ASTEROSEISMOLOGY of DELTA SCUTI STARS M. Breger 1

Home , Delta Scuti, Instability strip, S Scuti

Baltic Astronomy, vol. 9, 149-163, 2000.

M. Breger Institut für Astronomie, Universität Wien, Türkenschanzstr. 17, A-1180, Austria Received October 18, 1999

Abstract. This paper presents recent results for 5 Scuti stars based on measurements obtained by WET/Delta Scuti Network as well as theoretical modeling of the pulsation modes. In particular, the two stars in different stages of evolution, FG Vir and 4 CVn, are discussed. For 4 CVn, the XCOV13 campaign has revealed 34 frequencies, which sets a new record for 6 Scuti stars. Preliminary mode identifications are presented, indicating pulsation in low radial order and low degree (I = 0 to 2). The star shows strong amplitude variability with timescales of ten years or longer, although for neighbouring years the amplitudes usually are similar. The cyclic behavior of the amplitude variations excludes an evolutionary origin. The pulsation mode at 7.375 c/d exhibits the most rapid decrease found so far: the V amplitude dropped from the highest known value of 15 mmag in 1974 to 4 mmag in 1976 and 1 mmag in 1977. After that the mode has been increasing in amplitude. There exists a phase jump between 1976 and 1977, suggesting the growth of a new mode. Key words: stars: pulsating, Delta Scuti stars

1. INTRODUCTION The Ö Scuti stars are pulsators situated in the classical cepheid instability strip on the main sequence or moving from the main sequence to the giant branch. In general, the period range is limited to between 0.02 d and 0.25 d. This limit provides a good separa- tion from the neighboring or overlapping groups of pulsators in the Hertzsprung-Russell Diagram, such as roAp, Gamma Dor and RR Lyrae stars. 150 M. Breger

Some S Scuti stars are (pure) radial pulsators, while the major- ity pulsate with a large number of nonradial p-modes simultaneously. The nonradial pulsations of <5 Scuti stars found photometrically are low-degree (i < 3) and low-order (n = 0 to 7) p-modes, while spectroscopic studies have confirmed the presence of high-degree nonradial modes with I up to 20 (e. g. for the star r Peg, Kennelly et al. 1998). The 5 Scuti stars represent a transition between the cepheid- like large-amplitude radial pulsation of the classical instability strip and the ocean of nonradial pulsation occurring in the hot half of the Hertzsprung-Russell Diagram. Many excited modes show photometric amplitudes in excess of 0.001 mag, which makes it possible to study these stars photometrically. The position of S Scuti stars on and slightly above the main sequence permits the asteroseismological comparison between oscillation data and stellar models in a region where the basic stellar structure is regarded as relatively well known.

2. ASTEROSEISMOLOGY

At the risk of oversimplification, one can divide the different approaches to S Scuti star asteroseismology into three types:

(i) The minimal approach

One of the early successes of asteroseismology concerned the matching of the observed and computed period ratios of Population I high-amplitude 5 Scuti stars (HADS). Although 'only' two frequencies were observed, the accurate period ratios provided strong evidence for the validity of the OPAL/OP opacities. We note that this agreement is based on the fortunate situation that the HADS pulsate with low-order radial modes so that the mode-identification problem does not exist. This success leads to the question whether or not such a minimal approach could also work for nonradially pulsating stars. An example of the Minimal Approach is given in the study of HR 5437 by Liu et al. (1999). Two frequencies of pulsation were derived, while independent mode identifications were not available (a common situation). Reasonable values of and Teff were derived from narrowband uvby/3 photometry and a mass estimated. Stellar evolution and pulsation models were used to pick the modes with closest frequency match. For HR 5437, the two modes were identified with I — 0, n = 4; and t = 1, n = 1. The difficulty with this type of Asteroseismology of Delta Scuti stars 151

1 1 1 1 t i i i r

FG Vir

10 15 20 25 30 35

4 CVn

4 6 8 10 12 Frequency (c/d)

