Astron. Astrophys. 337, 447–459 (1998) ASTRONOMYAND

ASTROPHYSICS

Spectroscopic and photometric investigationsof MAIA candidate stars?

G. Scholz1, H. Lehmann2, G. Hildebrandt1, K. Panov3, and L. Iliev3

1 Astrophysikalisches Institut Potsdam, Telegrafenberg A27, D-14473 Potsdam, Germany (gscholz@aip.de, ghildebrandt@aip.de)2 Thuringer 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 theHipparcos photometry data, we investigate the radial velocityand brightness of suspected Maia variable stars which are clas-sified also in some examples as peculiar stars, mainly for theexistence of periodic variations with time-scales of hours. Theresults lead to the following conclusions:(1) Short-term radial velocity variations have been unambigu-ously proved for the A0 V starγ CrB and the A2 III starγ UMi.The stars pulsate in an irregular manner. Moreover,γ CrB showsa multiperiod structure quite similar to some of the best-studiedneighbouringδ Scu stars.(2) In the Hipparcos photometry as well as in our photometricruns we find significant short- and long-term variations in thestars HD 8441, 2 Lyn,θ Vir, γ UMi, andγ CrB. For ET And theHipparcos data confirm a short-period variation found alreadyearlier. Furthermore, we find changes of the colour index inθ Virandγ 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 be-haviour of our two best-investigated starsγ CrB andγ UMi istypical for pulsations in this region of the Hertzsprung-Russelldiagram, our observational runs are too short and the accuracyof the measurements too low to exclude such pulsations in theother stars, however.(4) The radial velocities of the binariesα Dra and ET And havebeen further used for a recalculation of the orbital elements. ForHD 8441 and 2 Lyn we estimated the orbital elements for thefirst time.(5) Zeeman observations of the starsγ Gem,θ Vir, α Dra, 4 Lac,and ET And give no evidence of the presence of longitudinalmagnetic 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 Thuringer Landessternwarte Tautenburg, Germany, and with the2 m telescope of the National Astronomical Observatory Rozhen, Bul-garia. For photometric investigations we used the 0.6 m telescope atRozhen and the Hipparcos and Tycho catalogues.

1. Introduction

Pulsations are a widespread phenomenon in early-type starsalong and near the main sequence. But in a small region of theHertzsprung-Russell diagram (HRD), bordered by theδ Scutistars and the slowly pulsating B stars (often named as 53 Perseistars), which are located on the cool side of theβ Cephei strip,stellar pulsations seem to be absent.

In the fifties Struve (1955) suggested that a sequence ofvariables with spectral and luminosity types between B7V-IIIand A2V-II might exist having periods of about 0.d1 to 0.d3.He called this group of stars ”Maia” stars after the presumedprototype Maia in the Pleiades. If the existence of such a groupof variables would be real then these variables would to a largeextent occupy the pulsational free zone between the 53 Per andtheδ Scu stars and pulsational variability would be then a moreor less common characteristic of stars located in the upper regionof the HRD down to the hot border of theδ Scuti instability strip.

Beginning already with Struve himself (later he found nei-ther a light nor a velocity variability in Maia), a long-lastingdispute occurred about the existence of the Maia stars as an au-tonomous class of variable stars. A compilation of the pros andcons of observational results related to the hypothetical Maiastars 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.d1(Panov 1978). But, after recent comments (Kuschnig et al. 1994,Breger 1995) the photometric variability should be due to thecomparison star used. If this statement is true, not a single starwould be known to pulsate in brightness with a period smallerthan about 0.d28 (28 Tau) in the domain of the HRD where theMaia stars should be expected.

Concerning the radial velocities of ET And the results arealso controversial. Gerth et al. (1984) during an observationalcampaign in 1981 at Rozhen Observatory found radial velocitychanges with a period of about 0.d2 and a semi-amplitude ofabout 4 km/s, whereas observations made in 1990 at the Obser-vatoire de Haute-Provence (Piskunov et al. 1994) do not confirmother radial velocity variations than those occurring from binarymotion 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) mv NS comparison check JD NP ttype [km/s] [mag] star star 2400000+ [min]

σ And 1404 A2V 110 4.6 19 θ And no 49621.50 77 15049623.50 64 150

8441 A2V 10 6.7 1423 Tau 23480 B6IV 250 4.2 20 Tau no 49621.60 32 80

49623.58 51 10049627.56 33 60

27 Tau 23850 B8III 200 3.6 20 Tau no 49253.52 15 14049254.54 12 9049256.52 18 120

28 Tau 23862 B8V 340 5.0 20 Tau no 49253.52 14 9049254.53 12 9049256.52 14 150

2 Lyn 43378 A2V 35 4.5 20γ Gem 47105 A0IV 10 1.9 148θ Vir 114330 A2V 10 4.4 43 21 Vir HD 109722 49830.35 47 120

49834.34 17 6049835.31 44 10049836.29 62 17049864.33 35 9049865.34 47 12050222.34 31 10050593.35 32 10050601.34 18 7050602.35 6 20

α Dra 123299 A0III 30 3.6 76γ UMi 137422 A2III 165 3.0 125 142105 no 49252.27 13 80γ CrB 140436 A0V 100 3.8 1490 138341 HD 136849 50222.40 165 270

50225.37 50 10050227.50 96 18050228.46 25 4050231.40 29 6050593.46 21 6050596.47 81 17050600.45 71 16050601.43 89 21050615.39 25 4550616.43 15 2750617.39 12 20

21 Aql 179761 B8III 20 5.1 17 179343 no 49255.25 27 12049620.26 25 16049621.27 74 130

θ Peg 210418 A2V 130 3.5 9 214923 no 49623.28 77 1804 Lac 212593 B9II 20 4.6 69 6 Lac 2 Lac 49252.38 16 70

49256.40 20 7049259.41 28 12049619.41 16 4049620.35 60 9049621.37 97 150

2 Lac 49623.38 77 15049624.34 62 9049627.40 52 90

ET And 219749 B9IV 80 6.3 34 219891 HD 219397 49253.30 75 27049624.51 30 180

219397 50322.55 27 10050358.45 69 23050360.45 79 26050388.35 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 than0.7 km/s.

