The rotation of the solar core inferred by genetic forward modeling

Genetic forward modeling is a genetic algorithm-based modeling technique that can be used to perform helioseismic inversions of the Sun's internal angular velocity profile. The method can easily accommodate constraints such as positivity and monotonicity and readily lends itself to the use of robust statistical goodness-of-fit estimators. After briefly describing the technique, we ascertain its performance by carrying out a series of inversions for artificial splitting data generated from a set of synthetic internal rotation profiles characterized by various small inward increases in angular velocity in the deep solar core (r/R. less than or equal to 0.5). These experiments indicate that the technique is accurate down to r/R. similar or equal to 0.2, and retains useful sensitivity down to r/R. similar or equal to 0.1. We then use genetic forward modeling in conjunction with the LOW degree L (LOWL) 2 year frequency-splitting data set to determine the rotation rate in the deep solar core. We perform a large set of one-dimensional and 1.5-dimensional inversions using regularized least-squares minimization, conventional least-squares minimization with a monotonicity constraint (partial derivative Omega/partial derivative r less than or equal to 0), and inversions using robust statistical estimators. These calculations indicate that the solar core rotates very nearly rigidly down to r/R. similar to 0.1. More specifically, on spatial scales greater than or similar to 0.04 R. we can rule out inward increases by more than 50% down to r/R. = 0.2, and by more than a factor of 2 down to r/R. = 0.1. Thorough testing of various possible sources of bias associated with our technique indicates that these results are robust with respect to intrinsic modeling assumptions. Consequences of our results for models of the rotational evolution of the Sun and solar-type stars are discussed.