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

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2. The GOLF signal

The sensitivity of the GOLF signal has recently been discussed by García et al. (2000) and Ulrich et al. (1998, 2000). Details of the system in terms of the magnetic field configuration, the properties of the scattering cell and the resultant scattering strengths are found in those papers. The objective of this paper is to evaluate solar factors which influence the GOLF measurement. There could be additional factors due to the instrument which might influence the signal dependence on position over the solar disk. During the commissioning phase of SOHO, the spacecraft performed off-set pointing tests which altered the optical path of the sunlight through the instrument. During these tests there was no detectable change in the GOLF signal (Gabriel et al. 1997). This off-set pointing performance demonstrates that there is no vignetting in the system and that the instrument responds uniformly to all parts of the solar disk. This performance is a result of the high degree of uniformity of the magnetic field in the scattering portion of the cell and the fact that the temperature of the scattering gas is sufficiently low that self-absorption within the cell is not a factor. The only instrument thermal effect which influences the spatial characteristics of the instrument response is that due to the cell temperature which changes the balance between the three scattering components. This temperature variation effect is included in the model. Other instrumental variations alter the overall gain of the signal but do not alter the spatial characteristics. For example, it has been hypothesized by Ulrich et al. (2000) that an interference fringe in one of the blocking filters is evolving and producing a sinusoid-like time dependence in the instrument throughput. Such a fringe could also introduce a wavelength and velocity dependent factor which might alter the spatial response. However, this effect is ruled out by comparison of the phase of the sinusoid-like function in the two states of magnetic modulation. No phase difference was detectible. Based on such considerations, we do not consider any instrumental factors as significant apart from those discussed below.

The discussion in this paper follows the formalism presented in the above earlier papers and extends that treatment to the case of a spatially resolved image. The GOLF instrument system utilizes both D1 and D2 lines. Telluric absorption components near the working point on the red wing of D2 complicate ground-based studies of this line. Since both members of the doublet are scattered into the detection chain, there are three separate wavelength bands combined to yield a single signal for every configuration of the GOLF instrument. We designate these components as [FORMULA], [FORMULA] and [FORMULA]. These longitudinal Zeeman components are offset from the non-magnetic wavelengths [FORMULA] nm and [FORMULA] nm (Reader & Corliss 1980) to wavelengths of

[EQUATION]

where GOLF's permanent magnetic field strength [FORMULA] is [FORMULA]40 gauss and there is an additional variable field coming from an electromagnet whose modulation amplitude is [FORMULA]1 gauss. Thus the wavelength increments are:

[EQUATION]

Following Boumier (1991) we have used the notation [FORMULA] to designate these components respectively. The precision of the above determination of the modulation amplitude applies to the offset in GOLF signal obtained during the two-wing period of operation and represents the shift necessary to yield equal line of sight velocity for two different combinations of intensity. The actual magnetic field in the instrument could be different. However, the determined parameter is the quantity which influences the analysis of the GOLF data according to the methods outlined here and it is well determined as indicated by the above quoted errors. The magnetic conversion factor A is [FORMULA] for magnetic fields in gauss and wavelengths in nm and we have neglected a small difference in the value of A for the D1 and D2 lines.

Following the notation of Ulrich et al. (2000) we distinguish between a realized intensity and a line profile function by representing the intensities as in a mathitalic notation such that for example [FORMULA] refers to the intensity in the blue wing with the positive state of the electromagnet. For a line profile function we use bold face and explicitly indicate the input quantity on which it depends: [FORMULA] is such a profile function for spectral line j depending on w which has dimensions of wavelength. We have explicitly indicated that the profile function depends on center-to-limb angle [FORMULA] and surface magnetic field strength B. In our case w is the wavelength difference between the scattering component at wavelength [FORMULA] and a centroid of the solar line at wavelength [FORMULA]. Each solar line profile [FORMULA] may depend on other parameters such as position within a supergranule cell. At present we use the profiles described in the following section and neglect this variation as well as that due to B so that they can be taken as a constant when averaged over long time periods.

The GOLF instrument selects the solar radiation by resonance scattering from the sodium atoms within a heated cell in a strong magnetic field. The scattering strength depends on cell temperature and the magnetic field structure and is represented here by a scattering function [FORMULA] for each of the scattering components. These functions are given by Boumier & Damé (1993). The signals observed by GOLF are then:

[EQUATION]

which yield:

[EQUATION]

where the intensity [FORMULA] includes the limb darkening which is the indicated function of [FORMULA] and the velocity [FORMULA] which is the total doppler shift of a point at coordinates [FORMULA] due to the Einstein gravitation red shift, the orbital sun-spacecraft velocity, the differential rotation and the convective limb shift effect. The [FORMULA] coordinate system is rectangular in the plane of the sky and can have a zero point defined to be at the solar disk center. The dimensions of x and y need to be consistent with those for [FORMULA] for the purpose of normalizing various integrals.

Eqs. (6) and (7) require knowledge of the line profiles over some range in v near each of the working points. For the full velocity range of the orbital motion of SOHO, the line profiles are significantly non-linear. For the purpose of the determination of the velocity sensitivity, we may consider a restricted range in which case the profile is nearly linear. We may then define a reference velocity [FORMULA] and consider [FORMULA] to be small. The magnetic field and its modulation correspond to the velocity shifts:

[EQUATION]

We may also remap the functional form of the line profile so that the input parameter is [FORMULA] instead of wavelength w: [FORMULA]. After adopting the following compact notation for the derivative with respect to velocity:

[EQUATION]

and defining:

[EQUATION]

and using a linear expansion about the reference velocity we obtain:

[EQUATION]

Two properties of these definitions are worth emphasizing: first, even though we have used a velocity scale for the argument of the line profile function, we have reversed the sign in order to account for the fact that the velocity appears with a negative sign in Eqs. (11 - 14); and second, the slopes [FORMULA] are positive while the slopes [FORMULA] are negative.

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© European Southern Observatory (ESO) 2000

Online publication: January 29, 2001
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