General Properties

Definitions

The $\delta $ Scuti stars are pulsators situated in the classical cepheid instability strip on the main sequence or are moving from the main sequence to the giant branch. In general, the period range is limited to between 0.02d and 0.25d. This limit provides a good separation from the neighboring or overlapping groups of pulsators in the Hertzsprung-Russell Diagram, such as roAp, $\gamma$ Dor and RR Lyrae stars.

 

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Figure 1: Sample light curves in the Stromgren $y$ and$v$ filters of a typical $\delta $ Scuti variable (FG Vir). The data were taken from a multisite campaign of FG Vir (Breger et al. 1998). The predicted variability is shown by a solid curve. Notice that the seemingly irregular light curves and bumps are caused by multiperiodicity.

Regrettably, one should not regard this simple definition and description to be complete. We must consider two additional astrophysical situations: (i) the evolved Pop. II stars inside the classical instability strip with $\delta $ Scuti-like periods (SX Phe stars, see below), and (ii) the massive stars evolving through the instability strip.

The massive (M $>$ 2M${_\odot}$) stars evolving from the main sequence towards the giant region cross the instability strip on nearly horizontal tracks at higher luminosities in the Hertzsprung-Russell Diagram. The evolutionary state identifies them as $\delta $ Scuti stars. But due to their high mass and luminosity, the periods are longer than those of average $\delta $ Scuti star and may get as large as 1d. Consequently, they overlap the RR Lyrae stars in period, which are in the post-giant stage of evolution and have low masses below 1 M${_\odot}$. We propose that these long-period $\delta $ Scuti stars be distinguished from RR Lyrae stars by considering the size of stellar rotation. The suggestion is based on the observation by Petersen, Carney & Latham (1996), who point out that RR Lyrae stars show no detectable rotation ($v\,\sin\,i \le$ 10 km s$^{-1}$), while evolved $\delta $ Scuti stars do. An example of a $\delta $ Scuti star with long periods is AC And (P$_{\rm o}$ = 0.71d, P$_1$ = 0.53d, P$_2$ = 0.42d (Fitch & Szeidl 1976, Fernie 1994).

$\delta $ Scuti stars can also be found among pre-main sequence stars. Examples are the two pulsators in the young cluster NGC 2264 (Breger 1972a) and the star HR 5999 (Kurtz & Marang 1995), which exhibits both $\delta $ Scuti and larger variability caused by variable dust obscuration.

Some $\delta $ Scuti stars are (pure) radial pulsators, while the majority pulsate with a large number of nonradial p modes simultaneously. The nonradial pulsations of $\delta $ Scuti stars found photometrically are low-degree ($\ell \leq$ 3) and low-order (n = 0 to 7) p modes, while spectroscopic studies have confirmed the presence of high-degree nonradial modes with $\ell $ up to 20 (e.g., for the star $\tau$ Peg, Kennelly et al. 1998).

The $\delta $ Scuti stars represent a transition between the cepheid-like large-amplitude radial pulsation of the classical instability strip and the ocean of nonradial pulsation occurring in the hot half of the Hertzsprung-Russell Diagram. Many excited modes show photometric amplitudes in excess of 0.001 mag, which makes it possible to study these stars photometrically. The position of $\delta $ Scuti stars on and slightly above the main sequence permits the asteroseismological comparison between oscillation data and stellar models in a region where the basic stellar structure is regarded as relatively well known.

 

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Figure 2: The position of the $\delta $ Scuti variables in relation to other types of variables of Pop. I in the hot part of the HRD. Some positions of the variables are tentative and some mode identifications and other recent information may be speculative. The position of the EC14026 = sdB stars was taken from Koen et al. (1998).

It is important to point out that $\delta $ Scuti pulsation is not an unusual phenomenon. On the contrary, the stable stars in the classical instability strip raise the question whether these stars might be variable with amplitudes below the present level of detection. In recent years, the discovery of new $\delta $ Scuti stars has been accelerating, especially due to the successes of large observing programs such as HIPPARCOS, MACHO and OGLE. Furthermore, many $\delta $ Scuti stars with large amplitudes have also been found in other galaxies, e.g., in the Carina Dwarf Spheroidal Galaxy at $V \sim$ 23 (Mateo, Hurley-Keller & Nemec 1998). If one also considers the fact that $\sim $50% of all main-sequence stars inside the instability strip are $\delta $ Scuti pulsators, it might become meaningless to compile complete catalogs containing the names of all stars discovered so far to be variable. Although the older list by the author (Breger 1979) is sometimes still used, more recent compilations containing hundreds of $\delta $ Scuti stars are available.1 Some excellent examples are:

The Delta Scuti Star Newsletter with news, discussions and papers, is published regularly by the Vienna group. The newsletter is sent to individuals active in the field, who have expressed a desire to receive it. The contents of previous newsletters, developments in the field of $\delta $ Scuti stars as well as the Delta Scuti Network can be found under http://dsn.astro.univie.ac.at. The site also makes it possible to upload and download recent papers on the subject of $\delta $ Scuti and related stars.