Fig. 1. Main pulsation frequencies for XX Pyx (near ZAMS), FG Vir (near ZAMS) and 4 CVn (evolved). The horizontal scale was adjusted for each star to correct for the different stellar mean densities. Detected pulsation frequencies which could be identified with combinations /¿± fj or 2/ terms were omitted. The diagram shows that the location and width of the excited frequency region varies from star to star even after the differences in mean densities have been corrected for. analysis is that neither the mode identifications nor the model fits are unique. (ii) Ensemble asteroseismology Here the problem of the relative lack of information on any in- dividual star is solved by the study of six or more stars in the same star cluster. These stars are expected to have a common age and metallicity. Furthermore, since the distance to the cluster is known, an additional uncertainty is reduced. The best examples of such studies are found for the variables in the Praesepe cluster (Arentoft 152 M. Breger et al. 1998, Michel et al. 1999). Michel et al. chose to omit mode identifications and to model the observed frequencies directly. This eliminates the uncertainties associated with mode identifications but increases the number of free parameters and the associated problem with uniqueness of the models. The initial results for the six stars considered are quite promising and already indicate that the value of the mixing-length parameter can be constrained.

(iii) The direct approach This method recognizes the fact that the successes of helioseis- mology are a consequence of the large amount of data available. Consequently, for a carefully chosen single 5 Scuti star a maximum of information is obtained with different techniques optimized for specific deductions. At the present stage, high-precision photometry is used to derive 30+ frequencies of pulsation per star. Because of cancellation effects across the stellar surface, the modes detected by photometry have low I values. If the photometry is multicolor, the phase differences can be used to identify the i values. Since millimag- accuracy photometry for most 5 Scuti stars can be obtained on a telescope of 1 m or smaller, a multisite campaign with hundreds of hours can be organized without major difficulties. This is not so for spectropic studies, for which larger telescopes are required. Conse- quently, the spectroscopic studies are generally only a week or two in length. The spectroscopic data are too few for reliable determina- tions of 30+ frequencies, but are essential for mode identifications. The line-profile analyses can identify both the I and m values. Finally, the large number of frequencies and mode identifications allow the astronomer to distinguish between a large number of different models. The uniqueness problem mentioned above is con- siderably reduced, but is strongly dependent on a sufficient number of mode identifications being available. Especially for the modes with amplitudes of 1 mmag or smaller these are difficult to obtain. The direct approach is applied by WET/Delta Scuti Network in their studies of S Scuti stars. Below we will present the results of two recent studies of FG Vir and 4 CVn, respectively. The results for a third star, XX Pyx, are presented in a separate paper in this volume. These three stars represent three different stages of evolution and are compared in Fig. 1. Asteroseismology of Delta Scuti stars 153

3.0 1 1 1 1 1 1 1 1 FG Vir 1995/6 data (494 hours) 2.5 Breger, Pamyatnykh, Pitali, Garrido. A&A 341, 151, 1999 230 Viskum, Kjeldsen, Bedding, et al. A&A 335, 549, 1998 20 244 106 (iHz <

"s" 1.5 147 X <

1.0

0.5

-10 -8 -6 -4 -2

Phase difference, <|>v-, in degrees

Fig. 2. Comparison of two mode identification methods for FG Vir. The points in the top left part correspond to i = 2, in the middle to I = 1, and in the bottom right part I = 0. The diagram shows that within the error bars, the agreement is excellent. The numbers refer to the frequencies expressed in /liHz. For the 271 ¿¿Hz (23.4 c/d) mode, the present data cannot distinguish between a i = 0 or 1 identification. Note that the theoretical models computed by Pamyathnykh indicate that the 271 ^Hz mode would be compatible with t = 1, but not 0.