Similar distinct discrepancies are also described in spectro-scopic and photometric observations of other presumed Maiastars. Probably, these differences have to be accepted becausethe errors indicated in the individual findings do not admit seri-ous doubts about the reality of the results published.

In the present paper we summarize our observations and in-vestigations of hypothetical Maia stars. For some stars the obser-vational results have already been discussed earlier (Lehmannet al., 1995, 1996, 1997). Here we complete these findings andinclude the results following from the Hipparcos photometry.

2. Observations and reductions

2.1. Spectroscopic and photometric observations

The photographic spectroscopic observations were performedwith the coude spectrographs of the 2 m telescopes of theKarl-Schwarzschild-Observatory at Tautenburg and of the Na-tional Astronomical Observatory Rozhen. The spectrogramsfrom Tautenburg were partially obtained with a Zeeman an-alyzer. Radial velocities (RV hereinafter) and magnetic fieldswere measured by a computer-controlled Abbe comparator us-ing lines in the spectral region between 3800 to 4800A. Addi-tionally, CCD observations were obtained at Tautenburg withthe coude spectrograph and with theechelle spectrograph andZeeman analyzer ’TRAFICOS’ (Hildebrandt et al. 1997) at-tached at the Nasmyth focus. CCD spectra have been reducedunder MIDAS with a specially developed reduction package.Because of the very different S/N ratio the error of a RV valueof a single line, possessing a line width equivalent to about80 km/s, is for the photographic plate about 3 km/s and for aCCD spectrogram 0.6 km/s. In the case that the RV correspondto the mean of several lines the errors are about 1 and 0.3 km/s,respectively.

The photometric observations were obtained with the 60 cmtelescope of the Rozhen Observatory using a set ofUBV fil-ters and an EMI 9789QB photomultiplier. Generally, the meanerror in the various colours of the photometric measurementsis about 0.005 to 0.006 magnitudes. In some cases the obser-vations include a check star as well as a comparison star. Ifonly a comparison star is used this one is very probably con-stant because no hint on the existence of brightness variationsis indicated in the literature. Further supplementary details ofthe observational parameters can be found in Lehmann et al.(1995).

Information on the stars investigated and the observing log isgiven in Table 1. Most columns are self-explanatory.NS andNPgive the number of the spectra and the number of the photometricmeasurements included in the run, respectively.t is the total timeinterval 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 (BT ,VT ) pho-tometric systems.λmax, λ1/2 give central wavelength and lower/upperwavelength at FWHM,4m give the accuracy for the mean value mea-sured on constant stars withmV ∼ 8 mag.

H BT VT

λmax [nm] 452 435 505λ1/2 [nm] 394 - 615 384 - 455 475 - 5714m [mmag] 1.5 12 12

epochs was acquired for all objects in the Hipparcos Catalogue(obtained by the main mission detector), and two-colour pho-tometry for nearly all objects in the Tycho Catalogue (obtainedby the star mapper detector). Whereas the Tycho data representJohnsonB andV magnitudes, the Hipparcos main instrumentobserved in a broad-band system in order to optimise the astro-metric signal. Although the photometry obtained with this sys-tem is limited in its astrophysical content, the precision of eachobservation is much higher than that of the Tycho Cataloguedata. Table 2 lists some basic photometric properties as givenin the Introduction to the Hipparcos and Tycho Catalogues. Adetailed explanation can be found there.

First, we investigated both the Hipparcos and the Tychophotometric data. Although the Tycho data include many morevalues, the photometric accuracy turns out to be not sufficientto find any periodic variation within our sample.

Fig. 1 shows the typical time distribution of the Hipparcosdata for the example star ET And. There are 161 data pointsspread over 1150 d, the largest continous data group contains35 measurements within 2 days. The data distribution shown inFig. 1 is typical for all of our target stars. Also the time intervalof observation is about the same. The window function shownin the lower part will be discussed in detail in the followingsection.

The Hipparcos catalogue lists only two of our target starsas variable - it gives the rotation period of ET And,Prot =1.d61891, and a period for HD 8441,P = 69.d92, which is pos-sibly an alias. Our period search in the Hipparcos photometryyields a periodic brightness variation for five of the stars. Ta-ble 4 lists the data sets used for our target stars as well as theresults of period searches.

3. Period searches

Basic considerations on the significance of periods derived byusual period finding techniques for unevenly spaced data can befound in Scargle (1982, SC) or in Horne & Baliunas (1986, HB).We consider here the Scargle periodogram and the least squaresfit by sine-waves (Valtier 1972, Lehmann et al. 1995). If weinspect one single frequencyf in a periodogram which containsno signal, the statistical probability that we found there a peakP (f) with a height above a certain valuez shall bePr[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

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])NI . (1)

F is the so-called false-alarm probability (FAP hereinafter), andNI is the number of statistically independent frequencies in-cluded in the periodogram. As stated by SC, if many frequen-cies are inspected for a spectral peak, expect to find a largepeak power even if no signal is present.Pr is determined bythe density distributionp(x) valid for the concrete form of theperiodogram used, it is

Pr[P (f) > z] = 1 −z∫

0

p(x) dx. (2)

For the Scargle periodogram in its normalized form (divided bythe sample variance) SC and HB give an exponential densitydistribution, whereas Koen (1990) showed thatp(x) can be bet-ter approximated by aF -distribution, especially in the case ofa smaller number of data:

p(x) =(

1 +2 x

n − 1

)− N+12

. (3)

