Measurements of frequencies of solar oscillations from the MDI Medium-l Program

Inversions of solar internal structure employ both the frequencies and the associated uncertainties of the solar oscillation modes as input parameters. In this paper we investigate how systematic errors in these input parameters may affect the resulting inferences of the sun's internal structure. Such systematic errors are likely to arise from inaccuracies in the theoretical models which are used to represent the spectral lines in the observational power spectra, from line blending, from asymmetries in the profiles of these lines, and from other factors. In order to study such systematic effects we have employed two different duration observing runs (one of 60 days and the second of 144 days) obtained with the Medium-l Program of the Michelson Doppler Imager experiment onboard the SOHO spacecraft. This observing program provides continuous observations of solar oscillation modes having angular degrees, l, ranging from 0 to ∼ 300. For this study intermediate-and high-degree p-mode oscillations having degrees less than 251 were employed. In the first of our tests we employed two different methods of estimating the modal frequencies and their associated uncertainties from the 144-day observational power spectra. In our second test we also repeated both methods of frequency estimation on the 60-day time series in order to assess the influence of the duration of the observed time series on the computed frequencies and uncertainties. In a third test we investigated the sensitivity of the computed frequencies to the choice of initial-guess, or 'seed' frequencies that are used in the frequency estimation codes. In a fourth test we attempted to investigate the possible systematic frequency errors which are introduced when the observational asymmetry in the p-mode peaks is ignored. We carried out this particular test by fitting simple models of asymmetric line profiles to the peaks in the observational power spectra. We were then able to compute the differences between those frequencies and our previous frequencies which had been obtained using the assumption that all of the observational peaks were symmetric in shape. In order to study the possible influence of the two different frequency estimation methods upon the radial profile of the internal sound speed, we carried out four parallel structural inversions using the different sets and subsets of frequency estimates and uncertainties as computed from the 144-day observing run as inputs. The results of these four inversions confirm the previous finding by the GONG project (Gough et al., 1996) and by the MDI Medium-l Program (Kosovichev et al., 1997) that, in a thin layer just beneath the convection zone, helium appears to be less abundant than predicted by theory. However, differences in our four inverted radial sound speed profiles demonstrate that the currently-available techniques for determining the frequencies of the Medium-l oscillation peaks introduce systematic errors which are large enough to affect the results of the structural inversions. Moreover, based upon the differences in these four inverted sound speed profiles, it appears that the choice of which subset of modes is included in a particular inversion and which modes are not included may also be introducing systematic errors into our current understanding of solar internal structure. Hence, it appears to be very important that consistent sets of modal selection criteria be employed. Finally, at least one of the two frequency estimation codes which we used was not sensitive to changes in the input 'seed' frequencies which were employed as initial guesses for that code. This result allays fears that the difference in the helium abundance between the sun and the reference solar model in the thin layer beneath the convection zone which was mentioned above might have been due to the particular seed frequencies which were employed in the earlier inversions. Since this thin layer may likely be the place where the solar dynamo operates, it will be extremely important to observe any possible evolution of this transition layer throughout the upcoming 11-year activity cycle.