Astron. Astrophys. 337, 447 459 (1998) Spectroscopic and photometric investigations of MAIA candidate stars ASTRONOMY AND ASTROPHYSICS G. Scholz 1, H. Lehmann 2, G. Hildebrandt 1,K.Panov 3, and L. Iliev 3 1 Astrophysikalisches Institut Potsdam, Telegrafenberg A27, D-14473 Potsdam, Germany (gscholz@aip.de, ghildebrandt@aip.de) 2 Thüringer Landessternwarte Tautenburg, D-07778 Tautenburg, Germany (lehm@tls-tautenburg.de) 3 Institute of Astronomy, Sofia, Bulgarian Academy of Sciences, Bulgaria (kpanov@bgearn.acad.bg, liliev@bgearn.acad.bg) Received 5 January 1998 / Accepted 22 June 1998 Abstract. Including our own observational material and the Hipparcos photometry data, we investigate the radial velocity and brightness of suspected Maia variable stars which are classified also in some examples as peculiar stars, mainly for the existence of periodic variations with time-scales of hours. The results lead to the following conclusions: (1) Short-term radial velocity variations have been unambiguously proved for the A0 V star γ CrB and the A2 III star γ UMi. The stars pulsate in an irregular manner. Moreover, γ CrB shows a multiperiod structure quite similar to some of the best-studied neighbouring δ Scu stars. (2) In the Hipparcos photometry as well as in our photometric runs we find significant short- and long-term variations in the stars HD 8441, 2 Lyn, θ Vir, γ UMi, and γ CrB. For ET And the Hipparcos data confirm a short-period variation found already earlier. Furthermore, we find changes of the colour index in θ Vir and γ CrB on a time-scale of days. (3) No proofs for the existence of a separate class of variables, designated as Maia variables, are found. If the irregular behaviour of our two best-investigated stars γ CrB and γ UMi is typical for pulsations in this region of the Hertzsprung-Russell diagram, our observational runs are too short and the accuracy of the measurements too low to exclude such pulsations in the other stars, however. (4) The radial velocities of the binaries α Dra and ET And have been further used for a recalculation of the orbital elements. For HD 8441 and 2 Lyn we estimated the orbital elements for the first time. (5) Zeeman observations of the stars γ Gem, θ Vir, α Dra, 4 Lac, and ET And give no evidence of the presence of longitudinal magnetic field strengths larger than about 150 gauss. Key words: binaries: spectroscopic stars: early-type stars: magnetic fields stars: oscillations Send offprint requests to: G. Scholz Based on spectroscopic observations taken with the 2 m telescope at the Thüringer Landessternwarte Tautenburg, Germany, and with the 2 m telescope of the National Astronomical Observatory Rozhen, Bulgaria. For photometric investigations we used the 0.6 m telescope at Rozhen and the Hipparcos and Tycho catalogues. 1. Introduction Pulsations are a widespread phenomenon in early-type stars along and near the main sequence. But in a small region of the Hertzsprung-Russell diagram (HRD), bordered by the δ Scuti stars and the slowly pulsating B stars (often named as 53 Persei stars), which are located on the cool side of the β Cephei strip, stellar pulsations seem to be absent. In the fifties Struve (1955) suggested that a sequence of variables with spectral and luminosity types between B7V-III and A2V-II might exist having periods of about 0 ḍ 1to0 ḍ 3. He called this group of stars Maia stars after the presumed prototype Maia in the Pleiades. If the existence of such a group of variables would be real then these variables would to a large extent occupy the pulsational free zone between the 53 Per and the δ Scu stars and pulsational variability would be then a more or less common characteristic of stars located in the upper region of the HRD down to the hot border of the δ Scuti instability strip. Beginning already with Struve himself (later he found neither a light nor a velocity variability in Maia), a long-lasting dispute occurred about the existence of the Maia stars as an autonomous class of variable stars. A compilation of the pros and cons of observational results related to the hypothetical Maia stars has been given by McNamara (1987a). In last years, the most quoted example of a Maia pulsator was the B9p star ET And with a photometric period of about 0 ḍ 1 (Panov 1978). But, after recent comments (Kuschnig et al. 1994, Breger 1995) the photometric variability should be due to the comparison star used. If this statement is true, not a single star would be known to pulsate in brightness with a period smaller than about 0 ḍ 28 (28 Tau) in the domain of the HRD where the Maia stars should be expected. Concerning the radial velocities of ET And the results are also controversial. Gerth et al. (1984) during an observational campaign in 1981 at Rozhen Observatory found radial velocity changes with a period of about 0 ḍ 2 and a semi-amplitude of about 4 km/s, whereas observations made in 1990 at the Observatoire de Haute-Provence (Piskunov et al. 1994) do not confirm other radial velocity variations than those occurring from binary motion and stellar rotation. If short-term radial velocity varia-
448 G. Scholz et al.: Spectroscopic and photometric investigations of MAIA candidate stars Table 1. Journal of the spectroscopic and photometric observations of presumed Maia candidates. Name HD spectral v sin(i) m v N S comparison check JD N P t type [km/s] [mag] star star 2400000+ [min] σ And 1404 A2V 110 4.6 19 θ And no 49621.50 77 150 49623.50 64 150 8441 A2V 10 6.7 14 23 Tau 23480 B6IV 250 4.2 20 Tau no 49621.60 32 80 49623.58 51 100 49627.56 33 60 27 Tau 23850 B8III 200 3.6 20 Tau no 49253.52 15 140 49254.54 12 90 49256.52 18 120 28 Tau 23862 B8V 340 5.0 20 Tau no 49253.52 14 90 49254.53 12 90 49256.52 14 150 2 Lyn 43378 A2V 35 4.5 20 γ Gem 47105 A0IV 10 1.9 148 θ Vir 114330 A2V 10 4.4 43 21 Vir HD 109722 49830.35 47 120 49834.34 17 60 49835.31 44 100 49836.29 62 170 49864.33 35 90 49865.34 47 120 50222.34 31 100 50593.35 32 100 50601.34 18 70 50602.35 6 20 α Dra 123299 A0III 30 3.6 76 γ UMi 137422 A2III 165 3.0 125 142105 no 49252.27 13 80 γ CrB 140436 A0V 100 3.8 1490 138341 HD 136849 50222.40 165 270 50225.37 50 100 50227.50 96 180 50228.46 25 40 50231.40 29 60 50593.46 21 60 50596.47 81 170 50600.45 71 160 50601.43 89 210 50615.39 25 45 50616.43 15 27 50617.39 12 20 21 Aql 179761 B8III 20 5.1 17 179343 no 49255.25 27 120 49620.26 25 160 49621.27 74 130 θ Peg 210418 A2V 130 3.5 9 214923 no 49623.28 77 180 4 Lac 212593 B9II 20 4.6 69 6 Lac 2 Lac 49252.38 16 70 49256.40 20 70 49259.41 28 120 49619.41 16 40 49620.35 60 90 49621.37 97 150 2 Lac 49623.38 77 150 49624.34 62 90 49627.40 52 90 ET And 219749 B9IV 80 6.3 34 219891 HD 219397 49253.30 75 270 49624.51 30 180 219397 50322.55 27 100 50358.45 69 230 50360.45 79 260 50388.35 69 220
