MULTIMODE PULSATIONS OF THE k BOOTIS STAR 29 CYGNI: THE 1995 AND 1996 MULTISITE CAMPAIGNS

The Astronomical Journal, 134:1713Y1727, 2007 October # 2007. The American Astronomical Society. All rights reserved. Printed in U.S.A. MULTIMODE PULSATIONS OF THE k BOOTIS STAR 29 CYGNI: THE 1995 AND 1996 MULTISITE CAMPAIGNS D. E. Mkrtichian, 1,2 A. V. Kusakin, 3,4 P. Lopez de Coca, 5 K. Krisciunas, 6 C. Akan, 7 V. P. Malanushenko, 8,9 M. Paparo, 10 J. Percy, 11 A. Rolland, 5 V. Costa, 5 J. I. Olivares, 5 V. A. Koval, 2 M. A. Hobart, 12 C. Ibanoglu, 7 A. Ozturk, 7 S. Thompson, 11 E. Paunzen, 13 G. Handler, 13 V. Burnashev, 8 W. W. Weiss, 13 K. S. Kuratov, 4 and Y. W. Kang 1 Received 2007 May 31; accepted 2007 July 8 ABSTRACT In this paper we present the results of multisite photometric and spectroscopic campaigns, carried out during the years 1995 and 1996, to study the pulsations of a typical k Bootis star, 29 Cyg. During the 1995 campaign we found welldefined multiperiodicity in 29 Cyg, which was studied in detail during a multilongitude campaign covering a 65 day time interval in 1996. The frequency analysis of the 1996 campaign s data easily revealed 11 excited low degree modes with frequencies of oscillation ranging from 20.3 to 37.4 cycles day 1 and mean photometric amplitudes ranging from 10.65 to 0.96 mmag in the V filter. After removing the well-identified frequencies, the discrete Fourier transform of the residuals showed excess power in the 20Y40 cycle day 1 domain, which indicates the probable existence of unresolved rich p-mode spectra with photometric Vamplitudes below 0.5 mmag. We found a regular spacing of 2.41 cycles day 1 within the modes of 29 Cyg, which was interpreted as the spacing of consecutive even and odd -values. The asteroseismic luminosity log L/L ¼ 1:12, calculated from the frequency spacing, is in good agreement with the Hipparcos luminosity log L/L ¼ 1:16 and with luminosities from photometric and spectroscopic calibrations. Using our multicolor photometry we tentatively identified the dominant f 1 ¼ 37:425 cycle day 1 mode as an ¼ 2, n ¼ 5mode, and made radial overtone identification for all frequencies. These ranged from n ¼ 2 to 5. Analysis of the photometric data shows the long-term (years) and probable short-term (days) variability of amplitudes for all of these modes in 29 Cyg. Using our multicolor WBVR filter photometry, we found the wavelength dependence of the pulsation amplitudes for the five highest amplitude modes. Based on the H line radial velocity observations of 29 Cyg, we detected multiperiodic radial velocity variations with frequencies of 38.36 and 29.99 cycles day 1 and semiamplitudes of 1.0 and 0.8 km s 1, respectively. These frequencies coincide within the errors with the photometric frequencies of the two highest amplitude modes, 37.425 and 29.775 cycles day 1. For the highest amplitude ¼ 2, n ¼ 5 mode (37.425 cycles day 1 ), the radial velocityytoylight amplitude ratio and velocity-to-light phase shift are equal to 2K(H)/V ¼ 94 km mag 1 s 1 and f 1 ¼ Vr V ¼þ0:08 0:01, respectively, and are in good agreement with values for Scuti stars. The rich multiperiodic spectrum makes 29 Cyg a promising target for future multisite campaigns. Key words: stars: individual (29 Cygni) stars: oscillations 1. INTRODUCTION The k Bootis (hereafter LB) stars are a class of apparently metal-poor, Population I, late-b to mid-f stars, close to the main sequence, that comprise about 1%Y2% of the stars that occupy the same region in the H-R diagram as do normal A-type, metallic 1 Astrophysical Research Center for the Structure and Evolution of the Cosmos, Sejong University, Seoul 143-747, Korea. 2 Astronomical Observatory, Odessa National University, Shevchenko Park, Odessa 650014, Ukraine. 3 Sternberg State Astronomical Institute, Universitetsky Prospect 13, Moscow 119899, Russia. 4 Fesenkov Astrophysical Institute of National Academy of Sciences of Kazakhstan, Kamenskoye Plato, 050068 Almaty, Kazakhstan. 5 Instituto de Astrofísica de Andalucia, CSIC, P.O. Box 3004, E-18080 Granada, Spain. 6 Cerro Tololo Inter-American Observatory, Casilla 603, La Serena, Chile. 7 Ege University Observatory, Bornova, Izmir, Turkey. 8 Crimean Astrophysical Observatory, Nauchny, Crimea 334413, Ukraine. 9 Isaac Newton Institute of Chile, Crimean Branch, Nauchny, Crimea 334413, Ukraine. 10 Konkoly Observatory, P.O. Box 67, H-1525 Budapest, Hungary. 11 University of Toronto, Mississauga, ON L5L 1C6, Canada. 12 Faculdad de Física, Universidad Veracruzana, 91000 Xalapa, Veracruz, Mexico. 13 Institut für Astronomie der Universität Wien, Türkenschanzstrasse 17, A-1180 Wien, Austria. 1713 and magnetic chemically peculiar stars (Paunzen 2000). The spectra of LB stars show significant underabundances of metals (except for C, N, O, and S; Venn & Lambert 1990; Stürenburg 1993). Accretion and diffusion/accretion hypotheses formulated by Venn & Lambert (1990) and Turcotte & Charbonneau (1993) suggest that LB stars are ZAMS stars accreting metal-depleted circumstellar gas. This theory implies an ongoing accretion rate larger than 10 14 M yr 1 of the gaseous component of the protostellar circumstellar matter. Nowadays, about 50 known stars are believed to be LB stars. The origin of the peculiarities, evolutionary status, and position in the H-R diagram of the k Bootis group has been discussed in a recent review by Paunzen (2004). The first suspicion of pulsational variability with a period of about 45 minutes in 29 Cyg (V1644 Cyg: V ¼ 4:955 and spectral type of A2 V), a member of the LB group, was reported by E. N. Walker (1973, private communication). Later, a definite detection of pulsations with a period of about 45 minutes and a full amplitude of about 0.03 mag in the V filter was confirmed by Gies & Percy (1977). Until the early 1990s no other pulsating LB stars were found, and no attempts were made for a detailed study of pulsational properties of 29 Cyg itself, as well as of stars comprising the LB class. Since the early 1990s, ScutiYtype pulsations have been detected in 33 LB stars comprising at least 70% of all LB stars inside

