Non-Variable Stars Inside the Zz Ceti Instability Strip S. O

Baltic Astronomy, vol.4, 157-165, 1995.

NON-VARIABLE STARS INSIDE THE ZZ CETI INSTABILITY STRIP

S. O. Kepler1,2, O. Giovannini1, A. Kanaan1,2, M. A. Wood3 and C. F. Claver2'4 1 Instituto de Física, Universidade Federal do Rio Grande do Sul, 91501- 970 Porto Alegre, RS, Brazil 2 Department of Astronomy and McDonald Observatory, The University of Texas, Austin, TX 78712, U.S.A. 3 Department of Physics and Space Sciences, Florida Institute of Technology, 150 W. University Blvd., Melbourne, FL 32901, U.S.A. 4 Kitt Peak National Observatory, Tucson, AZ 85726, U.S.A.

Received September 20, 1995.

Abstract. We are obtaining high signal-to-noise (S/N) optical spectra and time-series photometry of all known DA4 and DA5 white dwarfs brighter than B = 16.0 mag. Deriving their atmospheric pa- rameters, masses and limits of variability, we can study the statistics of the ZZ Ceti instability strip. We have found 14 non-variables in agreement with mass stratification of the instability strip, but also at least one non-variable star inside the instability strip that cannot be explained by total mass alone.

Key words: stars: white dwarfs - stars: variables

1. Introduction The ZZ Ceti or DAV stars are the pure hydrogen atmosphere variable white dwarfs. They show non-radial g-mode pulsations (Kepler 1984) with periods between ~ 100 and ~ 1000 seconds, and amplitudes ranging from 4 to 30 mma. Several investigations show that these variables lie in a narrow instability strip centered close to the temperature of maximum hydrogen opacity (Teff ~ 12 000 K), i.e. at the extension of the Cepheid instability strip down to the white dwarf sequence (McGraw 1979). Previous studies of the colors of these stars have shown that most and perhaps all DAs 158 S.O. Kepler, O. Giovannini, A. Kanaan et al.

are photometric variables in the approximate temperature range 13 200 K > Teff > 11 500 K (Fontaine et al. 1982, Greenstein 1982). The observed pulsations can be used to determine the structure of white dwarfs (WD) in great detail and with exquisite precision, but the observations must be matched to theoretical models. The recent models by Bradley & Winget (1994) predict that all white dwarfs should become pulsators when they cool down to the instability strip, but the theoretical blue edge depends on the stellar mass; the heaviest WDs pulsate earlier than lighter ones. However, we have found non-variable WDs in the instability strip, raising ques- tions about the validity of the models and about the results derived from them. Dolez, Vauclair & Koester (1991) and Kepler & Nelan (1993) have found a few non-variables inside the instability strip, but they did not measure their masses. The recent pulsation models predict that the mass can solve this problem. Bergeron, SafFer & Liebert (1992) and Bragaglia, Renzini & Bergeron (1995) have done a spec- troscopic determination of the mass distribution of DA WDs; even though the mass distribution is narrow and peaked around 0.6 M©, DAs masses vary from as low as 0.2 M© to higher than 1.0 MQ. Therefore, it is possible that the variable vs. non-variables issue will be resolved if the mass of the white dwarf is properly accounted for, and we propose to test this hypothesis. Our project is to study the fraction of variable vs. non-variables for each mass sample, to find if non-variables do exist in the same range and define the location of the observational instability strip for each mass. We have thus been conducting a campaign to observe with time-series photometry all DA white dwarfs close to and inside the instability strip to better define the boundaries of that strip, and to test if all stars inside the strip are variable. During the last 8 years we have been observing with time-series photometry all these stars to increase the statistical sample and re- examine the conclusions of Fontaine et al. (1982). The main difficulty is that, while existing (spectro)photometry is a good guide of which star to observe, it does not provide us with a sufficiently accurate determination of Teff. For example, the exis- tence of two different calibrations for Greenstein's (1976, 1984) mul- tichannel data (i.e., AB69 and AB79) affects critically the effective temperatures derived, changes the position of the instability strip by 1000 K, and can even change the relative order of stars in relation to temperature. We have therefore already obtained S/N >70 op- Non-variable stars inside the ZZ Ceti instability strip 159 tical spectra of 64 white dwarfs with colors in and around the ZZ Ceti instability strip, and fitted them with model atmospheres to obtain the effective temperature and log <7; the mass of the star is then derived using evolutionary models with thick hydrogen layers and carbon core (Wood 1995). Careful modeling of the blue optical spectrum of ZZ Ceti stars yields effective temperatures for these objects in most cases to within ~ 200 — 300 K for S/N ~ 70 (Daou et al. 1990, Bragaglia, Renzini & Bergeron 1995, Bergeron et al. 1995). But there is the effect of different parametrizations of convec- tion on the temperature determination, discussed in Bergeron et al. (1992, 1995) and Koester et al. (1995). Our analysis relies on the simultaneous fitting of H/3 and H7, which are temperature-sensitive, and Hi, H8, and H9, which are sensitive to log g. Our study will provide more secure boundary temperatures for the instability strip (the boundaries determined by Bergeron et al. 1995 are based on the analysis of a sample of known variables only), as well as a firm esti- mate of the frequency of non-variable stars inside of the strip. The analysis presented here makes use of the synthetic spectrum grid for cool DA white dwarfs developed in Montreal (Bergeron et al. 1990, Bergeron, Wesemael and Fontaine 1991, Bergeron et al. 1995). We also obtained time series photometry for 45 of these stars, to study their variability, and found one new variable star (Kanaan et al. 1992, with 1.03 M©). Considering that the theoretical instability strip is only 1000 K wide, for any given mas3, we are mapping the effect of mass on the position of the instability strip.

