The solar gravitational figure: J2 and J4
Abstract
The theory of the solar gravitational figure is derived including the effects of differential rotation. It is shown that J_{4} is smaller than J_{2} by a factor of about 10 rather than being of order J_{2} squared as would be expected for rigid rotation. The dependence of both J_{2} and J_{4} on envelope mass is given. High order pmode oscillation frequencies provide a constraint on solar structure which limits the range in envelope mass to the range 0.01 M_{E/solar} mass 0.04. For an assumed rotation law in which the surface pattern of differential rotation extends uniformly throughout the convective envelope, this structural constraint limits the ranges of J_{2} and J_{4} in units of 10 to the 8th power to 10 J_{2} 15 and 0.6 J_{4} 1.5. Deviations from these ranges would imply that the rotation law is not constant with depth and would provide a measure of this rotation law.
 Publication:

California Univ., Los Angeles Report
 Pub Date:
 1980
 Bibcode:
 1980ucla.rept.....U
 Keywords:

 Solar Gravitation;
 Solar Physics;
 Solar Rotation;
 Angular Acceleration;
 Centripetal Force;
 Convection;
 Momentum;
 Perturbation Theory;
 Poisson Equation;
 Solar Activity;
 Stellar Envelopes;
 Solar Physics