On measuring low-degree p-mode frequency splitting with full-disc integrated data

The standard method of measuring rotational splitting from solar full-disc oscillation data, based on maximum-likelihood fitting of multi-lorentzian p rofiles to oscillation power spectra, systematically overestimates the spli tting. One of the reasons is that the maximum likelihood estimators (MLE) b ecome unbiased only asymptotically as the number of data tends to infinity; for a finite data set they are often biased, inducing a systematic error. In this paper we assess by Monte Carlo simulations the amount of systematic error in the splitting measurement, using artificially generated power spe ctra. The simulations are carried out for multiplets of degree l = 1, 2 and 3 with various signal-to-noise ratios, linewidths and observing times. We address the possible use of non-MLE estimators that could provide a smaller or negligible systematic error. The implication for asteroseismology is al so discussed.