2. Observations

The medium resolution (3 - 7 A) high signal-to-noise optical spectra were obtained with CCD detectors on the Cassegrain spec- trographs of the 2.15 m telescope of the Kitt Peak National Observa- tory , the 2.7 m telescope of the McDonald Observatory, the 2.15 m telescope of the Complexo Astronomico de El Leoncito and the 1.5 m telescope of the Cerro Tololo Interamerican Observatory. To determine if a star is variable or not, one must observe its light curve for at least three consecutive hours, because modulation of the multiple periods of the ZZ Ceti stars can beat down the observed variations to undetectable levels for more than 40 minutes (Hesser, Lasker and Neupert 1976, McGraw 1977, Kepler et al. 1983). An- other important point is that, within the known variables, there are stars with amplitudes down to 0.4 % (= 4 mma), and therefore the 160 S.O. Kepler, 0. Giovannini, A. Kanaan et al. detection limit should be smaller than this value. We have therefore observed most stars in Table 1 for at least 3 h in our time-series photometry. We observed several stars in different nights to decrease the probability of the negative interference of pulsations, vis a vis that McGraw (1977) claimed that G 226-29 and BPM 37093, the two lowest amplitude variables, were not variables. Additional observations were made at a later epoch if the original observations were not of the required quality. In Table 1 we present the limits for the non-variable stars we have observed, as well as the results of the line profile fitting using the ML 2 (a = 1) model atmospheres to the observed spectra done to us by Pierre Bergeron from 1991 to 1993. It is important to notice that most stars have two Teff solutions, one hot and one cold. The double result arises from fitting the line profiles only; as the maximum line depth occurs around Teff — 13 000 K, two temperatures, one lower and one higher, fit the line profiles equally well. For the results reported here we have not used any photometry to distinguish between the hot and cold solution, recommended by Bergeron et al. (1995). Most of these observations were obtained with a 2-star photome- ter (target and comparison star, Nather 1973) on the 1.6 m telescope of Laboratorio Nacional de Astrofisica (LNA) in Brazil. The north- ern objects were observed with 2- or 3-star photometers on the 0.9 m and 2.1 m telescopes at the McDonald Observatory.

3. Discussion

The sample of DA white dwarfs studied in this analysis has 90 % of stars with Teff < 15 000 K; they are concentrated around 13 000 K, while the mass distribution samples used in previous analysis have a large range in Teff (Bergeron, Saffer & Liebert 1992, Finley 1995, Bragaglia, Renzini & Bergeron 1995). The mass distribution for our sample has a mean value of M — 0.60MQ with a standard deviation of A = 0.02 MQ. These values are very similar to the ones derived from the above studies, when DA evolutionary models are used, in- dicating that DAs keep their mass during the cooling sequence. Bradley & Winget (1994) show that all DA models become un- stable as their temperatures drop down to the instability strip. The theoretical blue edge for DA models moves- to hotter temperatures as the stellar mass is increased. It is 13 460 K for a 0.8 M© DA star, Non-variable stars inside the ZZ Ceti instability strip 161

