JJ Hermes edited sectionIntroduction_.tex  about 10 years ago

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These hydrogen-atmosphere pulsating WDs (so-called DAVs or ZZ\,Ceti stars) have spent hundreds of Myr passively cooling before reaching this evolutionary state. Global oscillations provide a unique window below the thin photosphere and deep into the interior of these relatively simple stars, enabled by matching the observed periods to theoretical models generated by adiabatic pulsation calculations.  Given the number of free parameters for full asteroseismic fits, the most reliable results requiresecuring  a large number of significant pulsation periods and uniquely identifying the oscillation modes. However, withtypical  $g$-mode periods ranging from $100-1400$ s, ground-based photometry suffers from frequent gaps in coverage, frustrating efforts to disentangle multiperiodic signals and alias patterns. Multi-site campaigns coordinated across the globe via the Whole Earth Telescope (WET, \citealt{1990ApJ...361..309N}) have proved the richness of well-resolved WD pulsation spectra. For example, less than a week of nearly continuous observations of the helium-atmosphere (DBV) GD\,358 revealed more than 180 significant periodicities in the power spectrum, providing exquisite constraints on the helium-envelope mass, $(2.0\pm1.0) \times 10^{-6}$\,\mstar, the overall mass, $0.61\pm0.03$\,\msun, and the magnetic field strength, $1300\pm300$\,G \citep{1994ApJ...430..839W}. Similarly, roughly 11 days of nearly continuous photometry on the pre-WD PG\,1159$-$035 revealed 125 individual periodicities, accurately constraining the mass, rotation rate and magnetic field of this DOV \citep{1991ApJ...378..326W}.  The hydrogen-atmosphere  DAVs have also been extensively studied by some half-dozen WET campaigns, with varying results. In part, this is a result of how pulsation modes excited in DAVs are characteristically influenced by the WD effective temperature: hotter DAVs tend to have fewer modes, lower amplitudes and shorter-period pulsations, while cooler DAVs driven by substantially deeper convection zones tend to have more modes at higher amplitude and longer periods \citep{2006ApJ...640..956M}. WET campaigns have observationally  borne this out. More than 5 days of nearly continuous monitoring of the hot DAV G226$-$29 revealed just one significant triplet independent  pulsation mode \citep{1995ApJ...447..874K}, whereas the cooler DAV G29$-$38 has more a dozen modes of relatively high amplitude \citep{1994ApJ...436..875K}. In fact, G29$-$38 illustrates the challenges faced to performing asteroseismology of cooler DAVs: although the WD exhibits at least 19 independent oscillation frequencies, there is significant amplitude and phase modulation of these modes, which change dramatically from year-to-year \citep{1990ApJ...357..630W,1998ApJ...495..424K}. Another excellent example of this complex behavior is the cool DAV HL\,Tau\,76 \citep{2006A&A...446..237D}, which shows 34 independent periodicities along with many oscillation frequencies at linear combinations of the mode frequencies. The complex mode amplitude and frequency variations are likely the result of longer-period pulsations having much shorter linear growth times, increasing the prevalence of amplitude and phase changes in cooler DAVs with longer periods (e.g., \citealt{1999ApJ...511..904G}).  The {\em Kepler} mission has already uniquely contributed to long-term distinctions between the handful of hot and cool DAVs eventually found in the original pointing. The longest-studied by {\em Kepler}, the cool DAV ($11{,}130$\,K) KIC\,4552982 discovered from ground-based photometry \citep{2011ApJ...741L..16H}, shows considerable frequency modulation in the long-period modes present between $770-1330$\,s (Bell et al. 2014, in prep.). A much hotter DAV was also observed for six months, KIC\,11911480 ($12{,}160$\,K), which shows at least six independent pulsation modes from $172.9-324.5$\,s that are incredibly stable and evidence consistent splitting from a $3.5\pm0.5$\,day rotation rate \citep{2014MNRAS.438.3086G}.  After the failure of a second reaction wheel in 2013\,May, the {\em Kepler} spacecraft has been repurposed as {\em K2} to observe fields in the direction of the ecliptic. {\em K2} is poised to begin uninterrupted observations of fields in the ecliptic for approximately 75\,days. As part of an initial test to monitor the two-wheel controlled {\em K2} two-wheel-controlled  pointing behavior on long timescales, short-cadence photometry was collectedevery minute  on the cool DAV GD\,1212 during a preliminary an  engineering run in 2014\,January 2014~January  and February. GD\,1212 ($V=13.3$ mag) was discovered to pulsate by \citet{2006AJ....132..831G}, with roughly 0.5\% relative amplitude photometric variability dominant at 1160.7\,s. The most recent model atmosphere fits to spectroscopy of GD\,1212 find this WD has a \teff\ $= 11{,}270\pm170$ K and \logg\ $= 8.18\pm0.05$, which corresponds to a mass of $0.71\pm0.03$ \msun\ \citep{2011ApJ...743..138G}. This puts GD\,1212 at a distance of roughly 17 pc, although GD\,1212 has the lowest proper motion of any WD within 25 pc of the Sun, $33.6\pm1.0$ mas yr$^{-1}$ \citep{2009AJ....137.4547S}.  In this paper we provide a preliminary analysis of the unique two-wheel controlled two-wheel-controlled  {\em Kepler} observations of GD\,1212. In Section 2 we outline the observations and reductions. We analyze the independent pulsation modes and nonlinear combination frequencies in Sections 3 and 4, respectively. We reserve Section 5 for conclude with  a preliminary asteroseismic interpretationof the results,  andconclude with  a discussion of these results in the context of a two-wheel controlled two-wheel-controlled  {\em Kepler} missionobserving into the ecliptic  in Section 6. 5.