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

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4. Evidence of asymmetry as a property of p-modes

In this section, we first show that a non-negligeable unexpected effect obtained when fitting the modes with Lorentzian profiles can be explained by the presence of asymmetry. We then checked that this asymmetry is not an apparent one, but is due to an intrinsic property of the p-modes.

4.1. Evidence of an effect

If we leave free the width of the two components of an [FORMULA]=1 mode, a Lorentzian fit gives a systematic and significant difference between the two widths. As shown by Fig. 2, this difference can reach a factor of 2. We show by fitting Lorentzian profiles to simulated asymmetric ones that this effect can be totally explained by the asymmetry of the profiles. We also checked that the widths of the two components of an [FORMULA]=1 mode converge to the same value when fitting with the asymmetric formula. As shown further, the [FORMULA]=0 modes exhibit an asymmetry of the same magnitude. This argues against the [FORMULA]=1 effect being due to a real difference between the width of the m components.

[FIGURE] Fig. 2. Linewidth of the components of the [FORMULA]=1 modes using a Lorentzian fit, when both widths are independent free parameters.

4.2. Solar activity

An apparent asymmetry of the profiles might arise as a result of a slow drift of the frequencies combined with a change in amplitude. Solar activity, by moving the outer boundary of the acoustic cavity, changes the propagation times and thereby the frequencies of the modes during the cycle. It has been estimated that, when the previous solar cycle approached maximum activity, the frequencies increased (Palle et al. 1989, Elsworth et al. 1990), up to about 0.4 [FORMULA] and at the same time the energies of the modes decreased by nearly 30% (Anguera Gubau et al. 1992). Although Fierry Fraillon et al.(1998) did not find any effect of activity on GOLF frequencies over the first 690 days of our series, we preferred to check the temporal stability of the asymmetry parameter. To do this,we have analysed separately seven subseries of 115 days duration. Fig. 3 shows clearly that the asymmetry factor is of the same magnitude for the subseries as for the entire series, even at solar minimum, confirming that change in activity over the 805 days observed is insufficient to account for our measured asymmetries.

[FIGURE] Fig. 3. The asymmetric parameter for independent successive 115 days sub-series (example of the mode [FORMULA]=0, n=20). The dashed line corresponds to the value obtained from the entire time series.

4.3. Influence of background

In the fitted range there exists a background signal due to the solar convective motion (Harvey 1985, Palle et al. 1995) as well as the far wings of all of the other modes. Our fitting assumes this background to be flat in the fitting window. To see whether the real slope could produce the apparent asymmetry, we performed an asymmetric fit on a synthetic p-mode Lorenzian profile superimposed with a curve simulating convective background slope. This slope was estimated in the 700-1100 [FORMULA] range, and then extrapolated to our domain of study. The apparent asymmetry, B, obtained is at most -0.0004 which is some 50 times lower than the values measured in real data (see Sect. 5).

On the other hand, to study the influence of the wings, we simulated synthetic spectra by adding all of the p-modes profiles determined by separate Lorentzian fits. Individual asymmetric fits were then made on this synthetic spectra. The asymmetry obtained is mostly positive with a maximum of 0.0008. This confirms that it is adequate to assume a flat background over the limited range used in our fitting technique.

4.4. Influence of high [FORMULA] modes

Finally, we have carried out tests to see whether the existence of higher degree modes might compromise our fitting procedures. For the simulations, we have taken values of the amplitude and frequencies of these modes derived by one of our authors in a separate study (T. Roca Cortés, private communication). The [FORMULA]=4 mode, which would tend to increase the apparent [FORMULA]=2 asymmetry, is not inside our fitting window. Our simulation shows that its wings have a negligible effect on the results we obtain.

For the [FORMULA]=5 mode, which would tend to decrease the apparent [FORMULA]=0 asymmetry, the window we use normally includes less than half of the mode structure. In this case the uncertainty on the anticipated amplitude of this mode is too large to be useful. Instead, we have investigated our fit with the real data, a fit in which we do not take account of the existence of the [FORMULA]=5 mode. We displace progressively the high-frequency limit of the fitting window, until it includes all of the anticipated [FORMULA]=5 mode. It is found that the resulting parameters for the pair [FORMULA]=0 - [FORMULA]=2 vary negligibly with the window size, indicating that there is a negligible effect from neglect of the [FORMULA]=5 mode.

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© European Southern Observatory (ESO) 2000

Online publication: March 9, 2000