High Precision Orthogonal Decomposition of the Solar Limb Darkening

Abstract

The Precision Solar Photometric Telescope (PSPT) at Mauna Loa Solar Observatory (MLSO) in Hawaii yields full disk solar images with high (approximately 0.1%) photometric precision. Determination of the solar limb darkening function and known image defects to the same level of precision presents fundamental conceptual and practical difficulties, but promises synoptic measurement of small variations in the mean thermodynamic stratification of the solar atmosphere. We describe a procedure which carefully identifies "quiet sun" in a PSPT image and uniquely determines a limb darkening function describing its radial intensity variation. The procedure performs a simultaneous least-squares fit to a truncated series of Legendre polynomials in radius and Fourier sine and cosine terms in central angle. The orthogonality of the functions allows capture, without mixing, of both the solar center to limb variation and any residual linear gradient present as an artifact. We demonstrate the accuracy and speed of the method on both simulated and real data.