Solar Oblateness and Differentially Rotating Polytropes

Abstract

Dicke and Goldenberg (1967a) measured the solar oblateness to be σ= (5±0.7) × 10-5 and subsequently interpreted this measurement as evidence that the solar interior rotates with a period of 1.d8. With this interpretation, they then showed that the observed oblateness causes an 8% discrepancy in the Einstein prediction of the perihelion advance of Mercury. The stability analysis of Goldreich and Schubert (1967) seems to preclude such a fast rotation of the solar interior although magnetic field effects could alter their conclusions (Dicke, 1967). More recently Goldreich and Schubert (1968) and Fricke (1969) have calculated upper bounds to the solar oblateness essentially by finding the steepest distribution of angular velocity that is consistent with secular stability at each point in the equatorial plane of the sun. Fricke’s result of σmax=1.4 × 10-5 is based on a stronger stability criterion than that of Goldreich and Schubert who found σmax=1.4 × 10-4; Fricke, however, suggests that this may be in error and should actually be σmax=3.4 × 10-5. In their calculations of σmax the above authors assumed that the outer convective layers of the sun are rotating uniformly and that the angular velocity in the interior is a function of the radial distance from the center of the sun only. We note that while these assumptions are reasonable, neither of them is supported by the observed solar rotation.