## 4. ResultsWe will now describe our final results of the fitting of the low
degree () p-mode parameters using the
GONG data and demonstrate that their determination is better than
others found in the literature. In summary, we fitted the Fourier
spectra instead of the power spectra for all By estimating accurately the low degree p-mode parameters using high spatial resolution data, we enabled the creation in the future of a homogeneous set of frequencies and rotational splittings for estimating the solar structure and rotation profile. ## 4.1. FrequenciesThe frequency results are shown in Table 1. We have identified
139 p modes with (81 with
) with an estimate of the
uncertainties on the fitted frequency of less than
0.2
We have compared our frequencies with those of the GONG project for a three-month time series starting on 6 June 1996, which is essentially contained within the period used here. In that analysis, the power spectra was fitted instead of the Fourier spectra and the leakage between the elements of a multiplet was not taken into account (Hill et al. 1996). Its number of identified modes for is very small. Out of the 55 frequency determinations in common with ours for , 93 coincide within 3 (using combined errors), 82 within 2 and 55 within 1. We have compared our frequencies with those of the GOLF instrument
on board the SOHO satellite (Lazrek et al. 1997) which performs
full-disk integrated light velocity measurements. They used an
eight-month observational period, of which four overlap with the GONG
observations used here. Their frequencies are in good agreement with
ours. Out of the 72 frequency determinations in common with ours for
, 100
coincide within 3 (using combined
errors), 93 within
2 and
71 within
1, meaning that the scatter is due
to a normally distributed noise. For
, the estimate of the uncertainties
on the fitted GOLF frequency is similar to ours for the same modes but
for , 2 and 3, they are significantly
larger than ours, approximately
times larger. This is due to a combination of different
signal-to-noise ratios, modes detected and length of observing time.
In addition, the GOLF frequency errors are the average of statistical
errors in the fittings done for different authors. Last but not least,
the time series for in the GONG
data analysis is calculated in a different way than the other degrees;
it is obtained through the spatial average of each solar image, in
such a way that, for , GONG
simulates an integrated light instrument. In the
fitting, the
modes were fitted simultaneously.
This is necessary not only for modes with
We also compared our results with the LOWL data, which is a one-site instrument. The data we used was velocity measurements (125 square pixels), starting in February 1995 and it is one-year long, thus having a six-month overlap with the GONG data used here (Tomczyk et al. 1995). Out of the 87 LOWL frequency determinations for , 93 coincide within 3 (using combined errors), 72 within 2 and 45 within 1. Despite the good agreement between the frequency determination, the
GONG frequencies are systematically lower than GOLF and LOWL
frequencies. The weighted average of the frequency differences between
our work and LOWL is
## 4.2. Splitting coefficientsFig. 6b shows the splitting coefficients results found for up to 6 as a function of the lower turning point position. The coefficients for and high-order modes are very scattered and have larger error bars than the others. The small number of elements in the multiplets and the very small value of the splitting, of the order of 10 times the uncertainty in the mode frequency, impose difficulties on the splitting determination. This scattering in the splitting coefficients determination is also present in the analysis of a very low spatial resolution instrument, LOI/SOHO (Appourchaux et al. 1998c), and in integrated light instruments. The splitting for the three-month GONG series is poorly determined.
This is probably due to the short period of observation and the
incorrect treatment of the mode leakage. However, it agrees with our
results towards higher degree modes. The weighted averages over
When compared with GOLF determinations (Lazrek et al. 1997), our error bars are smaller and our measurements are similarly scattered for modes. However, for and 3 modes, our data are less scattered and the error bars are much smaller. ## 4.3. LinewidthsFinally, the estimated linewidth
(Eq. 3) of the modes obtained from the fit are shown on Fig. 9. The
power-law behaviour of the linewidths is clearly visible for all
degrees at the low and high frequency limits:
(28 observations) for
© European Southern Observatory (ESO) 1999 Online publication: April 28, 1999 |