Subgroups

The vast majority of all $\delta $ Scuti stars are small-amplitude variables, pulsating mainly with nonradial p modes. In addition to these run-of-the-mill variables, it is astrophysically reasonable to define two subgroups of $\delta $ Scuti stars. The names of these two subgroups have been accepted by most workers in the field:

 
Table 1: Alternate names used for $\delta $ Scuti (DS) stars
Old name
(Used by)		 Present name Properties
DSCTC
(GCVS 4th ed.)		 DS average DS star
(as found in open clusters)
Dwarf Cepheid    

(Smith 1955)

 DS all known DS stars

(McNamara and others)

 HADS  V amplitude > 0.3 mag
RRs
(GCVS 3rd ed.)		 HADS V amplitude > 0.3 mag
AI Vel
(Bessell 1969)		 HADS V amplitude > 0.3 mag
USPC, USPV
(Eggen 1979)		 DS ultrashort period cepheids

 

(i) The high-amplitude $\delta $ Scuti stars (HADS) are the $\delta $ Scuti stars with $V$ amplitudes $\geq$ 0.30 mag. We shall show below that the pulsation of these stars differs from that of the average $\delta $ Scuti stars in other respects as well.

(ii) The SX Phe variables are the $\delta $ Scuti stars of Pop. II and old disk population. Since such old stars at $\sim $ 8500 K should have already evolved away and no longer exist in this part of the Hertzsprung-Russell Diagram, they are also unusual from an evolutionary point of view. They probably are in a post-giant branch stage of evolution and may be merged binary stars. Note that most SX Phe stars are also HADS, but not vice versa.

Finally, during the last decade, the existence of a new group of pulsators, the $\gamma$ Doradus variables, has been confirmed. The periods are longer than those of $\delta $ Scuti stars with typical periods near 1 or 2 days. The light variability of these stars is now known to be caused by g-mode pulsation, rather than surface spots rotating with the star. These stars are probably not a subgroup of $\delta $ Scuti stars and most $\gamma$ Doradus stars are cooler than the red edge of the $\delta $ Scuti instability strip. It is at present unclear whether or not some stars show both $\delta $ Scuti and $\gamma$ Doradus-type of variability, i.e., surface p and g modes at the same time. Breger & Beichbuchner (1996) examined the group of $\delta $ Scuti stars for possible candidates of both types of pulsation: new photometry of the most promising contender in that sample, BI CMi, shows some (weak) evidence in favor of the $\gamma$ Doradus-type of variability for this star. Also, Paparò et al. (2000), in their study of the $\delta $ Scuti star 57 Tau in the Hyades cluster, report two probable frequencies in the low-frequency, $\gamma$ Doradus domain.


The large-amplitude modes in the Pop. I and Pop. II HADS are radial modes (F, 1H, 2H), of which one or two are simultaneously excited with typical amplitudes of 0.5 mag. A connection between high amplitude and dominant radial pulsation therefore exists: the typical radial amplitude is a factor of 10 or 100 larger than the amplitudes of the typical nonradial pulsators.

This correlation raises the question whether or not radial modes with low amplitudes also exist. The answer here is a definite yes: radial modes have been identified in variables such as FG Vir and 4 CVn, where the radial modes have similar millimag amplitudes as the many simultaneously excited nonradial modes. Curiously, in these more rapidly rotating stars the amplitudes of the identified radial modes are smaller than those of $\ell $ = 1.

 

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Figure 3: Pulsational instability domains on the upper main sequence as computed by Pamyatnykh (1999). For the classical instability strip (right) the Blue Edge is shown. A few evolutionary tracks for different mass values are also presented. The plotted $\delta $ Scuti stars were taken from Garcia et al. (1995).

There also exists a group of the so-called monoperiodic variables. Because of their seeming monoperiodicity they resemble the HADS, but have smaller amplitudes. The question arises whether the group of small-amplitude monoperiodic pulsators are also radial pulsators. We can compare the two groups through the period-luminosity relation and find that they differ. The monoperiodic small-amplitude pulsators have smaller $Q$ values, i.e., they pulsate in higher overtones. These modes may not be radial: in the star 28 And, Rodriguez et al. (1998) identify the mode at 14.43 c/d as a nonradial p$_3$ $\ell $ = 2 mode. They also find amplitude variability and evidence for the existence of a second pulsation mode at 17.23 c/d. More modes at or below the present observational threshold may well exist. It is therefore likely that the so-called monoperiodic variables with low amplitudes are not radial pulsators and may not even be monoperiodic!

