## 3. Pulsation mode identifications from photometric phase differencesThe relative phase difference between the temperature and radius
variations of a pulsating star leads to an observable phase difference
between the light curves at different wavelengths. The sizes of these
phases differences depend not only on the properties of the star, but
also on the type of pulsation mode. The observed phase difference can
then be used for mode typing. This was already pointed out by Watson
(1988). Garrido et al. (1990) presented detailed calculations and
predictions for Scuti stars. They find that
measurements through different filters of the Strömgren
We have chosen the The resulting phase differences are shown in Table 2. The
phase errors (in degrees) were estimated from the formula
, where
We can now compare the observed phase differences with theoretical
modelling in order to determine the values. The
ATLAS9 models of Kurucz (1993) were used to construct a model
atmosphere for FG Vir. Garrido et al. (1990) presented calculations
using values of ranging from
to . For FG Vir, Viskum
(1997) determined a smaller range, viz. . This
allowed us to refine the calculations, although the results are very
similar. Another required constant, the deviation from adiabaticity,
R, has been changed slightly from the value used by Garrido et al.
(1990). Values of 0.20 (instead of 0.25) to 1.00 were used. This
change was indicated by measurements of high-amplitude
Scuti stars. The theoretical predictions are
shown in Fig. 2 together with the observations. The importance of
considering the dependence on the pulsation constant,
Our best mode identifications based on Strömgren photometry are shown in Table 2. We obtained five unambiguous values, while for three further modes we cannot distinguish between two adjacent values. The frequency , shown in the middle panel, is situated to the right of the = 0 by 1.9 . We note that the deviation is caused by only one subset of data (the CCD measurements from Siding Spring Observatory, see Stankov et al. 1998), without which a phase shift of is found. Irrespective of which of the two values for is accepted, an identification with radial pulsation is consistent within the statistical uncertainties. We can now compare the results from the photometric method with those derived from a promising new technique of examining the equivalent width variations of selected lines. Bedding et al. (1996) have shown that for low degree pulsation, the -values of pulsation modes can be inferred from simultaneous observations of several selected absorption lines combined with simultaneous photometric observations. Viskum et al. (1998) have applied this method to the star FG Vir. In particular, the equivalent-width changes of the H and H lines turned out to be good discriminators. In their paper, identifications have been presented for the eight dominant modes. We note that on the observational side the photometric and spectroscopic methods are independent. However, both methods rely on similar model-atmosphere calculations, so that they cannot be considered to be completely independent of each other. The agreement between the photometric and spectroscopic mode determinations is remarkable. It appears prudent to examine the comparison of the results of the two methods in more detail, especially with consideration of the (unavoidable) observational uncertainties. In order to compare independent parameters with each other, we pick the amplitude ratio of A(H)/A(FeI) given by Viskum et al. (1998). The comparison is shown in Fig. 3, where the numbers next to the points refer to the frequency numbering in Table 1. The figure shows that some of excellent agreement may be accidental once the observational uncertainties are considered. Nevertheless, the viability of both methods to determine values has been demonstrated and for at least six modes the values have been observationally determined. These determinations now need to be used as input for pulsation models.
© European Southern Observatory (ESO) 1999 Online publication: November 26, 1998 |