1714 MKRTICHIAN ET AL. Vol. 134 TABLE 1 Log of 1995 Observations HJD 2,449,000+ N Date ( UT) Start End Filter Observatory Observers 1... 1995 Jul 21 920.2143 920.2792 W, B, V, R TSAO KAV 2... 1995 Aug 6 936.7332 936.9373 v, b McD HG 3... 1995 Aug 10 940.6023 940.9311 v, b McD HG 4... 1995 Aug 13 943.1356 943.3705 W, B, V, R TSAO KAV 5... 1995 Aug 19 949.2166 949.3768 W, B, V, R TSAO KAV 6... 1995 Aug 25 955.2245 955.2951 W, B, V, R TSAO KAV 7... 1995 Aug 26 956.1354 956.3517 W, B, V, R TSAO KAV 8... 1995 Aug 27 957.1210 957.3379 W, B, V, R TSAO KAV 9... 1995 Sep 8 969.1108 969.4203 W, B, V, R TSAO KAV Note. Observers: ( KAV) A. V. Kusakin; ( HG) G. Handler. the classical instability strip ( Paunzen 2004). In 1995, the Central Asian Network (CAN) collaboration ( Mkrtichian et al. 1998a, 1998b) selected 29 Cyg as a key object for a detailed study of pulsation spectra. The motivation was a detailed study of the oscillation spectrum to provide the possibility of asteroseismological studies of its parameters. After a preliminary study of the pulsation spectrum in 1995 ( Kusakin & Mkrtichian 1996), during 1996, 1997, and 1998 multisite photometric and spectroscopic campaigns were initiated by the CAN with the collaboration of observers worldwide. In this paper we present the results of the 1995 two-site and the 1996 multisite photometric and spectral campaigns on 29 Cyg. The results of the 1997 and 1998 photometric and spectral campaigns will be the subject of a subsequent paper. 2. THE 1995 TWO-SITE CAMPAIGN 2.1. Observations The 1995 two-site observations were carried out by the Tien Shan Astronomical Observatory ( TSAO) node of the CAN collaboration and at McDonald Observatory ( McD) for a preliminary study of the pulsation spectrum of 29 Cyg. During 1995 JulyY September we obtained five nights of high-speed photometric observations of 29 Cyg with a four-channel WBVR photometer (Kornilov & Krylov 1990) on the 0.48 m reflector at TSAO. The comparison stars HD 192661 (G8 III, V ¼ 6:567) and HD 192538 (A0 V, V ¼ 6:468), earlier established as nonvariables during the Alma-Ata WBVR photometric survey (Kornilov et al. 1991), were used as comparison stars. Two nights of Strömgren vb photometry were also obtained in 1995 August, with a twochannel photometer on the 0.9 m telescope at McD (Paunzen & Handler 1996). One channel was used for differential photometry of 29 Cyg relative to the comparison stars HD 195050 (V ¼ 5:6, A3 V) and HD 188892 (V ¼ 4:9, B6 III). During 1995 a total of 43.5 hr of photometry was obtained at the two sites. The journal of all the 1995 observations is given in Table 1. The data were reduced using standard reduction procedures for differential data. The Strömgren b and v amplitudes are very close to the B-filter amplitude for 29 Cyg. As a result the two nights of Strömgren v data obtained at McD were merged for frequency analysis with the five nights of B-band observations from the TSAO. The B and v light curves obtained at the TSAO and McD are shown in Figure 1. 2.2. Frequency Analysis of 1995 Data The time-series analysis in this paper was carried out with Kurtz s modification (Kurtz 1985) of the discrete Fourier transform (DFT) algorithm of Deeming (1975) and the package of programs Four (Andronov 1994). The latter also uses a leastsquares multifrequency method for differential corrections, which fits a multifrequency signal simultaneously with set frequencies and their harmonics. At each step of the frequency analysis we prewhiten using all frequencies found in previous steps. For accurate determination of the significance of peaks we use a bootstrap randomization technique (e.g., Kürster et al. 1997). This technique randomly shuffles the magnitude measurements, keeping the times fixed. A Lomb-Scargle periodogram is calculated for each random data set, and these data are reshuffled. After a large number of these shuffles (in our case 0:5Y1 ; 10 5 ), the fraction of the periodograms having maximum power greater than the observed data periodogram over the frequency interval of interest represents the false alarm probability (FAP), or the chance that random noise can produce the observed power in the periodogram. Seven available nights of the 1995 data set distributed over a 49 day span result in a complex spectral window pattern with strong 1 cycle day 1 aliases. These complicate the frequency analysis, giving rise to a 1 cycle day 1 frequency uncertainty. The DFT analysis of data in both filters yields the highest peak in the W, B, V,andR data at a frequency of 37.426 cycles day 1.The frequencies of 29.773, 34.723, and 25.188 cycles day 1 were consecutively found above the noise level. For a simultaneous fourfrequency solution of the 1995 B- and V-band light curves, the precise frequency values in our paper were chosen based on accurate frequencies obtained later during the multisite 1996 campaign and given in Table 7. The frequency solution for the B- and V-band light curves of 1995 are given in Tables 2 and 3. In these tables and throughout the paper the nomenclature of frequencies and their values is given according to the hierarchy of amplitudes and more accurate frequency estimates for these frequencies found in the analysis of the 1996 campaign s data (see Table 7). 3. THE 1996 MULTISITE PHOTOMETRIC AND SPECTRAL CAMPAIGN Preliminary analysis of the 1995 B R color observations carried out by Kusakin & Mkrtichian (1996) had already revealed the multiperiodicity of 29 Cyg. Due to the expected rich pulsation spectrum of 29 Cyg, and also due to its brightness, suitable declination, and long duration of visibility in the northern hemisphere during the summer and autumn seasons, observations were continued in 1996 by the CAN group (Mkrtichian et al. 1998a) and collaborators. In order to detect the expected small-amplitude modes, increase frequency resolution, and reduce the aliasing,

