another search for maia variable stars

Another Search for Maia Variable StarsAuthor(s): John R. Percy and Joseph B. WilsonSource: Publications of the Astronomical Society of the Pacific, Vol. 112, No. 772 (June 2000),pp. 846-851Published by: The University of Chicago Press on behalf of the Astronomical Society of the PacificStable URL: http://www.jstor.org/stable/10.1086/316577 .

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PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF THE PACIFIC, 112 :846È851, 2000 June2000. The Astronomical Society of the PaciÐc. All rights reserved. Printed in U.S.A.(

Another Search for Maia Variable Stars

JOHN R. PERCY AND JOSEPH B. WILSON

Erindale Campus, and Department of Astronomy, University of Toronto, Mississauga, ON L5L 1C6, Canada ;jpercy=erin.utoronto.ca, joseph.wilson=utoronto.ca

Received 1999 October 6 ; accepted 2000 February 17

ABSTRACT. We have used the Hipparcos epoch photometry database, and autocorrelation analysis, tosearch for the elusive Maia variablesÈshort-period B7ÈA3 nearÈmain-sequence pulsating variable stars. Ofseveral hundred stars considered, and several dozen stars studied in detail, only a handful are possiblevariables : three are possible shallow eclipsing variables ; three have possible periods in the range 0.25È0.5day, but their amplitudes are so low that they are probably nonvariable. The most promising are HD 29573,with a period of 1.6 days (but possibly a rotating variable), and c CrB, with a period of 0.9 dayÈa period alsofound spectroscopically by Lehmann and coworkers. Sirius shows variations which are probably instrumen-tal. Two previously suspected Maia starsÈMaia and c UMiÈare photometrically constant. The MaiavariablesÈif they existÈare very rare and very elusive.

1. INTRODUCTION

The Maia variable stars were proposed by Struve (1955)as a ““ hypothetical ÏÏ group of variable B7ÈA3 stars, near themain sequence, with small amplitudes and periods of a fewhours. The apparent variability of the two original pro-posed members of the group (Maia and c UMi) was prob-ably largely instrumental in nature, and the proposedtimescale of a few hours was the timescale of the obser-vations. If the variability of the proposed Maia stars wasintrinsic and pulsational, thenÈby analogy with the knownradially pulsating b Cephei (B0ÈB3) and d Scuti (A7ÈF2)variablesÈperiods of a few hours might have beenexpected. Over the years, several suspected variables wereattributed to this class, but no concrete evidence of variabil-ity had been found up to the 1980s (McNamara 1987). Bythe 1990s, nonradial pulsation with periods of up to a dayor more had been found in the slowly pulsating B stars(mid-B) and c Doradus stars (mid-F), so intrinsic pulsa-tional variability with periods of a day or more might bepossible in the proposed Maia stars. Lehmann et al. (1995,1996, 1997, 1998) have revived interest in this class ; in alarger spectroscopic survey, they have reported short-termspectroscopic variations in two starsÈc CrB (A0 V) andc UMi (A3 III).

The identiÐcation of possible Maia variables is compli-cated by the presence of other types of variables in the sameregion of the H-R diagram. The peculiar A (Ap) stars arerotating variables with periods of 0.5 day and higher. Therapidly oscillating Ap (roAp) stars are a subset of thesewhich pulsate with periods of a few minutes. The slowly

pulsating B (SPB) stars are nonradially pulsating mid-Bstars with periods of 0.5È2 days. The d Scuti stars are pulsa-ting A7ÈF2 stars with periods of 1 to several hours. Thec Doradus stars are nonradially pulsating F0ÈF5 stars withperiods of about a day. There are also eclipsing and ellip-soidal variables of all spectral types, with periods of 0.5 dayor more. We would therefore deÐne the ““ hypothetical ÏÏMaia stars to be radial or nonradial pulsators with spectraltypes B7ÈA3, near the main sequence, but which were notSPB, d Scuti, or c Doradus stars. According to stellar pulsa-tion theory, there is no reason to expect a separate class ofpulsating variable stars with spectral types B7ÈA3Èthoughthis should obviously not deter observers from looking. Ifsuch a group of variables actually exists, then it is up totheoreticians to explain them.