We use a least squares fit by sine-waves and name our peri-odogram S-periodogram with

PS(f) = 1 − s2(f)/s20(f). (4)

s2 is the variance of the residuals of the least squares fit (reducedsum of squares) ands2

0 is the sample variance. The equivalenceof both methods, least squares fit and Scargle periodogram, wasshown by SC. It is

Pscargle(f) =N − 1

2PS(f). (5)

whereN is the number of data. From the F-distribution givenby Koen we derive the FAP for the S-periodogram:

F = 1 −[1 − (1 + z)− N−1

2

]NI

. (6)

The number of statistically independend frequenciesNI ishardly to determine in the case of unevenly spaced data. Koen(1990) investigated FAPs following from the exponential andfrom theF -distribution withNI=N and withNI=N/2. Herewe use theF -distribution withNI=N/2 which gives the largestFAP for a given number of data.NI=N/2 corresponds to thecase of evenly spaced data, where the periodogram is developedin N/2 frequencies up to the Nyquist frequency

fNy=(24t)−1 = N−12 T−1, (7)

where4t is the time interval between two equidistant timesteps andT is the total time span of the sample, respectively.For unevenly spaced data there exists no definition of a Nyquistfrequency. The periodogram can give valid information also atfrequencies aboveN−1

2 T−1, however, as we will show for theHipparcos photometry data. So, we tend to get an overestimationof the FAP, or an underestimation of the significance of our foundperiods, respectively.

The total time span of the Hipparcos photometry for ET Andis aboutT=1150 d, and within this time span there areN=161data points (Fig. 1). If we calculate a Nyquist frequency in anal-ogy to the evenly spaced case by Eq. 7, we get, with a meanseparation of the data points of 7.d2, fNy ∼ 0.07 cycles/d. Thelower part of Fig. 1 shows the window function of the data. Thereis a repetition of the course of the window function at about 34cycles/d (dashed lines), far beyond the calculated Nyquist fre-quency for the evenly spaced analogy. The window functionshown in Fig. 1 is typical for the Hipparcos photometry of all ofour target stars. We extend our period search up to 10 cycles/d,which is just below the frequency of the first sidelobe of thewindow function.

We regard all periodograms containing peaks with heightsabove the FAP limit of 1% as significant for the occurrence ofa periodicity in the data variation. The FAP alone does not al-low for an estimation of the significance of one peak found atone special frequency, however. Only if the periodogram of thedata pre-whitened for the period found (subtraction of the cor-responding sinusoidal variation from the data) shows no morepeaks higher than the assumed FAP limit, we regard the foundperiod as significant.

In all figures referring to the results of period searches, wegive in the following section the phase diagrams folded with thefound periods, the calculated optimized sinusoidal fit (whichpartly 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 forthe found periods. To observe a sufficient frequency resolution- a problem especially valid for the Hipparcos data - the pe-riodograms had been developed in up to105 frequencies. Inthe figures we had then to reduce the resulting amount of datawithout smoothing sharp maxima. This was done be a repeatedelimination of all local minima in the periodograms until therewere less than 8 000 frequency points per diagram left.

For one star (ET And) we find multiple frequencies. In thiscase 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 ofTable 1

HD 8441 P [d] 106.3334 ± 0.0041γ [km/s] +10.15 ± 0.94K [km/s] 27.65 ± 0.35e 0.130 ± 0.014To 2403733.4 ± 1.9ω [◦] 114.6 ± 5.9rms [km/s] 0.88

2 Lyn P [d] 20.8190 ± 0.0087γ [km/s] −4.51 ± 0.94K [km/s] 3.77 ± 0.33e 0.367 ± 0.089To 2447959.50 ± 0.68ω [◦] 8 ± 16rms [km/s] 0.93

α Dra P [d] 51.4162 ± 0.0008γ [km/s] −14.42 ± 0.98K [km/s] 48.33 ± 0.37e 0.4272 ± 0.056To 2442392.67 ± 0.15ω [◦] 21.5 ± 1.1rms [km/s] 1.7

ET And P [d] 48.3016 ± 0.0018γ [km/s] +4.1 ± 1.3K [km/s] 25.39 ± 0.47e 0.498 ± 0.014To 2443716.4 ± 1.4ω [◦] 67.1 ± 2.3rms [km/s] 4.3

To is the epoch of periastron passage

all frequencies simultaneously, using a specially developed it-erative procedure. Figures showing the results include then thevariation for one of the found periods, pre-whitened for all ofthe other periods.

4. Spectroscopic and photometric results

First we give two Tables containing the results of several can-didate stars, as a list of new or re-calculated orbital elements ofsome binaries (Table 3), and a compilation of all periods foundfrom the Hipparcos photometry (Table 4). The results will beincluded in the following discussion of the individual stars.

The entire RVs will be available in the Journal of Astronom-ical Data, Lehmann et al. (1998). In the brightness diagramsshown in this discussion dB represents the difference inB-magnitude (comparison star - object) and HJD the heliocentricJulian day.

4.1. Maia candidates without short-term variations

In Table 5 we have collected the Maia candidates for which ourinvestigations yield no significant changes on a short-time scale.The rms for the brightness of the Tauri stars correspond to ourobservations and the other ones are taken from Table 4. We

Table 4. Results of period search in the Hipparcos photometry. TheTable lists Hipparcos catalogue number, numberN of data used forour period search and mean rms of the photometry calculated from theindividual errors given in the catalogue. Beside the found periodsPwe give the corresponding half-amplitudesK.

star HIP N rms P K[mmag] [d] [mmag]

σ And 1473 101 4.1 - -HD 8441 6560 90 7.0 1.7237 102 Lyn 30060 83 4.3 0.236835 3γ Gem 31681 33 3.0 - -θ Vir 64238 50 4.2 0.697384 8α Dra 68756 110 3.4 - -γ UMi 75097 95 3.3 - -γ CrB 76952 116 3.8 0.445 521 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 4.121 Aql −5.51 ± 0.16 4.8θ Peg −46.65 ± 0.81 3.3γ Gem − ± 1.00 3.023 Tau − − 5.027 Tau − − 5.028 Tau − − 5.0

observed these stars only at the beginning of our campaign. Fordetails and the discussion of the results and the literature werefer to Lehmann et al. (1995). Forσ And, 21 Aql andθ Peg wecan conclude a constant behaviour of the RVs and give the meanvalues. A detailed description of the spectroscopic investigationof the binary starγ Gem can be found in Scholz et al. (1997).

