A BRIEF HISTORY

The Radial Era

The first mention of $\delta$ Scuti variability was made by Wright (1900), who announced the radial velocity of the star $\delta$ Scuti to be variable. It was only three decades later that Colacevich (1935) and Fath (1935) made their relatively accurate simultaneous radial velocity and photometric measurements of the star. They determined a period and placed $\delta$ Scuti in the $\beta$ Canis Majoris variable star group. Subsequent investigations suggested that $\delta$ Scuti resembled the cepheids, rather than the hotter $\beta$ Canis Majoris variables. The stars DQ Cep, CC And, and AI Vel were similar to $\delta$ Scuti and showed relatively large photometric amplitudes.

In an important development, Eggen (1956) pointed out the existence of a separate type of variable star with four proposed members (DQ Cep, CC And, $\delta$ Scuti, and $\rho$ Pup). Not surprisingly, the first $\delta$ Scuti stars discovered turned out to be unusual for their class because of their large photometric amplitudes. Only after 1965 could numerous discoveries of $\delta$ Scuti stars be made when photoelectric measurements with millimag precision became possible. Several systematic searches for more $\delta$ Scuti variables were made by Breger (1969ac), Danziger & Dickens (1967), Millis (1967), and Jorgensen, Johansen & Olsen (1971). These new discoveries made extensive review papers (Baglin et al. 1973; Breger 1979) necessary.

Most papers of that era examined the known $\delta$ Scuti stars in terms of radial pulsation. While this is justified for most high-amplitude variables, it is now known that even the star $\delta$ Scuti itself is a nonradial pulsator (Templeton et al. 1997).

In the second half of the Seventies, the research emphasis started to shift towards the study of nonradial modes. The end of the Radial Era can be illustrated with two publications:

Breger & Bregman (1975) computed the values of the pulsation constants, $Q$, for the different $\delta$ Scuti stars and compared them with the expected values for different radial modes by Cox, King & Stellingwerf (1972). On the assumption of radial pulsation, it was shown that the dominant pulsation would have a radial order of 1 or 2 for the hotter variables, and 0 or 1 for the cooler $\delta$ Scuti stars. This result provided some evidence that for blue edges for the different radial orders move towards hotter temperatures with increasing radial order.

Stellingwerf (1980) computed nonlinear pulsation models for radial pulsation modes. Pulsational instability was found and the observed radial periods confirmed. However, without artificially induced amplitude limits, the computed amplitudes were so large that the outer layers of the star approached escape velocity. This problem was termed by Stellingwerf `the Main-Sequence Catastrophe'. Subsequent calculations by Cox and others could include much deeper damping and the models no longer showed tendencies to grow to large unobserved amplitudes.

 

The Tidal Hypothesis

Fitch (1967) proposed that in many $\delta$ Scuti and $\beta$ Cephei pulsators, the intrinsic radial pulsation could be perturbed by tidal forces from a stellar companion in an elliptical orbit. This would explain the (relatively) long-period modulation of the radial modes observed in stars such as CC And. On the other hand, in circular orbits and synchronous rotation, tidal deformation would appear static in the rotating frame so that nonradial modes could grow to significant strength (Fitch 1976).

Tidal modulation must, of course, exist in some $\delta$ Scuti stars (see below). However, the lack of evidence for the binary nature of many of the stars with complex light curves meant that the tidal modulation hypothesis as a general explanation was not accepted.

Nevertheless, valuable information on stellar pulsation and structure can be obtained by studying pulsating close binaries. An example is the ellipsoidal $\delta$ Scuti star 14 Aur A with a short 3.8 day circular orbit, for which Fitch & Wisniewski (1979) modeled $\ell$ = 1, p$_5$ pulsation modes. For a system separated by only a few stellar radii, the companion has a profound influence on the excited nonradial modes.

Even in more widely separated binary systems, where the tidal influence of the companion may be negligible, the light-time effects in the orbit need to be considered. An example is the star $\theta^2$ Tau (Breger et al. 1989) with an orbit of 141 days, for which the extraction of the frequencies of pulsation from photometric data requires light-time corrections so that an erroneous report of unstable frequencies can be avoided. For even wider binary systems, the measured times of maximum light are affected so that the derivation of period changes from the (O-C) diagram needs to include the binary effects. An excellent example is the star SZ Lyn (P = 3.14 years, Barnes & Moffett 1975).