G. Scholz et al.: Spectroscopic and photometric investigations of MAIA candidate stars 449 tion would be present, its semi-amplitude should be smaller than 0.7 km/s. Similar distinct discrepancies are also described in spectroscopic and photometric observations of other presumed Maia stars. Probably, these differences have to be accepted because the errors indicated in the individual findings do not admit serious doubts about the reality of the results published. In the present paper we summarize our observations and investigations of hypothetical Maia stars. For some stars the observational results have already been discussed earlier (Lehmann et al., 1995, 1996, 1997). Here we complete these findings and include the results following from the Hipparcos photometry. 2. Observations and reductions 2.1. Spectroscopic and photometric observations The photographic spectroscopic observations were performed with the coudé spectrographs of the 2 m telescopes of the Karl-Schwarzschild-Observatory at Tautenburg and of the National Astronomical Observatory Rozhen. The spectrograms from Tautenburg were partially obtained with a Zeeman analyzer. Radial velocities (RV hereinafter) and magnetic fields were measured by a computer-controlled Abbé comparator using lines in the spectral region between 3800 to 4800 Å. Additionally, CCD observations were obtained at Tautenburg with the coudé spectrograph and with the échelle spectrograph and Zeeman analyzer TRAFICOS (Hildebrandt et al. 1997) attached at the Nasmyth focus. CCD spectra have been reduced under MIDAS with a specially developed reduction package. Because of the very different S/N ratio the error of a RV value of a single line, possessing a line width equivalent to about 80 km/s, is for the photographic plate about 3 km/s and for a CCD spectrogram 0.6 km/s. In the case that the RV correspond to the mean of several lines the errors are about 1 and 0.3 km/s, respectively. The photometric observations were obtained with the 60 cm telescope of the Rozhen Observatory using a set of UBV filters and an EMI 9789QB photomultiplier. Generally, the mean error in the various colours of the photometric measurements is about 0.005 to 0.006 magnitudes. In some cases the observations include a check star as well as a comparison star. If only a comparison star is used this one is very probably constant because no hint on the existence of brightness variations is indicated in the literature. Further supplementary details of the observational parameters can be found in Lehmann et al. (1995). Information on the stars investigated and the observing log is given in Table 1. Most columns are self-explanatory. N S and N P give the number of the spectra and the number of the photometric measurements included in the run, respectively. t is the total time interval and JD is the mean time of the run. 2.2. Hipparcos photometry Hipparcos data for most of our target stars are now available. Accurate broad-band photometry at an average of some 110 Table 2. Pass bands of the Hipparcos (H) and the Tycho (B T, V T ) photometric systems. λ max, λ 1/2 give central wavelength and lower/upper wavelength at FWHM, m give the accuracy for the mean value measured on constant stars with m V 8 mag. H B T V T λ max [nm] 452 435 505 λ 1/2 [nm] 394-615 384-455 475-571 m [mmag] 1.5 12 12 epochs was acquired for all objects in the Hipparcos Catalogue (obtained by the main mission detector), and two-colour photometry for nearly all objects in the Tycho Catalogue (obtained by the star mapper detector). Whereas the Tycho data represent Johnson B and V magnitudes, the Hipparcos main instrument observed in a broad-band system in order to optimise the astrometric signal. Although the photometry obtained with this system is limited in its astrophysical content, the precision of each observation is much higher than that of the Tycho Catalogue data. Table 2 lists some basic photometric properties as given in the Introduction to the Hipparcos and Tycho Catalogues. A detailed explanation can be found there. First, we investigated both the Hipparcos and the Tycho photometric data. Although the Tycho data include many more values, the photometric accuracy turns out to be not sufficient to find any periodic variation within our sample. Fig. 1 shows the typical time distribution of the Hipparcos data for the example star ET And. There are 161 data points spread over 1150 d, the largest continous data group contains 35 measurements within 2 days. The data distribution shown in Fig. 1 is typical for all of our target stars. Also the time interval of observation is about the same. The window function shown in the lower part will be discussed in detail in the following section. The Hipparcos catalogue lists only two of our target stars as variable - it gives the rotation period of ET And, P rot = 1 ḍ 61891, and a period for HD 8441, P =69 ḍ 92, which is possibly an alias. Our period search in the Hipparcos photometry yields a periodic brightness variation for five of the stars. Table 4 lists the data sets used for our target stars as well as the results of period searches. 3. Period searches Basic considerations on the significance of periods derived by usual period finding techniques for unevenly spaced data can be found in Scargle (1982, SC) or in Horne & Baliunas (1986, HB). We consider here the Scargle periodogram and the least squares fit by sine-waves (Valtier 1972, Lehmann et al. 1995). If we inspect one single frequency f in a periodogram which contains no signal, the statistical probability that we found there a peak P (f) with a height above a certain value z shall be Pr[P (f) > z]. Then the probability that we found such a peak inspecting
450 G. Scholz et al.: Spectroscopic and photometric investigations of MAIA candidate stars The number of statistically independend frequencies N I is hardly to determine in the case of unevenly spaced data. Koen (1990) investigated FAPs following from the exponential and from the F -distribution with N I =N and with N I =N/2. Here we use the F -distribution with N I =N/2 which gives the largest FAP for a given number of data. N I =N/2 corresponds to the case of evenly spaced data, where the periodogram is developed in N/2 frequencies up to the Nyquist frequency f Ny =(2 t) 1 = N 1 2 T 1, (7) Fig. 1. Top: Time distribution of the Hipparcos photometry of ET And. Bottom: Window function of the data. all (statistically independent) frequencies in the periodogram is (see e.g. SC) F =1 (1 Pr[P (f) >z]) N I. (1) F is the so-called false-alarm probability (FAP hereinafter), and N I is the number of statistically independent frequencies included in the periodogram. As stated by SC, if many frequencies are inspected for a spectral peak, expect to find a large peak power even if no signal is present. Pr is determined by the density distribution p(x) valid for the concrete form of the periodogram used, it is z Pr[P (f) >z]=1 p(x) dx. (2) 0 For the Scargle periodogram in its normalized form (divided by the sample variance) SC and HB give an exponential density distribution, whereas Koen (1990) showed that p(x) can be better approximated by a F -distribution, especially in the case of a smaller number of data: p(x) = ( 1+ 2 x n 1 ) N+1 2. (3) We