3. FG Vir

Based on the distance determination for FG Vir and the phase difference between v and y, the 12.15 c/d mode is identified with the radial fundamental. The modes at 9.20 and 9.66 c/d have been identified with t=2 modes of mixed p- and g-mode character (Breger et al. 1999a). The high Q values of these modes cannot be explained by pulsation with pure p modes. The star FGVir provides some of the best available observational confirmation of the presence of mixed p/g modes in 6 Scuti stars. It needs to be pointed out that from an observational point of view, a different explanation involving the errors in the derived Q values must be considered. In fact, if we use uvbyfi photometry 154 M. Breger alone, changing the Q value by only one standard deviation could identify the 12.15 c/d as the radial first overtone, rather than the fundamental mode. Note that the phase difference method fixes the radial nature of this mode (Fig. 2). Such a hypothetical change of the Q values from the radial fundamental to the first overtone mode would weaken the observational evidence for the required presence of mixed modes in the star. A much tighter constraint is provided by the Hipparcos parallax, which predicts an absolute magnitude of Mv = 1.95 ± 0.13, leading to Q = 0.035 ± 0.003 for the 12.15 c/d mode (see appendix). We have used 1.85 solar masses (derived from evolutionary models) and the temperature range of 7400 to 7500 K (derived from uvbyfi photometry). The identification of the 12.15 c/d mode with the radial first overtone can be rejected at the 3 standard deviation level.

4. THE EVOLVED STAR 4CVn

The star 4CVn is the best-studied cool, evolved S Scuti star so far (Breger et al. 1999b, Breger 2000). It may be typical for the stars in that part of the Hertsprung-Russell diagram: stars of similar luminosity and temperature such as HD 2724 = BB Phe (Mantegazza & Poretti 1999) and 5 Scuti (Templeton et al. 1997) show some of the same properties. During 1996 and 1997, the Delta Scuti Network obtained 529 hours of photometric data on three continents for the evolved S Scuti variable 4 CVn. 34 statistically significant frequencies were detected (see Table 1). Of these, 16 can be identified as linear combinations of other frequencies. All significant frequencies outside the 4.5 to 9 c/d (52 to 104 ¿/Hz) range can be identified with frequency combinations, fi ± fj, of other modes with generally high amplitudes. There exists a number of closely spaced frequencies with separations of ~ 0.06 c/d. Numerical tests indicate that this cannot be explained as an artefact of amplitude variability. The results for 4 CVn show that even for stars on and above the main sequence other than the Sun, a very large number of simultaneously excited nonradial oscillations can be detected by conventional means. For the ten modes with largest photometric amplitudes, mode identifications based on photometric phase differences between y and v have been derived. These are shown in the bottom panel of Fig. 3. The phase differences indicate p\ to P4 modes of I = 1 for four of these Asteroseismology of Delta Scuti stars

Table 1. Frequency spectrum of 4 CVn.

Frequency Amplitude in 1996 c/d //Hz/ID y filter v filter mmag mmag ± 0.09 ± 0.11 A 8.595 99.48 15.3 22.9 h 7-375 85.36 11.6 17.4 h 5-048 58.42 10.7 16.4 k 6-117 70.80 9.2 14.3 h 5-851 67.72 10.1 15.0 k 5-532 64.03 6.4 10.1 f7 6.190 71.64 5.7 8.1 h 6-976 80.75 5.0 7.4 h 4-749 54.96 3.2 4.9 AO7.552 87.41 3.3 4.9 /n 6.750 78.13 0.9 1.6 /i26.440 74.54 1.6 2.4 A35.986 69.29 0.8 1.4 /14 7.896 91.39 0.8 0.9 /i55.134 59.42 0.8 1.1 A65.314 61.51 0.8 1.0 /176.404 74.12 0.4 1.3 As6.680 77.32 0.2 0.5 Agll.649 = k+k 0.7 1.4 /2014.712 = h+ k 0.7 1.0 /2112.907 = f2+h 0.4 0.5 /2215.970 = A + /2 0.6 0.7 /2313.643 = A + /3 0.5 0.6 /2410.580 = h+k 0.6 0.8 /25H.973 = 2/13 0.4 0.5 /2613.492 = h+k 0.5 0.6 /2712.423 = f2+h 0.3 0.3 /283.063 = A ~ k 0.6 0.9 /291-069 = k - h 0.5 1.0 /30 2.327 = h - h 0.2 0.4 /311-258 = h~k 0.6 0.5 /321-929 = k~ h 0.5 0.5 /ss 1-185 = h~h 0.3 0.5 /341-220 = A "/2 0.5 0.5 156 M. Breger

