Parameters and Pulsation Constant of Cepheid.

The analysis of fifty empirical period-radius relations and forty-three empirical period-luminosity relations is performed for the Cepheids. It is found that most of these relations have significant systematic errors. A new metrological method is suggested to exclude these systematic errors using the new empirical metrological relations and the empirical temperature scale of the various samples of the Cepheids. In this regard, the reliable relations between the mass, radius, effective surface temperature, luminosity, absolute magnitude on the one hand, and the pulsation period on the other hand, as well as the reliable dependence of the radius on the mass are determined for the Cepheids of types δ Cephei and δ Scuti from the Galaxy. These reliable relations permit us to accurately determine the empirical value of the pulsation constant for the Cepheids of both types for the first time. It is found that the pulsation constant very weakly depends on the pulsation period of the Cepheid, contrary to the known theoretical calculation. Hence, the Cepheids pulsate almost as a unified whole and homogeneous spherical body in wide ranges of a star's mass and evolutionary state with an extremely inhomogeneous distribution of stellar substance over its volume. Therefore, it is first suggested that the pulsation of the Cepheid is, first of all, the pulsation of the almost unified whole and homogenous shell of its gravitational mass. This pulsation is triggered by well-known effects; for example, the local optical opacity of the stellar substance and overshooting, using the usual pulsation of the stellar substance. [ABSTRACT FROM AUTHOR]