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Astron. Astrophys. 364, 816-828 (2000)

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6. Magnetic field effects

An important additional task is the identification and quantification of the non-coherent magnetically induced signal seen by GOLF. For this purpose we need to use an independent set of information having time resolution in the frequency range of interest but which is derived from spatially resolved and magnetically sensitive measurements such as are available from the MDI experiment. The MDI instrument provides a line depth parameter which indicates the equivalent width of the [FORMULA]nm line and that this parameter is magnetically sensitive. However, it does not provide a definite one-to-one mapping to the magnetic field and is also subject to influence by non-magnetic effects, especially on some portions of the solar image (e.g. Henney et al. 1998) and is available only on a 12 minute cadence after anti-aliasing temporal filtering. In addition, the MDI instrument also provides magnetograms but only once every 90 minutes. Consequently, there is not a single dataset which provides adequate information for use in modeling the magnetic effects on the GOLF data stream. Nonetheless, it may be possible to combine these data streams in such a way as to mitigate the magnetic effects on the GOLF signal. In order to prepare for such analysis, we give here a treatment of the magnetic effects in a form which is consistent with the discussion above of the velocity modelling.

We define sensitivity functions for magnetic field effects in the form:


The key new quantities are the magnetic field derivatives in the numerators of these expressions. These can be written:


In order to evaluate these expressions and apply them to the case of the GOLF data, it is necessary to have measurements of the magnetic sensitivity of both D lines. Unfortunately, the telluric contamination of the D2 line compounds the difficulty of isolating magnetic effects on the line profile. As a result a set of resolved sun profile measurements adequate to evaluate the derivatives in Eqs. 37 and 38 is available only for the case of the D1 profile. Consequently, we are forced to neglect the separate contributions for the D2 line and assume that the variations in the D1 line are representative of the total effect on the GOLF instrument. This may be a resonable approach since at the position of the working point on the D1 line the line shape parameters are intermediate between those of the two working points on the D2 line. With this approximation we can write:


where the sensitivity coefficients [FORMULA] and [FORMULA] are:


The response of the D2 line could be included in similar formulae by replacing these sensitivity coefficients with appropriately weighted averages over the three components.

Two sets of data have been used to evaluate the sensitivity coefficients for the D1 line. First, during the period from Nov. 1, 1992 to Feb. 3, 1993, a sequence of line scans following the methods described in Sect. 3. These observations lead to a determination of [FORMULA] and [FORMULA] as a function of the velocity relative to the bisector velocity. Second, magnetograms taken in the D1 line were selected for good sky transparency and good distribution of magnetic activity and used to determine the correlation between bisector intensity and magnetic field strength in annular rings. These observations lead to a determination of G. The magnetograms from 25-Jun-2000 to 28-Jun-2000 along with those from 19, 20 and 24-Jul-2000 were used for the bisector intensity versus magnetic field strength correlation determination. Six annular rings were chosen having center-to-limb angle limits defined by [FORMULA] with [FORMULA]. The magnetograms utilize spectral selection ports having separations of 19.6 and 22.8 pm. The two GOLF bisector half-separations for the D1 line correspond to 10.72 and 11.09 pm. The correlation coefficients from the magnetograms were interpolated to correspond to 10.90 pm. The derived values of G are shown in Fig. 6. The error bars shown are from the changes between the different magnetograms utilized. The observations used for the line profile sensitivity determination are listed in Table 1. They were averaged in the groups indicated and the changes in the averages were normalized for a 100 gauss magnetic field difference. The derived [FORMULA] functions are shown in Fig. 7 and Fig. 8. Note that because the G and [FORMULA] functions tend to cancel, the magnetic effect tends to emphasize those parts of the solar disk which are closest to the bisector velocity.

[FIGURE] Fig. 6. The dependence of the bisector intensity correlation coefficient on the center-to-limb angle [FORMULA].

[FIGURE] Fig. 7. The dependence of [FORMULA] on the reference velocity (the velocity offset from the bisector point).

[FIGURE] Fig. 8. The dependence of [FORMULA] on the reference velocity.


Table 1. Line profile observations

The magnetic darkening process was discussed by Ulrich (1993) and the effect can be modelled in the GOLF data. The present results are consistent with this previous publication and provide more detail for application to modelling the effect. The MDI instrument provides a proxy based on the shape of the Ni line at [FORMULA]nm. The correspondence between this parameter and the solar magnetic field is not perfect and it may be necessary to combine high temporal cadence information from the line width parameter with lower temporal cadence information from the direct MDI magnetograms. The Mt. Wilson 150-foot solar tower utilizes a 24 channel system which permits the simultaneouos simulation of these MDI parameters - the magnetic field calculated from velocity images taken with opposite states of circular polarization and the line depth parameter [FORMULA] along with the measurement of [FORMULA], the magnetic field at the GOLF working points in the D1 line. From this data we estimate that the MDI magnetic field is about 80% as strong as that from the D1 line and that the derivative [FORMULA] (gauss)-1. For a fixed value of [FORMULA] the scatter in [FORMULA] is about 0.03 so that a simple conversion of [FORMULA] to a change in intensity at the GOLF working point could produce a noisy result.

Future instruments such as those under development by the GONG project will provide magnetic field measurements with adequate temporal cadence. Analysis of the shape of the temporal power spectrum of GOLF single-wing data shows that active regions are a major contributor in the frequency range of interest (Ulrich et al. 2000). This result lends urgency to the development of a full treatment of the active region effects.

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Online publication: January 29, 2001