The present study was carried out because of the avail-ability of the Hipparcos catalog of astrometry and epochphotometry (Perryman et al. 1997).1 The epoch photometryhas a time distribution which is inconvenient for some pro-jects but convenient for this oneÈthere are measurementsevery 20 minutes or so for several hoursÈsometimes up toa day or more. There may then be gaps of 20È30 days. TheHipparcos photometric system is broadband, covering theJohnson B and V and more.

Scholz et al. (1998) have recently published a com-prehensive photometric and spectroscopic analysis of a

ÈÈÈÈÈÈÈÈÈÈÈÈÈÈÈ1 The Hipparcos and Tycho Catalogues are available at the Hipparcos

Space Astrometry Mission Web site (http ://astro.estec.esa.nl/Hipparcos/hipparcos.html).

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SEARCH FOR MAIA VARIABLE STARS 847

sample of 14 possible Maia stars. They used both ground-based and Hipparcos photometry and photographic andCCD spectra. Our initial sample of stars was much larger,and our main method of analysis was autocorrelationanalysis, which we believe is better suited to the time dis-tribution of the Hipparcos photometric data than is Fourieranalysis. The two studies are therefore complementary.

2. SAMPLE OF STARS

We have examined the short-term (0.02È1 day or more)variability of stars in several samples of B7ÈA3 nearÈmain-sequence stars using the Hipparcos epoch photometry : (1)stars from the Ph.D. thesis of Gray (1986), which gavedetailed spectral classiÐcations of several hundred suchstars ; (2) stars chosen directly from the Hipparcos databasethrough the Celestia 2000 software (ESA SP-1220) orthrough the Hipparcos Web site ; (3) stars chosen from thePh.D. thesis of Winzer (1974), which was a comprehensivestudy of the photometric variability of a large sample of Apstars ; and (4) stars chosen from the literature. About 500stars in total were examined on the Hipparcos Web site ;about 60 with variability Ñags M (microvariable) or U(unsolved) were analyzed using autocorrelation analysis ; ofthese, there were 12 which were previously suspected ofbeing Maia stars and/or for which the results looked prom-ising. These are described in ° 4. The spectral types are fromGray (1986).

3. METHODS

The initial assessment of variability was based on anyvariability Ñags in the Hipparcos catalog (Perryman et al.1997) and on the scatter of the Hipparcos measurements(column 46 in the Hipparcos catalog). The mean error ofindividual measurements varies from 0.0029 at magnitude 3to 0.0058 at magnitude 6 (Perryman et al. 1997), which is therange of brightness of our program stars ; these numbers areconsistent with the mean *m values in our autocorrelationdiagrams as *t approaches zero. The primary methods ofanalysis were (1) short-term light curves using the Hipparcosepoch photometry and (2) autocorrelation analysis (Percy,Ralli, & Sen 1993) over time intervals of up to 1 day.

Autocorrelation detects characteristic timescales of varia-bility, even if the variability is not periodic. It measures theaverage absolute di†erence in magnitude of measurementstaken *t days apart. Typically, 50È200 *t ““ bins ÏÏ arechosen, from zero to the maximum timescale expected inthe star (or the maximum *t in the data, as in the presentstudy). Characteristic timescales in the measurements showup as minima in the autocorrelation diagram (Percy et al.

1993). For stars such as the hypothetical Maia stars whichare expected to have timescales of up to a day or two, theshort groups of Hipparcos measurements can be used. Thelong gaps between the groups are not a problem as theywould be in Fourier analysis (Scholz et al. 1998) because, toconstruct the autocorrelation diagrams, only pairs of mea-surements within the same groups are used. With thismethod, it is not possible to look for timescales greater thanthe length of the groups of measurements because there areno pairs of measurements with *t values in this range. Inautocorrelation analysis, there are no ““ alias ÏÏ periods asthere are in Fourier analysis, but there are minima at mul-tiples (P, 2P, 3P, etc.) of the basic period. Unfortunately, it isdifficult to assess the statistical signiÐcance of any minimumin the autocorrelation diagram because of the variablenumber of points in each bin.

