How Much Do Helioseismological Inferences Depend on the Assumed Reference Model?

We investigate systematic uncertainties in determining the proÐles of the solar sound speed, density, and adiabatic index using helioseismological techniques. We Ðnd that rms uncertainties (averaged over the Sun) of D0.02%È0.04% are contributed to the sound-speed proÐle by each of three sources : (1) the choice of assumed reference model, (2) the width of the inversion kernel, and (3) the measurement errors. The rms agreement between the standard solar model sound speeds and the best helioseismological determinations is about 0.07%. The proÐle of the adiabatic index, is determined to an accuracy of !1, about 0.02% with the Michelson Doppler Imager (MDI) data set. The density proÐle is about an order of magnitude less well determined by the helioseismological measurements. Five state-of-the-art models, each with a signiÐcant di†erence in the input physics or a parameter choice, all give comparably good agreement with global helioseismological measurements. We consider four deÐcient solar models that are constructed either using old input data, assuming the 3He] 4He fusion reaction does not occur, neglecting element di†usion, or artiÐcially mixing the interior of the Sun. When used as reference models in the inversion process, these deÐcient models yield sound speeds for the Sun that di†er only by 0.1% from the sound speeds obtained using the standard model. We conclude that even relatively crude reference models yield reasonably accurate solar parameters. Although acceptable for most purposes as reference models, nonstandard solar models in which the core is artiÐcially mixed or in which element di†usion is neglected are strongly disfavored by the p-mode oscillation data. These nonstandard models produce sound-speed proÐles with respect to the Sun that are 4.5 and 18 times worse, respectively, than the agreement obtained with the standard solar model. Subject headings : Sun: oscillations È Sun: interior