The domain of g Doradus variables in the Hertzsprung±Russell diagram

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1 Mon. Not. R. Astron. Soc. 309, L19±L23 (1999) The domain of g Doradus variables in the Hertzsprung±Russell diagram South African Astronomical Observatory, PO Box 9, Observatory 7935, South Africa Accepted 1999 July 30. Received 1999 July 30; in original form 1999 July 7 1 INTRODUCTION The g Doradus stars are a new class of pulsating variables. They are non-radial g-mode pulsators of high radial overtone with typical periods between 8 and 80 hours. In the HR diagram, they appear to cluster around the intersection of the red edge of the classical instability strip with the main sequence. On the basis of the 13 bona fide members of the class, Kaye et al. (1999a) gave an accurate description of the g Doradus variables. In particular, they pointed out that these pulsators can easily be confused with other variables, the light modulations of which are induced by p-mode pulsations, rotation or binarity. Consequently, Kaye et al. (1999a) provided guidelines which help to distinguish g Doradus stars from different groups of variable stars. Because of this potential confusion and, more importantly, since the pulsational driving mechanism of g Doradus variables is presently not understood, knowledge of the circumstances under which the observed pulsations can occur is highly desirable. In other words, the domain in the HR diagram occupied by g Doradus stars needs to be determined. Kaye et al. (1999a) noted that 13 stars are not sufficient to define an instability region. Aerts, Eyer & Kestens (1998) suggested that the g Doradus phenomenon extends to temperatures slightly higher than that of the Sun. A continuously updated so-called Master List of bona fide g Doradus stars, plus further candidates proposed in the literature, is made available to the community at the WWW site www:astro:univie:ac:at=,gerald=gdor:html; major revisions are announced whenever deemed necessary (Krisciunas & Handler ABSTRACT 70 new g Doradus candidates were identified from Hipparcos photometry, which represents more than a doubling of the presently known number. Selecting the objects with good evidence for multiperiodicity, it is found that these stars, together with bona fide members of the class, occupy a well-defined region in a colour±magnitude diagram. This domain corresponds to a range of 7200±7700 K on the zero-age main sequence (ZAMS) and 6900± 7500 K one magnitude above it, which partly overlaps with the instability strip of d Scuti stars. For the first time, g Doradus stars can be discussed as a group. They can be found over a significant fraction of the main sequence lifetimes for objects in the relevant temperature range. An upper limit on the surface metallicity of g Doradus stars is apparent, which may guide the search for their pulsation driving mechanism. The importance of possible objects exhibiting both g Doradus and d Scuti-type pulsations is discussed. Key words: Hertzsprung±Russell (HR) diagram ± stars: oscillations ± d Scuti ± stars: variables: other. 1995; Handler & Krisciunas 1997). While working on the latest update of this master list (Handler, Kaye & Krisciunas, in preparation), it was found useful to subdivide the proposed g Doradus variables. On the basis of the available time-series photometric data only (see Section 2 for details), the proposed objects were separated into `prime' and `other' candidates; no assumptions about `expected' temperatures, luminosities, etc. were made. When comparing the locations of the prime candidates with those of the bona fide g Doradus stars in a colour±magnitude diagram, excellent agreement was found: a clear indication for the existence of a well-defined instability domain. Encouraged by this result, it was decided to perform an extensive search for further g Doradus stars in the Hipparcos database (ESA 1997). Contrary to previous studies (Aerts et al. 1998; Eyer 1998), the `unsolved' Hipparcos variables were also included in the initial sample, following the idea that lack of a clear periodicity could be because of unrecognized multiperiodic light variations. The results of this effort are reported below. 2 CANDIDATE SELECTION AND CLASSIFICATION As a first step, all Hipparcos variables with spectral types of A±G, periods between 0.3 and 10 d (for the `periodic' variables), amplitudes less than 0.2 mag and brighter than H p ˆ 8:5 mag at minimum, which were not classified as supergiants were selected. This resulted in more than 1000 candidates. Then the individual light curves were examined and obvious non-g Doradus stars (e.g. q 1999 RAS

