Period-luminosities relation of classical Cepheids

A new PL-relation (10) — Figure 2 for the Cepheids in the Galaxy, the Magellanic Clouds and M31 has been constructed. On deriving this relation both the period-radius (3) and period-colour relations (7), (8) and (9) are essentially used. The PC-relation (7) determined after the colours of 88 galactic cepheids (Table I), which are obtained from the colour-spectrum relation (6) — Figure 1, common for Cepheids and non-variable supergiants, are used also for the M31 Cepheids, whereas (8) and (9) are for the Large and Small MC Cepheids, respectively, all three PC-relations having a common slope. The comparison of the relations (8) and (9) with (7) shows that the LMC and SMC Cepheids are bluer than the galactic ones with 0^m.04 and 0^m.19, respectively, probably because of their metal-poor abundance. The places of thes-Cepheids in Figure 2 show that these Cepheids possess a dissimilar PL-relation with a different slope. The reason for such a difference is that thes-Cepheids are first harmonic pulsators. The distance moduli of the three galaxies under discussion are obtained from the PL-relation (10). The colour-coefficient of period-colour-luminosity-relation is briefly discussed. The general conclusion based on a comparison of the PL-relation in the present paper with those by other authors (Table V) is that our PL-relation differs in the zero-point by less than 0^m.2; therefore, the manner of constructing the PL-relation by means of PR and PC-relations is reasonable and useful.