JSTOR

1. INTRODUCTION

Cousins & Warren (1963) discovered that the bright F0 V star γ Doradus was variable over a range of several hundredths of a magnitude with two principal periods (0 733 and 0 757). The star γ Doradus has an absolute magnitude similar to that of a δ Scuti star but is somewhat cooler, and thus for many years it was deemed a “variable without a cause.” Cousins (1992) stated: “The suggested W‐UMa type no longer seems a possibility, but rotation with starspots and/or tidal distortion might account for the variability. The light‐curve and dual periodicity would favor some form of pulsation, but the period is much longer than expected for a δ Scuti star.” Balona, Krisciunas, & Cousins (1994) tried to model the star using two starspots and differential rotation. They found that the large size of the required spots and the high stability of their periods did not bode well for the starspot hypothesis. Furthermore, they found evidence of a third period, later confirmed by Balona et al. (1996), which further diminishes the likelihood of the starspot hypothesis.

9 Aurigae (=HD 32537), a star very similar to γ Doradus, was first noted to be variable by Krisciunas & Guinan (1990). Krisciunas et al. (1993) found evidence for two photometric periods between 1.2 and 3 days. Using infrared and International Ultraviolet Explorer data, Krisciunas et al. (1993) found no evidence for a close companion nor for a lumpy ring of dust surrounding the star, but they could not rule out the idea of starspots.

Over the past decade, more than 40 variable stars with spectral types and luminosity classes similar to γ Doradus have been discovered that exhibit variability on a timescale that is an order of magnitude slower than that of δ Scuti stars. Mantegazza, Poretti, & Zerbi (1994), Krisciunas (1994), and Hall (1995) suggested that these objects may constitute a new class of variable stars. Breger & Beichbuchner (1996) investigated whether any known δ Scuti stars also showed γ Doradus–type behavior and found no clear‐cut examples of stars that show both “fast” and “slow” variability; Figure 1 of their paper nicely illustrates the locations of the two kinds of variables on the color‐magnitude diagram. However, not all of their γ Doradus stars are regarded as bona fide members of the group.

Krisciunas (1998) provides a good summary of our knowledge of γ Doradus stars as a new class, but to date there is no publication in the refereed journal literature which summarizes and “defines” the characteristics of the class itself. It was quite evident early on that significant advancement in the understanding of the physical nature of γ Doradus stars could be made only on the basis of a large observational effort. Hence, activities were concentrated on international multilongitude photometric and spectroscopic campaigns.

On the basis of extensive photometry, radial velocities, and line‐profile variations, it has been proven that 9 Aurigae (Krisciunas et al. 1995b; Zerbi et al. 1997a; Kaye 1998a), γ Doradus (Balona et al. 1996), HD 164615 (Zerbi et al. 1997b; Hatzes 1998), HR 8330 (Kaye et al. 1999b), HD 62454 and HD 68192 (Kaye 1998a), and HR 8799 (Zerbi et al. 1999) are indeed pulsating variable stars. Given the nature of the observed variability in these stars, the cause must be high‐order (n), low‐degree (l), nonradial g‐modes. We assert this on the basis of evidence for nonradial g‐modes and the lack of convincing evidence for other explanations, including starspots. Furthermore, we argue that since this small (but growing) group of objects all have similar physical characteristics and show broadband light—and line‐profile variations resulting from the same physical mechanism—they form a new class of variable stars. In this paper, we indicate the cohesiveness of this group and its differences from other variable star classes. Finally, we provide a set of criteria by which new candidates may be judged.

2. GENERAL CHARACTERISTICS OF THE CLASS

Our list of bona fide γ Doradus stars is complete to 1999 April, and all objects of this class have extensive enough photometric and/or spectroscopic data sets to rule out other variability mechanisms. A complete, commented, up‐to‐date list of all proposed candidates for this group, as well as their observational history, is maintained by G. Handler and K. Krisciunas.1

Table 1 lists the observed quantities of each of the 13 objects used to define this new class of variable stars. Column (1) gives the most common name of each object. Column (2) provides the best available value of b−y; columns (3) and (4) list the average apparent visual magnitude of each object (〈V〉) and the best determined spectral type. Column (5) lists the best available value of the projected equatorial velocity, , in km s⁻¹. Column (6) reports the Hipparcos trigonometric parallax in milliarcseconds (ESA 1997).