2 L20 Table 1. Prime g Doradus candidates. Star Periods (d) References HD H99 HD : H99 HD : H99 HD : H99 HD ? H99 HD : H99 HD ? H99 HD AEK HD : E98 HD E98 HD H99, K99 HD : H99 HD : H99 HD : H99, K99 HD H99 HD : H99 HD ? H99 HD H99 HD H99 HD H99 HD AEK HD H99 HD H99 HD H99 HD H99 HD H99 HD : AEK HD : AEK HD H99 HD H99 HD : H99 HD : AEK, PM HD H99 HD H99 HD H99 HD : AEK HD / ? E98 HD H99 HD E98 HD : H99 HD H99 HD ? H99, K99 HD AEK HD H99 HD H99 M34 UVa KP References: H99: this paper, AEK: Aerts et al. 1998, E98: Eyer 1998, PM: Paunzen & Maitzen 1998, K99: Koen, private communication, KP: Krisciunas & Patten 1999.Notes: Entries labelled with colons denote average values of several possible further periods; question marks label uncertain periods. d Scuti stars, eclipsing binaries, low-amplitude Cepheids, rotationally modulated Ap stars, etc.) were rejected. For the remainder of the stars (< 450 objects), a period search was performed (utilizing the programs of Breger 1990 and Martinez & Koen 1994) and g Doradus candidates were selected. These stars were required to exhibit variations on a time-scale longer than the fundamental radial mode period. The remaining 70 stars and candidates proposed in the literature (see Handler et al., in preparation, and references therein) were subdivided into two groups on the basis of the appearance of their amplitude spectra. The prime candidates had to fulfill a number of criteria as follows. (i) Good evidence for multiperiodicity had to exist. After prewhitening with the frequency leaving the smallest residuals in Table 2. Further new g Doradus candidates. Star Period (d) Comment HD : d Sct star? HD 21788, 5 period uncertain HD : d Sct star? HD d Sct star? HD ? period uncertain HD : weak signal HD d Sct star? HD singly periodic? HD : weak signal HD : weak signal HD ? 2.9? period uncertain HD singly periodic? HD : weak, complicated signal HD d Sct star? HD weak signal HD weak signal HD singly periodic? HD d Sct star? HD : singly periodic? HD singly periodic? HD singly periodic? HD d Sct star? HD ? complicated signal HD : weak signal HD spotted star? HD d Sct star? HD : weak, complicated signal HD singly periodic? HD Am or Ap star? HD d Sct star? HD : complicated signal HD d Sct star? HD d Sct star? HD weak signal HD singly periodic? HD d Sct star? Notes: same as those for Table 1. the data, the resulting amplitude spectrum had to show at least a second peak or significant residuals in the same frequency range as that of the first frequency. In this way, possibly singly-periodic g Doradus stars are not considered, 1 but this effectively discriminates against all other causes of variability besides pulsation. (ii) Stars for which two frequencies were found which were harmonically related were rejected, as this could be because of rotational modulation or ellipsoidal variations. (iii) If two close frequencies (within a few per cent) were determined, the corresponding stars were not judged to be prime candidates, as this could be an artifact owing to starspot evolution or differential rotation of a spotted star (e.g. see Strassmeier & Bopp 1992). (iv) Stars for which the actual time-scale of light variation could not be unambiguously determined were not considered as prime candidates. As a result of the sampling of the Hipparcos photometry (cf. Eyer & Grenon 1998), strong aliasing is present in amplitude spectra. This can mimic spurious signals in the frequency range of interest for g Doradus stars, especially for 1 Kaye et al. (1999b) pointed out that about 30 per cent of the bona fide g Doradus stars are singly periodic. Since these objects do not have any remarkable features in any other respect, no systematic bias is expected for the present study owing to the possible exclusion of such stars.

3 The domain of g Doradus variables in the Hertzsprung±Russell diagram L21 objects which actually vary with periods around two hours, i.e. some d Scuti stars. The most reliable g Doradus candidates from our study and from the investigation of stars proposed in the literature are summarized in Table 1 together with the results of our period search. New objects considered in this work, which may be g Doradus stars, but whose nature remained uncertain, can be found in Table 2 with a comment explaining possible doubts. Eyer & Grenon (1998) pointed out that a search for multiple periods in Hipparcos photometry is difficult and can lead to spurious results. However, it was found useful to quote the time-scales present in the variations of the different stars. To allow the reader to judge the classification, plots with amplitude spectra for the individual stars have been placed at gdoratlas.html. The new g Doradus candidates listed in Tables 1 and 2 more than double the number of related objects presently known. We note that Hipparcos data are available for all `bona fide' g Doradus stars. We recovered some of them in our search, but for most objects the accuracy of the Hipparcos photometry was insufficient to claim variability. 