use a least squares fit by sine-waves and name our periodogram S-periodogram with P S (f) =1 s 2 (f)/s 2 0(f). (4) s 2 is the variance of the residuals of the least squares fit (reduced sum of squares) and s 2 0 is the sample variance. The equivalence of both methods, least squares fit and Scargle periodogram, was shown by SC. It is P scargle (f) = N 1 P S (f). (5) 2 where N is the number of data. From the F-distribution given by Koen we derive the FAP for the S-periodogram: ] F =1 [1 (1 + z) N 1 NI 2. (6) where t is the time interval between two equidistant time steps and T is the total time span of the sample, respectively. For unevenly spaced data there exists no definition of a Nyquist frequency. The periodogram can give valid information also at frequencies above N 1 2 T 1, however, as we will show for the Hipparcos photometry data. So, we tend to get an overestimation of the FAP, or an underestimation of the significance of our found periods, respectively. The total time span of the Hipparcos photometry for ET And is about T =1150 d, and within this time span there are N=161 data points (Fig. 1). If we calculate a Nyquist frequency in analogy to the evenly spaced case by Eq. 7, we get, with a mean separation of the data points of 7 ḍ 2, f Ny 0.07 cycles/d. The lower part of Fig. 1 shows the window function of the data. There is a repetition of the course of the window function at about 34 cycles/d (dashed lines), far beyond the calculated Nyquist frequency for the evenly spaced analogy. The window function shown in Fig. 1 is typical for the Hipparcos photometry of all of our target stars. We extend our period search up to 10 cycles/d, which is just below the frequency of the first sidelobe of the window function. We regard all periodograms containing peaks with heights above the FAP limit of 1% as significant for the occurrence of a periodicity in the data variation. The FAP alone does not allow for an estimation of the significance of one peak found at one special frequency, however. Only if the periodogram of the data pre-whitened for the period found (subtraction of the corresponding sinusoidal variation from the data) shows no more peaks higher than the assumed FAP limit, we regard the found period as significant. In all figures referring to the results of period searches, we give in the following section the phase diagrams folded with the found periods, the calculated optimized sinusoidal fit (which partly includes also the first harmonic) is drawn by a solid line, as well as the S-periodograms of the data together with the 1% FAP limit and the periodograms of the data pre-whitened for the found periods. To observe a sufficient frequency resolution - a problem especially valid for the Hipparcos data - the periodograms had been developed in up to 10 5 frequencies. In the figures we had then to reduce the resulting amount of data without smoothing sharp maxima. This was done be a repeated elimination of all local minima in the periodograms until there were less than 8 000 frequency points per diagram left. For one star (ET And) we find multiple frequencies. In this case we optimized the amplitude contributions and phases of
G. Scholz et al.: Spectroscopic and photometric investigations of MAIA candidate stars 451 Table 3. New orbital elements of the presumed Maia candidates of Table 1 HD 8441 P [d] 106.3334 ± 0.0041 γ [km/s] +10.15 ± 0.94 K [km/s] 27.65 ± 0.35 e 0.130 ± 0.014 T o 2403733.4 ± 1.9 ω [ ] 114.6 ± 5.9 rms [km/s] 0.88 2Lyn P [d] 20.8190 ± 0.0087 γ [km/s] 4.51 ± 0.94 K [km/s] 3.77 ± 0.33 e 0.367 ± 0.089 T o 2447959.50 ± 0.68 ω [ ] 8 ± 16 rms [km/s] 0.93 α Dra P [d] 51.4162 ± 0.0008 γ [km/s] 14.42 ± 0.98 K [km/s] 48.33 ± 0.37 e 0.4272 ± 0.056 T o 2442392.67 ± 0.15 ω [ ] 21.5 ± 1.1 rms [km/s] 1.7 ET And P [d] 48.3016 ± 0.0018 γ [km/s] +4.1 ± 1.3 K [km/s] 25.39 ± 0.47 e 0.498 ± 0.014 T o 2443716.4 ± 1.4 ω [ ] 67.1 ± 2.3 rms [km/s] 4.3 T o is the epoch of periastron passage all frequencies simultaneously, using a specially developed iterative procedure. Figures showing the results include then the variation for one of the found periods, pre-whitened for all of the other periods. 4. Spectroscopic and photometric results First we give two Tables containing the results of several candidate stars, as a list of new or re-calculated orbital elements of some binaries (Table 3), and a compilation of all periods found from the Hipparcos photometry (Table 4). The results will be included in the following discussion of the individual stars. The entire RVs will be available in the Journal of Astronomical Data, Lehmann et al. (1998). In the brightness diagrams shown in this discussion db represents the difference in B- magnitude (comparison star - object) and HJD the heliocentric Julian day. 4.1. Maia candidates without short-term variations In Table 5 we have collected the Maia candidates for which our investigations yield no significant changes on a short-time scale. The rms for the brightness of the Tauri stars correspond to our observations and the other ones are taken from Table 4. We Table 4. Results of period search in the Hipparcos photometry. The Table lists Hipparcos catalogue number, number N of data used for our period search and mean rms of the photometry calculated from the individual errors given in the catalogue. Beside the found periods P we give the corresponding half-amplitudes K. star HIP N rms P K [mmag] [d] [mmag] σ And 1473 101 4.1 - - HD 8441 6560 90 7.0 1.7237 10 2 Lyn 30060 83 4.3 0.236835 3 γ Gem 31681 33 3.0 - - θ Vir 64238 50 4.2 0.697384 8 α Dra 68756 110 3.4 - - γ UMi 75097 95 3.3 - - γ CrB 76952 116 3.8 0.445 5 21 Aql 94477 83 4.8 - - θ Peg 109427 63 3.3 - - 4 Lac 110609 147 4.7 - - ET And 115036 161 8.0 1.618767 7 0.103966 5 Table 5. Observed Maia candidates with constant behaviour. star RV rms rms [km/s] [km/s] [mmag] σ And 14.09 ± 0.36 4.1 21 Aql 5.51 ± 0.16 4.8 θ Peg 46.65 ± 0.81 3.3 γ Gem ± 1.00 3.0 23 Tau 5.0 27 Tau 5.0 28 Tau 5.0 observed these stars only at the beginning of our campaign. For details and the discussion of the results and the literature we refer to Lehmann et al. (1995). For σ And, 21 Aql and θ Peg we can conclude a constant behaviour of the RVs and give the mean values. A detailed description of the spectroscopic investigation of the binary star γ Gem can be found in Scholz et al. (1997). For all of the stars listed in Table 5, the photometric runs were too short to exclude possibly occurring temporal phases of brightness fluctuations as observed for some of the stars. So, McNamara (1987b) found for the listed Pleiades stars that the stars are variable. 23 Tau, e.g., exhibits a stable period of 0 ḍ 49 which was also confirmed by Balona (1990). 4.2. Maia candidates with short-term variations In this section we discuss the variations observed of the individual stars. Some results of the investigation of the Maia candidate stars have already been separately reported, and the remarks on those can therefore be confined here to the most important facts.