No. 4, 2007 MULTIMODE PULSATIONS OF 29 CYG 1715 Fig. 1. The 1995 campaign data: TSAO B-filter (circles) and McD b-filter (crosses) light curves. a two-stage photometric and spectroscopic multisite campaign was undertaken from 1996 July 27 to September 30 at observatories well distributed over the globe. The August multisite photometric run was carried out around the dates of 1996 August 11Y12, scheduled for spectroscopic observations on the 2.6 m telescope of the Crimean Astrophysical Observatory (CrAO), Ukraine. The 1996 September 18Y22 multisite run was organized around the nights of scheduled photometry on the 0.6 m telescope of the University of Hawaii ( UH) at Mauna Kea Observatory. According to the initial strategy of the campaign, from July 27 to September 30, 29 Cyg was continuously monitored photometrically at TSAO on the 0.48 m telescope on all available clear nights. The distribution of sites participating in the 1996 campaign is listed in Table 4. The Johnson V filters were used for observations. The observations obtained at CrAO with the 0.8 m Ritchey-Chrétien telescope were carried out with a spectrophotometric grating scanner working in the bandpass of 3200Y8500 8. The scanner was positioned at the effective wavelength of the Johnson V filter (5500 8) and used as a single-channel photometer with a 50 8 bandpass from about 5475 to 5525 8. The technique of observations at different sites and the choice of comparison stars were on the whole the same as for the 1995 observations. This includes measurements of the sky background and variable, comparison, and check stars. In total, 48 photometric and 2 spectroscopic nights at observatories in Ukraine, Kazakhstan, Turkey, Hungary, Canada, and the USA were acquired during the two stages of this campaign. The best 42 high-accuracy photometric nights were finally selected for further reduction and frequency analysis. At the same time, unknown to the CAN and its collaborators, an independent two-site photometric campaign on 29 Cyg from two continents was organized by P. Lopez de Coca ( Instituto de Astrofísica de Andalucia, Spain) and her collaborators. This campaign was carried out in Spain and Mexico using, respectively, the 0.9 m telescope at the Observatorio de Sierra Nevada (SNO) and the 1.5 m telescope at the San Pedro Martír Observatory (SPM). The stars HD 193369 and HD 192538 were used as companion stars; their magnitudes are given in Table 5. In total, during the two-site Spain-Mexico campaign, 14 high-quality nights, well complementing other multisite data, were acquired. The Spanish and Mexican observations were merged with other data for further analysis and are also listed in Tables 4 and 6. The zero-point adjustment of the magnitude differences between the variable and comparison stars obtained at the different sites has been carried out. We also removed the small-amplitude long-term trends in some nights at TSAO produced by uncertainties in the atmospheric extinction coefficient. For nights with a marginal quality and for intervals with guiding errors, the bad points were omitted. The original data points were summed to TABLE 2 B-Band Frequency and Amplitude Solution for 1995 Data TABLE 3 V-Band Frequency and Amplitude Solution for 1995 Data Label Frequency (cycles day 1 ) f (cycles day 1 ) Semiamplitude (mag) A (mag) Label Frequency (cycles day 1 ) f (cycles day 1 ) Semiamplitude (mag) A (mag) f 1... 37.4237 0.0004 12.65 0.3 f 4... 25.1907 0.0006 6.19 0.3 f 3... 29.7688 0.0009 4.58 0.3 f 2... 34.7339 0.0010 3.71 0.3 f 1... 37.4262 0.0003 10.44 0.2 f 4... 25.1881 0.0005 5.70 0.3 f 3... 29.7735 0.0006 4.84 0.3 f 2... 34.7231 0.0007 4.15 0.3

1716 MKRTICHIAN ET AL. TABLE 4 1995 and 1996 Campaign Observing Sites Site Location Longitude Latitude Telescope TSAO... Kazakhstan +76 57 +43 11 0.48 m McD... Texas, USA 104 01.3 +30 40.3 0.6 m 1995 1996 TSAO... Kazakhstan +76 57 +43 11 0.48 m CrAO... Crimea, Ukraine +34 01 +44 43.7 2.6 m, 0.8 m EUO... Bornova, Turkey +27 17 +38 24 0.48 m Konkoly Obs. ( KO)... Pisz esteti, Hungary +19 54 +47 55 0.5 m SNO... Granada, Spain 3 23.2 +37 03.8 0.9 m Toronto Univ. ( TU)... Toronto, Canada 79 24 +43 40 0.4 m SPM... Mexico 115 27.8 +31 02.6 1.5 m UH... Mauna Kea, Hawaii, USA 155 28.8 +19 49.6 0.6 m Note. Units of longitude and latitude are degrees and arcminutes. about 40Y60 s total integration time for every measurement of a star. These data were finally combined and used for further reduction and analysis. The 1996 combined data set covers a 65 day baseline and consists of 312.9 hr of usable V-band data. The data-point distribution echelle diagram of the 1996 campaign is shown in Figure 2. Corresponding to this data-point distribution, the spectral window function is inserted in Figure 4 (top). The multisite V-band light curves are shown in Figure 3; different symbols denote data obtained at different observing sites (see the legend). The observations obtained at different sites which overlap in time match well and show a good coincidence of photometric systems and the correctness of the data reduction. 3.1. Time-Series Analysis of 1996 Data The constancy of the comparison (HD 192538: A0 V, V ¼ 6:468) and check (HD 199661: G8 III, V ¼ 6:567) stars was established during the work on the W, B, V, R Catalog of Bright Northern Stars ( Kornilov et al. 1991) and also during the previous observations of 1995 (Kusakin & Mkrtichian 1996). The DFT frequency analysis of the 7530 V-band data points of 1996 was performed using the prewhitening technique described above for the 1995 data. The amplitude spectra of the 1996 V-band data, computed after each step of the prewhitening procedure, are presented in the panels of Figure 4 from top to bottom (note the different scale for the magnitude axes starting with the sixth panel). As a result of our analysis, 10 frequencies were found. Using 47,000 shuffles we established FAP 1:5 ; 10 3 for the lowest amplitude (0.96 mmag) peak at a frequency f 10 ¼ 32:6577 cycles day 1. The frequencies, amplitudes, and phases TABLE 5 Comparison Stars for the 29 Cyg 1995 and 1996 Campaigns Star V B Spectral Type C1: HD 192661... 6.567 7.907 G8 III C2: HD 192538... 6.458 6.473 A0 V C1: HD 195050 a... 5.636 5.704 A3 V C2: HD 188892 a... 4.943 4.854 B5 IV C1: HD 193369 b... 5.573 5.626 A2 V C2: HD 192538 b............ a Used at McD in 1995. b Used at SNO and SPM in 1996. found are listed in Table 7. The schematic frequency spectrum of the 1996 V-band data is shown in Figure 5. We also carried out a frequency analysis for the JD 2,450,316Y 2,450,330 subset of homogeneous high-quality V-band data obtained with the largest aperture photometric telescopes used during the campaign at the SNO (0.9 m) and SPM (1.5 m). These data provided a lower noise level and a higher signal-to-noise ratio than what is seen in the amplitude spectra in Figure 6 outside the domain where the modes are excited. We found consecutively the first six high-amplitude frequencies: f 1 ¼ 37:425, f 2 ¼ 34:7178, f 3 ¼ 29:7883, f 4 ¼ 25:1923, and f 6 ¼ 27:4983 cycles day 1 and a new low-frequency peak at f11 ¼ 20:34 cycles day 1 (the nomenclature of frequencies with asterisks follows the nomenclature given earlier, but asterisks denote their detection only in SNO- SPM data). The next steps of frequency analysis were complicated due to the series of peaks in the amplitude spectrum in the range of 19Y 40 cycles day 1, which very probably is due to an unresolved complex and dense spectrum of modes in 29 Cyg and the spectral window pattern of the SNO-SPM data. The FAP for the highest peaks calculated using 100,000 shuffles is below 10 5, and these peaks are real. However, the frequency uncertainty in the selection of real peaks may result in an incorrect frequency solution. Nevertheless, having in mind that subsequent frequencies found may be of lower significance and not correct, we continued the analysis of residuals to search for potential new frequencies and compare the results obtained from the whole data set. We consecutively resolved additional low-amplitude peaks at frequencies f 5 ¼ 28:132, f12 ¼ 32:896, f 13 ¼ 32:065, f 9 f9 ¼ 35:117, and f 7 ¼ 25:455 cycles day 1. The frequencies f12 ¼ 32:896 and f13 ¼ 32:065 cycles day 1 do not directly coincide with any ones found in the whole data set but may relate to frequencies f 10 and f 8, as they are relatively close to them. In spite of the relatively small FAP values (FAP < 1 ; 10 4 ) of other remaining peaks, due to the complexity of the DFT, the analysis was stopped when the visual inspection of the residual amplitude spectrum did not permit the selection of new, wellisolated peaks. The DFT amplitude spectrum of residuals indeed shows an excess of signal in the domain 20Y40 cycles day 1. This unresolved signal may be considered to be an indication of an extended, small-amplitude p-mode spectrum excited in 29 Cyg. That conclusion is in formal agreement with the spectroscopic finding by Bohlender et al. (1999) that, in 29 Cyg, there is an