Excitation Mechanism

The excitation mechanism of $\delta $ Scuti stars is the same as that for the other stars in the classical instability strip: the $\kappa$ mechanism (Baker & Kippenhahn 1962, 1965; Zhevakin 1963). During each cycle the kinetic energy of pulsation is supplied from the internal energy of the mixture of gas and radiation in the ionization zones of abundant elements such as He and H. The excitation of pulsation in these zones, in particular the HeII ionization zone near 48000 K, is enough to counterbalance the damping in the underlying layers. Almost three decades ago, Chevalier (1971) showed the pulsational instability from computing a $\delta $ Scuti star model. Note that in $\delta $ Scuti stars, the H and HeI ionization zones near 15000 K are located near the stellar surface and may not play an important role.

 

In Fig. 3, more recent computations of the stellar instability regions are presented for the stars on the upper main sequence. Note that Slowly Pulsating B stars are unstable to nonradial high-order gravity modes. A similar instability was found for massive stars in addition to the p-mode $\beta$ Cep-type instability.

Incidence of pulsation in the Lower Instability Strip

Only between 1/3 and 1/2 of the stars situated in the Lower Instability Strip show photometrically detectable light variability due to pulsation with an amplitude limit between 0.003 and 0.010 mag, depending on the details of the photometric studies. The position of the stars found to be variable and nonvariable is shown in Fig. 4. Since the majority of $\delta $ Scuti stars were not detected in surveys, inclusion of all stars in this diagram would falsify the relationship between variable and nonvariable stars. Consequently, the stars used in the figure were restricted to the stars studied in unbiased variability surveys which treated the variables and nonvariables similarly (Breger 1969ac, 1970, 1972ab; Danziger & Dickens 1967; Millis 1967; Jorgensen, Johansen & Olsen 1971; Slovak 1978; Paunzen et al. 1998). The large number of variables with amplitudes near the detection limit indicates that many of the so-called constant stars are also variable.

 

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Figure 4: Incidence of photometric variability in the Lower Instability Strip. Only stars discovered during variability surveys were plotted. Detectable pulsation occurs in less than 50% of the stars, although many constant stars are probably variable with amplitudes lower than the observational limit of a few millimag. The blue and red edges of the instability strip were drawn to include the certain $\delta $ Scuti variables.

Leung (1970) and Eggen (1970) suggested that the $\delta $ Scuti stars form two separate luminosity groups: variables near $M_v$ = 1.9 and 0.6, respectively. However, the distribution of a larger sample of variables showed no such separation (e.g., Breger 1979). Consequently, the view that $\delta $ Scuti pulsation is a general property of stars in the lower instability strip seemed to be confirmed.

The stellar parallaxes obtained with the Hipparcos astrometry satellite have allowed a more accurate determination of absolute magnitudes of relatively nearby stars. This has led to a number of studies which incorporated these new, and (usually) more accurate distances. A number of astronomers reported that the nearby $\delta $ Scuti stars indeed appear to fall into a high-luminosity and low-luminosity groups. Antonello & Mantegazza (1997) have examined the grouping of $\delta $ Scuti stars with known Hipparcos parallaxes in the Hertzsprung-Russell Diagram. They confirm the groupings for nearby stars. However, they also find that the distinction between the groups disappears once the sample is enlarged by including more distant stars. This argues against the existence of two separate groups.

The present picture that pulsation is a normal phenomenon in the Lower Instability Strip should not be interpreted to mean that all stars have the same probability of pulsating with a particular amplitude. In fact, stellar rotation and chemical peculiarity have a strong influence on the incidence, mode selection and amplitudes of pulsation. In a study of the incidence of pulsation in both field and cluster stars, Breger (1970) found that the classical Am stars do not pulsate, but the evolved Am stars (the $\delta $ Del = $\rho$ Pup stars) do. In fact, the behavior of the classical Am stars could be understood by the diffusion hypothesis. Here the amount of helium in the HeII ionization zone, which is required by pulsational instability, is reduced, leading to increased stellar stability (Breger 1972c).

 

Since 1972, considerably more information on the variability for individual Am stars and other chemically peculiar stars has become available. The behavior of the different types of chemically peculiar stars inside the instability strip is very complex. The increased sample of Am stars shows that it is possible for an Am star to pulsate (e.g., HD 1097, Kurtz 1989), but that pulsation among the classical Am stars is rare and of small amplitude. Another significant discovery was the rapid pulsation in Ap stars by Kurtz (1982). This group is now called the rapidly oscillating Ap (roAp) stars.