The Extraction of Rotational Splittings from Monte Carlo Simulations of Unresolved Low-` Data

We have generated in the time domain, and then tted in the frequency domain, artiicial representations of low-` p-mode pairs (quadrupole-monopole, and octupole-dipole), covering the range n 9 to 26. These data were designed to mimic those collected from unresolved observations of the solar disc. At each simulated radial order, some 250 independent realizations of the same basic mode pair have been tted. From the distribution of tted rotational splittings at each n, we nd: (i) an increasing tendency for the formal error in the splitting (returned by the mode-tting procedure) to be anti-correlated with the extracted splitting as n increases; and (ii) a tendency for the mean of the tted splitting distribution to increasingly overestimate the actual, input splitting, again as n increases. This latter eeect is more marked in the weighted mean of each high-n distribution (as opposed to the unweighted or median estimate) owing to the splitting-uncertainty anti-correlation. Further , both eeects are more severe at lower`, owing to the closer spacing in frequency of the sectoral components of the modes (which are the strongest in any data derived from unresolved helioseismic observations).