TABLE 6 Log of the 1996 Photometric Observations HJD 2,450,000+ N Date ( UT) Start End Filters Observatory Observers 1... 1996 Jul 27 292.3335 292.4397 W, B, V, R TSAO KAV 2... 1996 Jul 28 293.2225 293.4127 B, V, R TSAO KAV 3... 1996 Jul 29 294.1617 294.4307 B, V, R TSAO KAV 4... 1996 Jul 30 295.1649 295.2019 W, V TSAO KAV 5... 1996 Aug 3 299.1583 299.4297 B, V, R TSAO KAV 6... 1996 Aug 6 302.1765 302.4201 B, V, R TSAO KAV 7... 1996 Aug 9 305.3785 305.5751 V KO MP 8... 1996 Aug 10 306.3250 306.5552 V EUO AC, IC, OA 9... 1996 Aug 10 306.3269 306.5828 V KO MP 10... 1996 Aug 11 307.2829 307.5370 V EUO AC, IC, OA 11... 1996 Aug 12 308.2794 308.5463 V EUO AC, IC, OA 12... 1996 Aug 12 308.2988 308.4287 5500 8 CrAO KAV, BV, MDE 13... 1996 Aug 13 309.3129 309.5783 V EUO AC, IC, OA 14... 1996 Aug 14 310.2866 310.5518 V EUO AC, IC, OA 15... 1996 Aug 15 311.2735 311.3697 5500 8 CrAO BV, KAV 16... 1996 Aug 15 311.2777 311.5806 V EUO AC, IC, OA 17... 1996 Aug 16 312.6707 312.7405 V TU PP, TS 18... 1996 Aug 20 316.3567 316.6034 V SNO LCP, AR, VC, JIO, SFGB 19... 1996 Aug 22 318.3481 318.6346 V SNO LCP, RA, CV, OJI, GBSF 20... 1996 Aug 23 319.1487 319.3311 W, B, V, R TSAO KAV 21... 1996 Aug 23 319.3513 319.6459 V SNO LCP, RA, CV, OJI, GBSF 22... 1996 Aug 24 320.1173 320.6307 V SNO LCP, RA, CV, OJI, GBSF 23... 1996 Aug 24 320.1173 320.6307 W, B, V, R TSAO KAV 24... 1996 Aug 25 321.3833 321.6295 V SNO LCP, RA, CV, OJI, GBSF 25... 1996 Aug 25 321.7677 321.8912 V SPM HMA 26... 1996 Aug 26 322.2578 322.3574 W, B, V, R TSAO KAV 27... 1996 Aug 26 322.3577 322.4480 V SNO LCP, RA, CV, OJI, GBSF 28... 1996 Aug 26 322.7661 322.8982 V SPM HAM 29... 1996 Aug 27 323.1183 323.3092 W, B, V, R TSAO KAV 30... 1996 Aug 27 323.3391 323.6326 V SNO LCP, RA, CV, OJI, GBSF 31... 1996 Aug 27 323.7914 323.8498 V SPM HMA 32... 1996 Aug 28 324.1406 324.3387 W, B, V, R TSAO KAV 33... 1996 Aug 28 324.3400 324.5805 V SNO LCP, RA, CV, OJI, GBSF 34... 1996 Aug 29 325.4841 325.5764 V SNO LCP, RA, CV, OJI, GBSF 35... 1996 Aug 30 326.4240 326.5948 V SNO LCP, RA, CV, OJI, GBSF 36... 1996 Sep 1 328.3370 328.5491 V SNO LCP, RA, CV, OJI, GBSF 37... 1996 Sep 2 329.2781 329.4886 V EUO AC, IC, OA 38... 1996 Sep 3 330.3496 330.5623 V SNO LCP, RA, CV, OJI, GBSF 39... 1996 Sep 5 332.2004 332.4620 W, B, V, R TSAO KAV 40... 1996 Sep 6 333.1103 333.4132 W, B, V, R TSAO KAV 41... 1996 Sep 7 334.1070 334.4452 W, B, V, R TSAO KAV 42... 1996 Sep 8 335.0974 335.2276 W, B, V, R TSAO KAV 43... 1996 Sep 9 336.1682 336.2270 W, B, V, R TSAO KAV 44... 1996 Sep 13 340.1843 340.3531 W, B, V, R TSAO KAV 45... 1996 Sep 15 342.0817 342.4206 W, B, V, R TSAO KAV 46... 1996 Sep 16 343.2799 343.3919 W, B, V, R TSAO KAV 47... 1996 Sep 17 344.2160 344.2661 W, B, V, R TSAO KAV 48... 1996 Sep 18 345.2739 345.4821 V KO PM 49... 1996 Sep 18 345.3501 345.4034 W, B, V, R TSAO KAV 50... 1996 Sep 18 345.5830 345.7340 V TU PJ, TS 51... 1996 Sep 18 345.7363 345.8432 V UH KK 52... 1996 Sep 19 346.8360 346.8679 V UH KK 53... 1996 Sep 21 348.7182 348.8473 V UH KK 54... 1996 Sep 22 349.7449 349.8536 V UH KK 55... 1996 Sep 22 349.0753 349.3304 W, B, V, R TSAO KAV 56... 1996 Sep 29 356.0667 356.4080 W, B, V, R TSAO KAV 57... 1996 Sep 30 357.0600 357.2383 W, B, V, R TSAO KAV Note. Observers: (AC) C. Akan; ( BV) V. Burnashev; (CV) V. Costa; (GBSF) S. F. Gonzalez-Bedolla; ( IC) C. Ibanoglu; ( HMA) M. A. Hobart; ( KK) K. Krisciunas; ( KAV) A. V. Kusakin; ( KVA) V. A. Koval; ( LCP) P. Lopez de Coca; ( MVP) V. P. Malanushenko; ( MDE) D. E. Mkrtichian; (OJI) J. I. Olivares; (OA) A. Ozturk; ( PM) M. Paparo; ( PJ) J. Percy; (RA) A. Rolland; (TS) S. Thompson.

