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1. Introduction

The SOHO mission consists of a three axis stabilized spacecraft with eleven scientific instruments that studies the Sun (Domingo & Poland 1988). It offers an unprecedented opportunity to study the deep interior of the Sun through Helioseismology under ideal conditions at the Lagrange L1 point. Here, no terrestrial atmospheric effects are present, continuous exposures to the Sun are possible and there is a low Sun-spacecraft line-of-sight velocity. On this spacecraft there are three Helioseismic instruments: GOLF, MDI and VIRGO. Their first objective is the determination of the internal structure and dynamics of the Sun. In particular, GOLF measures the disk integrated radial velocity of the Sun in a frequency range of 10-7 to tex2html_wrap_inline1109 Hz. It is specially designed to detect the low frequency waves that correspond to the low order p-modes (below 2 mHz) and the g-modes with a sensitivity better than 1 mm/s in 20 days and a frequency resolution better than 16 nHz in a two years mission. These modes have not already been detected from the Earth due, mainly, to a combination of two effects: an increase of the atmospheric solar and terrestrial noise at low frequencies and a very low amplitude expected for them. As a secondary objective, GOLF also measures the longitudinal component of the line-of-sight global magnetic field of the Sun with an accuracy better than 1 mGauss.

The instrument is a disk integrated sunlight resonant scattering spectrophotometer. This is an earth-based proved technique that measures the Doppler shift of the solar sodium D lines (tex2html_wrap_inline1113 5896 and tex2html_wrap_inline1113 5890 Å) due to a non zero relative Sun-instrument line-of-sight velocity. This technique has been successfully used in solar physics by several researchers (Snider 1970; Brookes et al. 1978a; Fossat & Roddier 1971). The latest two groups have pioneered the work on helioseismology and, nowadays, the instruments used by helioseismic networks such as IRIS and BISON are based, with some differences, on this kind of technique.

Briefly, the solar absorption line (half-width tex2html_wrap_inline1117500 mÅ) traverses through a sodium vapor cell, placed in a longitudinal magnetic field of 5000 Gauss, which has an intrinsic (thermal) absorption line-width of the order of 25 mÅ. The light is absorbed and reemitted in all directions. This scattered light is symmetrically split into its Zeeman components displaced by tex2html_wrap_inline1119 mÅ from the rest wavelength (D1 case), allowing a measurement on either side on the wings of the solar absorption profile (see Fig. 1 (click here)). Switching between both wings, by moving appropriately a quarter wave plate and a linear polarizer, alternates the measurement of the intensity on them and therefore, measuring its Doppler shift. The observed velocity is proportional to a normalized difference of intensities that measures the shift.

Compared to the earth-based ones, GOLF incorporates two important improvements. The first one is the possibility of sampling the solar absorption profile at four points by adding a modulating magnetic field of tex2html_wrap_inline1123100 Gauss. Therefore, it can measure the slopes on each wing enabling an instantaneous calibration of the instrument's sensitivity (Isaak & Jones 1988). The second one is the ability to measure the longitudinal component of the line-of-sight global magnetic field of the Sun by adding a fixed quarter wave plate in front of the other two polarizing elements of the experiment. A full description of the instrument used is to be found in Gabriel et al. (1995). Even though this is a known technique, many items of the existing instruments have never been clearly quantified and correctly understood, as it can be seen from the description of earlier versions of such spectrophotometers (Brookes et al. 1978a; Grec et al. 1991).

Figure 1:   Diagram of the physical principle of the resonant scattering spectrophotometry shown only on one of the sodium D lines. a) The relative velocity between the Sun-spacecraft is zero. b) There is a non-zero velocity field between them, therefore the solar line is Doppler shifted; this is how the earth-based instruments work. c) A variable magnetic field in the spectrophotometer is placed, enabling 4 sampling points over the solar profile. d) When a quarter wave plate is placed at the GOLF's entrance, it is able to separate the circular polarized components of the solar light

Due to the fact of the four sampling points as opposed to the classical two for the earth-based instruments, several definitions of velocity signals can be extracted. Some new parameters can be derived from this new information as the measures of the integrated profile slopes or the new magnetic ratio. For the GOLF spectrophotometer, a quantitative description of the physics of the instrument is to be found in Boumier (1991) and Boumier & Damé (1993). A scientific breadboard of this kind of spectrophotometer was built and tested with the real Sun (Boumier et al. 1994). Although some new information could be gained from this experiment, the obvious non-identical working conditions prevented firm conclusions regarding GOLF instrument working at L1. As the final design of the GOLF instrument has not been tested with the Sun before launch, a full numerical simulation became a necessity.

As a consequence, the numerical model simulates the experiment working at ideal conditions at L1. It observes the surface of the Sun with the most important and appropriate velocity fields which constitute its velocity background "noise'' spectrum. Finally, the simulation of realistic low tex2html_wrap_inline1091 p-mode and predicted g-mode oscillations also include the true "signal'' we are interested in.

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