Table 1. Results of the spectroscopy and photometry

Limit T ff t>Tef[ M WD Var Alias e logfir 8logg (mma) (K) (K) (Mq) 1247+553 GD319A 32366 689 6.11 0.26 sdB 1033+464* GD 123 29800 2039-682 NV 1.9 BPM 13491 17119 254 8.36 0.04 0.84 1119+385* NV 3.0 PG 16500 140 7.98 0.04 0.61 2311+552* NV 5.0 GD 556 16106 286 7.64 0.06 0.44 0413-077 40 Eri B 15957 196 7.82 0.04 0.52 1654+637* NV 4.1 GD 515 15812 174 7.85 0.04 0.54 1919+145 GD 219 15000 117 8.08 0.03 0.66 1555-089* NV 2.5 G 152-B4B 14878 133 7.89 0.02 0.55 1550+183 NV 3.3 GD 194 14847 284 8.31 0.02 0.81 2047+372 G 210-36 14800 393 8.16 0.05 0.71 1448+077* NV 3.9 G 66-32 14702 132 7.81 0.02 0.51 0637+447 GD 77 14609 603 8.06 0.06 0.65 1610+116 GD 196 14600 121 7.82 0.03 0.52 0938+286* TON 20 14544 172 7.86 0.03 0.53 1418-005 NV 5.4 PG 14446 225 7.82 0.04 0.51 1022+050* NV 1.4 PG 14400 101 7.44 0.04 0.36 1026+023* NV 3.0 PG 14300 141 7.75 0.03 0.48 1129+071 PG 14200 298 7.91 0.05 0.56 1253+482 GD 320 14200 224 7.67 0.07 0.44 1327-083 NV 2.8 G 14-58 14200 107 7.82 0.02 0.52 0401+250 NV 1.6 G 8-8 14115 265 7.74 0.04 0.48 0151+017 NV 2.0 G 71-41 14043 281 7.71 0.04 0.46 1911+135 NV 2.2 G 142-B2A 14000 195 7.83 0.03 0.52 2149+372 NV 2.9 GD 397 14000 304 7.91 0.05 0.56 2341+322* NV 1.9 G130-5 13993 281 7.73 0.04 0.47 1355+340 G 165-B5B 13976 301 7.94 0.04 0.58 2322+205 NV 5.5 PG 13890 408 7.77 0.05 0.49 1827-106 NV 7.3 G155-19 13800 206 7.61 0.04 0.42 0951-035 NV 3.0 G161-36 13762 248 7.86 0.04 0.54 1101+364* NV 2.7 PG 13660 50 7.29 0.02 0.31 1716+020* NV 3.4 G 19-20 13618 180 7.87 0.03 0.54 1636+160 NV 3.3 GD 202 13532 126 7.94 0.03 0.57 162 S.O. Kepler, O. Giovannini, A. Kanaan et al.

Table 1 continued

Limit T g ¿>Teff M WD Var Alias e logg ¿logg (mma) (K) (K) (Mo) 1116+026 NV 2.7 GD 133 13476 137 7.87 0.03 0.54 1555-089* NV 2.5 G 152-B4B 13446 119 7.97 0.03 0.59 0943+441 NV 5.1 G 116-52 13444 143 7.50 0.02 0.37 1448+077* NV 3.9 G 66-32 13439 125 7.87 0.03 0.54 0938+286* TON 20 13436 130 7.92 0.03 0.57 1606+422 NV 1.8 CASE 2 13334 163 7.65 0.03 0.43 1026+023* NV 3.0 PG 13258 113 7.92 0.03 0.56 0339+523 NV 1.6 RUBIN 70 13226 312 7.06 0.07 0.29 2126+734 NV 1.4 G 261-43 13165 128 7.98 0.04 0.60 1647+591 V G 226-29 13029 113 8.19 0.02 0.73 0103-278 NV 6.0 G 269-93 12970 100 8.00 0.02 0.58 0921+354 V G 117-B15A 12845 186 7.96 0.04 0.59 1101+364* NV 2.7 PG 12660 71 7.26 0.04 0.30 1654+637* NV 4.1 GD 515 12626 159 8.05 0.04 0.64 1119+385* NV 3.0 PG 12600 159 8.24 0.06 0.75 2337-760 NV 3.0 BPM 15727 12548 273 7.58 0.11 0.40 0133-116 V R548 12527 219 8.01 0.06 0.61 1022+050* NV 1.4 PG 12400 98 7.54 0.04 0.38 2226+061 NV 2.2 GD 236 12260 136 8.01 0.06 0.61 0104-464 V BPM 30551 12247 1058 8.32 0.20 0.81 0341-459 V BPM 31594 12220 214 8.08 0.06 0.65 2311+552* NV 5.0 GD 556 11770 191 7.95 0.06 0.58 1559+369 V R808 11656 138 8.02 0.02 0.61 2105-820 NV 2.9 BPM 1266 11522 275 8.32 0.10 0.81 0033+016 NV 3.7 G 1-7 11214 133 8.70 0.06 1.04 1244+149 NV 3.0 G61-17 11066 81 7.98 0.04 0.59 2246+223 NV 2.5 G 67-23 10770 50 8.78 0.03 1.08 2136+229 NV 4.6 G126-18 10550 52 8.17 0.05 0.71 0255-705 NV 2.8 BPM 2819 10507 120 8.09 0.09 0.66 1507-105 NV 3.0 GD 176 10402 51 7.61 0.05 0.41 1637+335 G180-65 10383 39 8.15 0.03 0.70 2258+406 NV 4.7 G216-B14B 10281 90 8.37 0.07 0.84 1147+255* NV 4.0 G121-22 10264 51 8.09 0.04 0.66 1840-111 NV 3.0 G 155-34 10230 38 8.18 0.04 0.71 1539-035 NV 2.0 GD 189 10228 49 8.34 0.04 0.82 Non-variable stars inside the ZZ Ceti instability strip 163