452 G. Scholz et al.: Spectroscopic and photometric investigations of MAIA candidate stars Fig. 2. Orbital solution for HD 8441. Fig. 4. Orbital solution for 2 Lyn. Fig. 3. Hipparcos photometry of HD 8441. Top: Phase diagram folded with the period of 1 ḍ 7237. Centre: Periodogram, the peak at 1 ḍ 7237 is more pronounced than the peak at 69 ḍ 69 favoured in the Hipparcos catalogue. Bottom: Periodogram after pre-whitening the data for the 1 ḍ 7237 period. In all periodograms the 1% false alarm probability limit is marked by a dashed line. 4.2.1. HD 8441 Only spectroscopic observations could be secured for HD 8441. There are no significant variations in the RV in the course of a run covering a time interval of more than 300 min. From eight spectra we get (-14.96 ± 0.16) km/s as the mean of the measured RV. According to Babcock (1957) the star should be a spectroscopic binary. Adding our values to Babcock s RVs we calculated for the first time the orbital elements noted in Table 3. Fig. 2 shows the corresponding orbital curve. In the Hipparcos catalogue a period of 69 ḍ 92 is listed, which, obviously, bears no relation with the binary period of 106 ḍ 33. Our period search within the Hipparcos data revealed a photometric period of 1 ḍ 7237. This period is slightly more pronounced than the 70 d period. Fig. 3 shows the results of the period search. After pre-whitening the data for the period found, no further periodicity is indicated. Considering the stellar parameters (Table 1) we can conclude that only the 1 ḍ 723 period can arise from the rotation of the star. If this is correct, HD 8441 Fig. 5. Hipparcos photometry of 2 Lyn, folded with the period of 0 ḍ 236835. Panels as in Fig. 3. is seen nearly pole-on and the 69 ḍ 92 period is probably an alias arising from the data sampling. 4.2.2. 2 Lyn (HD 43378, HR 2238) In our spectroscopic run covering 240 min the radial velocity was found to be constant, RV = (0.2 ± 0.6) km/s. Recently, Caliskan and Adelman (1997) have published some new RV measurements. Accordingly, the authors suggest that the star might be a spectroscopic binary. Combining their and our RVs (we omit other RVs because a correction to the IAU standard or an estimation of the accuracy seems not possible), we find three orbital solutions with periods of 21, 33 and 87 days. Here we give the solution for the 21 ḍ orbit (Table 3, Fig. 4). This is the orbital solution with the smallest residuals. Further observations to prove its validity are necessary, however. After pre-whitening the data for the binary motion, no further RV periodicity could be found. Our search in the Hipparcos photometry gives a variation with the period of 0 ḍ 237. The results of the period search are illustrated in Fig. 5.
G. Scholz et al.: Spectroscopic and photometric investigations of MAIA candidate stars 453 Fig. 6. Results of period search in the RV values of θ Vir. Top: Phase diagram folded with the period of 0 ḍ 0614. Bottom: Periodogram of the data (solid curve) and of the residuals after pre-whitening the data for the period found (dashed curve). The two straight dashed lines give the limits for 1% and for 5% false alarm probability, respectively. Table 6. Periods found in RV and photometry of θ Vir. data P [d] half amplitude RV 0.0614 0.4 km/s Hipparcos photometry 0.697384 8 mmag B (UBV photometry) 0.65785 100 mmag 4.2.3. θ Vir (HD 114330, HR 4963) The star is a spectroscopic binary, and provisional orbital elements have been derived by Beardsley and Zizka (1977). Apart from the radial velocity variation occurring from the orbital motion the authors found periodic velocity variations of 0 ḍ 15 raising the question of what type of pulsating star θ Vir might be. However, the short-period variation was present in all the observations made at the Allegheny Observatory during the time interval between 1962 and 1974. Because a later effort to confirm the short-period variation with another telescope and spectrograph did not give any changes of the expected kind (Wolff 1983), the period is very probably based on an instrumental effect. For our spectroscopic investigation we have observed the very sharp-lined star during a run of about 180 min, obtaining a sequence of 40 CCD spectra. The search for period gives a well defined period of 0 ḍ 0614 with an amplitude of 0.4 km/s, being of the same order as the error of the individual RV values (Fig. 6). But, further observations are necessary to prove finally this finding. Comparing our RV values with the ones expected from Beardsley and Zizka s orbital elements clear differences are apparent. Shobbrook et al. (1972) suspected θ Vir to be a photometric variable star with a period longer than one day. Recently Adelman (1997) carried out uvby photometry of θ Vir and concluded, that this star would not be variable. His individual data, how- Fig. 7. Hipparcos photometry of θ Vir, folded with the period of 0 ḍ 697384. Panels as in Fig. 3. ever, show remarkable scatter, which could possibly indicate real variations. In the Hipparcos data we find a period of 0 ḍ 7 which is perhaps a harmonic of the rotational period (Fig. 7 and Table 6). We have observed θ Vir photometrically in 1995, 1996, and 1997. As comparison and check star we used 21 Vir and HD 109722, respectively. The measurements seem to indicate a photometric variability on a time scale comparable to that found from the Hipparcos data. Fig. 8 shows the result of the period search. Because of the very broad window function we can only derive an approximated period of about 0 ḍ 66 (s. Table 6) taking the largest peak in the periodogram. After pre-whitening the data for this period the residuals give a periodogram with signals distinctly larger than the 1% false alarm probability limit. Since the periodogram is completely dominated by the 1 ḍ alias, we cannot find any further period, however. Although we observed a period comparable to the period found in the Hipparcos photometry we regard the large amplitude present in our UBV photometry with great caution. Assuming the indicated brightness variation would be real the nightly colours seem to show a variation, too. Taking into account the values V = 5.48 mag, (B V ) = -0.03 mag, and (U B) = -0.10 mag for the comparison star 21 Vir as given in the Bright Star Catalogue (Hoffleit & Warren 1991), we obtain the nightly colours of θ Vir, listed in Table 7. The large amplitude of the brightness variation which we see in the UBV data seems not to be compatible with the small variation of only some mmag present in the Hipparcos photometry. A possible explanation could be the existence of active and inactive phases, as is meanwhile known from other Maia candidate stars, especially from γ CrB. But, based on its negative declination the star has in our observations always an only small altitude over the horizon, which is usually insufficient for