Frequency in cycles per day 0 2 4 6 8 10 12 14 16 1 1 1 1 1 1 1 1 1 1 1 1 ' 1 1 1 Combination Main pulsation region Combination modes modes f,f. f.+ f. I I f -f. 1 J

i i i , I

1 1 1 1 1 I = 0

2 2 2 2

1 • i 5 6 7 8 9 Frequency in cycles per day Fig. 3. Top: pulsation structure of 4 CVn in the frequency domain. The diagram shows that the detected pulsation frequencies fall into three distinct regions. All frequencies outside the main pulsation region from 4.5 to 9 c/d can be identified with expected frequency combinations. These combination modes are not observational artefacts but intrinsic to the star. Bottom: preliminary photometric mode identification. The spacing 1.2 c/d) of the four successive radial orders of t = 1 and the rotational splitting of the I = 2 triplet are in general agreement with predictions from the mean density and measured v sin i values.

modes. The average frequency difference between these successive radial orders is in agreement with the expected value from the mean density of the star. Furthermore, incomplete rotationally split groups are seen for I = 1 and I — 2. At the present time, spectroscopic line-profile measurements of 4 CVn are not yet available, so that a confirmation of the photometric mode identification as well as a determination of m values are not yet possible. Nevertheless, the present results already show that with a relatively small increase in data it might be possible to identify complete triplets or quintuplets in order to provide observationally measured rotational splitting. Asteroseismology of Delta Scuti stars 157

Since all pulsation modes with photometric amplitudes of 1 mmag or larger have now been detected for this star, a presently unknown mode selection mechanism must exist to select between the 1000+ of low-degree modes predicted to be excited for this (and many other) evolved stars. In fact, the preliminary mode identification of the detected modes of 4 CVn indicates a relatively simple pattern involving almost evenly spaced adjacent radial orders of low-degree modes with rotational splitting.

Fig. 4. Amplitude variability of 4 CVn from 1966 to 1997 based on a re-analysis of the available data. The amplitudes are given by the height of the peaks. For the different years, thresholds based on the quality and quantity of the available data were determined and marked with 'ND'. Amplitudes smaller than these limits are not shown.

The presently ununderstood mode selection mechanism operat- ing in 4 CVn also applies to other S Scuti stars. We note that 6 out of the 13 known frequencies of HD 2724 have values within 0.05 c/d of frequencies known for 4 CVn. Since chance agreements can be mathematically proven to be surprisingly (at least to the author) common, we have calculated the probability of such a chance agree- 158 M. Breger ment between the two stars: the probability is essentially zero. The agreement does not mean that there are magic frequency values: a simple interpretation is that the stars share a similar mean density and mode selection mechanism. We now turn to the amplitude variability of 4 CVn. The are con- siderable amounts of photometric data available covering the years 1966 to 1997. The knowledge of the frequency spectrum from the two years 1996 and 1997 makes it possible to reanalyse the available data from the previous decades in order to see which of the 34 known frequencies are also present in the older data and to examine the amplitude variability in these earlier years. The results of the reanalysis (Breger 2000) are shown in Fig. 4 and can be summarized as follows: (i) 4 CVn shows strong amplitude variability with time-scales of ten years or longer, although for neighbouring years the amplitudes usually are similar. Seven of the eight dominant modes show annual variability of ~ 12%. The variability increases to ~40 % over a decade. (ii) The cyclic behaviour of the amplitude variations excludes an evolutionary origin of the amplitude variability. Here the word 'cyclic' means that the amplitude changes reverse themselves again on a time-scale of a decade or longer. (iii) The pulsation mode at 7.375 c/d exhibited the most rapid decrease found so far: the V amplitude dropped from the highest known value of 15 mmag in 1974 to 4 mmag in 1976 and 1 mmag in 1977. After that the mode has been increasing in amplitude. The extensive new data from 1996/7 make it possible to derive a value of 7.3752 c/d. The frequency fits both the 1974-1976 and 1977-1978 data well, but there exists a phase jump of 0.48 ±0.02 c/d between 1976 and 1977. This is demonstrated in Fig. 5. This result suggests, but does not prove, the re-excitation of the mode between 1976 and 1977. Another interpretation in terms of nonlinear mode interactions could be considered: Moskalik (1985) examined the problem of resonant coupling of an unstable mode to two lower frequency stable modes. For 5 Scuti stars such an approach means that a low-order radial or nonradial unstable mode interacts with two stable gravity modes. The coupling can result in a periodic amplitude modulation as well as a large, sudden jump of pulsation phase. Asteroseismology of Delta Scuti stars 159

