Astron. Astrophys. 355, 743-750 (2000)

2. Mode asymmetry

The use of an arbitrary asymmetric form for the fitting profile may serve to improve the quality of the fit, but it cannot provide us with a valid resonance frequency. By assuming a physical basis for the asymmetry and adopting a derived parametric form for the fitting profile, the resonance frequency is obtained as one of the parameters in the fitting process. This frequency corresponds neither with the maximum, nor the centroid of the profile, but is systematically to one side. It is for this reason that fitting an asymmetric resonance with a Lorentzian profile leads to systematic errors in frequency.

In many areas of physics, the mixing of a resonant frequency with the nearby spectral continuum leads to an asymmetric profile, when the continuum is correlated with the resonance. This arises because the reversal of phase at the resonant frequency leads to a switch from addition to subtraction with the continuum. This effect, well-known in atomic spectroscopy, produces the familiar Fano profiles in autoionising lines, seen in absorption (Fano 1961).

In helioseismology, asymmetry has been interpreted by a number of authors (Duvall et al. 1993, Abrams & Kumar 1996) as due to the interaction between the resonant cavity mode and the local emission from discrete sources. However, this effect alone failed to explain the observation that the sign of the asymmetry is reversed when viewed in intensity and velocity. Recently, Nigam & Kosovichev (1998) modified the principle by adding also a correlation between the resonance and the background continuum, or solar noise. Since the solar noise, or granulation, is regarded as the source of excitation of the modes, it is reasonable to suppose that a part of this noise would be correlated with the modes. After some simplifying approximations, they offer the expression:

suitable for fitting to the observed spectrum where and are the mode amplitude, linewidth, central frequency and uncorrelated linear background noise respectively. The parameter B, which controls the asymmetry, contains the effects of correlated noise and of the source, the two factors that are claimed to be responsible for asymmetry. It is with the use of this expression that Toutain et al. (1998) have successfully explained the difference in sign between VIRGO and MDI asymmetries, confirming Nigam's predictions. Until the availability of this formula, we had been studying the asymmetry in GOLF using the Fano profiles (Thiery 1997), which include only the effect of interaction with the continuum. The present work has been carried out using Nigam's formula. Fig. 1 shows a typical example of a Lorentzian and an asymmetric fitting to a GOLF resonance.

Fig. 1a and b. Example of fitting (modes =0, 15 and =2, 14) using Lorentzian profiles a and Nigam profiles b . Note the improved agreement (visible in the wings) between the fit and data when the asymmetry is taken into account. The resolution for the plot is reduced to 0.29 .

© European Southern Observatory (ESO) 2000

Online publication: March 9, 2000
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