On Nonlinear Radial Adiabatic Pulsations of Polytropes

Abstract: In [arXiv: 1312.1118] the author has found the formal series describing radial adiabatic pulsations of polytropes. These series include a time-dependent function, unknown yet. If a polytrope is uniform this function is obtainable; it is governed by the well-known equation of Bhatnagar and Kothari. In the present work it is shown that the pulsations of a polytrope with a near-equilibrium stratification are described by the same equation. These pulsations are nonlinear and their periods do not equal to the periods of the standard model. The periods of the vanishingly small pulsations are obtained; using them, the period-mass-radius relation is deduced. This relation is used to estimate masses of 11 chosen Cepheids with firmly known radii; all the masses found are between 5 and 11 solar masses that correlate well with the results of the stellar evolution theory.