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3 Discussion

In order to carry out the previously described techniques, the photometric values in the standard system presented in the section of Observations were used first to determine reddening. This was done using specific techniques which have been previously described (see, for example, Peña et al. 1993) and which are based on a calibration by Nissen (1988) based, in turn, on the fundamental calibrations of Crawford and his co-workers (1975, 1979) for A and F stars. This is applicable since, as is well-known, the $\delta$ Scuti stars are within these spectral limits in the HR diagram. For both types, Crawford derived empirical calibrations for Mv and (b-y)0 and in the latter case, also the [Fe/H] metallicity. With these calibrations, slightly modified by Nissen (1988), a computing code was written to determine reddening and unreddened parameters for each set of photometric data. A slight interpolation would be necessary since the H$\beta$ values differ slightly in time from uvby photometry. However, since the difference is so small, in practice they were treated as if they were taken at the same time.


 
Table 2: Mean Strömgren indices and the range of the variation for each star

.D..-1
\begin{tabular}
{l.....}
\hline\noalign{\smallskip}
 &\multicolumn{1}{r}{BP Peg}...
 ...2.690 & 2.697 & 2.700 & 2.708 & 2.715\\ \noalign{\smallskip}
\hline\end{tabular}


A brief description for each star is given which emphasizes the main characteristics relevant to the findings of the present paper:

BP Peg. Broglia (1959) reported a linear ephemeris with a period of 0.10954347 d, detecting also a possible variation of the period between the 1953 and 1958 and 1959 observations. Furthermore, they found a modulation period on the order of 0.37 d with an amplitude in the maxima of 0.45 mag in the visual. Rodríguez (1989) presented uvby observations of this star and identified two main frequencies, 9.1260 and 11.8303 c/d corresponding to the fundamental mode and to the first overtone. Kim et al. (1989) secured new $uvby-\beta$ and spectroscopic observations of this star. They determined a photometric reddening value of E(b-y) equal to 0.067 mag. A superficial gravity value of 3.85 and a ratio [Fe/H] of -0.08 were obtained. An average $T_{\rm e}$ of 7470 K was determined from their photometry and theoretical grids. From this and theoretical models, a bolometric magnitude of $M_{{\rm 
bol}}\ 1.4$ mag, a mass of $1.85~M_\odot$ and an age of $1.3 \ 
10^9$ yr were finally derived. Rodríguez et al. (1992) also reported uvby-$\beta$ of three large amplitude $\delta$ Scuti stars, BP Peg, among them. They were able to determine the same parameters previously established with their photometry.

CY Aqr. Detre & Chang (1960) and Hardie & Tolbert (1961) reported an ephemeris with a negative quadratic term. Percy (1975) reported that the period remained constant between 1934 and 1951, when it suffered a drastic change and then remained constant. Elst (1972) determined a modulation period of 0.1222 d, but with a very small amplitude. Fitch (1973) suggested the modulation period might be 0.17766 d, which could be explained by the pulsational theory, whereas Elst's (1972) period, could not. Percy (1975) found that the modulation period proposed by Elst (1972) was not real but merely a result of its method of analysis. Geyer & Hoffmann (1974, 1975) did not find any modulation period. Mahdy & Szeidl (1980) derived an abrupt change of the period of $-18.1 \ 10^{-8}$ d around 1952, the period being constant before and after this date. Rolland et al. (1986) and Peña et al. (1987), proposed a period decay consistent with the theoretical model of a pre-white dwarf of $0.2~M_\odot$ in opposition to the abrupt period changes suggested. Rodríguez (1989) determined a linear ephemeris for his data and, in a later study, (Rodríguez et al. 1990) determined some observational parameters such as effective temperature of Te 7590 K, superficial gravity of $\log g = 3.89$ and metallicity [Fe/H] = - 0.7. Besides these values, they determined, considering pulsation, the following: $R_*=2.34~R_\odot$, $M = 1.49 ~M_\odot$, $M_{{\rm bol}} = 1.71$ and an age of $1.7 \ 10^9$ yr. Coates et al. (1994) determined a period change and concluded that the star was pulsating with only one period. This conclusion is not supported by the study of Powell et al. (1995) which stated that the new data did not present significant variations from cycle to cycle, but that an abrupt period change occurred in 1989 and that the star is now pulsating with a period of 0.061038612 d.