For all of the stars listed in Table 5, the photometric runswere too short to exclude possibly occurring temporal phasesof brightness fluctuations as observed for some of the stars. So,McNamara (1987b) found for the listed Pleiades stars that thestars are variable. 23 Tau, e.g., exhibits a stable period of 0.d49which was also confirmed by Balona (1990).

4.2. Maia candidates with short-term variations

In this section we discuss the variations observed of the individ-ual stars. Some results of the investigation of the Maia candidatestars have already been separately reported, and the remarks onthose 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. 3. Hipparcos photometry of HD 8441.Top: Phase diagram foldedwith the period of 1.d7237.Centre: Periodogram, the peak at 1.d7237is more pronounced than the peak at 69.d69 favoured in the Hipparcoscatalogue.Bottom: Periodogram after pre-whitening the data for the1.d7237 period. In all periodograms the 1% false alarm probability limitis 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 arun covering a time interval of more than 300 min. From eightspectra we get (-14.96± 0.16) km/s as the mean of the measuredRV.

According to Babcock (1957) the star should be a spectro-scopic binary. Adding our values to Babcock’s RVs we calcu-lated 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.d92 is listed, which,obviously, bears no relation with the binary period of 106.d33.Our period search within the Hipparcos data revealed a pho-tometric period of 1.d7237. This period is slightly more pro-nounced than the 70 d period. Fig. 3 shows the results of the pe-riod search. After pre-whitening the data for the period found,no further periodicity is indicated. Considering the stellar pa-rameters (Table 1) we can conclude that only the 1.d723 periodcan arise from the rotation of the star. If this is correct, HD 8441

Fig. 4. Orbital solution for 2 Lyn.

Fig. 5. Hipparcos photometry of 2 Lyn, folded with the period of0.d236835. Panels as in Fig. 3.

is seen nearly pole-on and the 69.d92 period is probably an aliasarising from the data sampling.

4.2.2. 2 Lyn (HD 43378, HR 2238)

In our spectroscopic run covering 240 min the radial velocitywas found to be constant, RV = (0.2± 0.6) km/s. Recently,Caliskan and Adelman (1997) have published some new RVmeasurements. Accordingly, the authors suggest that the starmight be a spectroscopic binary. Combining their and our RVs(we omit other RVs because a correction to the IAU standard oran estimation of the accuracy seems not possible), we find threeorbital solutions with periods of 21, 33 and 87 days. Here wegive the solution for the 21.d orbit (Table 3, Fig. 4). This is theorbital solution with the smallest residuals. Further observationsto prove its validity are necessary, however. After pre-whiteningthe data for the binary motion, no further RV periodicity couldbe found.

Our search in the Hipparcos photometry gives a variationwith the period of 0.d237. The results of the period search areillustrated 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 ofθ Vir. Top: Phasediagram folded with the period of 0.d0614.Bottom: Periodogram ofthe data (solid curve) and of the residuals after pre-whitening the datafor the period found (dashed curve). The two straight dashed lines givethe limits for 1% and for 5% false alarm probability, respectively.

Table 6. Periods found in RV and photometry ofθ Vir.

data P [d] half amplitudeRV 0.0614 0.4 km/sHipparcos 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 ele-ments have been derived by Beardsley and Zizka (1977). Apartfrom the radial velocity variation occurring from the orbitalmotion the authors found periodic velocity variations of 0.d15raising the question of what type of pulsating starθ Vir might be.However, the short-period variation was present in all the ob-servations made at the Allegheny Observatory during the timeinterval between 1962 and 1974. Because a later effort to con-firm the short-period variation with another telescope and spec-trograph did not give any changes of the expected kind (Wolff1983), the period is very probably based on an instrumentaleffect.

For our spectroscopic investigation we have observed thevery sharp-lined star during a run of about 180 min, obtaininga sequence of 40 CCD spectra. The search for period gives awell defined period of 0.d0614 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 finallythis finding. Comparing our RV values with the ones expectedfrom Beardsley and Zizka’s orbital elements clear differencesare apparent.

Shobbrook et al. (1972) suspectedθ Vir to be a photometricvariable star with a period longer than one day. Recently Adel-man (1997) carried out uvby photometry ofθ Vir and concluded,that this star would not be variable. His individual data, how-

Fig. 7. Hipparcos photometry ofθ Vir, folded with the period of0.d697384. Panels as in Fig. 3.

ever, show remarkable scatter, which could possibly indicatereal variations.

In the Hipparcos data we find a period of 0.d7 which is per-haps a harmonic of the rotational period (Fig. 7 and Table 6).

We have observedθ Vir photometrically in 1995, 1996,and 1997. As comparison and check star we used 21 Vir andHD 109722, respectively. The measurements seem to indicate aphotometric variability on a time scale comparable to that foundfrom the Hipparcos data. Fig. 8 shows the result of the periodsearch. Because of the very broad window function we can onlyderive an approximated period of about 0.d66 (s. Table 6) takingthe largest peak in the periodogram. After pre-whitening thedata for this period the residuals give a periodogram with sig-nals distinctly larger than the 1% false alarm probability limit.Since the periodogram is completely dominated by the 1.d alias,we cannot find any further period, however. Although we ob-served a period comparable to the period found in the Hippar-cos photometry we regard the large amplitude present in ourUBV photometry with great caution.

