3 Data analysis

The plots of the data of the three Cepheids phased with the periods given by Payne-Gaposchkin & Gaposchkin (1966) showed immediately that in the cases of HV 1777 and HV 1353 these periods are wrong (Fig. 5, left panels).

Least-squares power spectra (Antonello et al. 1986) were computed for the four variables (Fig. 6). In these spectra we see typically 3 peaks corresponding to the true period and to its (1d^-1+1/P) and (1d^-1-1/P) aliases. Indeed we found that the previously known periods of HV 1777 and HV 1353 (marked with an arrow in the figure) are the (1d^-1-1/P) aliases of the true ones. The data phased with the correct periods are shown in the right panels of Fig. 5. In the case of HV 1763 we see that this star has a periodic light curve and that the dominant peak is at 0.47d^-1, and it is partially blended with its (1d^-1-1/P) alias. This star is a short-period Cepheid too, a not unexpected fact since its apparent magnitude is very similar to those of the other three Cepheids (see Fig. 4). The light curves of HV 1353 and HV 1763 phased according to their periods are shown in Fig. 7.

  

Figure 5: V light variations of HV 1777 (upper panels) and HV 1353 (bottom panels) phased with previous periods (left) and with the correct ones (right)

  

Figure 6: Least-squares power spectra of the 4 Cepheids. Arrows mark the positions of the periods reported by Payne-Gaposchkin & Gaposchkin (1966)

  

Figure 7: V light curves of HV 1779 (top panel) and HV 1763 (bottom panel)

  

Table 2: Period and relevant data of observed Cepheids

  

Table 3: Fourier decomposition coefficients and their formal errors

The light curves of the three known Cepheids are very different from those reported by Payne-Gaposchkin & Gaposchkin (1966). This is obvious for HV 1777 and HV 1353, because of the wrong periods, but it is also the case of HV 1353; while Payne-Gaposchkin & Gaposchkin (1966) give a descending branch steeper than the ascending one, the opposite is true according to our data. Table 2 summarizes for each star the periods as obtained from our data, the mean V magnitude, the amplitude and the observed time of maximum brightness.

The adopted formula for the Fourier decomposition was

$$V=V_0 + \sum A_i ~ \cos [2{\pi}if(t-T_0) + \phi_i].$$ (1)

The Fourier parameters, that is phase differences $\phi_{i1}=\phi_i-i\phi_1$ and amplitude ratios R_i1=R_i/R₁, are reported in Table 3, besides the rms residual of the fit. This residual is in good agreement with the accuracies estimated from Fig. 4.