Astron. Astrophys. 323, 235-242 (1997)

4. Comparisons and results

4.1. - diagram

Rather than compare the individual frequencies of several data sets, we have chosen to compare the classical helioseismic parameters and from the asymptotic approximation of frequencies. These two parameters are easy to derive from the frequency datasets and have widely accepted definitions. We have compared the four sets of frequencies from the IRIS network with the BiSON network p-mode frequencies (Elsworth et al. 1994), with the LOWL frequencies (Tomczyk et al. 1996), with two sets of theoretical frequencies computed by the Nice Observatory team (Morel et al. 1996), and another set computed by the Saclay group (Turck-Chièze et al. 1993).

We derived the "big separation," , using a second order polynomial fit of the echelle-diagram of the datasets from to , and the parameter from a first order fit to the ("small separation") quantity as previously described (Scherrer et al. 1983; Christensen-Dalsgaard 1988; Gelly et al. 1988), taking .

Fig. 5 summarizes our results. As a general comment, all observations are consistent with the same value of and are also compatible with all the models. For the errors bars are so small that they are not visible at the scale of the figure. Clearly all the observations lie on the left side of the figure and all the theoretical values on the right side. Simply using the meaning of in the asymptotic approximation, we interpret this discrepancy to some weakness in the treatment of the surface layers of the solar models. Comparisons of other seismological parameters derived from the same frequency tables lead to the same conclusion (Pantel 1996).

Fig. 5. plot using 4 IRIS frequency tables (), Bison frequency table (), LOWL frequency table (), P. Morel et al. theoretical frequency tables () for models with and without diffusion, and S. Turck-Chièze et al. theoretical frequency table () for a model without diffusion.

4.2. Solar cycle effects

The three years 1989-91 correspond to the maximum phase of solar activity, with a peak in the summer of 1989. In 1992 (last year of our study) solar activity underwent a precipitous fall toward its minimum. We have evaluated the frequency decrease due to solar cycle effects from 1989 to 1992 by computing the average frequency difference over a selected range of n: . Fig. 6 shows that the mean shift was for and p modes for n in the range . This is in good agreement with the BiSON result (Elsworth et al. 1994).

Fig. 6. P-mode frequency shift from 1989 to 1992 showing the same mean shift of for all and modes, except , .

The frequency dependence of the shift seen by other authors (Libbrecht et al. 1990) and the possible dependence (Palle et al. 1989, Anguera Gubau et al. 1991) are not discernable here because of the limited number of modes and the small number of power spectra. Such a study would require more data, but the quality of the individual frequencies measurement already allows a good determination of the mean frequency shift during this 3-year interval.

© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998

helpdesk.link@springer.de