Uncovering the Bias in Low-Degree p-Mode Linewidth Fitting

Abstract

Obtaining reliable estimates of linewidths in the power spectra of low-degree p modes is problematic at low frequency. In this regime, the mode coherence time increases with decreasing frequency, often causing the modes to be unresolved in relatively long duration spectra. The signal-to-noise ratio is also less favourable at low frequency, resulting in fits to power spectra underestimating the true linewidth of the p modes owing to the tails of the Lorentzian peaks becoming dominated by the background noise. We use a numerical simulation approach to assess the effect of this bias on the fitted widths of p-mode peaks and calculate observational duration limits required to obtain an unbiased estimate of the p-mode linewidth as a function of frequency. This is done in four different cases, where the precision of the artificial data is set at 0.25, 0.50, 0.75, and 1.00 m s⁻¹ by adding random scatter to increase the sample standard deviation per 40-second measurement. In all cases, the observational duration required to accurately obtain width estimates increases beyond that required for sufficient spectral resolution below a certain threshold frequency. For modes at ≈ 1500 μHz, with an amplitude of approximately ten times the background, observations of up to 972 days are required to obtain an unbiased estimate of the linewidth. This is equivalent to ≈ 18 times the coherence time of the corresponding p modes.