is the coefficient of radiative conductivity. As usual, a is the radiation pressure constant, c is the speed of light, and k is the coefficient of opacity per unit mass.

In the following we shall consider a mixture of blackbody radiation and a simple ideal gas. Neglecting the ionization and excitation energies, we thus replace Eqs. (2.13) and (2.14) by

p and

ix 3

For isentropic motions, Eq. (2.11) becomes

thus expressing that the specific entropy of each fluid particle remains a constant along its path (although this entropy may differ from one path line to another). Equation (3.9) can be written also in the form

Here we have let

where p = pg/(pg + pr) is the ratio of gaseous pressure to total pressure. One can also write

where -2 and -3 are related to — by the following relations:

The variation of the ratio p is given by

The -s reduce to the usual adiabatic exponent y = cp/cV in the limit pr ^ pg; they reduce to 4/3 for blackbody radiation alone (pg ^ pr). For a mixture of an ideal gas and blackbody radiation, the generalized adiabatic exponents are intermediate in value between 4/3 and y .

3.2.1 The Poincare-Wavre theorem

The simplest model of a rotating star we can make is to assume that the configuration rotates about a fixed direction in space with some assigned angular velocity. Assume further that the star is axially symmetric and that the motion is steady in time. Let the star rotate about the z axis, and take the center of our inertial frame of reference at the center of mass. Then, in cylindrical polar coordinates (m, z), the velocity v has the form v = Qm(3.15)

where \9 is the unit vector in the azimuthal direction. By virtue of our assumptions, Eq. (3.3) is identically satisfied. Since we have neglected any large-scale motion in meridian planes passing through the rotation axis, the y component of Eq. (3.1) is identically satisfied also. The remaining components of this equation imply that

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