20 1 1 I I I 123 d 3(0 E - E _ 59 d _ ' 86d

0.0 I I i i I 1974 1975 1976 1977 1978 Fig. 5. Amplitude variability and phase shifts of the 7.375 c/d mode of 4CVn using the frequency value of 7.37521 c/d accurately determined from the 1996-1997 data. The formal errors are the vertical lines inside the open circles. The length of the annual measurements are given by the numbers above the circles. The data indicate that a sudden phase shift occurred between 1976 and 1977 when the amplitude decayed.

ACKNOWLEDGMENTS. This investigation has been supported by the Austrian Fonds zur Förderung der wissenschaftlichen Forschung, project number S7304. It is a pleasure to thank Alosha Pamyatnykh and Mike Montgomery for helpful discussions.

REFERENCES

Arentoft T., Kjeldsen H., Nuspl J. et al. 1998, A&A, 308, 909 Balona L. A. 1994, MNRAS, 268, 119 Breger M. 1977, PASP, 89, 55 Breger M. 1990, Delta Scuti Star Newsletter (Vienna), 2, 13 Breger M. 2000, MNRAS, in press Breger M., Pamyatnykh A.A., Pikall H., Garrido R. 1999a, A&A, 341, 151 Breger M., Handler G., Garrido R. et al. 1999b, A&A, 349, 225 Crawford D.L. 1975, AJ, 80, 955 Crawford D. L. 1979, AJ, 84, 1858 Kennelly E. J., Brown T. M., Kotak R. et al. 1998, ApJ, 495, 440 Liu Z.L., Zhou A.Y., Jiang S. Y. et al. 1999, A&AS, 137, 445 160 M. Breger

Mantegazza L., Poretti E. 1999, A&A, 348, 139 Michel E., Hernandez M. M., Houdek G. et al. 1999, A&A, 342, 153 Moon T. T., Dworetsky M. M. 1985, MNRAS, 217, 305 Moskalik P. 1985, Acta Astron., 35, 229 Pamyatnykh A. A. 1998, private communication Philip A.G.D., Relyea L. 1979, AJ, 84, 1743 Smalley B., Kupka F. 1997, A&A, 328, 349 Templeton M.R., McNamara B. J., Guzik J.A. et al. 1997, AJ, 114, 1592 Villa P. 1998, unpublished, Master Thesis, Univ. of Vienna, Austria Asterò seismology of Delta Scuti stars 161

APPENDIX

Preparing for asteroseismology: determining atmospheric parameters from observations The comparison of observed frequencies with pulsation models requires the determination of the values of the pulsational constant, Q, for each frequency, i.e. the stellar mean density needs to be known. The Q value can be computed from

logQ = - log / + 0.5 logg + O.lA/boi + logreff - 6.456, (1) where the frequency, /, is measured in c/d. Narrow band uvbyfi photometry is superbly suited towards de- riving these values. However, two separate calibrations need to be applied: the absolute magnitude calibrations by Crawford (1975, 1979) and separate model atmosphere calibrations to derive g and Teff. It is not always recognized that there exist some difficulties with this procedure, which can lead to surprisingly large uncertainties. A number of different model-atmosphere calibrations have been carefully established to derive the values of the surface gravity, g, and temperature, Teff. They differ from each other in a systematic way based on the assumptions used for the model-atmosphere calcu- lations as well as which ZAMS was adopted. Note that the ZAMS established by Crawford for the absolute magnitude calibrations is usually not identical to the ZAMS obtained by stellar evolution models. This incompatibility can lead to strange results. It is possible to estimate the uncertainties caused by this problem by computing a consistency mass *, A4, from the atmospheric parameters by