454 G. Scholz et al.: Spectroscopic and photometric investigations of MAIA candidate stars Fig. 9. Top: Hipparcos photometry of γ UMi. A slight decrease in brightness of about 2 mmag/year can be seen. Bottom: Behaviour of γ UMi within one photometric run in B. Fig. 8. UBV photometry of θ Vir, B values folded with the period of 0 ḍ 65785. Panels as in Fig. 3. Table 7. Variable nightly mean colours of θ Vir. J.D. B V U B 2 440 000+ [mag] [mag] θ Vir 9830.35 0.027 ± 0.046 +0.036 ± 0.044 9834.34 0.034 ± 0.013 +0.007 ± 0.012 9835.31 0.026 ± 0.016 +0.005 ± 0.020 9836.29 0.021 ± 0.013 +0.004 ± 0.013 9864.33 0.028 ± 0.017 +0.014 ± 0.013 9865.34 0.040 ± 0.027 0.025 ± 0.034 10222.34 0.005 ± 0.006 0.035 ± 0.009 10593.35 +0.030 ± 0.012 0.011 ± 0.016 10601.34 +0.003 ± 0.007 0.025 ± 0.008 10602.35 0.030 ± 0.018 0.091 ± 0.017 accurate photometric measurements. Without a doubt further observations under optimal conditions are necessary. 4.2.4. α Dra (HD 123299, HR 5291) We have got only spectroscopic observations of this star. The chronological distribution of the RV observations is insufficient to prove a variability on time scales of hours. The few RV values obtained in the same night do not show variations which conspicuously deviate from the orbital motion. To check for this impression more precisely, we first calculated once more the orbital elements of α Dra adding to our old RV data 20 recently measured values from photographic spectra and 16 values from échelle spectra. The new elements are given in Table 3. A period analysis of the residuals of the RV, after subtracting the binary motion, gives no hint at the existence of periods on time scales of hours, and only a slight hint at the period of 3 ḍ 56, which was found in an earlier investigation by Lehmann & Scholz (1993). The reason is that the mean deviation of the RV residuals of 1.7 km/s has the same magnitude as the value of ±1.5 km/s, typical of the error of the photographic spectra. 4.2.5. γ UMi (HD 137422, HR 5735) The results of a period search with 125 photographic spectra and the analysis of earlier observations of other authors have been already published by Lehmann et al. (1995). The star pulsates with a fundamental period of about 0 ḍ 1 and a semi-amplitude of not quite 2 km/s. As in the case of γ CrB, the amplitude of the RV variations of γ UMi is not stable over a long time interval. In contrast to γ CrB, the small number of spectra of γ UMi does not allow us to derive a set of frequencies for the explanation of the presumed amplitude modulation. The light variation of γ UMi shows an irregular behaviour on a time scale of about 0 ḍ 14 and an amplitude smaller than 0.05 mag (Baker 1926, Meyer 1936, Baglin et al. 1973). Joshi et al. (1969) found nearly the same period and a repetition of the shape of the light curve after 21 cycles. In contrast to these findings Percy (1978) found no variation greater than 0.02 mag during a run of a single night. Our observational run reveals an increase of the brightness of 0.02 mag in the U,B, and V pass bands, as shown in Fig. 9. The change could be consistent with any period discussed. In addition to the irregular short-term changes, the Hipparcos data also show a long-term trend. 4.2.6. γ CrB (HD 140436, HR 5849) From a frequency analysis of 1490 spectra we have shown that the velocity of the star changes with at least three periods and in a manner quite similar to that of the neighbouring δ Scu stars. The results and a possible multiple frequency model describing our observational findings are discussed in Lehmann et al. (1997a). The period which dominates the RV-variations is 0 ḍ 445. The probable rotation period of the star is twice that period, or 0 ḍ 89,
G. Scholz et al.: Spectroscopic and photometric investigations of MAIA candidate stars 455 Fig. 11. Two colour diagram (nightly mean values) of γ CrB. Table 8. Variable nightly mean colours of γ CrB Fig. 10. Hipparcos photometry of γ CrB, folded with the period of 0 ḍ 445. Panels as in Fig. 3. and the observed short-term periods are arranged in a triplet around 0 ḍ 1. Our interpretation of the observed frequencies in terms of rotationally split nrp-modes is still valid, but we had to revise the deduced azimuthal quantum numbers through the existence of bumps observed in the line profiles from high-resolution spectra. These bumps traverse the line profiles with a crossing time of 0 ḍ 445. From the number of bumps seen in the profiles one can estimate that the intrinsic pulsation frequency is about 6 times the rotational frequency (Lehmann 1997b). A further nice confirmation of the proposed pulsation model we find now in the Hipparcos data. The period search clearly yields the value of 0 ḍ 445, as is shown in Fig. 10. During the twelve nights of our photometric observations we found from the averaged values of these runs that the colours change from +0.03 mag to -0.05 mag in (B V ) and from 0.00 mag to 0.07 mag in (U B). For the comparison star HD 138341 we took the values V = 6.46 mag, (B V )= 0.19 mag and (U B) = 0.14 mag as listed in the Bright Star Catalogue, from which we calculated the mean nightly magnitudes and colours for γ CrB (Table 8). Fig. 11 shows the path in the two-colour-diagram. In the diagram the star is moving across the main sequence. A similar behaviour is shown by some Be stars, e.g. φ Per. A period analysis of this variation gives a value of 25 d for all spectral regions with the largest amplitude of about 0.1 mag in the B pass band (Fig. 12). There is no phase shift between the variations in U,B, and V, but the amplitude of the variation in B is more than twice as large as the amplitudes in U and V. The periodograms of the UBV data are seriously influenced by the broad window function of the data and dominated by the 1 d aliasing. So the period of 25 d found from the periodograms in U, B, and V (Fig. 12), which was not previously observed, could also be feigned by the aliasing. We suppose that this pe- J.D. B V U B 2 440 000+ [mag] [mag] γ CrB 10222.40 +0.026 ± 0.005 0.001 ± 0.006 10225.37 +0.008 ± 0.011 +0.012 ± 0.020 10227.50 +0.001 ± 0.010 +0.025 ± 0.010 10228.46 0.008 ± 0.009 +0.030 ± 0.014 10231.40 0.050 ± 0.011 +0.065 ± 0.011 10593.46 0.053 ± 0.007 +0.065 ± 0.008 10596.47 +0.010 ± 0.009 +0.020 ± 0.007 10600.45 +0.069 ± 0.011 +0.019 ± 0.008 10601.43 +0.023 ± 0.015 +0.010 ± 0.007 10615.39 0.055 ± 0.009 +0.064 ± 0.007 10616.43 0.057 ± 0.004 +0.064 ± 0.005 10617.39 0.049 ± 0.004 +0.055 ± 0.008 riod is produced by underlying multiple frequencies which we cannot resolve because of the poor data sampling. In Lehmann et al. (1997a) we tried to estimate the spectral type of γ CrB from the parallaxe, the semi-major axis and the difference in magnitude of the binary. Now we can make use of the much more accurate data from the Hipparcos satellite: Π= (22.48 ± 0.67) mas, m = 1.56 ± 0.01. The semi-major axis of the orbit is 735 mas. Assuming a mass-luminosity exponent of 3.8, it follows that the masses are (2.4 ± 0.3)M for the primary and (1.7 ± 0.2)M for the secondary. The real errors of the derived masses may be somewhat larger, because we use here a statistical mean for the mass-luminosity exponent. But our assumption that γ CrB is an A0 main sequence star with a mass which does not exceed 3 solar masses is well confirmed. 4.2.7. 4 Lac (HD 212593, HR 8541) Altogether we have investigated 69 photographic spectra. We looked for periodic variations on time-scales of hours in 44 spectra, obtained on four nights. In each night a time period of about 270 min is covered. The results of the measurements are summarized in Table 9. N is the number of spectra. The RVs, determined from about 35 spectral lines, show a remarkable agreement between the individual series. In all spectra, the Ca ii lines 3933.7/3968.5 Å differ distinctly from all other lines measured. The simplest explanation of this finding could be an interstellar contribution in the measured Ca II RVs, but observations of high resolved spectral lines are necessary to answer
