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# PRECISION ASTEROSEISMOLOGY OF THE WHITE DWARF GD 1212 USING A TWO-WHEEL CONTROLLED KEPLER SPACECRAFT

Abstract

We present a preliminary analysis of the cool pulsating white dwarf GD1212, enabled by more than 11.5 days of space-based photometry obtained during an engineering test of a two-reaction wheel controlled Kepler spacecraft. We detect at least 21 independent pulsation modes, ranging from $$369.8-1220.8$$s, and at least 17 nonlinear combination frequencies of those independent pulsations. Our longest uninterrupted light curve, 9.0 days in length, evidences coherent difference frequencies at periods inaccessible from the ground, up to 14.5hr, the longest-period signals ever detected in a pulsating white dwarf. These results mark some of the first science to come from a two-wheel controlled Kepler spacecraft, proving the capability for unprecedented discoveries afforded by extending Kepler observations to the ecliptic.

# Introduction

The endpoints of stellar evolution, white dwarf (WD) stars provide important boundary conditions on the fate of all stars with masses $$\leq 8$$ $${M}_{\odot}$$, as is the case for more than 97% of all stars in our Galaxy, including our Sun. When a WD cools to the appropriate effective temperature to foster a hydrogen partial ionization zone, roughly $$12{,}000$$K, global oscillations driven as non-radial $$g$$-modes become unstable and reach observable amplitudes.

These hydrogen-atmosphere pulsating WDs (so-called DAVs or ZZCeti 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 require securing a large number of significant pulsation periods and uniquely identifying the oscillation modes. However, with typical $$g$$-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, Nather et al. 1990) 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) GD358 revealed more than 180 significant periodicities in the power spectrum, providing exquisite constraints on the helium-envelope mass, $$(2.0\pm1.0) \times 10^{-6}$$$${M}_{\star}$$, the overall mass, $$0.61\pm0.03$$$${M}_{\odot}$$, and the magnetic field strength, $$1300\pm300$$G (Winget et al., 1994). Similarly, roughly 11 days of nearly continuous photometry on the pre-WD PG1159$$-$$035 revealed 125 individual periodicities, accurately constraining the mass, rotation rate and magnetic field of this DOV (Winget et al., 1991).

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 (Mukadam et al., 2006). WET campaigns have borne this out. More than 5 days of nearly continuous monitoring of the hot DAV G226$$-$$29 revealed just one significant triplet pulsation mode (Kepler et al., 1995), whereas the cooler DAV G29$$-$$38 has more a dozen modes of relatively high amplitude (Kleinman et al., 1994).

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 (Winget et al., 1990; Kleinman et al., 1998). Another excellent example of this complex behavior is the cool DAV HLTau76 (Dolez et al., 2006), 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., Goldreich et al. 1999).

The 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 Kepler, the cool DAV ($$11{,}130$$K) KIC4552982 discovered from ground-based photometry (Hermes et al., 2011), 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, KIC11911480 ($$12{,}160$$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 (citation not found: 2014MNRAS.438.3086G).

After the failure of a second reaction wheel in 2013May, the Kepler spacecraft has been demonstrated a mission concept using two reaction wheel control, observing fields in the direction of the ecliptic. This mission conecpt aims to obtain uninterrupted observations of fields in the ecliptic for approximately 75days. As part of an initial test to monitor the two-wheel controlled pointing behavior on long timescales, short-cadence photometry was collected every minute on the cool DAV GD1212 during a preliminary engineering run in 2014January and February.

GD1212 ($$V=13.3$$ mag) was discovered to pulsate by Gianninas et al. (2006), with roughly 0.5% relative amplitude photometric variability dominant at 1160.7s. The most recent model atmosphere fits to spectroscopy of GD1212 find this WD has a $${T}_{\mathrm{eff}}$$ $$= 11{,}270\pm170$$ K and $$\log{g}$$ $$= 8.18\pm0.05$$, which corresponds to a mass of $$0.71\pm0.03$$ $${M}_{\odot}$$ (Gianninas et al., 2011). This puts GD1212 at a distance of roughly 17 pc, although GD1212 has the lowe