3 RESULT A colour±magnitude diagram including all g Doradus candidates is shown in Fig. 1. The StroÈmgren b 2 y colour index was used as a temperature indicator (dereddened whenever necessary), since it is available for most of the stars. For the remainder, b 2 y was estimated from the Hipparcos B 2 V using the relations of Caldwell et al. (1993). Absolute magnitudes were determined from the Hipparcos parallaxes whenever available or were calculated from StroÈmgren photometric indices. In Fig. 1, the location of all the `prime' candidates identified by us (again, selected by the appearance of their frequency spectra only) is strikingly similar to that of the bona fide g Doradus variables. This strongly suggests that most of these stars are indeed g Doradus stars and it is clear evidence that these objects occupy a well-defined small region in the HR diagram. The cool boundary of this region is defined more clearly than its hotter counterpart, simply because there are more stars available. One object (HD ) lies outside the blue edge. There is no doubt that it is a g Doradus star, since it is the only object for which four frequencies from the Hipparcos photometry could be determined (three are independent, one is a linear combination), but when comparing its published b 2 y with the corresponding H b index and with its B 2 V it appears that b 2 y is too small by 0.015±0.020 mag. Hence, this object was not considered for defining the blue edge. Clearly, new StroÈmgren photometry of HD needs to be obtained. Consequently, the instability region for g Doradus stars can be outlined for the first time. Its extent is indicated in Fig. 1. Using the model atmosphere results of Kurucz (1991), it can be translated into an effective temperature range of 7200±7700 K on the ZAMS log g < 4:33, while the luminous end occurs about 1 magnitude above it log g < 4:0 between effective temperatures of 6900 and 7500 K. 4 DISCUSSION One of the most widespread ideas about the g Doradus phenomenon is that it is related to stellar age. For instance, Krisciunas (1998) gave arguments that g Doradus stars are younger than 300 Myr. In Fig. 1, several objects well above the ZAMS (up to 1.3 mag) can be discerned, suggesting that g Doradus-type pulsations can exist in somewhat evolved mainsequence stars, unless these g Doradus stars are binaries or premain sequence objects. The binary hypothesis can be checked by comparing the absolute magnitudes derived from parallaxes with those calculated from StroÈmgren photometry (see Crawford 1975, 1979). Fig. 2 shows the results of such a comparison. For most of the stars the absolute magnitudes determined using Figure 1. The colour±magnitude diagram of the presently known or suspected g Doradus variables. Star symbols: bona fide g Doradus stars, dots: prime candidates from the literature, open circles: other candidates from the literature (see Handler et al., in preparation), filled triangles: prime candidates from this paper, open triangles: further candidates from this work. The observed zero-age main sequence (ZAMS: Crawford 1975, 1979) is shown together with the boundaries of the d Scuti star instability strip (thin lines almost normal to the ZAMS, Breger 1979). The domain of g Doradus stars is indicated with thick lines approximately normal to the ZAMS; the single filled-triangle outlier is likely to have an erroneous b 2 y colour index (see text).

4 L22 both methods agree well within the errors (rms of about ^0:3 mag for the photometric absolute magnitudes, mean rms approximately ^0:25 for the Hipparcos absolute magnitudes). A few objects may indeed be binaries, but not all of the more luminous objects in Fig. 1 can be explained by this hypothesis. It is therefore suggested that the g Doradus phenomenon can occur over a significant fraction of the main sequence lifetime of stars in the relevant temperature range. One of the arguments in favour of the idea that g Doradus stars are very young objects came from the apparent absence of such pulsators in the Hyades (Krisciunas et al. 1995). The Hyades are also relatively metal-rich. It is therefore logical to ask whether metallicity could play a role for g Doradus-type pulsation. This is examined in Fig. 3. On the average, g Doradus stars have metallicites comparable to that of the Sun (using Smalley's (1993) calibration, [M/H] is found to be between 20:37 2 and 0:12). Objects enriched in metals are absent; this is different from the situation for d Scuti stars. 3 In fact, there may be a strict upper limit on the metallicity of g Doradus stars. In Fig. 3 it can also be seen that hotter objects seem to have a larger range in metal abundance than cooler stars. This can shed some light on the driving mechanism for the pulsations of g Doradus stars. Kaye, Guzik & Bradley (1999) outline a possible k-mechanism located in a zone of iron enhancement due to diffusion and radiative levitation as found in models by Turcotte, Richer & Michaud (1998). The observation that g Doradus stars are only found in a certain range of surface metallicity can then be taken as a clue that diffusion processes (settling of metals) may indeed play an important role for the excitation of their pulsations. It would be interesting to perform detailed abundance analyses of g Doradus stars in order to check whether they show any peculiarities in their chemical composition. Kaye et al. (1999) also discuss a conjectured mode selection mechanism operating in the surface convection zone. This requires a weak, but non-negligible stellar dynamo, i.e. a Rossby number (ratio of stellar rotation period to convective turnover time) of order unity. Consequently, Kaye (1998) suggested