The autocorrelation method has been used in a study ofthe short-term and long-term photometric variability of theBe star NW Ser using ground-based and Hipparcos data(Percy et al. 1999) and in a study of short-term variability ofB-type eclipsing binaries using Hipparcos data (Percy &Au-Yong 2000).

4. RESULTS

HIP 16083 (HD 21364, m T au, B9 IV n).ÈThis object hasa scatter of only 0.004, but the long-term light curve (Fig. 1)shows several instances when the star is up to 0.1 fainterthan normal. This suggests that it may be a shallow eclips-ing variable. According to the Y ale Catalogue of BrightStars (Hoffleit 1982), this star is ““ a triple spectroscopicsystem of two sharp-lined stars revolving in 7.1466 days ;this pair revolves in 145.10 days around a broad-lined B7star. ÏÏ The interval between the Ðrst two deepest minima is19.00 cycles of the 7.1466 day period and 0.94 cycle of the145.10 day period. The interval between the second twodeepest minima is 29.50 cycles of the 7.1466 day period and

FIG. 1.ÈLong-term Hipparcos light curve of HIP 16083 (m Tau)showing occasional fadings which suggest that this star may be a shalloweclipsing binary.

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848 PERCY & WILSON

FIG. 2.ÈAutocorrelation diagram for Hipparcos photometry of HIP17573 (Maia) ; there is no evidence for minima greater than 0.001.

1.45 cycles of the 145.10 day period. These results are con-sistent with eclipses of the 7.1466 day system. The star is notlisted in Batten, Fletcher, & McCarthyÏs (1989) catalog ofspectroscopic binaries.

HIP 17573 (HD 23408, HR 1149, 20 T au, Maia,B7 III).ÈThis object has a low scatter (0.003), as do theother bright Pleiads 17 Tau (0.004), 19 Tau (0.004), 23 Tau(0.005), 25 Tau (0.004), and 27 Tau (0.006). The autocorrela-tion diagram is Ñat to within 0.001 mag (Fig. 2). We con-sider this star to be photometrically constant.

HIP 21644 (HD 29573, HR 1483, A2 IV ÈV ).ÈThis objectshows a scatter of 0.012. The autocorrelation diagram (Fig.3) has minima at 1.6 and 3È4 days. This suggests that thisstar is a low-level variable with a period of about 1.6 days ;recall that the autocorrelation method produces minima atmultiples of the basic period. This period is consistent withthe short-term light curves. It could be a rotating (Ap) vari-able ; Gray (1986) classiÐes the spectrum as normal, butthere are Ap-type variables whose spectral peculiarities aremarginal (Winzer 1974). Alternatively, it could be a non-radial pulsator, in which case we would deÐne it as a Maia

FIG. 3.ÈAutocorrelation diagram for Hipparcos photometry of HIP21644 (HR 1483). Note the minima at about 1.6 and 3.2 days, whichsuggest a period of 1.6 days.

FIG. 4.ÈHipparcos light curve of HIP 30675 (HR 2328), showing apossible fading into a shallow eclipse.

star. It is not possible to distinguish between the rotationaland pulsational hypothesis with the data which are avail-able. The star is, however, variable.

HIP 30675 (HD 45380, HR 2328, B9 V an).ÈThis objecthas a scatter of 0.014. There is no evidence in the autocor-relation diagram for timescales from 0 to 3 days ; the curverises smoothly from 0.008 to 0.012 with no minima in thisrange. However, in the light curve there are instances (e.g.,Fig. 4) when the star appears to be entering or exiting ashallow (0.05 mag) eclipse ; this star may be a shallow eclips-ing binary. On the other hand, there is no other evidence forthis suggestion. The star is not listed as a spectroscopicbinary by Batten et al. (1989) or Hoffleit (1982).

HIP 32349 (HD 48915, HR 2491, a CMa, Sirius, A0mA1V a).ÈThis object shows a large scatter ; the autocorrelationdiagram shows a minimum at 4 days ; the light curve showsvariations of several hundredths of a magnitude on thistimescale. The baseline scatter in the autocorrelationdiagram (as *t approaches zero) is 0.02, however, whichsuggests that the variability is instrumental and due to theexceptional brightness of the star.