TABLE 1 Observational Parameters of the Confirmed γ Doradus Variables

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Table 2 presents derived properties of the 13 objects. Estimates for the total metallicity ([Me/H]) are derived from the relations of Nissen (1988) and Smalley (1993), which are precise to within 0.1 dex in [Me/H] and are listed in column (2). The absolute visual magnitudes (col. [3]) are calculated from the Hipparcos parallaxes. Luminosities, using bolometric corrections listed in Lang (1992, p. 138) and (Allen 1973, p. 161), are presented in column (4). The effective temperatures are determined from the new calibration of Strömgren photometry by Villa (1998), for which we estimate errors of ±100 K (col. [5]); stellar radii precise to ±0.05 R_⊙ are then calculated (col. [6]). Finally, masses which are precise to ±0.03 M_⊙ (internal model error) are inferred by comparison with solar‐metallicity evolutionary tracks by Pamyatnykh et al. (1998) (col. [7]). The final row in Table 2 represents the unweighted average of each of the columns; presumably, these are the physical parameters of a “typical” γ Doradus variable.

TABLE 2 Calculated and Inferred Basic Properties of the Confirmed γ Doradus Variables

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We present a color‐magnitude diagram of all 13 stars, using the Hipparcos parallaxes to calculate accurate values of in Figure 1. The observed zero‐age main sequence (Crawford 1975) and the observed edges of the δ Scuti instability strip (Breger 1979) are shown as a solid line and dashed lines, respectively.

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Fig. 1.— Color‐magnitude diagram showing the positions of the confirmed γ Doradus stars. Solid points indicate the position of each object, the solid line represents the observed zero‐age main sequence, and the boundaries of the observed δ Scuti instability strip are indicated by dashed lines.

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The truly intriguing characteristic of γ Doradus stars is that they are variable; considering the part of the Hertzsprung‐Russell (HR) diagram in which they lie, previous pulsational models say they should not be. The outer convection zones of these stars are too shallow to generate and sustain a large magnetic dynamo, thus making starspots improbable. Most of the γ Doradus stars are multiperiodic; the average period is close to 0.8 days. The observed variations are not necessarily stable and may be highly dynamic (Kaye & Zerbi 1997). Typical amplitudes cluster around 4% (= 0 04) in Johnson V and may vary during the course of an observing season by as much as a factor of 4. For the best‐studied stars (e.g., γ Doradus itself, 9 Aurigae, and HR 8330), line‐profile variations with periods equal to the photometric periods have been confirmed (Balona et al. 1996; Kaye 1998a; Kaye et al. 1999b). No high‐frequency signals have been detected in either the photometry or the spectroscopy, indicating a lack of the p‐mode pulsation common in δ Scuti stars.

Despite their commonality, a small subset of γ Doradus stars shows remarkably peculiar pulsation characteristics. In several objects (e.g., HD 224945: Poretti et al. 1996; HD 224638: Mantegazza et al. 1994; and 9 Aurigae: Krisciunas et al. 1995b; Zerbi et al. 1997a; Kaye 1998a), amplitude variability of order 50% over a few years is observed. Other objects (e.g., γ Doradus: Cousins 1992; HD 164615: Zerbi et al. 1997b; and HR 8799: Zerbi et al. 1999) show amplitude modulation selectively located at the moment of maximum brightness, a characteristic of variability that is new to the field of stellar pulsation. Still other objects (e.g., HD 68192) show remarkably constant periods and amplitudes over long timescales. Clearly, these peculiarities within the γ Doradus class need many more long‐term observations to be explained.

3. DEFINING A NEW CLASS

We argue that the qualities and characteristics of the 13 above named and described stars form a homogeneous set based on their physical characteristics and their mechanism for variability and, thus, form the basis for a new class of variable stars.

