4 Analysis

Simultaneous $uvby-\beta$ photoelectric photometry for the $\delta$ Scuti stars CY Aqr, DY Peg, YZ Boo, BP Peg, and DY Her has been secured. The application of the previously described technique from Peña et al. (1993) to the data for each star provides the reddening for each set of colors obtained at the same time. A mean value of the reddening was considered and from this, unreddened indexes were obtained. Once the unreddened indexes have been evaluated, (Tables 3 to 7 for BP Peg, CY Aqr, DY Her, DY Peg and YZ Boo, respectively) the location of each data point was determined in the theoretical grids of Relyea & Kurucz (1978) for solar abundance and lower. From the photometry, superficial gravity and effective temperatures as well as metallicity, absolute magnitude and distance have been derived for each star and the variations in $T_{\rm e}$ and log g during the pulsation cycle for the large amplitude stars is presented in Table 8. A compilation of the values reported in the literature has been done and the derived values compared well with those determined previously (Table 9). In particular CY Aqr and DY Peg show low metallicity, a characteristic of Pop II stars whereas DY Her and YZ Boo have Pop I metallicity.

 

Table 7: Unreddened photometry of YZ Boo

Since the values of metallicity found for BP Peg differ from those previously compiled, a careful analysis was carried out: a direct comparison with another source of uvby - $\beta$ (KMJ, 1989) was done. Since significant values for determining physical quantities are those between phases 0.3 to 0.75 (Breger et al. 1978; McNamara 1997), phase diagrams were constructed with the KMJ photometry of the longest nights (2447413 & 20) to avoid the beating phenomena that could arise from the two determined frequencies in BP Peg. What was immediately evident, was that most of the measured $\rm H\beta$ values for BP Peg from the two sources were above the 2.72 limit that establishes the difference between A and F type stars since [Fe/H] can be determined only for F type (Nissen 1988). Mean values and the standard deviations were determined (Table 10) for the considered photometric data (KMJ and the present paper's) between these phase limits and, within these uncertainties, the magnitude and colors are practically the same. With these values a metallicity of -0.093 and 0.764 respectively, was calculated. Emphasis should be made on the fact that photometry in the present paper was carried out simultaneously in all the filters and that the dispersion is lower.

 

Table 8: Variations in $T_{\rm e}$ and $\log g$ during the pulsation cycle for the large amplitude stars

 

Table 9: Comparison with the previously reported data in the literature

PP Present paper McN & F McNamara & Feltz (1978) GKA

Andreasen (1983) KJ Kim & Joner (1994b) MB Breger (1980)

J & McN Joner & McNamara (1983) ER Rodríguez (1989)

BC & R Breger et al. (1978) EA Antonello (1990)

PLC López de Coca (1986) K & R Kilambi & Rahman (1993)

KMcN & J Kim et al. (1989) McN McNamara (1997).

In view of the apparently large discrepancy, the determination of the metal content [Fe/H] of BP Peg was also done considering the relations 4.6.8 and 4.6.9 provided by Rodríguez (1989). From these, the metal content for each set of data was $0.459 \pm 0.372$ for the photometry in present paper and $-0.400 \pm 0.738$ for the KMJ values for the 4.6.8 equation and, analogously, of $0.359 \pm 0.275$ and $-0.235 \pm 0.451$ for the 4.6.9 relation which when calculated from the standard deviations in the considered range phases, give the same values of metallicity within the uncertainties.

From the determined values for the pulsational constant (Breger et al. 1996), as well as from their position in the period -luminosity-color diagrams (López de Coca et al. 1990), it has been determined that BP Peg, DY Her and YZ Boo are pulsating in the fundamental mode whereas CY Aqr and DY Peg do so in higher overtones (2H from the former method and between 2H and 3H, from the last one). The derived mass values are 1.85, 2.1, 1.7, 0.21 and $0.225~M_\odot$, respectively.

What is immediately evident when comparing the physical parameters obtained from $uvby-\beta$ photometric data with those reported in the literature, is the significant spread of values of the physical characteristics. The principal sources have been listed at the bottom of Table 9. The comparison of the pulsational and evolutionary theories are in excellent agreement if the results derived by each method are examined. From these methods it was found that BP Peg, DY Her and YZ Boo are classical $\delta$ Scuti stars and fit the determinations of other authors, except for the metallicity found for YZ Boo. On the other hand, CY Aqr and DY Peg appear to be SX Phe stars of an older population than the $\delta$ Scuti stars. The scenario for these stars would be that they are in a more advanced evolutive stage which could correspond to pre-white dwarfs as the lower absolute magnitude indicates. No significant changes in the position of these stars in the HR diagram are expected because no significant changes have been found from the previously determined physical characteristics.

Acknowledgements

We would like to thank the staff of the OAN for their assistance in securing the observations. This work was partially supported by Conacyt through grants 3925E, E130-3059 and a previous collaboration program with CSIC which allowed the visit of R. Garrido to the OAN in 1986. Special recognition for his support in securing the observations of DY Her is acknowledged. Typing and proofreading were done by J. Orta and J. Miller, respectively. C. Guzman assisted us in the computing. This is part of the work for obtaining the Masters Degree of DG. We would like to acknowledge both fuitful discussions with Carlos Chavarría and suggestions of the referee which improved this paper.

 

Table 10: Mean values and standard deviations for BP Peg between phases 0.3 and 0.75