1718 MKRTICHIAN ET AL. and in the observations made in 1976 by Gies & Percy (1977). The V-band semiamplitudes of the 29.78 and 37.42 cycle day 1 modes in Gies & Percy s (1977) (JD 2,442,931Y2,442,968) data set were A 29 ¼ 7:5 and A 37 ¼ 6:4 mmag, respectively, and the ratio was R 1976 ¼ A 29 /A 37 ¼ 1:17. On the other hand, the V-band amplitude ratios for these modes are R 1995 ¼ A 29 /A 37 ¼ 0:46 and R 1996 ¼ A 29 /A 37 ¼ 0:295, respectively, in the 1995 and 1996 data sets, i.e., the 29.788 cycle day 1 mode has a larger amplitude in 1977 than the 37.425 cycle day 1 mode, whereas during 1995Y1996 this ratio is the opposite, with an essentially smaller amplitude for the 29.788 cycle day 1 mode. This is strong evidence of the long-term amplitude variability of the modes in 29 Cyg. Further multisite observations of 29 Cyg are necessary to study the annual and short-term variability of the modes. Fig. 2. The 1996 campaign V-band data-point distribution echelle diagram for 29 Cyg. The corresponding spectral window function is an inset in the top panel in Fig. 4 excited spectrum of high-degree (m 14) modes that should have very small photometric amplitudes and are actually hidden. The frequencies and amplitudes found in the SNO and SPM data are listed in Table 8. 3.2. Short-Term Amplitude Variability In order to check the hypothesis relating to the short-term amplitude variability of the high-amplitude modes in 29 Cyg, we did the following. Using the available large number (N ¼ 7530) of V-band data points, we divided the whole 65 day data set into seven subsets of data having several days duration to search for amplitude variability of the pulsation modes. The resulting time intervals and number of points in each subset are given in Table 9. Knowing precisely the frequencies of the modes obtained for a stationary frequency solution of the whole data set, in order to limit the number of degrees of freedom we fixed the frequencies and phases of oscillations at the values found in the analysis of the whole data set. In order to obtain a correct least-squares solution for the selected data subsets in our amplitude variability analysis, we also limited the number of frequencies to the first five high-amplitude (>1.4 mmag) modes. The resulting amplitude variability in 29 Cyg is shown in Figure 7. As is seen, the amplitudes of all the modes show mainly uncorrelated amplitude variability, which are for some intervals 5Y6 times larger than the formal errors of the least-squares solution. 3.3. Long-Term Amplitude Variability The long-term amplitude variability of the high-amplitude modes in 29 Cyg was reported by Kusakin & Mkrtichian (1996) based on their preliminary analysis of the amplitude ratio of the 37.425 and 29.788 cycle day 1 modes found in their 1995 data 3.4. Wavelength Dependence of the Pulsation Amplitudes The dependence of the pulsation amplitudes at different wavelengths has so far not been established in any pulsating LB star. Knowledge of the wavelength-amplitude and color-phase dependencies for wide spectral intervals allows us to discriminate the spherical degree of the nonradial modes ( Watson 1988). To determine these dependencies for the relatively high amplitude modes excited in 29 Cyg, we considered the subset of homogeneous multicolor WBVR photometry obtained at TSAO between JD 2,450,292 and 2,450,357. We found the amplitude solution using the precise frequencies known from analysis of the whole data set and listed in Table 7. The resulting amplitude-wavelength dependencies for the first five high-amplitude modes are shown in Figure 8. The f 1 mode has the highest amplitude in the Johnson B filter and decreases at longer wavelengths (in the V and R bands). The amplitude in the W filter of the Straižis system (which is narrower than the Johnson U filter and measures the Balmer jump better) is slightly less than in the B filter but remains higher than in V and R. This is typical for amplitude distribution in Scuti stars. For other frequencies the amplitudes in the W and B filters are close to each other within the formal rms errors, and the amplitudes also decrease at longer wavelengths. 3.5. H Line Spectroscopy The initial aim of our spectral observations during the 1996 campaign was a pulsational line profile analysis of 29 Cyg to search for higher degree nonradial modes and radial velocity ( RV) variations. However, the weather conditions at CrAO during the first spectral night did not allow us to obtain a high enough S/N ratio in the blue region of the spectra. That forced us during the first night to change the strategy of the spectral observations and focus our work on the H line RV investigations. The spectral observations of 29 Cyg were carried out at the coudé focus of the 2.6 m telescope of the CrAO during two consecutive nights, 1996 August 11Y12 and 12Y13. The spectra were obtained with the coudé spectrometer with a linear dispersion of 0.13 8 pixel 1. The spectral resolution was about 0.4 8. Asa detector we employed a 1024 ; 256 pixel liquid-nitrogen-cooled CCD camera. A spectral region of k ¼ 130 8 centered on the H line was used. The exposure time was 4 minutes. The S/N was 80Y100 for the individual spectra. During two consecutive nights, we collected two sets of observations with 118 and 256 minute durations (22 and 45 usable spectra, respectively). During the first night (August 11Y12) the spectroscopic observations at CrAO were supported by parallel photoelectric observations with the 0.48 m telescope at the Ege University Observatory (EUO) in Turkey. During the second spectroscopic

