*Astron. Astrophys. 355, 743-750 (2000)*
## 3. Fitting the GOLF data
The GOLF series used covers the 805 days between April 11, 1996 and
June 25, 1998, with more than 99% continuity. The GOLF raw data have
been converted to velocities using the calibration techniques
described by García (private communication) prior to carrying
out an FFT transform on the entire series, with a sampling time of 80
seconds. Only the GOLF detector PM2 has been used in this
analysis.
The classical fitting technique in this domain consists of fitting
a simple Fourier power spectrum, often using codes derived from those
offered by Appourchaux et al. (1998). For such a spectrum,
statistics are applicable and the
fitting is then by the *maximum likelihood method* .
The entire analysis was limited to the spectral range 2000
to 3600
. Our objective requires very high
precision, which we cannot obtain reliably outside of this range.
Above 3600 the modes overlap
seriously. Below 2000 , the signal to
solar background ratio is smaller and, more importantly, the number of
bins which contribute to the line is small due to the smaller
linewidth. These limitations are particularly critical for the
asymmetry parameter.
A critical point is the choice of the spectral window used for
fitting the p-modes profiles, i.e. how much of the spectrum we fit at
a time. Some workers choose to fit the entire *p*-mode spectrum,
arguing that this is the only way to correctly take account of the
effect of the far wings from distant modes (Roca Cortes et al. 1998).
This can be done only if the model profile assumed for the modes is
valid everywhere in the window or if the residual errors are
negligible compared with errors due to the stochastic noise. It also
assumes that the overlapping far wings are additive on a scale of
spectral power, which is not evident. As the Nigam formula used in
this paper is obtained by a Taylor expansion around the eigenfrequency
of the mode (Nigam & Kosovichev 1998), we adopted the approach of
fitting only those close multiplets that have an evident overlap, i.e.
fitting was carried out over limited spectral ranges with the
neighbouring =0 and
=2 grouped together, as were the
=1 and
=3. The choice of a precise window is
discussed in Sect. 5 and corresponds to a trade off between the
effects of the stochastic noise and of the validity of the formula.
This alternative to a fit of the whole spectrum has the cost of
considering the contribution of other resonances as a flat
"background". In all cases, there exists an unknown continuous
component due to solar noise (plus perhaps instrumental noise) for
which arbitrary parameters are used. In the present work, we performed
tests and simulations to quantify the errors due to our assumptions.
These include that the background is represented by a constant value,
the slope being assumed to be zero over the limited range of window.
All of the components in the fitted range were assumed to have the
same asymmetry factor, but the linewidth was allowed to vary with the
degree. The relative amplitude of the mode components was taken as a
fixed empirical function of
m,
which was derived by taking a mean over observations from different
orders. For =2, we use
(*m*=2)/(*m*=0)=1.7
and for =3,
(*m*=3)/(*m*=1)=1.7
(Lazrek, private comunication).
Here, the splitting is defined as the mean for each multiplet of
the separation between the modes
*m*=1.
The uncertainty quoted here for each parameter determined is the
statistical error obtained from the fitting program, using
appropriately the covariance matrix of the fit. We performed Monte
Carlo simulations (based on a method developed by Fierry Fraillon et
al. 1997) which confirm the reality of these uncertainties.
© European Southern Observatory (ESO) 2000
Online publication: March 9, 2000
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