* With the luminosity derived from atmospheric parameters alone (such as uvby(3 photometric indices), the real mass of the star is not found. The procedure of calculating the mass, A4, involves a circular argument: the photometric luminosity calibration is based on the assumption that the star has a 'normal' Population I value of the mass. With correct and consistent calibrations, only this implicitly assumed value can be found. Any deviations found from the 'normal' value are a sign of imperfect calibrations and not the stellar properties. Consequently, the stellar mass value required for the theoretical models should not be determined from Equation (2). 162 M. Breger

We have chosen a number of different commonly used g, Teff calibrations and calculated the consistency mass values across the Crawford ZAMS. The hoped-for agreement with the evolutionary masses is not found.

Evolutionary tracks (Pamyatnykh, 1998) 0.48 —•— Final calibration —•— Balona (1994) 0.40 —•— Breger (1977) —A— Moon & Dworetsky (1985) —X— Philip & Relyea (1979) 0.32

0.24 o

i 0.16 o> o 0.08

0.00

-0.08

-0.16 6000 6500 7000 7500 8000 8500 (K)

Fig. 6. Derived consistency ZAMS masses for different calibrations of uvby/3 photometry. The ZAMS values by Crawford (1975, 1979) were used. The expected evolutionary masses are shown for comparison. Note that the deviations from the expected evolutionary mass can be as large as 0.2 in log Ai or ~50 % in mass. This translates to an error of up to 25 % in the computed Q-value.

This is shown in Fig. 6, which compares these consistency masses for different calibrations. The curve called 'Final calibration' refers to an unpublished new calibration by Villa (1998) and the author. This calibration attempts to shift the theoretical Smalley & Kupka (1997) grid by using the known temperature and gravity values of standard stars. The Figure shows that a consistency problem still exists for all calibrations, indicating uncertainties with the values of Asteroseismology of Delta Scuti stars 163

Crawford ZAMS or the model atmopsheres. At this stage, a rec- ommendation of which calibration is most reliable cannot be made. The present author uses the Breger (1977) grid, while the Moon & Dworetsky (1985) grid has also been applied by some workers in the field. To summarize, the standard method of calculating Q values from photometric parameters alone, is subject to systematic errors as large as ~ 25 % based on uncertain and incompatible calibrations. For the average star in the instability strip, the uncertainty is smaller, viz. ~10%. This uncertainty is on top of a random uncertainty of ~18% caused by the standard photometric observing uncertainty of the uvby/3 parameters (Breger 1990). These uncertainties must be taken into consideration when the observed frequency spectrum is compared with different models. It is advisable to replace the uncertain log g value, which is often afflicted by systematic errors, by a stronger dependence on Mboi and the introduction of a (small) mass term. Such a scheme is especially useful if an accurate (Hipparcos) parallax is available, i. e. M\>0\ is accurately known.

If we substitute the solar values Mbd,© = 4.75 and Teff<0 = 5770 K into the period-luminosity-temperature-mass relation (Equa- tion 2), and rearrange the terms, we find

log Q = - log / + 0.3Mboi + 3 log Teff + 0.5 log(M/M&) - 12.7085, where / is the frequency in c/d. Note that the constants used here are the same as used for Equation 1. For stars with accurately determined distances, the most im- portant term, Mbd, is known. The temperature is usually obtained from one of the available model atmosphere calibrations, while the mass term can be estimated from the evolutionary models, i. e., the position of the star in the Hertzsprung-Russell diagram.