Assuming the indicated brightness variation would be realthe nightly colours seem to show a variation, too. Taking intoaccount the valuesV = 5.48 mag, (B − V ) = -0.03 mag, and(U − B) = -0.10 mag for the comparison star 21 Vir as given inthe Bright Star Catalogue (Hoffleit & Warren 1991), we obtainthe nightly colours ofθ Vir, listed in Table 7.

The large amplitude of the brightness variation which wesee in theUBV data seems not to be compatible with the smallvariation of only some mmag present in the Hipparcos photom-etry. A possible explanation could be the existence of activeand inactive phases, as is meanwhile known from other Maiacandidate stars, especially fromγ CrB. But, based on its nega-tive declination the star has in our observations always an onlysmall altitude over the horizon, which is usually insufficient for

454 G. Scholz et al.: Spectroscopic and photometric investigations of MAIA candidate stars

Fig. 8. UBV photometry ofθ Vir, B values folded with the period of0.d65785. Panels as in Fig. 3.

Table 7.Variable nightly mean colours ofθ Vir.

J.D. B − V U − B2 440 000+ [mag] [mag]

θ Vir 9830.35 −0.027± 0.046 +0.036± 0.0449834.34 −0.034± 0.013 +0.007± 0.0129835.31 −0.026± 0.016 +0.005± 0.0209836.29 −0.021± 0.013 +0.004± 0.0139864.33 −0.028± 0.017 +0.014± 0.0139865.34 −0.040± 0.027 −0.025± 0.034

10222.34 −0.005± 0.006 −0.035± 0.00910593.35 +0.030± 0.012 −0.011± 0.01610601.34 +0.003± 0.007 −0.025± 0.00810602.35 −0.030± 0.018 −0.091± 0.017

accurate photometric measurements. Without a doubt furtherobservations under optimal conditions are necessary.

4.2.4.α Dra (HD 123299, HR 5291)

We have got only spectroscopic observations of this star. Thechronological distribution of the RV observations is insufficientto prove a variability on time scales of hours. The few RV valuesobtained in the same night do not show variations which con-spicuously deviate from the orbital motion. To check for thisimpression more precisely, we first calculated once more theorbital elements ofα Dra adding to our old RV data 20 recentlymeasured values from photographic spectra and 16 values fromechelle spectra. The new elements are given in Table 3. A periodanalysis of the residuals of the RV, after subtracting the binarymotion, gives no hint at the existence of periods on time scalesof hours, and only a slight hint at the period of 3.d56, which was

Fig. 9. Top: Hipparcos photometry ofγ UMi. A slight decrease inbrightness of about 2 mmag/year can be seen.Bottom: Behaviour ofγ UMi within one photometric run inB.

found in an earlier investigation by Lehmann & Scholz (1993).The reason is that the mean deviation of the RV residuals of1.7 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 andthe analysis of earlier observations of other authors have beenalready published by Lehmann et al. (1995). The star pulsateswith a fundamental period of about 0.d1 and a semi-amplitudeof not quite 2 km/s. As in the case ofγ CrB, the amplitude of theRV variations ofγ UMi is not stable over a long time interval.In contrast toγ CrB, the small number of spectra ofγ UMi doesnot allow us to derive a set of frequencies for the explanation ofthe presumed amplitude modulation.

The light variation ofγ UMi shows an irregular behaviouron a time scale of about 0.d14 and an amplitude smaller than0.05 mag (Baker 1926, Meyer 1936, Baglin et al. 1973). Joshiet al. (1969) found nearly the same period and a repetition ofthe shape of the light curve after 21 cycles. In contrast to thesefindings Percy (1978) found no variation greater than 0.02 magduring a run of a single night.

Our observational run reveals an increase of the brightnessof 0.02 mag in theU ,B, andV pass bands, as shown in Fig. 9.The change could be consistent with any period discussed. Inaddition to the irregular short-term changes, the Hipparcos dataalso show a long-term trend.

4.2.6.γ CrB (HD 140436, HR 5849)

From a frequency analysis of 1490 spectra we have shown thatthe velocity of the star changes with at least three periods and in amanner quite similar to that of the neighbouringδ Scu stars. Theresults and a possible multiple frequency model describing ourobservational findings are discussed in Lehmann et al. (1997a).The period which dominates the RV-variations is 0.d445. Theprobable rotation period of the star is twice that period, or 0.d89,

G. Scholz et al.: Spectroscopic and photometric investigations of MAIA candidate stars 455

Fig. 10. Hipparcos photometry ofγ CrB, folded with the period of0.d445. Panels as in Fig. 3.

and the observed short-term periods are arranged in a tripletaround 0.d1.

Our interpretation of the observed frequencies in terms ofrotationally split nrp-modes is still valid, but we had to revisethe deduced azimuthal quantum numbers through the existenceof ’bumps’ observed in the line profiles from high-resolutionspectra. These bumps traverse the line profiles with a crossingtime of 0.d445. From the number of bumps seen in the profilesone can estimate that the intrinsic pulsation frequency is about6 times the rotational frequency (Lehmann 1997b).

A further nice confirmation of the proposed pulsation modelwe find now in the Hipparcos data. The period search clearlyyields the value of 0.d445, as is shown in Fig. 10.

