asteroseismology to study the interior structure of these stars. Our approach for deriving information on the depth of the convection zone and its temperature sensitivity is based on the seminal numerical work of Brickhill (1992) and on the complementary analytical treatment of Goldreich & Wu (1999) and Wu (2001). Essentially, we take a hybrid of these two approaches, and it is this model which we describe below.