We report the discovery of a new hydrogen atmosphere variable white dwarf (DAV; ZZ Ceti), G30-20, a high-amplitude, long-period pulsator. The Fourier transform of its light curve shows power around 1050-1125 s. We suspect the existence of multiple periodicities in this region, probably corresponding to different radial order (k) modes, but our observations are not long enough to resolve them. This discovery increases the number of known DAVs to 32. Our best fit to its optical spectrum gives T-eff = 11; 070 +/- 180 K and log g = 7.95 +/- 0.06. This implies that G30-20 is the coolest known DAV.NSF AST-9876730NASA NAG 5-9321STSI GO-08254Astronom

Bergeron, P.

Kepler, S. O.

Mukadam, Anjum S.

Winget, D. E.

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A NEW ZZ CETI WHITE DWARF PULSATOR: G30-20Anjum S. Mukadam,1,2 S. O. Kepler,3 D. E. Winget,1,2 and P. Bergeron4Received 2002 February 25; accepted 2002 July 23ABSTRACTWe report the discovery of a new hydrogen atmosphere variable white dwarf (DAV; ZZ Ceti), G30-20, ahigh-amplitude, long-period pulsator. The Fourier transform of its light curve shows power around 1050–1125 s. We suspect the existence of multiple periodicities in this region, probably corresponding to diﬀerentradial order (k) modes, but our observations are not long enough to resolve them. This discovery increasesthe number of known DAVs to 32. Our best ﬁt to its optical spectrum gives Teff ¼ 11; 070 180 K andlog g ¼ 7:95 0:06. This implies that G30-20 is the coolest knownDAV.Subject headings: stars: individual (G30-20,WD 2347+128) — stars: oscillations —stars: variables: other — white dwarfs1. INTRODUCTIONWhite dwarfs are the end points of most stars in the uni-verse, and their structure provides constraints on their priorevolution. Their high gravity and temperature make themgood cosmic laboratories to study physics under extremeconditions. As white dwarfs cool, they pass through aninstability strip in which we observe them as nonradial g-mode pulsators. Pulsating white dwarfs oﬀer us a chance tostudy their internal structure through the techniques ofasteroseismology.As 80% of all white dwarf stars have atmospheres domi-nated by hydrogen (DAs), to understand the pulsating DAs(DAVs) is to understand the most common type of whitedwarf. DAVs are not defective or special in any way. AllDAs have been shown to pulsate when their temperaturesreach the ZZ Ceti instability strip (Robinson 1979; Fontaineet al. 1985), i.e., pulsation is an evolutionary phase.The DAV strip is empirically found between 11,200 and12,500 K, log g  8, using model atmospheres (Bergeron etal. 1995b) that treat convection withML 2= ¼ 0:6 (see x 5).The DAV white dwarfs are also known as ZZ Ceti starsafter ZZ Ceti, the prototype of the class. Their observedperiods typically range from 100 to 1000 s, which is consis-tent with nonradial g-mode pulsations (see the review paperWinget 1998 and references therein). As each mode weobserve gives us information on a diﬀerent part of the star,the more modes we detect, the better our understanding ofthe stellar structure. Clemens (1993) was the ﬁrst to combinedata from diﬀerent hot DAVs (HDAVs) to paint a coherentpicture of them as a group. Kleinman et al. (1998) observedG29-38, a cool DAV (CDAV), over many observing sea-sons, combining modes that come and go with time to pro-vide the largest coherent set of modes seen in any singleDAV. We currently know 31 DAVs; additional pulsatorsand additional modes in known pulsators will help usunderstand the DAVs as a class.Pulsation models indicate that the limits of the ZZ Cetiinstability strip depend on the eﬀective temperature andmass of the star (Bradley & Winget 1994). The blue edge ofthe strip is expected to vary from 13,460 K for a 0.8M DAto 12,000 K for a 0.4M DA star for an interior ML 3 con-vection prescription (Kepler & Bradley 1995). Most modelatmospheres of DAV stars treat convection with a mixinglength prescription assuming some parameterization, thechoice of which can shift the edges of the instability strip intemperature by a few thousand K (Bergeron et al. 1995b;Koester & Allard 2000). Pulsation models predict a red edgeat temperatures as low as 8000–10,000 K (Winget 