During the twelve nights of our photometric observations wefound from the averaged values of these runs that the colourschange from +0.03 mag to -0.05 mag in(B − V ) and from0.00 mag to 0.07 mag in(U − B). For the comparison starHD 138341 we took the valuesV = 6.46 mag, (B − V ) =0.19 mag and (U−B) = 0.14 mag as listed in the Bright Star Cat-alogue, from which we calculated the mean nightly magnitudesand colours forγ CrB (Table 8). Fig. 11 shows the path in thetwo-colour-diagram. In the diagram the star is moving acrossthe main sequence. A similar behaviour is shown by some Bestars, e.g.φ Per. A period analysis of this variation gives a valueof 25 d for all spectral regions with the largest amplitude ofabout 0.1 mag in theB pass band (Fig. 12). There is no phaseshift between the variations inU ,B, andV , but the amplitude ofthe variation inB is more than twice as large as the amplitudesin U andV .

The periodograms of theUBV data are seriously influencedby the broad window function of the data and dominated by the1 d aliasing. So the period of 25 d found from the periodogramsin U , B, andV (Fig. 12), which was not previously observed,could also be feigned by the aliasing. We suppose that this pe-

Fig. 11. Two colour diagram (nightly mean values) ofγ CrB.

Table 8.Variable nightly mean colours ofγ CrB

J.D. B − V U − B2 440 000+ [mag] [mag]

γ CrB 10222.40 +0.026± 0.005 −0.001± 0.00610225.37 +0.008± 0.011 +0.012± 0.02010227.50 +0.001± 0.010 +0.025± 0.01010228.46 −0.008± 0.009 +0.030± 0.01410231.40 −0.050± 0.011 +0.065± 0.01110593.46 −0.053± 0.007 +0.065± 0.00810596.47 +0.010± 0.009 +0.020± 0.00710600.45 +0.069± 0.011 +0.019± 0.00810601.43 +0.023± 0.015 +0.010± 0.00710615.39 −0.055± 0.009 +0.064± 0.00710616.43 −0.057± 0.004 +0.064± 0.00510617.39 −0.049± 0.004 +0.055± 0.008

riod is produced by underlying multiple frequencies which wecannot resolve because of the poor data sampling.

In Lehmann et al. (1997a) we tried to estimate the spectraltype ofγ CrB from the parallaxe, the semi-major axis and thedifference in magnitude of the binary. Now we can make use ofthe much more accurate data from the Hipparcos satellite:Π =(22.48 ± 0.67) mas,4m = 1.56 ± 0.01. The semi-major axisof the orbit is 735 mas. Assuming a mass-luminosity exponentof 3.8, it follows that the masses are(2.4 ± 0.3)M� for theprimary and(1.7 ± 0.2)M� for the secondary. The real errorsof the derived masses may be somewhat larger, because we usehere a statistical mean for the mass-luminosity exponent. Butour assumption thatγ CrB is an A0 main sequence star with amass 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. Welooked for periodic variations on time-scales of hours in 44spectra, obtained on four nights. In each night a time periodof about 270 min is covered. The results of the measurementsare summarized in Table 9.N is the number of spectra. TheRVs, determined from about 35 spectral lines, show a remark-able agreement between the individual series. In all spectra, theCaii lines 3933.7/3968.5A differ distinctly from all other linesmeasured. The simplest explanation of this finding could be aninterstellar contribution in the measured Ca II RVs, but obser-vations of high resolved spectral lines are necessary to answer

456 G. Scholz et al.: Spectroscopic and photometric investigations of MAIA candidate stars

Fig. 12. B magnitudes ofγ CrB. Top: Phase diagram folded withthe period of 25.d09. Center: Periodogram. For a better comparisonwith the window function it is extended to negative frequencies.Bot-tom: Window function of the data.

Fig. 13. Photometric behaviour of 4 Lac inB

Table 9.Radial velocity observations of 4 Lac

run RV [km/s] RV [km/s] Nmean Caii

1994 Sept. 23/24 −28.31± 0.16 −20.45± 0.28 101994 Sept. 24/25 −28.10± 0.26 −20.23± 0.25 161994 Sept. 25/26 −28.63± 0.23 −20.92± 0.29 111995 Oct. 10 −24.31± 0.21 −18.21± 0.46 7

this supposition. Moreover, a long-time variation seems to bepresent as the comparison of the runs in 1994 and 1995 shows.

Our photometric observations obtained in Sept. 1993 andSept. 1994 show no variations. This is in agreement with inves-tigations by Harmanec et al. (1994) that repeated observationsover several years give a stable reproduction ofUBV magni-tudes. 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 controver-sial statements concerning the existence of short-term RV vari-ations. In an attempt to overcome the contradictions we first

Fig. 14. Top:Orbital solution of ET And.Bottom: Periodogram of theentire data set indicating the 1 d alias of the rotation period at 0.d616.

Table 10. Data sources for the orbital solution for ET And.

author/instrument Number zero-pointof RVs correction [km/s]

Ondrejov 93 ±0.00Haute Provence 16 −0.76Palmer 6 +0.48Hube 26 −0.28Duflot 4 +3.55Rozhen 113 −4.20

recalculate the orbital solution for ET And, combining all avail-able RV data. To count for an eventual difference in the RVzero-points between the data of different authors, we developeda special reduction program. Starting with given initial values,the program calculates differential corrections to all of the or-bital elements including the orbital period, and to a difference inthe instrumental zero-points which is the same for all data fromone author. The iterative procedure converges after about 4 to5 cycles. Table 10 lists the sources of the data included and thecorrections obtained (for the sending of a collection of the RVswe thank Dr.Ziznovsky, 1993). Table 3 gives the new orbitalelements, and Fig. 14 the orbital solution.

The search for short-term periods in the residuals after sub-tracting the orbital solution from the RVs was carried out withinthe entire data set, the set of RVs containing alone the Rozhenvalues, and within four individual subsets of the Rozhen dataeach obtained in close time intervals of 1 to 3 nights. As a resultwe found one significant period of 0.d618105 in the entire dataset, which is exactly the 1 d and 1 year alias of the known rota-tion period of ET And of 1.d61887, and the rotation period itselfin one of the data subsets. We did not find any further significantshort-term period in the RV values, however. Nevertheless, thelarge scatter of the residuals of the RVs after subtracting the or-bital solution compared to the intrinsic accuracy of the Rozhendata of about 1 km/s lets us assume at least the existence ofspontaneously occurring RV fluctuations.

