By George W. Collins
This textbook designed for complicated undergraduate scholars covers the rules and ideas within the box, and provides the required heritage for complex classes. starting with a survey of a few of the basics of statistical mechanics, Collins builds up the physics of stellar constitution st
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Extra resources for The Fundamentals of Stellar Astrophysics
Some additional property of the system will have to be invoked to relate the last generated higher moment to one of lower order, in order to close the system of equations and allow for a solution. To demonstrate this process, we show how the equation of continuity, the Euler-Lagrange equations of hydrodynamic flow, and the virial theorem can all be obtained from moments of the Boltzmann transport equation. Continuity Equation and the Zeroth Velocity Moment Although most moments, particularly in statistics, are normalized by the integral of the distribution function itself, we have chosen not to do so here because the integral of the phase density f over all velocity space has a particularly important physical meaning, namely, the local spatial density.
Sooner or later the equation of state must change over to the fully relativistic equation of state. 19) 30 1. 16), then the radius also disappears and M ~ constant . 20) Thus, for a fully relativistic degenerate gas, there is a unique mass for which the configuration is stable. Should mass be added beyond this point, the star would be forced into a state of unrestrained gravitational collapse. Much later we shall see that a further change in the equation of state, which occurs when the density approaches that of nuclear matter, can halt the collapse, allowing the formation of a neutron star.
With this notion that ( Q/dT)│α is the specific heat at constant α , we make the generalized definition of polytropic change to be 43 1. 6) where C is some constant. 7) Now for an ordinary gas it is common to define the ratio of specific heats (CP/CV) as γ. 1)]. 2)], which means the gas behaves adiabatically. If C = 4, then the gas is isothermal. The polytropic equation of state provides us with a highly specific relationship between P and ρ. However, hydrostatic equilibrium also provides us with a specific relationship between P and ρ, and we may use the two to eliminate the pressure P, thereby obtaining an equation in ρ alone which describes the run of density throughout the configuration.