Fig. 3. Multisite photometry of 29 Cyg obtained during the 1996 campaign. The symbols denote the observations obtained at TSAO ( filled circles), SNO and SPM ( plus signs), Konkoly Observatory (open circles), EUO ( filled squares), Toronto University (open squares), CrAO (crosses), and UH. The 10 frequency fit is shown as a solid line.

Fig. 3 Continued 1720

Fig. 3 Continued 1721

1722 MKRTICHIAN ET AL. Vol. 134 Label TABLE 7 10 Frequency Solution and Approximate Overtone Identification for 1996 Multisite Data Frequency (cycles day 1 ) f Semiamplitude (cycles day 1 ) (mmag) A (mmag) Q (days) Radial Order n f 1... 37.42551 0.00007 10.65 0.07 0.0125 5 f 2... 34.72125 0.00017 4.19 0.07 0.0135 4Y5 f 3... 29.77514 0.00022 3.14 0.08 0.0157 4 f 4... 25.18958 0.00028 2.59 0.07 0.0185 3Y2 f 5... 28.15890 0.00050 1.45 0.07 0.0166 3 f 6... 27.50362 0.00052 1.37 0.08 0.0177 3 f 7... 25.45789 0.00061 1.18 0.08 0.0183 3 f 8... 32.62539 0.00059 1.21 0.08 0.0143 4 f 9... 34.91194 0.00070 0.99 0.07 0.0134 5Y4 f 10... 32.65773 0.00074 0.96 0.08 0.0143 4 a thorium comparison spectrum. To increase the accuracy of the wavelength calibration the RVs of the central parts (k ¼ 3:1 8) of the H line were determined relative to 16 atmospheric H 2 O lines. The accuracy of the RV determinations depended on the S/N ratio and was about 0.01Y0.015 8 for a single spectrum, which corresponds to about 0.5Y0.7 km s 1 for the RVs. We present in Figure 9 the RV variations of the H line ( filled circles) for two nights, JD 2,450,307 and 2,450,308. In Figure 9 (bottom panels) are shown the parallel photometric observations for these dates obtained at EUO (open circles) andatcrao (crosses). RV variations with a full amplitude of about 4 km s 1 areclearlyseeninthefigure.infigure10ispresentedthefrequency analysis of the JD 2,450,307 and 2,450,308 simultaneous RV (left panels) and V-filter (right panels) data. The RV data show the existence of two main peaks at frequencies of 38:36 0:06 and 29:99 0:08 cycles day 1, with semiamplitudes of 1:0 0:2 and0:8 0:2 kms 1, respectively. Due to the spectral window 1 cycle day 1 pattern the peaks of the RV amplitude spectra do not directly coincide with the highest known photometric frequencies, f 1 ¼ 37:425 and f 3 ¼ 29:775 cycles day 1, but these RV periodicities are undoubtedly the result of pulsations in the same modes. The amplitude spectra of the simultaneous photometric V-band data are shown in the right panels in Figure 10. The highest peaks correspond to the frequency f 1. In the middle panel is shown the spectrum of the residuals. The second highest peak in this subset of V-band data corresponds to the frequency f 2. The bottom panels (left and right) show the resulting RV and photometric amplitude spectra obtained after removing the corresponding two highest amplitude frequencies mentioned above. The small-amplitude (about 2 mmag) signal at frequency f 3 is Fig. 4. The 1996 campaign V-band amplitude DFT spectra. Note the different scale for the magnitude axis starting with the sixth panel. night, August 12Y13, parallel photoelectric observations were carried out with the neighboring 0.8 m Ritchey-Chrétien telescope of CrAO, as well as the 0.48 m telescope at EUO. The journal of spectroscopic observations is given in Table 10. The spectra were processed in the standard way by applying flat-field corrections, with normalization and wavelength calibration from Fig. 5. Schematic frequency spectrum of 29 Cyg.