G. Scholz et al.: Spectroscopic and photometric investigations of MAIA candidate stars 457

Fig. 15. Phase diagrams of the Hipparcos photometry of ET And.Top: Folded with the rotation period of 1.d6188.Bottom: Residualsafter subtracting the rotation period, folded with 0.d103966.

Fig. 16. Periodograms for the Hipparcos photometry of ET And.Top: Original data indicating the rotation period of 1.d6188. Cen-tre: Residuals after subtracting the rotation period showing a clearpeak at 0.d103966.Bottom: Residuals after pre-whitening the data forboth periods.

About 15 years ago Panov (1978) and Hildebrandt (1981)reported on photometric observations with a variability of about0.d1 which is superposed on the 1.d61887 variation caused by therotation of this peculiar Si star. However, according to Kuschniget al. (1994) and Breger (1995) the short-term variability shouldbe attributed to the comparison star HD 219891. We have testedthese remarks, on the one hand, by making further observationswith another comparison star, and, on the other hand, by theinvestigation of the Hipparcos photometry.

From the Hipparcos measurements, having no relation toany comparison star, we determine the periods of 1.d618767,which is unambiguously the rotation period, and of 0.d103966,which is quite near to the questionable pulsation period (Figs. 15and 16). Accordingly, we now have no doubts that ET And pul-sates with a period of about 150 min, but probably with a chang-

Table 11. Effective magnetic field strength and radial velocity ofγ Gem,θ Vir , α Dra, and 4 Lac

HJD Beff RV2 400 000+ [gauss] [km/s]

γ Gem 50465.4666 +80± 150 −14.10± 0.2950465.5149 −160± 160 −13.40± 0.2550466.4688 −140± 70 −11.86± 0.2450494.3520 +130± 160 −12.38± 0.34

θ Vir 50465.6864 +140± 150 −4.68± 0.27α Dra 50465.7229 −140± 260 +46.15± 0.43

50466.7098 +150± 320 +33.60± 1.2050470.7425 +450± 320 −6.68± 0.73

4 Lac 46694.3559 −270± 60 −25.82± 0.4146697.3979 +120± 80 −26.54± 0.9946698.4159 +210± 50 −26.59± 0.5946699.4055 +140± 50 −26.38± 0.5947078.4107 −80± 80 −25.43± 0.6047083.3620 +320± 150 −24.21± 0.8947099.4738 +110± 140 −23.47± 0.9048490.5152 −80± 200 −25.61± 1.02

ing amplitude. ET And can be in fact a representative of theMaia stars, as was proposed for the first time by Kuschnig et al.(1990).

5. Magnetic fields

In past for some Maia candidates the existence and the behaviourof a strong organized magnetic field have been discussed. Mem-bers of this group are the starsγ Gem (Scholz et al. (1997)),α Dra (Lehmann and Scholz (1993)), 4 Lac (Gerth (1988)) andET And (Gerth and Bychkov (1994)). Because doubts existabout the reality of the findings we have made some polari-metric observations of these stars and the sharp-lined target starθ Vir.

For the search of longitudinal magnetic fields at our disposalare spectroscopic observations made with a Zeeman analyzer aswell as hydrogen magnetometer measurements. We obtained8 photographic Zeeman spectra of 4 Lac at the coude focusand furthermore, 11, 4, and 1 Zeemanechelle spectra ofα Dra,γ Gem, andθ Vir with ’TRAFICOS’ at the Nasmyth focus ofthe 2 m telescope in Tautenburg, respectively. Additionally, 22magnetometer measurements of ET And were taken at the 6 mtelescope in Special Astrophysical Observatory Zelenchuk. Ta-ble 11 collects the values of the effective magnetic fieldBeff andthe RVs, derived from about 35 metallic lines in each spectro-gram of 4 Lac andγ Gem, about 10 lines ofθ Vir and 5 lines ofα Dra. The magnetometer values ofBeff for ET And are listedin a paper by Gerth and Bychkov (1994).

Forγ Gem andθ Vir our results agree quite well with Land-street’s (1982) valueBeff = (−165± 120) gauss forγ Gem andBeff = (−9 ± 30) gauss forθ Vir determined also by measure-ments of the circular polarization. Considering the data forBefflisted in Table 11, no evidence for the existence of a longitudinalmagnetic field larger than about 150 gauss can be detected.

458 G. Scholz et al.: Spectroscopic and photometric investigations of MAIA candidate stars

Our result aboutγ Gem disagrees with the assumption ofa global magnetic field strength of nearly 2800 G estimated byTakada-Hidai and Jugaku (1993) using a theoretical relationbetween the strength of the magnetic field and the equivalentwidths of the Fe II doublet at 6147.7/6149.2A underlying dif-ferent magnetic intensification due to the partial Paschen-Backeffect. Such a relation, based on empirical data and valid for alimited range of the magnetic field strength, was proposed byMathys & Lanz (1992) and holds only for Ap stars. It is un-suitable for a search for global magnetic fields in normal stars.This aspect can be illustrated by ourechelle Zeeman spectra ofγ Gem.

The equivalent widths of the two neighbouring Fe II lineswe measured to beW (6147.7) = (46.9± 1.2) mA andW (6149.2) = (41.4± 2.4) mA.The equivalent widths noted are means of both Zeeman chan-nels and of the four spectra, as we cannot find any systematicdifferences between these spectra. Using Mathys and Lanz’s re-lation a global magnetic field of (3200± 1500) gauss follows,having nearly the same magnitude as the value estimated byTakada-Hidai and Jugaku. But this value is incompatible withthe magnitude ofBeff determined from the measurements ofthe circular polarization. Therefore, taking into account thesefindings, we conclude thatγ Gem is probably a non- or a weak-magnetic star.

