5 Discussion and conclusions

Studying carefully the frequency values in Table 3, one may find that f₁, f₃ correspond to the periods of 0.17836376 and 0.1428041 days which were identified by Fitch (1955) and Cox et al. (1984), while f₆ corresponds to the beat period of 0.716292 days. However, more frequencies are proved to be present in the pulsation of VZ Cnc! We may find that $f_2\approx 2f_1$, $f_4\approx 3f_1$, and $f_5\approx f_3+f_1, f_6\approx f_3-f_1$.Thus, if we label f₁ as $\nu _0=5.6066$ c/d and f₃ as $\nu _1=7.0022$ c/d, the other frequencies can be marked in terms of $\nu _0$ and $\nu _1$. The identification results are listed in the last column of Tables 3 and 4 within small errors. At the same time, it may be found that the frequencies $\nu _0$ and $\nu _1$ are usually associated with the first and second overtones of radial pulsation based on the similarity of their period ratio (0.801) to the theoretically expected value of 0.810. The analysis of the light curves of VZ Cnc also shows that the pulsation frequencies of this star are quite stable while the amplitudes are changing slightly from 1950 to 1993.

The results of multiple frequency analyses show that the star VZ Cnc oscillates simultaneously with two modes of first and second overtones, and some harmonics and cross-frequencies generated by the nonlinear effects. About the large scatter in the $\rm O-C$ diagram under the supposition of two modes, although we do not give firm and definitive explanation, the discovery of more than 2 frequencies in the power spectrum of the light curve of this star might give one possibilility.