In following with the informal discussions at the “Astrophysical Applications of Stellar Pulsation” conference (Stobie & Whitelock 1995) held in 1995 at Cape Town, South Africa, and in recent papers in the literature (see, e.g., Krisciunas et al. 1993; Balona et al. 1996; Zerbi et al. 1997a; Poretti et al. 1997; Kaye 1998a; Kaye et al. 1999b), we propose that this type of variable star henceforth be known and recognized by the name γ Doradus variable stars. The extent of the γ Doradus phenomenon, as it is currently known, consists of variable stars with an implied range in spectral type A7–F5 and in luminosity class IV, IV‐V, or V; their variations are consistent with the model of high‐order (n), low‐degree (l), nonradial, gravity‐mode oscillations. Although it is conceivable that variations such as those of the stars in this class may occur outside of this region, it is likely that other mechanisms of variability would then dominate, and thus this combination of spectral type, luminosity class, and (most importantly) variability mechanism forms a suitable definition.

From an observational point of view, the g‐mode oscillations seen in γ Doradus variable stars are characterized by periods between 0.4 and 3 days and peak‐to‐peak amplitudes ≲0 1 in Johnson V. The presence of multiple periods and/or amplitude modulation is common among these stars, but this is not included in the formal definition presented here. Spectroscopic variations are also observed, and these manifest themselves both as low‐amplitude radial‐velocity variations (that cannot be attributed to duplicity effects) and as photospheric line‐profile variations.

In addition to these features, we stress that any object put forth for consideration as a confirmed γ Doradus variable star must not vary exclusively by other mechanisms, including p‐mode pulsations (e.g., δ Scuti stars), rotational modulation of dark, cool, magnetically generated starspots; rotational modulation of bright, hot, abundance‐anomaly regions; duplicity‐induced variations; or other rotational effects. Obviously, dual‐nature objects (e.g., pulsating stars showing both γ Doradus– and δ Scuti–type behavior) must not be rejected. Prime candidates for γ Doradus stars should therefore not be primarily variable as a result of the rotational modulation occuring in Am, Ap, Fm, RS CVn, or BY Dra stars. However, candidates may be members of a spectroscopically defined class (e.g., λ Boötis stars; see, e.g., Gray & Kaye 1999a).

4. CONCLUDING PERSPECTIVE

The γ Doradus stars constitute a new class of variable stars because they all have about the same mass, temperature, and luminosity and the same mechanism of variability. They are clearly not a subclass of any of the other A/F‐type variable or peculiar stars in this part of the HR diagram, and they may offer additional insight into stellar physics when they are better understood (e.g., they may represent the cool portion of an “iron opacity instability strip” currently formed by the β Cephei stars, the slowly pulsating B stars, and the subdwarf B stars; they may also offer insight into the presence of g‐modes in solar‐like stars). Modeling by Kaye et al. (1999a) is beginning to shed light on the theoretically required interior structure and on the specific physics driving the observed variability, but much theoretical work lies ahead.

To understand the behavior of γ Doradus stars and to investigate how they differ from the δ Scuti variables and spotted stars, we need to investigate a number of star clusters of differing ages, perhaps up to as old as 1 Gyr. The fact that the Hyades have no γ Doradus variables (Krisciunas et al. 1995a) may be a quirk of the Hyades rather than proof that stars ≈600 Myr old are too old to exhibit γ Doradus–type behavior. Clearly, the “outliers” of the γ Doradus candidates that would extend the limits of the region of the HR diagram in which these new variables are found should be checked carefully for both photometric and spectroscopic evidence indicative of pulsations versus starspots, duplicity effects, and other causes of variability not consistent with the definition presented above (see, e.g., Aerts, Eyer, & Kestens 1998). Finally, additional observations of individual γ Doradus stars are clearly warranted in order to understand better the nature of these objects. After all, 13 objects does not an instability strip make. In the meantime, we must keep an open and critical mind about these variables.