Table 1 continued

Limit T f[ $T ff M WD Var Alias e e logflr Slogg (mma) (K) (K) (Mo) 1857+119 NV 4.7 G141-54 10070 47 7.98 0.05 0.59 1537+651 GD 348 9831 42 8.13 0.04 0.68 1655+215 G 169-34 9472 30 8.20 0.04 0.72 2115-560 NV 2.6 BPM 27273 9427 75 8.02 0.10 0.62 1001-033 GD 110 8632 41 8.26 0.06 0.76

* indicates a star with two Teff solutions, one hot, one cold, t binary stars. Notes: GD 77 is a magnetic WD; 40 Eri B is a ROSAT source; PG 1022+050 is a pre-cataclysmic variable.

12 950 K for 0.7 M®, 12 770 K for 0.6 M®, 12 300 K for 0.5 M® and 12 000 K for 0.4 M®. Their models drop back to stability after about 1000 K span of instability. Table 1 shows 18 non-variable inside the theoretical instability strip (13 460 K > > 11 000 K). 14 of those are compatible with the predictions of the mass dependence of the instability strip. But 4 non-variable stars inside the instability strip (PG 1119+385, GD 515, GD 236, GD 556) have masses that indicate they should pulsate. Of these 4 stars, only GD 236 does not have an alternative higher temperature fit that would place it outside the instability strip. When we are analyzing such statistics, a few effects must be taken in account: (1) the obvious effects of observational errors, which due to the nar- rowness of the instability strip could put a star inside the instability strip; (2) certain combinations of the indices of the spherical harmonics t and m, when viewed from special aspects, show no luminos- ity variations, because the surface brightness distribution over the observable hemisphere of the star averages out in time. For example, when the inclination angle of the rotation axis of a variable star is seen pole on, the pulsation modes which are symmetrical about the pole cancel out, and we see no observable variations, even though the star is variable. If the modes are rotationally split, on the other hand, the effect will make modes with different ra-values have different amplitudes, but probably 164 S.O. Kepler, O. Giovannini, A. Kanaan et al.

not cancel out all the variations (Pesnell 1985). This factor cannot explain any substantial percentage of non-variables because it requires very specific orientations; (3) there is an observational limit on the detectable pulsational amplitude. Considering that some known pulsators have very small amplitudes (0.6 % ~ 6 mma for G 226-29, 0.4 % ~ 4 mma for BPM 37093), we could claim that a pulsating star is non-variable if its amplitude is below our detection limit. Our basic conclusion is that the large majority of non-variable stars (14 out of 18) inside the theoretical instability strip are in per- fect agreement with the recent pulsation models prediction of mass stratification of the instability strip. However, there are non-variable stars inside the ZZ Ceti instability strip that cannot be explained using only the total mass of the star. This work was partially supported by grants from CNPq, FINEP & FAPERGS (Brazil), by the National Science Foundation under grant AST 92-17988, through the Florida Institute of Technology, and NSERC & FCAR (Canada) during S.O. Kepler's and M.A. Wood's stay in Montreal.

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