Constrained estimates of low-degree mode frequencies and the determination of the interior structure of the Sun

Low-degreep-modes penetrate to the solar centre and provide direct information about the core. However, the high observational accuracy that is required to resolve the details of the structure of the core is difficult to achieve because the oscillation power spectrum is significantly distorted by stochastic forcing of the oscillations, which appears as multiplicative noise. Here, an attempt is reported to reduce uncertainties of spectral parameter estimation by incorporating constraints imposed by smooth behaviour of some of the parameters (e.g., linewidths, background noise, rotational splitting) over a group of lines. Instead of estimating these parameters independently for each line, we determine them as smooth functions of frequency. It is expected that this procedure gives more accurate estimates of the average frequencies of any multiplet in the power spectrum, to which we have applied no constraints. We give some examples of the procedure for whole-disk measurements by the IPHIR space experiment. It is shown that the additional constraints do not result in significant changes in the frequency estimates, except for one mode whose peak in the power spectrum has the lowest signal-to-noise ratio. However, the uncertainty in the frequency of that mode does not influence substantially the results of the structure inversion in the core. Inversions of the IPHIR datasets are compared with corresponding inversions of data from the Birmingham Solar Oscillation Network (BISON). The IPHIR data indicate a sharp increase towards the centre of the deviation of the squared sound speed of the sun from that of a standard solar model, whereas the BISON data show a decrease. The difference between the IPHIR and BISON inversions is significant, preventing any definite conclusion about the deviation of the structure of the solar core from that of the model.