1981;Winget et al. 1982; Dolez & Vauclair 1981; Hansen, Winget,&Kawaler 1985).As models cool below the blue edge, the partial ionizationzone moves deeper into the star, and driving is provided formodes of lower and lower frequency. The models stopshowing excited modes with periods shorter than or equalto 1500 s at temperatures of 8000 K. Longer period modescould still exist at even lower temperatures. The surface at-mospheric layers may not reﬂect internal waves well at longtimescales, and the energy of an excited mode may leakthrough the surface, eventually damping it (Hansen et al.1985). Brickhill (1983) showed that for a given model, therestricted frequency interval where pulsations of largeamplitude are observable moves into a frequency rangesmaller than the critical value for all g-modes, as the eﬀec-tive temperature of the models is decreased. At this criticalvalue, the surface ﬂux amplitudes of pulsation modesdecrease as the delay associated with the convective zoneincreases as a result of turbulent viscosity, and large changesin radial and pressure perturbations are produced in mod-els. Brickhill (1983) found the red edge at models withTeff ¼ 11; 000 K and log g ¼ 8. Bradley & Winget (1994)were unable to ﬁnd a red edge with their models. Wu &Goldreich (1999) get a maximum period of about 2300 sfrom nonadiabatic calculations of overstable modes.Including convective overshoot, they get a maximum periodof 1400 s for overstable modes, which is comparable to theobserved maximum period of 1200 s for detected modes inCDAVs. Determining the location of the red edge is madediﬃcult by convective overshoot and nonlinear eﬀects.Observable amplitudes of detected modes in CDAVsdecline for periods in excess of 1000 s (see, e.g., Fig. 5 fromClemens 1995). This suggests that the observational red1 University of Texas at Austin, 17.310 RLM Hall, Austin, TX 78712;anjum@astro.as.utexas.edu, dew@bullwinkle.as.utexas.edu.2 McDonald Observatory, Fort Davis, TX 79734.3 Instituto de Fı´sica, Universidade Federal do Rio Grande do Sul, 91501970 Porto Alegre, RS Brazil; kepler@if.ufrgs.br.4 De´partement de Physique, Universite´ de Montre´al, CP 6128,Succ. Centre-Ville, Montre´al, QC, H3C 3J7, Canada; bergeron@ASTRO.UMontreal.CA.The Astrophysical Journal, 580:429–433, 2002 November 20# 2002. The American Astronomical Society. All rights reserved. Printed in U.S.A.429edge at a maximum period of 1200 s is genuine. Kanaan etal. (2000) and Kanaan, Kepler, & Winget (2002) concludethat the observed red edge for the ZZ Ceti instability strip at11,000 K is not an observational selection eﬀect, as theupper limit set by noise is a factor of 50 smaller than typicalpulsation amplitudes. The blue edge of the instability strip iscurrently deﬁned by GD 165 (Koester & Allard 2000) orG226-29 (Bergeron et al. 1995b). The red edge of the strip isobservationally deﬁned by three ZZ Ceti stars R808, GD154, and G38-29 (Bergeron et al. 1995b; Koester & Allard2000). Wu &Goldreich (1999, 2001) suspect that convectivedriving allows velocity variations to become more observ-able than luminosity variations toward the red edge. Kotaket al. (2002) got time-resolved spectra of three nonpulsatingDA white dwarfs with temperatures slightly cooler than theZZ Ceti strip, but did not detect any signiﬁcant periodicvelocity variations. Finding more DAVs at diﬀerent temper-atures and masses will improve our observational determi-nation of the edges of the ZZ Ceti strip, as well as determineits mass dependence (Kepler et al. 2000).The HDAV stars are found to exhibit extreme amplitudeand frequency stability, making them reliable clocks. Whensuch stable clocks have an orbiting planet around them,their reﬂex motion around the center of mass of the systembecomes measurable, providing a means to detect the planet(Kepler et al. 1990, 1991; Mukadam, Winget, & Kepler2001). The success of a planet search project based on thistechnique rests on ﬁnding a statistically signiﬁcant numberof HDAV stars. We discovered G30-20 in our search foradditional HDAV stars.2. G30-20: A HIGH-PRIORITY ZZ CETI CANDIDATEGreenstein & Liebert (1990) published high signal-to-noise spectrophotometric data for G30-20 (WD 2347+128;EGGR 405; B ¼ 