456 G. Scholz et al.: Spectroscopic and photometric investigations of MAIA candidate stars Fig. 14. Top: Orbital solution of ET And. Bottom: Periodogram of the entire data set indicating the 1 d alias of the rotation period at 0 ḍ 616. Table 10. Data sources for the orbital solution for ET And. Fig. 12. B magnitudes of γ CrB. Top: Phase diagram folded with the period of 25 ḍ 09. Center: Periodogram. For a better comparison with the window function it is extended to negative frequencies. Bottom: Window function of the data. author/instrument Number zero-point of RVs correction [km/s] Ondřejov 93 ±0.00 Haute Provence 16 0.76 Palmer 6 +0.48 Hube 26 0.28 Duflot 4 +3.55 Rozhen 113 4.20 Fig. 13. Photometric behaviour of 4 Lac in B Table 9. Radial velocity observations of 4 Lac run RV [km/s] RV [km/s] N mean Ca ii 1994 Sept. 23/24 28.31 ± 0.16 20.45 ± 0.28 10 1994 Sept. 24/25 28.10 ± 0.26 20.23 ± 0.25 16 1994 Sept. 25/26 28.63 ± 0.23 20.92 ± 0.29 11 1995 Oct. 10 24.31 ± 0.21 18.21 ± 0.46 7 this supposition. Moreover, a long-time variation seems to be present as the comparison of the runs in 1994 and 1995 shows. Our photometric observations obtained in Sept. 1993 and Sept. 1994 show no variations. This is in agreement with investigations by Harmanec et al. (1994) that repeated observations over several years give a stable reproduction of UBV magnitudes. Fig. 13 shows one of these runs in the B pass band. 4.2.8. ET And (HD 219749, HR 8861) We have already mentioned in the introduction the controversial statements concerning the existence of short-term RV variations. In an attempt to overcome the contradictions we first recalculate the orbital solution for ET And, combining all available RV data. To count for an eventual difference in the RV zero-points between the data of different authors, we developed a special reduction program. Starting with given initial values, the program calculates differential corrections to all of the orbital elements including the orbital period, and to a difference in the instrumental zero-points which is the same for all data from one author. The iterative procedure converges after about 4 to 5 cycles. Table 10 lists the sources of the data included and the corrections obtained (for the sending of a collection of the RVs we thank Dr. Žižňovský, 1993). Table 3 gives the new orbital elements, and Fig. 14 the orbital solution. The search for short-term periods in the residuals after subtracting the orbital solution from the RVs was carried out within the entire data set, the set of RVs containing alone the Rozhen values, and within four individual subsets of the Rozhen data each obtained in close time intervals of 1 to 3 nights. As a result we found one significant period of 0 ḍ 618105 in the entire data set, which is exactly the 1 d and 1 year alias of the known rotation period of ET And of 1 ḍ 61887, and the rotation period itself in one of the data subsets. We did not find any further significant short-term period in the RV values, however. Nevertheless, the large scatter of the residuals of the RVs after subtracting the orbital solution compared to the intrinsic accuracy of the Rozhen data of about 1 km/s lets us assume at least the existence of spontaneously occurring RV fluctuations.
G. Scholz et al.: Spectroscopic and photometric investigations of MAIA candidate stars 457 Table 11. Effective magnetic field strength and radial velocity of γ Gem, θ Vir,αDra, and 4 Lac Fig. 15. Phase diagrams of the Hipparcos photometry of ET And. Top: Folded with the rotation period of 1 ḍ 6188. Bottom: Residuals after subtracting the rotation period, folded with 0 ḍ 103966. HJD B eff RV 2 400 000+ [gauss] [km/s] γ Gem 50465.4666 +80 ± 150 14.10 ± 0.29 50465.5149 160 ± 160 13.40 ± 0.25 50466.4688 140 ± 70 11.86 ± 0.24 50494.3520 +130 ± 160 12.38 ± 0.34 θ Vir 50465.6864 +140 ± 150 4.68 ± 0.27 α Dra 50465.7229 140 ± 260 +46.15 ± 0.43 50466.7098 +150 ± 320 +33.60 ± 1.20 50470.7425 +450 ± 320 6.68 ± 0.73 4 Lac 46694.3559 270 ± 60 25.82 ± 0.41 46697.3979 +120 ± 80 26.54 ± 0.99 46698.4159 +210 ± 50 26.59 ± 0.59 46699.4055 +140 ± 50 26.38 ± 0.59 47078.4107 80 ± 80 25.43 ± 0.60 47083.3620 +320 ± 150 24.21 ± 0.89 47099.4738 +110 ± 140 23.47 ± 0.90 48490.5152 80 ± 200 25.61 ± 1.02 ing amplitude. ET And can be in fact a representative of the Maia stars, as was proposed for the first time by Kuschnig et al. (1990). 5. Magnetic fields Fig. 16. Periodograms for the Hipparcos photometry of ET And. Top: Original data indicating the rotation period of 1 ḍ 6188. Centre: Residuals after subtracting the rotation period showing a clear peak at 0 ḍ 103966. Bottom: Residuals after pre-whitening the data for both periods. About 15 years ago Panov (1978) and Hildebrandt (1981) reported on photometric observations with a variability of about 0 ḍ 1 which is superposed on the 1 ḍ 61887 variation caused by the rotation of this peculiar Si star. However, according to Kuschnig et al. (1994) and Breger (1995) the short-term variability should be attributed to the comparison star HD 219891. We have tested these remarks, on the one hand, by making further observations with another comparison star, and, on the other hand, by the investigation of the Hipparcos photometry. From the Hipparcos measurements, having no relation to any comparison star, we determine the periods of 1 ḍ 618767, which is unambiguously the rotation period, and of 0 ḍ 103966, which is quite near to the questionable pulsation period (Figs. 15 and 16). Accordingly, we now have no doubts that ET And pulsates with a period of about 150 min, but probably with a chang- In past for some Maia candidates the existence and the behaviour of a strong organized magnetic field have been discussed. Members of this group are the stars γ Gem (Scholz et al. (1997)), α Dra (Lehmann and Scholz (1993)), 4 Lac (Gerth (1988)) and ET And (Gerth and Bychkov (1994)). Because doubts exist about the reality of the findings we have made some polarimetric observations of these stars and the sharp-lined target star θ Vir. For the search of longitudinal magnetic fields at our disposal are spectroscopic observations made with a Zeeman analyzer as well as hydrogen magnetometer measurements. We obtained 8 photographic Zeeman spectra of 4 Lac at the coudé focus and furthermore, 11, 4, and 1 Zeeman échelle spectra of α Dra, γ Gem, and θ Vir with TRAFICOS at the Nasmyth focus of the 2 m telescope in Tautenburg, respectively. Additionally, 22 magnetometer measurements of ET And were taken at the 6 m telescope in Special Astrophysical Observatory Zelenchuk. Table 11 collects the values of the effective magnetic field B eff and the RVs, derived from about 35 metallic lines in each spectrogram of 4 Lac and γ Gem, about 10 lines of θ Vir and 5 lines of α Dra. The magnetometer values of B eff for ET And are listed in a paper by Gerth and Bychkov (1994). For γ Gem and θ Vir our results agree quite well with Landstreet s (1982) value B eff =( 165 ± 120) gauss for γ Gem and B eff =( 9 ± 30) gauss for θ Vir determined also by measurements of the circular polarization. Considering the data for B eff listed in Table 11, no evidence for the existence of a longitudinal magnetic field larger than about 150 gauss can be detected.
