Stability in the Light Curves of High‐Amplitude δ Scuti Stars: Selected Monoperiodic Stars

For each star, every analyzed data set consists of observations from one author collected over a period of less than 1 year. A comparison was made of the amplitudes obtained for different years. When necessary, the observations collected by the same author, over 2 consecutive years, were analyzed together as only one data set.

Table 1 lists the seven monoperiodic high‐amplitude δ Scuti stars we selected together with their pulsation periods and the order of the fit used in the corresponding Fourier decompositions. First, the data corresponding to each data set were phased from 0 to 1 using a linear ephemeris with the periods listed in Table 1. In order to avoid possible phase shifts in the phased data, due to the uncertainties in the published periods or possible secular variations, the origin in time T₀, for each linear ephemeris, was chosen in the same epoch of the observations. For this, we use or derive one time of light maximum from the corresponding data. Nevertheless, in the case of SZ Lyn the ephemeris which describes well its period variation contains both a secular increase of the period and binary variation (Soliman et al. 1986) with a relatively short orbital period (1173.5 days) and a large semiamplitude (0.00569 days). This binary contribution is too large and must be taken into account. In this case, we use the full ephemeris derived by these authors to phase all the data sets of SZ Lyn. Thus, we avoid problems of dispersion in the phased data due to real phase shifts.

After one data set has been phased, we make a Fourier decomposition of the light curve with a fixed order for the fit. For each star, several data sets were proved to know the best order of the fit. Using the matching Fourier decomposition, we build the corresponding synthetic light curve phased from 0 to 1 and determine the amplitude (as determined by Fourier analysis, i.e., semiamplitude) of the full light curve (containing all the harmonics of the fit). By comparing the observed and synthetic full light curves, we derived the σ (calculated as standard deviations of the residuals on 0.1 phase around both the time of maximum and minimum) and errors (as standard errors) listed in the columns (5) and (4) of Tables 2–pasp_111_760_709tb33pasp_111_760_709tb44pasp_111_760_709tb55pasp_111_760_709tb66pasp_111_760_709tb778, respectively.

Tables 2–8 show that the majority of the photometric data available in the literature were collected using the Johnson BV filters. In addition, some observing runs were carried out using other filters and photometric systems. For the sake of homogeneity, all the resulting amplitudes are transformed to equivalent amplitudes into the Johnson V filter.

2.2.1. Johnson ΔB Amplitudes

2.2.2. Str ömgren Δv, Δb, Δy Amplitudes

2.2.3. Hipparcos ΔH_p Amplitudes

Recently, Harmanec (1998) has derived a relationship to transform Hipparcos H_p magnitudes into Johnson V magnitudes. Using this, we can approximate the corresponding amplitudes as

Alternatively, we can use the relation derived by Cousins (1987), between the Johnson and Strömgren color indices, to obtain

In addition, we can write the following equation using Table 1b from Garrido et al. (1990) where the amplitude ratios, between observed b−y and V variations, were determined for a large sample of high‐amplitude δ Scuti stars:

Thus, using these three formulae, the corresponding Hipparcos ΔH_p and Johnson ΔV amplitudes can be related using the equation

Note that the estimated transformation errors in the amplitudes, due to approximations in the equations, are of only a very few thousandths of a magnitude. This is smaller than the errors produced by the equation (4) itself and has negligible influence on the results which we obtain for the final ΔV amplitudes. This is true also for all the relationships derived below.

2.2.4. Walraven ΔB_W, ΔV_W Amplitudes

When we are dealing with data collected into the Walraven photometric system, we can make use of the relation given in Diethelm (1985). Thus, the amplitudes in the two systems satisfy the following equation where V_W and (V−B)_W are also in magnitudes:

Assuming that Δ(V−B)_W = -Δ(B−V) and using the relations (2) and (3), we can write

This relationship agrees very well with the results obtained by Diethelm (1985) for the high‐amplitude δ Scuti star RY Lep. In addition, by comparing the curves of this star in the filter B and B_W, a similar equation can be derived for the corresponding ΔB and ΔB_W amplitudes as

2.2.5. Geneva ΔB_G, ΔV_G Amplitudes

For observations collected using the filter V_G of the Geneva photometric system, we can use the relation derived by Rufener & Maeder (1971) for the clusters of Pleiades and Praesepe. Thus, the Johnson V and Geneva V_G amplitudes can be related by the following equation. As can be seen, the coefficient is practically unity due to both central wavelengths being very close to each other (Arp 1961; Matthews & Sandage 1963; Rufener 1964):

For photometry relating to Geneva B_G magnitudes, no relationships were found in the literature to transform into the Johnson photometric system. However, we can make a linear approximation, taking into account the central wavelengths of the different filters and the amplitude ratios calculated by Garrido et al. (1990) for a large sample of observed high‐amplitude δ Scuti stars using Strömgren photometry. This way, we assume that the central wavelengths for the Strömgren vb, Johnson V, and Geneva B_G filters are 4110, 4670, 5550, and 4250 Å, respectively (Straizys 1992; Arp 1961; Rufener 1964). Then, the Johnson V and Geneva B_G amplitudes satisfy the equation

2.2.6. Other Filters

A number of photometric data available in the bibliography were not collected using "standard" filters. Examples are those observations carried out by Broglia & Masani (1957) on YZ Boo using blue and yellow filters centered at λ = 4250 Å and λ = 5400 Å, Binnendijk (1968) on SZ Lyn using B and V filters centered at λ = 4420 Å and λ = 5300 Å, etc. For these cases we have made use of the same method described for the Geneva B_G filter in the preceding section. The following relations are then obtained to relate the corresponding amplitudes. Note that the relation obtained for B₄₂₅₀ is the same as for B_G as both filters are centered at the same wavelength.