HIP 45526 (HD 79931, HR 3683, 24 Hya, B8.5 III).ÈThis object shows a scatter of only 0.005 ; the autocorrela-tion diagram has a number of gaps ; the evidence forvariability is marginal at best.

HIP 54682 (HD 97277, HR 4343, b Crt, A2 IV ).ÈThisobject shows a scatter of only 0.005, but the autocorrelationdiagram (Fig. 5) shows evidence of minima at 0.4 and 0.9day, which suggests that there may be a period of 0.4È0.5day with an amplitude of 0.01 mag (recall that the autocor-relation method gives minima at multiples of the basicperiod). The light curve (Fig. 6) is consistent with variabilityon this timescale, but the variability is small and irregular.Assuming that the variability is real, it is not possible todetermine its nature from the present data.

HIP 71762 (HD 129174, HR 5475, n Boo, B9 III~ HgMnmetallic lines).ÈThis object shows a scatter of 0.005, and theautocorrelation diagram is Ñat from 0 to 0.5 day, but there

2000 PASP, 112 :846È851




FIG. 5.ÈAutocorrelation diagram for Hipparcos photometry of HIP54682 (b Crt). Note the minima at about 0.4 and 0.9 day, which suggest apossible period of 0.4È0.5 day. The amplitude, however, is very small, andthe variability is therefore uncertain.

are a few measurements which are a few hundredths of amagnitude fainter than normal, so there is a slight chancethat this star is a shallow eclipsing binary. On the otherhand, the Bright Star Catalogue (Hoffleit 1982) lists this staras an HgMn star with a spectroscopic (line strength) periodof 2.2445 days, so the photometric variability may be con-nected with this presumably rotational period.

HIP 75097 (HD 137422, HR 5735, c UMi, A3 III).ÈThisobject is a suspected Maia star. It has a scatter of only 0.004.Lehmann et al. (1995) reported spectroscopic variations ona timescale of 0.1 day. The autocorrelation diagram is Ñat towithin 0.001 mag, on a timescale of 0.0È0.2 day ; the star isphotometrically nonvariable on these timescales. Longerterm variations are not ruled out by our analysis, becausethe lengths of the groups of Hipparcos measurements are 0.2day or less. The scatter in the short-term light curves isconsistent with the observational error.

HIP 76952 (HD 140436, HR 5849, c CrB, A0 IVcomposite?).ÈThis object has a scatter of 0.007. Lehmann etal. (1995) recently found spectroscopic variations withperiods of 0.9 days and fractions thereof. The autocorrela-

FIG. 6.ÈHipparcos light curve of HIP 54682 (b Crt), showing possiblevariations on a timescale of 0.4 day.

FIG. 7.ÈAutocorrelation diagram for Hipparcos photometry of HIP76952 (c CrB). Note the minimum at 0.9 day, and the possible minimum at0.3 day. The spectroscopic period is also 0.9 day.

tion diagram suggests a period of 0.9 day (Fig. 7) in thesense that there is a minimum in the autocorrelationdiagram around *t \ 0.9 day. There is also a minimum at0.3 day, but it is based on one point in the diagram; unfor-tunately, there are no measurements with time di†erences inthe range 0.45È0.8 day. The short-term light curves (Figs. 8aand 8b) suggest a period of 0.3 day, but the evidence for thistimescale is marginal at best. Note that it is very difficult toconstruct phase curves for short periods in Hipparcos databecause of the long gaps between groups of measurements,unless the period is known precisely and unless the variabil-ity is highly periodic. This star is a close visual double ; thecompanion is A3 V, about 1A away.

HIP 99770 (HD 192640, HR 7736, 29 Cyg, A0.5 V a~j Boo).ÈThis object is a well-known j Bootis star with aphotometric period of about 45 minutes and an amplitudeof 0.01È0.02. The scatter of 0.012 is consistent with this.Unfortunately, the time distribution of the measurements isnot suitable for investigating the period, since measure-ments are obtained only twice per cycle. There is someslight evidence in the autocorrelation diagram for a periodof 50 days, but this may be an artifact of the long gapsbetween groups of measurements ; we mention it only forcompleteness.

HIP 109268 (HD 209952, HR 8425, a Gru, B7IV n).ÈThisobject shows a scatter of 0.005, but there is marginal evi-dence for a minimum in the autocorrelation diagram at 0.3day, but this timescale is not apparent in the short-termlight curves. This star is not a likely Maia candidate.

