Pubs.GISS: Abstract of Canuto and Hsieh 1981

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Canuto and Hsieh 1981

Canuto, V.M., and S.-H. Hsieh, 1981: Scale covariant gravitation. VI. Stellar structure and evolution. Astrophys. J., 248, 801-812, doi:10.1086/159204.

Using the scale covariant theory of gravitation, we derive results of interest to stellar structure and evolution.

We first derive the radiative transport equation which finds an immediate application in the study of stellar evolution with a variable gravitational "constant" G.

We show that the Sun's absolute luminosity scales as L ~ G*M/κ, where κ is the stellar opacity. Taking into account that the Earth-Sun distance is also affected by a variable G, it is then shown that the Earth's effective temperature scales like T_eff ~ (G²*M/κ)^(1/4). Comparisons with previous estimates, based on simple Newtonian framework, are presented and discussed.

A third result that follows from this analysis is that a polytropic equation of state of the form p ~ ρ^γ is incompatible with a variable G, the correct result being p ~ ρ^γ*(G/β²)^(γ-1), where β is the gauge function relating atomic to gravitational times.

Finally, we derive a formula for the age of globular clusters as a function of G, using the previously derived expression for the absolute luminosity.

Numerical estimates are presented.