 

The USPV Hypothesis

After examining nine small-amplitude $\delta$ Scuti stars in his Hyades moving group and in the old disk population, Eggen (1970) proposed that all these variables with P $\leq$ 0.2 days should be called ultrashort-period cepheids or variables (USPV). Furthermore, he could not confirm the period-luminosity-color relation proposed by Breger (1969b). In turn, he suggested the existence of two separate groups of ultrashort-period variables separated by luminosity, at $M_{\rm v}$ = 0.6 and 1.9 mag, respectively. The position in the Hertzsprung-Russell Diagram of the nine variables studied by him indeed supports the division.

However, a recent plot of a larger sample of $\delta$ Scuti stars (see Breger 1979) shows no such separation. Furthermore, in spite of the uncertainties connected with the definition of a characteristic period for a multiperiodic star, the larger sample also obeys a very clear period-luminosity-color relation.

 

Are the variations irregular or multiperiodic?

The question of whether or not $\delta$ Scuti stars show stable pulsation frequencies, as opposed to quasiperiodic or even irregular variations, is astrophysically very important. Le Contel et al. (1974) and Valtier et al. (1974), in reporting their photometry on HR 432, 515, 812, 8006 and 9039, suggested that periods in $\delta$ Scuti stars have meaning only in a statistical sense. The evidence was reviewed by Fitch (1976) and found to be contradictory. Fitch speculated that even ten nights of observations would be insufficient to extract the multiple pulsation frequencies, so that an impression of irregularity would be created. In fact, for the stars listed above, only 5 to 13 nights of observations were available.

Kurtz (1980) analyzed the star $\theta$ Tuc and reviewed the best candidates for irregular variability. He argued convincingly against the reported variable frequencies in other stars as well.

The very extensive photometric campaigns carried out ten or twenty years later for specific $\delta$ Scuti stars and the discovery of dozens of stable frequencies (see below) show that the variability of $\delta$ Scuti stars is multiperiodic and regular in frequency.

 

Hundreds of modes: the Nonradial Mixed Mode Era

Considerable evidence has now become available that in $\delta$ Scuti stars, hundreds (or more) of nonradial pulsation modes are simultaneously excited. This can be illustrated by two recent papers, which have examined the problem from completely different angles.

Kennelly et al. (1998) have obtained extensive spectroscopic time-series observations of the rapidly rotating star $\tau$ Peg. They find a rich mode spectrum with degrees up to $\ell$ = 20 and with frequencies below about 35 c/d. A good correlation exists between the modes in a diagram plotting observed frequency against nonradial degree. After transformation to a frame of reference co-rotating with the star, those modes with the largest (spectroscopic) amplitudes have frequencies that lie within a narrow band near 18 c/d. They interpret these modes as prograde modes with $\vert$m$\vert$ = $\ell$. (Note that the change from the observer to a co-rotating frame of reference considerably changes the values of the frequencies of modes of large $\vert$m$\vert$ values: low-degree modes are affected much less). If we consider that many additional modes are not geometrically favored for detection, the number of excited nonradial modes of high degree in $\tau$ Peg should be very much larger than the 30 detected modes.

Breger et al. (1998) detected at least 24 significant pulsation modes of low degree, $\ell$ = 0 to 2 or 3, in the star FG Vir after analyzing over 650 hours of photometric data. Furthermore, the residuals show a rich power spectrum with many additional peaks in the limited frequency region in which the pulsation modes are excited. If one also considers the fact that only the low-degree modes could be photometrically detected, one must conclude that literally hundreds of pulsation modes are excited, although generally with small amplitudes.

Pulsation models (Dziembowski 1995) show that most of these excited modes are mixed modes with a p-mode character in the envelope and g-mode character in the stellar core. This property makes such $\delta$ Scuti stars extremely valuable for asteroseismology. Such applications require that the detected frequencies can be identified with specific pulsation modes. The work in progress on FG Vir has already shown that the observed photometric phase differences between different colors give consistent $\ell$ identifications. Furthermore, the photometric identification of the mode at 12.15 c/d with the radial fundamental mode predicts the correct distance for the star (as measured by Hipparcos). This in turn confirms the g-mode nature of the detected frequencies at lower values.