5. DISCUSSION

Of the several hundred stars which we considered for thisproject, only a few dozen merited more detailed exami-nation, and only a dozen produced interesting results. Twosuspected Maia starsÈc UMi and Maia itselfÈappear to

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850 PERCY & WILSON

FIG. 8.ÈShort-term Hipparcos light curve of HIP 76952 (c CrB) on (a) JD 2,447,856 and (b) JD 2,447,857 showing possible variations on a timescale of 0.3day.

be photometrically constant. (This result is not necessarilyinconsistent with Lehmann et al.Ïs [1995] observation ofspectroscopic variability in the latter star ; if the spectro-scopic variability is due to high-order nonradial pulsation,then cancellation e†ects would probably make the photo-metric variability negligible.) A well-known j BootisstarÈ29 CygÈhad a short period which was inconvenientfor analysis. Sirius, the brightest star in the night sky,showed evidence for variability, but this is likely due toinstrumental e†ects.

Three starsÈm Tau, HD 45380, and HD 129174Èwereslightly fainter than normal on a few occasions and may beshallow eclipsing variables. The Ðrst of these stars is aknown spectroscopic binary ; the third may possibly be arotating variable, rather than an eclipsing one, as it isknown to be a spectrum-variable Ap star.

Three starsÈHD 79931, HD 97277, and HD 209952Èshow evidence for variability on a timescale of 0.25È0.5 dayand may therefore be pulsating variables. In each case, theamplitude is very low (0.01 or less), so the evidence is veryweak.

HD 29573 shows strong evidence for variability with aperiod of 1.6 days. It could be a rotating variable, related tothe Ap stars, though Gray (1986) classiÐes the spectrum asabsolutely normal (A2 IVÈV). Alternatively, the star couldbe a nonradial pulsator related to the slowly pulsating Bstars.

HD 140436 (c CrB) is perhaps the most interesting case.Lehmann et al. (1995) found spectroscopic variations withperiods of 0.9 day and fractions thereof. We Ðnd a photo-metric period of 0.9 day and possibly 0.3 day. If the 0.9 dayperiod represents a low-order nonradial pulsation mode,and Lehmann et al.Ïs shorter periods represent higher ordermodes, then we would not expect to observe them photo-metrically because of cancellation e†ects on the stellarsurface. Lehmann et al. proposed that 0.9 day was the rota-tion period of the star and that nonradial pulsations werebeing carried around the star with this period.

Other than c CrB and c UMi, there is virtually no overlapbetween our Ðnal sample of suspected Maia variables andthe sample of Scholz et al. (1998)Èeither because their starsfell outside our original sample or because the scatter s inthe Hipparcos catalog was sufficiently small as to suggestthat the star was nonvariable. Scholz et al. (1998) have sug-gested periods for Ðve of the stars in their sample, on thebasis of Fourier analysis. With the exception of c CrB,however, none of the periods has peaks in the power spectrawhich stand out conspicuously.

6. CONCLUSIONS

We have used the Hipparcos epoch photometry databaseto search for Maia starsÈB7ÈA3 nearÈmain-sequence pul-sating variable stars with periods of up to a day. We havemade extensive use of autocorrelation analysis, which iswell suited for looking for short-term variability in thisdatabase. Out of several hundred stars considered, only Ðveshowed evidence for Maia-type variability ; in three of these,the evidence was weak. The two remaining cases are HD29573, which may possibly be a rotating variable, and HD140436 (c CrB), for which there is independent evidence forspectroscopic variability on timescales of 0.9 day and less.Careful simultaneous spectroscopic and photometric obser-vations of this star would be worthwhile.

We conclude (as other authors have done) that if theMaia variables exist at all, they are very rare and veryelusive.

J. B. W. was a participant in the Research OpportunitiesProgram at the University of Toronto. We thank theNatural Sciences and Engineering Research Council ofCanada for a Research Grant (to J. R. P.) and a SummerUndergraduate Research Award (to J. B. W.). We alsothank Dr. K. S. OÏFlaherty (Hipparcos Science Team) forher assistance.

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