that under this hypothesis, the instability region for g Doradus stars in the HR diagram should be tilted from hot to cool and more luminous to less, i.e. tilt upward and to the left. The reader is referred to the two references above for more details. Based on the available data, the color-magnitude diagram shown in Fig. 1 is not consistent with this theoretical prediction. The instability region for g Doradus stars partly overlaps with that of d Scuti stars. For the latter objects, the blue edge is generated by the driving region being too close to the stellar surface, while the red edge is believed to be caused by surface convection becoming effective. The physical mechanisms responsible for the hot and cool borders of the g Doradus instability region are not obvious. 2 For the l Bootis star HR 8799, the object with the largest positive dm 1 in Fig. 3, Gray & Kaye (1999) determined M=HŠ ˆ20:47 by spectral synthesis. 3 A t-test shows that the metallicity distribution of the stars in Fig. 3 is different from that of d Scuti stars (taken from the latest catalogue by Zechner, private communication) in the same temperature range to the 99.9 per cent confidence level. We caution, however, that our candidate selection process discriminated against Ap/Fp stars (but not Am/Fm stars) and therefore this value may be too high. Figure 2. The Hipparcos absolute visual magnitude versus the same quantity derived from StroÈmgren photometry. Plot symbols are the same as in Fig. 1, but only bona fide g Doradus stars and prime candidates are considered. Figure 3. The StroÈmgren metallicity parameter dm 1 versus colour index b 2 y for the bona fide g Doradus stars and prime candidates. No metalrich object is found. A correlation between metallicity and temperature can be discerned. The possible connection between the g Doradus and d Scuti variables has been discussed by Breger & Beichbuchner (1996), based on a much smaller sample of g Doradus variables than available to date. The question then arises, is there is an exclusion between the two groups (and if so, what causes it) or do `hybrid' objects exist? If stars exhibiting simultaenous g Doradus and d Scuti-type pulsations could be found, this would greatly increase the possibilities for asteroseismology of both classes of variable star. The pulsation modes in the higher-frequency region may easily be identified, since main-sequence d Scuti stars should mainly show the signatures of pure p-mode pulsation. Hence, their position in the HR diagram can be tightly constrained (e.g. see Handler et al. 1997). Then the g Doradus-type g-modes (whose radial order is practically impossible to be derived without further constraints because the high-order g-mode spectrum is very dense) can be used to probe the deep interior of the stars.

5 The domain of g Doradus variables in the Hertzsprung±Russell diagram L23 ACKNOWLEDGMENTS This work would not have been undertaken without the input of a number of colleagues, especially Tony Kaye and Chris Koen. The author is grateful for constructive comments on draft versions of this paper by Don Kurtz, Michel Breger, Luis Balona and, again, Tony Kaye. He also thanks Stephen Potter for improving the English style of the manuscript and Renate Zechner for permission to use her catalogue of d Scuti stars prior to publication. REFERENCES Aerts C., Eyer L., Kestens E., 1998, A&A, 337, 790 (AEK) Breger M., 1979, PASP, 91, 5 Breger M., 1990, Comm. Asteroseism, 20, 1 (Univ. Vienna) Breger M., Beichbuchner F., 1996, A&A, 313, 851 Caldwell J. A. R., Cousins A. W. J., Ahlers C. C., van Wamelen P., Maritz E. J., 1993, SAAO Circ., 15, 1 Crawford D. L., 1975, AJ, 80, 955 Crawford D. L., 1979, AJ, 84, 1858 ESA, 1997, The Hipparcos and Tycho catalogues, ESA SP-1200 Eyer L., 1998, PhD thesis, Univ. Geneva (E98) Eyer L.,Grenon M., 1998, in Deubner F. et al., eds, New Eyes to See Inside the Sun and Stars. p. 291 Gray R. O., Kaye A. B., 1999, AJ, submitted Handler G., Krisciunas K., 1997, Delta Scuti Star Newsletter, 11, 3 (Univ. Vienna) Handler G. et al., 1997, MNRAS, 286, 303 Kaye A. B., 1998, PhD thesis, Georgia State Univ. Kaye A. B., Guzik J. A., Bradley P. A., 1999, in Ibanoglu C., ed., Variable Stars as Important Astrophysical Tools. NATO-ASI, in press Kaye A. B., Handler G., Krisciunas K., Poretti E., Zerbi F., 1999a, PASP, 111, 840 Kaye A. B. et al., 1999b, AJ, submitted Krisciunas K., 1998, in Deubner F. L. et al., eds, New Eyes to See Inside the Sun and Stars. p. 339 Krisciunas K., Handler G., 1995, Inf. Bull. Variable Stars, 4195 Krisciunas K., Patten B. M., 1998, Inf. Bull. Variable Stars, 4705 (KP) Krisciunas K., Crowe R. A., Luedeke K. D., Roberts M., 1995, MNRAS, 277, 1404 Kurucz R. L., 1991, Van Vleck Obs. Contr., 11, 27 Martinez P., Koen C., 1994, MNRAS, 267, 1039 Paunzen E., Maitzen H. M., 1998, A&AS, 133, 1 (PM) Smalley B., 1993, A&A, 274, 391 Strassmeier K. G., Bopp B. W., 1992, A&A, 259, 183 Turcotte S., Richer J., Michaud G., 1998, ApJ, 504, 559 This paper has been typeset from a TEX/LATEX file prepared by the author.

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