Distortion of the p-mode peak profiles by the solar-cycle frequency shifts: do we need to worry ?

We seek to address whether solar-cycle frequency shifts of the Sun's low-l p modes 'distort' the underlying shapes of the mode peaks, when those peaks are observed in power frequency spectra made from data spanning large fractions, or more, of the cycle period. We present analytical descriptions of the expected profiles, and validate the predictions through use of artificial seismic time-series data, in which temporal variations of the oscillator frequencies are introduced. Our main finding is that for the Sun-like frequency shifts the distortion of the asymmetrical Lorentzian-like profiles is very small, but also just detectible. Our analysis indicates that by fitting modes to the usual Lorentzian-like models - which do not allow for the distortion - rather than new models we derive, there is a bias in the mode height and linewidth parameters that is comparable in size to the observational uncertainties given by multi-year data sets. Bias in the frequency parameter gives much less cause for worry, being over an order of magnitude smaller than the corresponding frequency uncertainties. The distortion discussed in this paper may need to be considered when multiyear Sun-like asteroseismic data sets are analysed on stars showing strong activity cycles.