From all CCD Zeeman spectra ofα Dra we have determinedthe RV, but only a few spectra were used to check for the exis-tence of a magnetic field. The spectra possess a quite insufficientS/N ratio, so that we note in Table 11 only the values of the longi-tudinal magnetic field derived from the three best spectrograms.At first sight the quoted result does not agree with the detectionof a variable longitudinal magnetic field of the semi-amplitudeof about 1500 gauss established by Lehmann and Scholz (1993)from photographic Zeeman spectra. However, considering alsothe other CCD spectra, in some of them we observe single lineswith distinct displacements. Unfortunately, at the moment weare not able to give further details about the different behaviourof the spectral lines.

For ET And the individual values ofBeff , listed in a tableby Gerth and Bychkov (1994), scatter remarkably in time inter-vals of minutes, both in the magnitude as well as in the polarity.The authors assumed that the errors of the single magnetic fieldvalues are distinctly smaller than their dispersion. After theirperiod search they postulated the presence of three periods ontime scales of several tens of minutes. But rather serious doubtsexist concerning the significance of the derived periods: on theone hand, corresponding to our period search the ”most signif-icant” period gives a false alarm probability of about 50 % (themethod for the determination of the significance is described byLehmann et al. 1995 and in Sect. 3 of this paper), and on the otherhand, no reasonable reason can be found to explain the extraor-dinary polarity reversal on time scales of minutes. Therefore,we prefer to interpret the unusual scattering of the data as aresult produced by observational errors alone. In this case, thesimple mean ofBeff is (110± 240) gauss. Two observations

by Bohlender et al. (1993) give similar values, namely for J.D.2447394.7Beff = (470 ± 470) gauss and for J.D. 2447395.8Beff = (−380± 480) gauss so that at present no significant hintof the existence of a magnetic field for ET And exists.

6. Discussion

The main result of this investigation is the confirmation thatsome A0 stars are able to pulsate with periods of hours. Ourbest studied example is the starγ CrB, for which we have unam-biguously detected a multiple period behaviour. The rotationalperiod ofγ CrB is 0.d89 which is a fundamental period in theobserved frequency set. All short-term periods are nearly multi-ples of this period. The observation of bumps traversing the lineprofiles with a crossing time of 0.d445 as well as the highv·siniof 112 km/s support our assumption that these multiples are dueto rotationally split modes of non-radial pulsation, and not dueto surface inhomogeneities. The period of 0.d445 which domi-nates the RV-variation ofγ CrB is also found in the brightnessvariation of the Hipparcos data. The period of 25.d dominatingthe periodograms inUBV seems not to be in agreement withthe predictions of the pulsational model ofγ CrB. If we try toinclude yet this period in our frequency model it is necessaryto assume a further short-term period of about 0.d16. Most re-markable would be then the ratio of the obtained 0.d89 (rotation)period to this short-term period. It is near to 6 as we predictedin Lehmann et al. (1997b) from the observation of the bumpsfor the intrinsic non-radial pulsation period of the star. Unfor-tunately, the poor data sampling of the photometric values doesnot allow to give a reliable statement.

The present accuracy of its stellar parameters doubtless lo-catesγ CrB in the pusational-free zone of the HRD expectedhitherto between the borders of the 53 Per and theδ Scu stars.

From our observations especially ofγ CrB, and partiallyof γ UMi and ET And, we now know that pulsations in thesestars can be detected only at definite times. This is certainlythe main reason for the conflicting results found by differentauthors and for the enormous amount of observing time thatis necessary to secure at least the reality of the existence of thepulsations. Furthermore, to establish the multi-frequency modelof γ CrB, coordinated observations at two different longitudes(the Thuringer Landessternwarte Tautenburg and the DominionAstrophysical Observatory, Lehmann et al. 1997a) were carriedout.

For the other stars the amplitudes of possibly existing RVvariations must be smaller than the precision of our measure-ments, say about 1.5 km/s. A special case is obviously the starET And considering the large scatter of the residuals of the RVsafter subtracting the orbital motion. In this star different veloc-ity variations could be present acting simultaneously with thebinary motion and pulsation, as the velocity progression showsindicated in some earlier spectra investigated.

Because the photometric amplitudes of the short-term vari-ations have only few mmag for the discovery of light changes ofthis amplitude, observations with the very best meteorologicalconditions 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 spec-troscopic and photometric campaign confirm unambiguouslythe existence of occasional pulsations in our best-studied starγ CrB and there is strong evidence that pulsations exist also inγ UMi and ET And. But, the establishment of a special groupof pulsational variables (the so-called Maia group) seems notto be justified, at present. If such a group would really exist theprototype could be thenγ CrB and not the star Maia, where nopulsations have been detected.

Acknowledgements.This work was essentially supported by theDeutsche Forschungsgemeinschaft, Aktenzeichen 436 BUL 113/72/0, and the Bulgarian Academy of Sciences. GS and GH thank the direc-tor of the Thuringer Landessternwarte, Prof. J. Solf, for the generousallocation of 2 m telescope time with ourechelle Zeeman spectrograph’TRAFICOS’. The authors also thank the other participants in the ob-servations. Here we name from Tautenburg the colleagues S. Klose andespecially M. Woche, and from Rozhen Observatory D. Kolev, N. To-mov, and T.Tomov. Furthermore we thank E. Gerth for some spectrumreductions. The authors are also very grateful to Prof. J. Hearnshawfor his suggestions and the careful proofreading of the manuscript,and the referee, Dr. B.J. McNamara, for providing us with very usefulcomments.

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