458 G. Scholz et al.: Spectroscopic and photometric investigations of MAIA candidate stars Our result about γ Gem disagrees with the assumption of a global magnetic field strength of nearly 2800 G estimated by Takada-Hidai and Jugaku (1993) using a theoretical relation between the strength of the magnetic field and the equivalent widths of the Fe II doublet at 6147.7/6149.2 Å underlying different magnetic intensification due to the partial Paschen-Back effect. Such a relation, based on empirical data and valid for a limited range of the magnetic field strength, was proposed by Mathys & Lanz (1992) and holds only for Ap stars. It is unsuitable for a search for global magnetic fields in normal stars. This aspect can be illustrated by our échelle Zeeman spectra of γ Gem. The equivalent widths of the two neighbouring Fe II lines we measured to be W (6147.7) = (46.9 ± 1.2) må and W (6149.2) = (41.4 ± 2.4) må. The equivalent widths noted are means of both Zeeman channels and of the four spectra, as we cannot find any systematic differences between these spectra. Using Mathys and Lanz s relation a global magnetic field of (3200 ± 1500) gauss follows, having nearly the same magnitude as the value estimated by Takada-Hidai and Jugaku. But this value is incompatible with the magnitude of B eff determined from the measurements of the circular polarization. Therefore, taking into account these findings, we conclude that γ Gem is probably a non- or a weakmagnetic star. From all CCD Zeeman spectra of α Dra we have determined the RV, but only a few spectra were used to check for the existence of a magnetic field. The spectra possess a quite insufficient S/N ratio, so that we note in Table 11 only the values of the longitudinal magnetic field derived from the three best spectrograms. At first sight the quoted result does not agree with the detection of a variable longitudinal magnetic field of the semi-amplitude of about 1500 gauss established by Lehmann and Scholz (1993) from photographic Zeeman spectra. However, considering also the other CCD spectra, in some of them we observe single lines with distinct displacements. Unfortunately, at the moment we are not able to give further details about the different behaviour of the spectral lines. For ET And the individual values of B eff, listed in a table by Gerth and Bychkov (1994), scatter remarkably in time intervals of minutes, both in the magnitude as well as in the polarity. The authors assumed that the errors of the single magnetic field values are distinctly smaller than their dispersion. After their period search they postulated the presence of three periods on time scales of several tens of minutes. But rather serious doubts exist concerning the significance of the derived periods: on the one hand, corresponding to our period search the most significant period gives a false alarm probability of about 50 % (the method for the determination of the significance is described by Lehmann et al. 1995 and in Sect. 3 of this paper), and on the other hand, no reasonable reason can be found to explain the extraordinary polarity reversal on time scales of minutes. Therefore, we prefer to interpret the unusual scattering of the data as a result produced by observational errors alone. In this case, the simple mean of B eff is (110 ± 240) gauss. Two observations by Bohlender et al. (1993) give similar values, namely for J.D. 2447394.7 B eff = (470 ± 470) gauss and for J.D. 2447395.8 B eff =( 380 ± 480) gauss so that at present no significant hint of the existence of a magnetic field for ET And exists. 6. Discussion The main result of this investigation is the confirmation that some A0 stars are able to pulsate with periods of hours. Our best studied example is the star γ CrB, for which we have unambiguously detected a multiple period behaviour. The rotational period of γ CrB is 0 ḍ 89 which is a fundamental period in the observed frequency set. All short-term periods are nearly multiples of this period. The observation of bumps traversing the line profiles with a crossing time of 0 ḍ 445 as well as the high v sini of 112 km/s support our assumption that these multiples are due to rotationally split modes of non-radial pulsation, and not due to surface inhomogeneities. The period of 0 ḍ 445 which dominates the RV-variation of γ CrB is also found in the brightness variation of the Hipparcos data. The period of 25 ḍ dominating the periodograms in UBV seems not to be in agreement with the predictions of the pulsational model of γ CrB. If we try to include yet this period in our frequency model it is necessary to assume a further short-term period of about 0 ḍ 16. Most remarkable would be then the ratio of the obtained 0 ḍ 89 (rotation) period to this short-term period. It is near to 6 as we predicted in Lehmann et al. (1997b) from the observation of the bumps for the intrinsic non-radial pulsation period of the star. Unfortunately, the poor data sampling of the photometric values does not allow to give a reliable statement. The present accuracy of its stellar parameters doubtless locates γ CrB in the pusational-free zone of the HRD expected hitherto between the borders of the 53 Per and the δ Scu stars. From our observations especially of γ CrB, and partially of γ UMi and ET And, we now know that pulsations in these stars can be detected only at definite times. This is certainly the main reason for the conflicting results found by different authors and for the enormous amount of observing time that is necessary to secure at least the reality of the existence of the pulsations. Furthermore, to establish the multi-frequency model of γ CrB, coordinated observations at two different longitudes (the Thüringer Landessternwarte Tautenburg and the Dominion Astrophysical Observatory, Lehmann et al. 1997a) were carried out. For the other stars the amplitudes of possibly existing RV variations must be smaller than the precision of our measurements, say about 1.5 km/s. A special case is obviously the star ET And considering the large scatter of the residuals of the RVs after subtracting the orbital motion. In this star different velocity variations could be present acting simultaneously with the binary motion and pulsation, as the velocity progression shows indicated in some earlier spectra investigated. Because the photometric amplitudes of the short-term variations have only few mmag for the discovery of light changes of this amplitude, observations with the very best meteorological conditions and from satellites are necessary.