This star was photometrically observed through the 1960s by Churms & Evans (1961), Leung (1968), and Chambliss (1971) and in the 1970s by Balona & Martin (1978) using the Johnson photometric system. After this, only the observations collected by the Hipparcos satellite (ESA 1997) for the period 1990–1992 are available. Mean values of 0.2047(±0.0042) and 0.1618(±0.0042) mag are obtained for the amplitudes in the B and V bands, respectively. Then, a factor of F = 0.790(±0.037) is used to transform the amplitudes from B into V. We derive a mean value for the equivalent amplitude in the Johnson V filter of 〈ΔV〉 = 0.1590 mag with a mean standard error of 〈ε〉 = 0.0069 mag. As can be seen in Table 2, the results obtained for the final amplitudes seem to be in very good agreement. The only exception is the amplitude derived from the Hipparcos 1990–1991 data set. It seems to be slightly smaller than the others.

This star shows the largest amplitude among the seven high‐amplitude δ Scuti stars which have been considered in this paper. EH Lib has been observed by many authors over a period of 32 years, from 1960 to 1992. The largest data set was collected in 1975 by Broglia & Conconi (1977) using the Johnson BV filters. In total, 27 data sets have been found in the literature for this star. A factor F of 0.779(±0.028) was derived to transform the ΔB amplitudes into ΔV. The mean value obtained for the ΔV equivalent amplitude through all the data sets was of 0.2651(±0.0091) mag.

This star was recently discovered as being variable, in 1986 by Oja (1987). The time span of observations is relatively short, only 12 years from 1986 to 1998. Nevertheless, there are data sets available in the literature for almost all of these years, mainly due to observations carried out by Kiss & Szatmary (1995, 1998). In general, we found that these data had the smallest dispersions. To transform the ΔB amplitudes into ΔV, the factor F was found to be 0.775(±0.015) mag and the 〈ΔV〉 equivalent amplitude obtained was 0.1989(±0.0040) mag.

The earliest reliable data set of photometric observations found in the bibliography for YZ Boo is that carried out by Broglia & Masani (1957) in the year 1956. Since this, 22 other observation runs have been considered in our study. The largest data set corresponds to Szeidl & Mahdy (1981) in 1959 using Johnson BV photometry. These authors also observed this star during 1975 and 1979 using the same filters. The largest dispersion was found for the data from Schmidt et al. (1995), who collected only 28 points through 16 nights using the V filter. However, the corresponding Fourier decomposition seems to be reliable. From Table 5 we find a factor F = 0.813(± 0.031) mag and 〈ΔV〉 = 0.2090(± 0.0119) mag as the equivalent amplitude for the V band.

The largest amount of data has been collected for SZ Lyn. For this star, we found 42 photometric data sets spanning 29 years, between 1962 and 1991. The longest data set was obtained by Szeidl (1983), who observed this variable for several years during the 1960s and 1970s. However, the largest data set in only one observing run was obtained in 1963 by Broglia (1963) using Johnson photometry. For this star, we find a factor F of 0.768(±0.015) mag to transform ΔB amplitudes into ΔV and 〈ΔV〉 = 0.2567(± 0.0055) mag as equivalent amplitude. Note that the data set from Fernley et al. (1984) consists of only 20 points. These points are "normal" points obtained by averaging the observed data, each 0.05 cycles, over the whole pulsation cycle.

The variability of AD CMi was discovered in 1959 by Abhyankar (1959) using the Johnson photometric system. The majority of the observations were carried out during the 1970s and 1980s using Johnson and Strömgren photometry. Finally, Yang et al. (1992b) collected the largest data set in 1992 using only the Johnson V filter. F = 0.740(± 0.016) mag and 〈ΔV〉 = 0.1477(± 0.0040) mag are obtained. Note that the 18 points listed for the data set from Burchi et al. (1993) correspond to "normal" points obtained from 121 individual measurements collected on three nights.

DY Her gave the longest time span of photometric observations. We have data sets from 1954 to 1991. Its variability was discovered by Hoffmeister (1935), but the first reliable photometric data set available in the literature was collected in 1954 by Broglia & Masani (1955). From 1965 until 1985, we found only two data sets: those from Szeidl & Mahdy (1981) and Breger et al. (1978) obtained in 1972 and 1977 using Johnson and Strömgren photometry, respectively. The longest data set was collected by Milone et al. (1994) from 1985 to 1991. For this star, we find F = 0.741(± 0.036) mag and 〈ΔV〉 = 0.2361(± 0.0112) mag.

The author thanks Dr. L. L. Kiss for making available his unpublished data on BE Lyn and Dr. L. Balona for his valuable comments. This research was supported by the Junta de Andalucía and the Dirección General de Enseñanza Superior (DGES) under project PB96‐0840. This research has made use of the Simbad database, operated at CDS, Strasbourg, France. Acknowledgments are also especially made to M. C. Romero for making available many papers used in this investigation and to V. G. Brown for proofreading.