Variable stars in nearby galaxies - VI. Frequency-period distribution of Cepheids in IC 1613 and other galaxies of the Local Group

The frequency-period distribution and other properties of Cepheids in IC1613 are discussed and compared with those of stars in our Galaxy (Milky Way), LMC, SMC, M31 and M33. Taking into account the observational limitations and related incompleteness, it is concluded that the frequency{period distribution of Cepheids in IC1613 is similar to that of SMC; we suspect that a much larger number of stars exist in IC1613 with a period of less than 2 d that have not yet been detected. A discussion of the deficiency of fundamental mode Cepheids with periods in the range 8{10 d in the Milky Way, M31 and M33 is reported. The present data are not sufficient to verify if this is produced by a real bimodal frequency{period distribution or whether depends on the lack of pulsating stars in such a period range due to pulsational stability reasons. Some arguments are presented in favor of a bimodal distribution that is a function of the average metallicity. The Milky Way, M31 and M33 have the two maxima located at the same periods, about 5 and 13 d, respectively. A comment on very long period Cepheids is also given.