G. Scholz et al.: Spectroscopic and photometric investigations of MAIA candidate stars 459 Restricted to our sample of stars, the results of our spectroscopic and photometric campaign confirm unambiguously the existence of occasional pulsations in our best-studied star γ CrB and there is strong evidence that pulsations exist also in γ UMi and ET And. But, the establishment of a special group of pulsational variables (the so-called Maia group) seems not to be justified, at present. If such a group would really exist the prototype could be then γ CrB and not the star Maia, where no pulsations have been detected. Acknowledgements. This work was essentially supported by the Deutsche Forschungsgemeinschaft, Aktenzeichen 436 BUL 113/72/0, and the Bulgarian Academy of Sciences. GS and GH thank the director of the Thüringer Landessternwarte, Prof. J. Solf, for the generous allocation of 2 m telescope time with our échelle Zeeman spectrograph TRAFICOS. The authors also thank the other participants in the observations. Here we name from Tautenburg the colleagues S. Klose and especially M. Woche, and from Rozhen Observatory D. Kolev, N. Tomov, and T.Tomov. Furthermore we thank E. Gerth for some spectrum reductions. The authors are also very grateful to Prof. J. Hearnshaw for his suggestions and the careful proofreading of the manuscript, and the referee, Dr. B.J. McNamara, for providing us with very useful comments. References Adelman S.J, 1997, A&AS 125, 497 Babcock H.W., 1957, ApJS 3, 141 Baglin A., Breger M., Chevalier C., Hauck B., le Contel J.P., Sareyan J.P., Valtier J.C., 1973, A&A 23, 221 Baker R.H., 1926, PASP 38, 86 Balona L.A., 1990, MNRAS 245, 92 Beardsley W.R., Zizka E.R., 1977, Rev. Mexicana de Astronomia y Astrofisica 3, 109 Bohlender D.A., Landstreet J.D., Thompson I.B., 1993, A&A 269, 355 Breger M., 1972, ApJ 176, 367 Breger M., 1995, in A.S.P. Conf. Series 83, 70 Caliskan H., Adelman S.J., 1997, MNRAS 288, 501 Gerth E., 1988, in Magnetic Stars, Publ. Spec. Astrophy. Obs., Zelenchuk, 78 Gerth E., Bychkov V.,D., 1994, in Chemically Peculiar and Magnetic Stars, Astron. Inst. Slovak Academy of Sciences, Tatranska Lomnica 1994, 40 Gerth E., Scholz G., Panov K.P., 1984, Astron. Nachr. 305, 79 Harmanec P., Horn J., Juza K., 1994, A&AS 104, 121 Hildebrandt G., 1981, in Magnetic Stars, Publ. Spec. Astrophys. Obs., Zelenchuk, 74 Hildebrandt G., Woche M., Scholz G., Rendtel J., Lehmann H., 1997, Astron. Nachr., 318, 291 Hoffleit D., Warren Jr W.H., 1991, The Bright Star Catalogue, 5th Revised Ed., Yale Univ. Obs. Joshi S.C., Gurtu S.K., Joshi M.C., 1969, Observatory 89, 112 The Hipparcos and Tycho Catalogues, Vol. 17, 1997, ESA SP-1200 Horne J. H., Baliunas S. L., 1986, ApJ 302, 757 Koen C., 1990, ApJ 348, 700 Kuschnig R., Weiss W.W., Piskunov N.E., Ryabchikova T.A., Kreidl T.J., Alvarez M., Bedolla S.G., Bus S.J., Guo Z., Hao J., Huang L., Kupka F., Le Contel D., Le Contel J.M., Osip D.J., Panov K.P., Polosukchina N.S., Sareyan J.P., Schneider H., Valtier J.C., Zboril M., Zižňovský J., Zverko J., 1994, in IAU Symp. No. 162: Pulsation, rotation and mass loss in early-type stars, 43 Kuschnig R., Weiss W.W., Kreidl T.J., et al., 1990, in A.S.P. Conf. Series 11, 348 Landstreet J.D., 1982, ApJ 258, 639 Lehmann H., Scholz G., 1993, in A.S.P. Conf. Series 44, 612 Lehmann H., Scholz G., Hildebrandt G., Klose S., Panov K.P., Reimann H.-G., Woche M., Ziener R., 1995, A&A 300, 783 Lehmann H., Scholz G., Hildebrandt G., 1996, A&A 312, 508 Lehmann H., Scholz G., Hildebrandt G., Yang S., 1997a, A&A 325, 529 Lehmann H., Scholz G., Yang S., Hildebrandt G., 1997b, in A half century of stellar pulsation interpretations, Los Alamos, A.S.P. Conf. Series, in press Lehmann H., Scholz G., Yang S., 1998, J. of Astron. Data, in press Mathys G., Lanz T., 1992, A&A 256, 169 Meyer E.J., 1936, Astron. Nachr. 259, 237 McNamara B.J., 1987a, in Stellar Pulsation, Lecture Notes in Physics, edts. A.N. Cox et al., Springer Berlin, 274, 92 McNamara B.J., 1987b, ApJ 312, 778 Panov K.P., 1978, Publ. Astron. Inst. Czechoslov. Acad. Sciences, No.54, 19 Percy J.R., 1978, PASP 90, 703 Piskunov N., Ryabchikova T.A., Kuschnig R., Weiss W.W., 1994, A&A 291, 910 Scargle J. D., 1982, ApJ 263, 835 Scholz G., Lehmann H., Harmanec P., Gerth E., Hildebrandt G., 1997, A&A 320, 791 Shobbrook R.R., Lomb N.R., Herbison-Evans E.D., 1972, MNRAS 156, 165 Struve O., 1955, Sky and Telescope, 14, 461 Takada-Hidai M., Jugaku J., 1993, A.S.P. Conf. Series 44, 310 Valtier J. C., 1972, A&A 16,38 Wolff S.C., 1983, in The A-type stars: problems and perspectives. NASA SP-463, p.29 Žižňovský J., 1993, priv. comm.