DY Her. Since its discovery as a variable star in the thirties it has been a subject of considerable interest. In works by McNamara (1978) with spectra and by Breger et al. (1978) from $uvby-\beta$, a value of $2.7~R_\odot$ was determined. Szeidl (1979) stated that the radius should be larger than that previously reported. Breger et al. (1978) determined the effective temperature and superficial gravity with Strömgren photometry with a one channel photometer. Rodríguez (1989) determined the metallicity of the star with simultaneous Strömgren photometry. López de Coca et al. (1990) included it in a comprehensive review of the observational characteristics of all the $\delta$ Scuti stars known. Antonello (1990) carried out a comparison with theoretical models concerning the Strömgren m1 index. For DY Her he derived $\langle 
T_{\rm e}\rangle$ of 7360 K, $\log \langle g\rangle$ of 3.87 and [Fe/H] of 0.16. The physical parameters of mass, bolometric magnitude and age were later determined from $uvby-\beta$ photometry by Rodríguez et al. (1990). Dawei et al. (1993) confirmed the period change of DY Her based on studies by Madhy & Szeidl (1980) with a compilation of 60 maxima from 1938 up to 1979. Yang et al. (1993) made a compilation of 30 years of observations determining a variation in the period of P0 = 0.14863130 d, $1/p({\rm d}p/{\rm d}t) = -5.2\
 10^{-9}$ yr. Milone et al. (1994) derived the mean radius and bolometric luminosity of $2.77~R_\odot$ and $M_{{\rm bol}} = 1.41$ mag, respectively, from visual and infrared photometry and the effective temperature derived by Breger et al. (1978).

DY Peg. An excellent review of the previous observations can be found in Rodriguez (1989). Between 1966 and 1975 several observers obtained new photometric data with the purpose of confirming light curve variations. Quigley & Africano (1979, 1981) derived a quadratic ephemeris which predicted a decrease in the period. Peña & Peniche (1986) derived a decrease in the period, consistent with the theoretical models of Dziembowski & Kozlowski (1974) for a pre-white-dwarf in opposition to the abrupt period changes proposed by Percy (1975) and Mahdy & Szeidl (1980). Rodriguez (1989) reported observations of DY Peg in the Strömgren system determining a period of 0.0729 d. Recently, Kilambi & Rahman (1993) presented UBV observations and determined mass, radius, gravity and variations of the temperature over one cycle of pulsation. Rodriguez et al. (1993) reported light curves in the $uvby-\beta$ system.

 
Table 3: Unreddened photometry of BP Peg

\begin{tabular}
{lccclccc}
\hline\noalign{\smallskip}
Time & $(b-y)_0$\space & $...
 ...\noalign{\smallskip}
\multicolumn{8}{l}{HJD = time + 2446670.0.}\\ \end{tabular}


 
Table 4: Unreddened photometry of CY Aqr

\begin{tabular}
{lccclccc}
\hline\noalign{\smallskip}
Time & $(b-y)_0$\space & $...
 ...\noalign{\smallskip}
\multicolumn{8}{l}{HJD = time + 2444494.0.}\\ \end{tabular}


 
Table 5: Unreddened photometry of DY Her

\begin{tabular}
{lccclccc}
\hline\noalign{\smallskip}
Time & $(b-y)_0$\space & $...
 ...\noalign{\smallskip}
\multicolumn{8}{l}{HJD = time + 2446645.0.}\\ \end{tabular}


 
Table 6: Unreddened photometry of DY Peg

\begin{tabular}
{lccclccc}
\hline\noalign{\smallskip}
Time & $(b-y)_0$\space & $...
 ...\noalign{\smallskip}
\multicolumn{8}{l}{HJD = time + 2448925.0.}\\ \end{tabular}

YZ Boo. Studies by Szeidl & Mahdy (1981) led them to conclude that YZ Boo had suffered a period change. Joner & McNamara (1983) derived its physical parameters ($T_{\rm e}= 7590$ and $\log g =3.95$, [Fe/H]= -0.025, $M_{{\rm bol}} = + 1.7$) through UBV and Strömgren photometry and concluded that it is a dwarf Cepheid of Pop I, which, according to Breger (1979) could be considered to be $\delta$ Scuti star. Since the period changes can provide information on the evolutive stage of the stars, several studies have been done with this goal in mind: this star was first studied by Szeidl & Mahdy (1981), later by Peniche et al. (1985); Jiang (1986), determined new ephemeris with a quadratic term. Peniche et al. (1985) concluded that it is impossible to decide if the period is constant or not with the currently available data bases. Kim & Joner (1994a) reported photometric observations in Coussins VRc system and in a later paper Kim & Joner (1994b) determined Te = 7410 K, $\log g 
= 3.71$ and a metallicity [M/H] = -0.025.


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