No. 4, 2007 MULTIMODE PULSATIONS OF 29 CYG 1723 TABLE 8 Multifrequency and Multiamplitude Solution for SNO and SPM Observations Label Frequency (cycles day 1 ) f (cycles day 1 ) Semiamplitude (mmag) A (mmag) f 1... 37.4256 0.0004 10.06 0.1 f 2... 34.7178 0.0011 4.28 0.1 f 3... 29.7883 0.0015 3.27 0.1 f 4... 25.1923 0.0015 2.90 0.1 f 6... 27.4936 0.0019 2.57 0.1 f 11... 20.343 0.003 1.32 0.1 f 5... 28.132 0.004 1.19 0.1... 32.896 0.005 1.13 0.1 f13... 32.065 0.005 0.97 0.1 f14... 35.117 0.005 0.89 0.1 f 7... 25.455 0.004 1.29 0.1 f 12 Notes. The frequencies with asterisks denote those frequencies found only in SNO and SPM data. The nomenclature of frequencies follows the sequence of frequencies that were found during the analysis of the whole data set. Frequencies without asterisks denote other frequencies found in the analysis of the whole data set (see Table 7). phases, is shown in Figure 9 by the solid line. The velocity-toamplitude ratio for the 37.425 cycle day 1 mode is equal to 2K(H)/V ¼ 94 km s 1 mag 1, and the phase shift between the inverse RV and V-band light curves is f 1 ¼ Vr V ¼ þ0:08 0:01, in agreement with the phase lag values +0:09 0:015 found earlier for Scuti stars with predominant radial pulsations (Breger et al. 1976). 4. FREQUENCY SPACING AND MODE IDENTIFICATION Visual inspection of the schematic frequency spectrum of 29 Cyg in Figure 5 shows regular frequency spacing and resembles that of XX Pyx (Handler et al. 1997, 2000) very closely. To search for preferred frequency separations, 10 mode frequencies from Table 7 and one ( f11 ) from Table 8 were taken, and the same analysis as described by Handler et al. (1997, 2000) was done. The resulting power spectrum of spectral windows of frequencies is shown in Figure 11. The result is a highly significant mean frequency spacing of 2.41 cycles day 1 (27.89 Hz) within the modes of 29 Cyg. If we assume that the mean frequency spacing of 27.89 Hz is the spacing of consecutive even or odd -values or half the spacing of 0 ¼ 55:78 Hz between consecutive overtones of the same degree of, and using the better than 10% accuracy calibration for main-sequence stars with masses between 1 and 2.0 M (Gabriel et al. 1985), 0 ¼ 0:205 GM 1=2 R 3 Hz; ð1þ TABLE 9 Time Intervals for Short-Term Variability Search Fig. 6. DFT amplitude spectrum of merged SNO and SPM data. Note the changing scale of the amplitude axis. visible in the photometry panel but at lower S/N. Other frequencies known from the photometry are not visible above the noise level in both the RVand V-band data spectra of the residuals due to their small amplitudes and limited S/ N ratio. The least-squares fit of the RV data with the known photometric frequencies of 37.425 and 29.77 cycles day 1, using optimized amplitudes and HJD 2,450,000+ Start End Data Points N 292.3335... 295.2019 500 305.3785... 311.5806 941 316.3567... 320.6307 1081 321.3833... 324.5805 1324 326.4240... 330.5623 464 332.2004... 335.2276 715 342.0817... 345.8432 857

1724 MKRTICHIAN ET AL. Fig. 7. Amplitude variability of the highest amplitude modes f 1, f 2, f 3, f 4, and f 5 vs. time during the 1996 campaign. Fig. 8. Pulsation semiamplitude vs. wavelength obtained from the TSAO W, B, V, and R data of 1996. where the mass M,radiusR, and gravitational constant G are given in SI units, we get an asteroseismic mean density of 0.264. The absolute magnitude M V ¼ 1:89 and luminosity log L/L ¼ 1:16 obtained from the Hipparcos parallax ¼ 24:37 mas and magnitude V ¼ 4:955 for 29 Cyg are in good agreement with the values obtained from multicolor Strömgren photometry, which gives the following estimates: absolute magnitude M V ¼ 1:85, luminosity log L/L ¼ 1:23, temperature log T ea ¼ 3:907, and surface gravity log g ¼ 4:1 (Iliev & Barzova 1993). The spectroscopic estimates of the fundamental parameters log T e ¼ 3:892 and log g ¼ 4:0 (Heiter 1998) are close to the photometric ones. Both place 29 Cyg about 0.9 mag above the ZAMS in the log T e YM V diagram, well inside the instability strip. With log T ea ¼ 3:9, log g ¼ 4:10, and the asteroseismic mean density for 29 Cyg, this implies from evolutionary tracks a mass of about 1.9 M, and hence, we get a radius of 1.94 R and a luminosity of log L/L ¼ 1:13, in good agreement with the Hipparcos and Strömgren photometric calibration results. This suggests that deriving asteroseismic luminosities from frequency spacings for LB stars works well. In an attempt to independently determine the degrees of the modes, we carried out a frequency analysis on a subset of the multicolor observations (JD 2,450,292Y2,450,357) obtained at TSAO. The frequency spectrum of the B V data is shown in Figure 12. Only the highest amplitude mode, f 1 ¼ 37:425, cycles day 1 has a signal-to-noise ratio greater than 4 in the amplitude spectrum, and only this mode allows us to obtain phase and amplitude estimates for the application of Watson s (1988) method of (tentative) mode identification. The amplitude ratio and phase shift between the B V and V light curves are given in Table 11. The amplitude ratio A B V /A V ¼ 0:21 0:06 and the large negative phase shift ¼ (B V ) V ¼ 17:29 3:6 obtained from the multicolor TSAO data locate the f 1 mode on the A B V /A V - (B V ) V plane in the area of interest for ¼ 2modes. Thus, the tentative -degree identification of the 37.425 cycle day 1 frequency is the ¼ 2 nonradial mode. The identification of other modes found in the photometry requires additional information on the degrees of the modes and pulsation model calculations relating to the theoretical frequency spectrum of 29 Cyg. TABLE 10 Journal of 1996 Spectroscopic Observations HJD 2,450,000+ Date ( UT) Start End Number of Spectra Observers 1996 Aug 11... 307.4320 307.5105 24 MVP, MDE 1996 Aug 12... 308.3945 308.5723 52 MVP, MDE Note. Observers: ( MVP) V. P. Malanushenko; ( MDE) D. E. Mkrtichian.

Fig. 9. Parallel H line RVs (top panels) and V-band light curves of 29 Cyg (bottom panels). Crosses, CrAO 0.8 m telescope; circles, EUO 0.48 m telescope. Fig. 10. Frequency analysis of the JD 2,450,307Y2,450,308 H line RVs (left panels) and photometric V-filter data (right panels). Top left: Amplitude spectrum of the original RV data. The highest peak corresponds to the f 1 ¼ 37:425 cycle day 1 mode. Middle left: Amplitude spectrum of the residuals. The second peak related to f 3 ¼ 29:775 cycles day 1 is easily visible. Bottom left: Amplitude spectrum after the subtraction of the two frequencies f 1 and f 3. The excess of signal at frequency 20 Y21 cycles day 1 may be an indication of the presence of the oscillation modes found in the photometry. Top right: Amplitude spectrum of the original EUO and CrAO V-filter data. The highest peak corresponds to the f 1 ¼ 37:425 cycle day 1 mode. Middle right: Amplitude spectrum of the residuals. The second peak related to f 2 ¼ 34:721 cycles day 1 is easily visible. Bottom right: Amplitude spectrum after the subtraction of the two frequencies f 1 and f 2. Note that the relative spectroscopic amplitude of f 3 is higher than f 2.

