With the software that we have just described we have produced two series of one year long each. The first corresponds to the status of the Sun in 1986, a year of minimum solar activity that it is a good example of what we found in 1996 when GOLF has begun its operations. The other one, is based on the sunspots recorded in 1991 which was a year of a maximum solar activity, which can be considered as a top limit of the activity GOLF is going to face in its lifetime.
The data products of the simulation have been organized in files of one day long. Each one has 1080 blocks of 80 seconds (one GOLF measurement cycle) consisting of one time and 16 intensities. This structure is the same than the one of the real scientific data files.
For each magnetic configuration of the sodium cell (B+ and B-, see
Fig. 1 (click here)) a definition of a "classical'' ratio of the mean
intensities can be made, similar to the standard two points ratio used by
earth-based spectrophotometers:
Where , are the intensities directly measured by GOLF (see
Fig. 1 (click here)).
An average of the two ratios, r(B+) and r(B-), is performed since both
have the same behaviour, and the statistical noise will decrease (a
comparison with this and other calibration methods can be seen in
García
et al. 1995). This ratio,
, is not linearly proportional
to the velocity along the year. Therefore, a correction for these non
linearities can be empirically calculated following
Pallé et al.
(1993):
where r' is the linearized ratio and V the radial velocity. To calculate
it, we have substituted V by V' (), which
corresponds to the known velocities and neglecting the other terms which are
sufficiently small. The calibrated velocity is obtained by a linear fit of
r' to (a+b V').
In Table 1 we show the value of each coefficient (a, b, c, d) obtained for the whole year. We have also included similar coefficients for the IRIS spectrophotometer (IRIS apparatus in Tenerife only measures the D1 component of the sodium doublet).
Coefficients | 1991 | IRIS | |
a | 3.436 ![]() ![]() | ||
b ![]() | 0.20403 ![]() | 0.13 | |
c ![]() | 3.78 ![]() ![]() | 4.5 | |
d ![]() | -9.37 ![]() ![]() | 2.6 |
The linealization expression (Eq. 12 (click here)) has been stopped at the 4th power of the velocity because it is enough to model the central part of the solar lines where the GOLF working points are located, within the earth based observational errors. On the other hand, we have proved that the more terms we add, the more dependent the coefficients are to the initials values introduced. The last term considered, V4, introduces only a small correction to the previous one, V2, so the next, V6, can be neglected, and the possible corrections would begin to characterize the "noise''.
Figure 4: Example of the simulated velocity residuals obtained
for a year with high solar activity
The coefficients are equal in the simulations of both series and there is also a general agreement between the coefficients of the simulation and these from IRIS. The most significative difference is in the b coefficient. This can be explained because GOLF is not only measuring in a different part of the solar line, but also because it measures in the three components of the sodium doublet, which changes significantly the measured slope. There is also the possiblity of small errors due to the not enough precise knowledge of the shape of the Solar sodium lines. A smaller value in b for the IRIS experiments can be explained by an effect of the parasitic light that has not been taken into account in the simulation, giving a higher value of the denominator (IR + IB) and, therefore, a lower value of b.
The velocity residuals () are obtained directly substituting
the calculated coefficients in the expression:
In Fig. 4 (click here) we can see the calibrated residuals in velocity. The
long time variations correspond to the velocity induced by the active
regions passing over the solar disk (compare with Fig. 2 (click here)), while
the small trends are a combination of and
.