On the universal stellar law for extrasolar systems

• We have developed the statistical theory of gravitating spheroidal bodies.
• We have introduced the universal stellar law (USL) for the planetary systems.
• We have estimated temperature of the stellar corona for different types of stars.
• We have derived the known Hertzsprung–Russell׳s dependence based on USL.
• We have testified the obtained results for multi-planet extrasolar systems.

In this work, we consider a statistical theory of gravitating spheroidal bodies to derive and develop an universal stellar law for extrasolar systems. Previously, it has been proposed the statistical theory for a cosmogonic body forming (so-called spheroidal body). The proposed theory starts from the conception for forming a spheroidal body inside a gas-dust protoplanetary nebula; it permits us to derive the form of distribution functions, mass density, gravitational potentials and strengths both for immovable and rotating spheroidal bodies as well as to find the distribution function of specific angular momentum. If we start from the conception for forming a spheroidal body as a protostar (in particular, proto-Sun) inside a prestellar (presolar) nebula then the derived distribution functions of particle as well as the mass density of an immovable spheroidal body characterize the first stage of evolution: from a prestellar molecular cloud (the presolar nebula) to a forming core or a protostar (the proto-Sun) together with its shell as a stellar nebula (the solar nebula). This paper derives the equation of state of an ideal stellar substance based on conception of gravitating spheroidal body. Using this equation we obtain the universal stellar law (USL) for the planetary systems connecting temperature, size and mass of each of stars. This work also considers the solar corona in the connection with USL. Then it is accounting under calculation of the ratio of temperature of the solar corona to effective temperature of the Sun׳ surface and modification of USL. To test justice of the modified USL for different types of stars, temperature of the stellar corona is estimated. The prediction of parameters of stars is carrying out by means of the modified USL as well as the known Hertzsprung–Russell׳s dependence is derived from USL directly. This paper also shows that knowledge of some characteristics for multi-planet extrasolar systems refines own parameters of stars. In this connection, comparison with estimations of temperatures using of the regression dependences for multi-planet extrasolar systems testifies the obtained results entirely.