1726 MKRTICHIAN ET AL. Vol. 134 TABLE 11 Amplitude Ratio, Phase Shift, and Tentative Mode Degree Identification for the 37.425 Cycle Day 1 Mode Parameter Value A(B V )/A(V )... 0.21 A (deg)... 0.063 (B V ) (V ) (deg)... 17.29 (deg)... 3.6 Degree... 2 Fig. 11. Search for a preferred frequency separation within 11 pulsation modes detected in 29 Cyg. The highest peak in the power spectrum corresponds to a frequency spacing of 2.41 day 1 (27.89 Hz). This spacing corresponds to half of the spacing between consecutive overtones of the same. Information on precise absolute values of the frequencies obtained in our work, as well as on the asteroseismic estimate of the mean density of the star, gives the possibility of an approximate tentative determination of the radial order of the modes by means of the pulsation constant, Q ¼ Pð= Þ 0:5 ; ð2þ where and are the mean densities of the star and the Sun; Q varies slowly with spectral type for any acoustic mode, with fixed quantum numbers (, m, n) determining its spatial structure (Unno et al. 1989). Substitution of the asteroseismically determined mean density and periods into equation (2) gives the pulsation constants for the detected modes in the range of the second to fifth overtones, which are given in the last column in Table 7. The pulsation constant for the 11th f11 mode is 0.0245, which relates this mode to the first or second overtone. 5. CONCLUSIONS Based on new multisite data we confirmed the multiperiodicity and found a rich spectrum of multiperiodic oscillations in 29 Cyg. We found 11 pulsation frequencies and suspect additional low-amplitude ones in the interval of 20Y60 cycles day 1. Analysis of the frequency spectrum showed regular spacing of 2.41 cycles day 1 within the modes of 29 Cyg, which was interpreted as the spacing of consecutive even or odd -values. The asteroseismic calibrations of the mean spacing of consecutive overtones were used for the determination of the mean density of the star, which was used for an asteroseismic determination of the luminosity. We show that the asteroseismic luminosity is in good agreement with the luminosity from the Hipparcos parallax and photometric and spectroscopic calibrations. An analysis of seven subsets of data was undertaken to check the hypothesis of amplitude variability of the modes. Our analysis shows strong and uncorrelated amplitude variability higher than the formal errors of least-squares analysis on timescales of several days for all analyzed modes. The comparison with observations obtained earlier shows the long-term amplitude variability of the frequencies. Using the B V and V-bandphaseshifts,wemadeatentative identification of the highest amplitude mode at 37.425 cycles day 1 as an ¼ 2, n ¼ 5 mode, and made a radial overtone identification for all 11 frequencies. These range from n ¼ 2to5. Based on spectroscopic observations of 29 Cyg we found pulsational RV variability of the H line at two frequencies, with amplitudes of 1.0 and 0.8 km s 1. These coincide, respectively, with two known high-amplitude photometric modes having frequencies of 37.425 and 29.775 cycles day 1. The velocity-to-light amplitude ratio and velocity-to-light phase shift for the highest amplitude ¼ 2, n ¼ 7 mode at 37.425 cycles day 1 are equal to 2K(H)/V ¼ 94 km s 1 mag 1 and f 1 ¼ Vr V ¼ 0:08 0:01, respectively, both in agreement with previously found relations for Scuti stars. The residual data show an excess of power in the 20Y40 cycle day 1 domain that indicates the existence of an unresolved rich p-mode spectrum with photometric V-band amplitudes below the 0.5 mmag level. This makes 29 Cyg a promising target for future multisite campaigns. Fig. 12. Amplitude frequency spectrum of a subset of the TSAO B V data. The smooth horizontal line shows the S/N ¼ 4:0 level. M. D. E. and K. Y. W. acknowledge their work as part of the research activity of the Astrophysical Research Center for the Structure and Evolution of the Cosmos, which is supported by the Korean Science and Engineering Foundation. The participation of G. H., E. P., and W. W. was supported by the Austrian Fonds zur Förderung der wissenschaftlichen Forschung under grant S-7303. The spectroscopic observations described in this publication were made possible in part by grants R2Q000 and U1C000 from the International Science Foundation and by grant A-05-067 from the ESO C&EE programme. This work was supported in part by US Civilian and Research Development Foundation grant UP2-317.

No. 4, 2007 MULTIMODE PULSATIONS OF 29 CYG 1727 Andronov, I. L. 1994, Odessa Astron. Publ., 7, 49 Bohlender, D. A., Gonzalez, J.-F., & Matthews, J. M. 1999, A&A, 350, 553 Breger, M., Hutchins, J., & Kuhi, L. V. 1976, ApJ, 210, 163 Deeming, T. J. 1975, Ap&SS, 36, 137 Gabriel, M., Noels, A., Scuflaire, R., & Mathys, G. 1985, A&A, 143, 206 Gies, D. R., & Percy, J. R. 1977, AJ, 82, 166 Handler, G., et al. 1997, MNRAS, 286, 303. 2000, MNRAS, 318, 511 Heiter, U. 1998, Contrib. Astron. Obs. Scalnate Pleso, 27, 403 Iliev, I. K. & Barzova, I. S. 1993, Ap&SS, 208, 277 Kornilov, V. G., & Krylov, A. V. 1990, Astron. Zh., 67, 173 Kornilov, V. G., et al. 1991, Trudy GAISH, 63, 399 Kürster, M., Schmitt, J. H. M. M., Cutispoto, G., & Dennerl, K. 1997, A&A, 320, 831 REFERENCES Kurtz, D. W. 1985, MNRAS, 213, 773 Kusakin, A. V., & Mkrtichian, D. E. 1996, Inf. Bull. Variable Stars, 4314, 1 Mkrtichian, D. E., et al. 1998a, Contrib. Astron. Obs. Scalnate Pleso, 27, 238. 1998b, Contrib. Astron. Obs. Scalnate Pleso, 27, 476 Paunzen, E. 2000, Ph.D. thesis, Vienna Univ.. 2004, in IAU Symp. 224, The A-Star Puzzle, ed. J. Zverko et al. ( New York: Cambridge Univ. Press), 443 Paunzen, E., & Handler, G. 1996, Inf. Bull. Variable Stars, 4318, 1 Stürenburg, S. 1993, A&A, 277, 139 Turcotte, S., & Charbonneau, P. 1993, ApJ, 413, 376 Unno, W., Osaki, Y., Ando, H., Saio, H., & Shibahashi, H. 1989, Nonradial Oscillations of Stars (2nd ed.; Tokyo: Univ. Tokyo Press) Venn, K. A., & Lambert, D. L. 1990, ApJ, 363, 234 Watson, R. D. 1988, Ap&SS, 140, 255