15:9). Dolez, Vauclair, & Koester (1991)ﬁtted this data to a grid of pure hydrogen model atmos-pheres with local thermal equilibrium (LTE) and found atemperature of Teff ¼ 11;000 100 K with log g ¼ 8:500:10 for G30-20.Greenstein (1982) found that 14 DAs lie in the strip,0:41  GR  0:29, on the AB 79 scale (Oke & Gunn1983) and concluded that (GR) color proves to be an excel-lent temperature indicator for DAs. From the magnitudesgiven by Greenstein & Liebert (1990), we compute the fol-lowing color indices: VI ¼ 0:415, GR ¼ 0:28,UV ¼ 0:43, UG ¼ 0:49, and BV ¼ 0:05. G30-20with GR ¼ 0:28 is close to the red edge of the instability-0.6 -0.4 -0.2 00.80.60.40.20Fig. 1.—Pure hydrogen DAmodels by Bergeron et al. (2001) plotted as a function of the color indices GR and UV, with Teff indicated in units of 103 Kand log g values of 7.0 (bottom) to 9.0 (top). For G30-20, we obtainedGR ¼ 0:28,UV ¼ 0:43 from high signal-to-noise spectrophotometric data (Green-stein & Liebert 1990), with an assumed uncertainty of 0.04 mag. The location of G30-20 in the ZZ Ceti instability strip is shown, along with the error bars. Wehave plotted the known ZZCeti stars fromGreenstein (1984) as crosses to show the mass dependence of the instability strip.430 MUKADAM ET AL. Vol. 580strip. Colors for pure hydrogen DA model atmospherespublished by Bergeron, Wesemael, & Beauchamp (1995a)and Bergeron, Leggett, & Ruiz (2001) allow us to estimatethe temperature of G30-20 to be 10; 700 300 K withlog g ¼ 8:0 0:3, as indicated in Figure 1.3. OBSERVATIONSWe obtained time-series aperture photometry on G30-20in 2001 December at the 2.1 m telescope at McDonaldObservatory. The data were acquired using ‘‘ P3Mudgee,’’ athree-star photometer (Kleinman, Nather, & Phillips 1996).We observed unﬁltered light to maximize the signal-to-noiseratio; g-mode pulsations in white dwarfs do not changephase with wavelength (Robinson, Kepler, & Nather 1982).We present the journal of observations in Table 1.Dolez et al. (1991) state that G30-20 is a nonvariable, set-ting amplitude detection limits at a few mmag.5 Our lightcurve of the star clearly shows beating eﬀects; beating candestroy pulsations in the light curve for up to a few hours,depending on the amplitude of the pulsation and the magni-tude of the star, both of which dictate the signal-to-noiseratio. It is possible to obtain an essentially constant lightcurve of G30-20 for up to an hour, depending on the time ofobservation. Hence, our observations are not inconsistentwith their observations.TABLE 1Journal of Observations for Data Acquired on G30-20 in 2001 DecemberObserving RunDate(UTC)Time(UTC)Duration(hr)Integration Time(s)asm-0094............ 2001 Dec 19 01:15:00 2.21 10asm-0099............ 2001 Dec 20 01:03:10 2.95 5Note.—Data acquired at the 2.1 m telescope of McDonald Observatory with athree-star photometer.Fig. 2.—Reduced light curves of G30-20 obtained on 2001 December 19 and 20, respectively, at the 2.1 m telescope of McDonald Observatory, using athree-star photometer. The top panel shows a 2.21 hr long light curve with an integration time of 10 s. The bottom panel shows a 2.95 hr long light curve withan integration time of 5 s.5 1 mmag equals 0.1086% change in intensity.No. 1, 2002 NEW ZZ CETI WD PULSATOR: G30-20 4314. DATA REDUCTIONWe reduced and analyzed the data in a manner describedby Nather et al. (1990) and Kepler (1993), correcting forextinction and sky variations. After this preliminary reduc-tion, we brought the data to the same fractional amplitudescale and converted the times of observations to barycentriccoordinated time TCB (Standish 1998). The light curves ofthe two runs reduced in this manner are shown in Figure 2.We computed a discrete Fourier transform (DFT) for eachindividual run and the combined data. These are shown inFigure 3, along with the corresponding ‘‘ window ’’ pattern,which is what a single frequency in that data set should looklike.We conclude that this ZZ Ceti star is a high-amplitudelong-period variable. Cool ZZ Ceti stars show high ampli-tudes in the range of 10–50 mma (milli–modulation ampli-tude), where 1 mma equals 0.1% change in intensity. Forexample, O’Donoghue, Warner, & Cropper (1992) detectedan amplitude of 56 mma for the 617.87 s period in BPM31594, while Dolez (1998) detected a period at 541 s in HLTau 76 with an amplitude of 37.3 mmag. Our observationsare not long enough to resolve the power evident in theregion 1050–1125 s. We suspect the existence of multipleperiodicities in this region that might correspond to diﬀerentk modes. The combined DFT from both data sets shows apeak at 1068 s, with an amplitude of 13.8 mma. It will benecessary to observe G30-20 long enough to resolve its pul-sation spectrum in order to be able to use the pulsations tostudy its structure.5. COOLEST KNOWN DAV YETBergeron et al. (1995b) considered various parameteriza-tions of the mixing-length theory (MLT) to treat convectionin models of ZZ Ceti stars. Bo¨hm & Cassinelli (1971)describe the ML 2 version of convection, assuming the ratioof the mixing length (l) to the pressure scale height (H ),  l=H ¼ 1. Bergeron et al. (1995b) analyzed optical andultraviolet (UV) spectrophotometric data of ZZ Ceti starsand found that model atmospheres calculated using the ML2 version, assuming  ¼ 0:6, provide an internal consistencybetween the optical and UV temperature estimates, theobserved photometry, the trigonometric parallax measure-ments, and the gravitational redshift masses. We obtained abest value of Teff ¼ 11;070 180 K and log g ¼ 7:95 0:06by ﬁtting Balmer line proﬁles from a high signal-to-noiseﬂux–calibrated optical spectrum of G30-20, obtained byC. K. J. Moran, with these model atmospheres. The modelﬁts are shown in Figure 4. Bergeron et al. (1995b) haveargued that the Balmer line proﬁles from H to H9 are thebest estimators of temperature and surface gravity.Fig. 3.—Top two panels show the discrete Fourier transform (DFT) of G30-20 from the individual runs on 2001December 19 and 20, respectively. The bot-tom panel shows the DFT from combining the two runs. The inset in each panel shows the ‘‘ window ’’ pattern, which is how a single frequency in that data setshould look.432 MUKADAM ET AL. Vol. 580The formal 1  internal errors of the ﬁtting parametersare 60 K in Teff and 0.04 in log g. Such small internal errorsonly represent the ability and the sensitivity of the modelspectra to match the observed spectra (Bergeron et al.1995b). The error budget is actually dominated by externalerrors, which originate mostly from uncertainties of the ﬂuxcalibration. We have estimated this external error by ﬁttingthe four ZZ Ceti stars (G38-29, GD 66, G238-53, and G29-38) found in common between the sample from which thespectrum of G30-20 was drawn and that of Bergeron et al.(1995b). The standard deviations between these independentsamples are 180 K in Teff and 0.06 in log g, which we adopthere as our formal errors of the ﬁt to G30-20.G30-20 is currently the coolest known DAV atTeff ¼ 11;070 K with log g ¼ 7:95 among the ZZ Ceti starsthat do have a published temperature determination (Brad-ley 2000; Bergeron et al. 1995b).6 Using theoretical evolu-tionary models (Wood 1995) with thick hydrogen layers, wederive a mass of M ¼ 0:58 M, an absolute visual magni-tude ofMv ¼ 11:8, and a distance of d ¼ 70 pc from Earth.G30-20 is thus close to the observational red edge of the ZZCeti instability strip.We acknowledge and thank C. K. J. Moran for takinghigh signal-to-noise spectroscopic data that led to a betterdetermination of the temperature of this star, quoted in thispaper. We also acknowledge the NSF grant AST-9876730,NASA grant NAG 5-9321, and STSI GO-08254 for theirfunding and support. 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Koester &K.Werner (Berlin: Springer), 41Wu, Y., &Goldreich, P. 1999, ApJ, 519, 783———. 2001, ApJ, 546, 4696 The ZZ Ceti stars KUV 08368+4026, KUV 11370+4222, EC140121446, and EC 234872424 do not yet have published temperaturedeterminations (Bradley 2000).Fig. 4.—High signal-to-noise optical spectrum of G30-20, obtained byC. K. J. Moran, yielded a best ﬁt of Teff ¼ 11;070 180 K withlog g ¼ 7:95 0:06, using theML 2model atmospheres with  ¼ 0:6.No. 1, 2002 NEW ZZ CETI WD PULSATOR: G30-20 433

A New ZZ Ceti White Dwarf Pulsator: G30-20

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A New ZZ Ceti White Dwarf Pulsator: G30-20

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