Astron. Astrophys. 364, 799-815 (2000)

1. Introduction

1.1. General background

The GOLF instrument is a resonant scattering spectrophotometer which measures the intensity of solar radiation at selected positions within the sodium doublet lines. The integrated sunlight is scattered by sodium vapor in a temperature controlled cell which is inside a permanent magnet at a position where the magnetic field is nearly uniform. The scattered wavelengths are governed by the magnetic field strength and by a combination of polarizing elements. An electromagnet modulates the magnetic field permitting the selection of two closely spaced positions on the line wings. Two of the polarizing elements include mechanisms which can rotate these elements in steps of 90 degrees to select either the blue or red wing of the sodium doublet lines. Full descriptions of the instrument and its early performance are to be found in Gabriel et al. (1995, 1997), and a discussion of system stability is given in Robillot et al. (1998). Due to occasional malfunction of the rotating mechanisms, the polarizers were stopped on 11 April 1996 at positions which select the blue wings of the lines and have been left fixed subsequently. The usual operation of a resonance cell system provides intensity measurements for both the blue and red line wings and the velocity is found from the ratio of the intensity difference to the intensity sum. In the stopped or single-wing mode no observations are available from the red side of the lines so that we cannot calculate the above ratio which leads to a velocity measurement where absolute photometric effects cancel out. Data taken between January 19 and April 1, 1996 include observations of both wings and this data is very helpful in determining instrumental properties.

Subsequent to April 11, 1996 the instrument functions largely in a photometric mode where variations over various time scales are combinations of intensity and velocity fluctuations. The purpose of this work is to show how the photometric signal can be converted to an effective velocity with a well determined scale. Essential to the success of this method is knowledge of the modulation of the field strength by the electromagnet. This method deduces the solar line profile from a combination of the magnetic modulation and the orbital velocity variations. There are basically two steps in the analysis: first, the raw signal C is converted to a photometric signal P through the correction for known instrumental and geometric effects as will be described by García et al. (2000) and second, a solar profile corrected signal S is calculated from P by correcting for the deduced variation in the net solar profile intensity. Although no temporal filtering is required in the calculation of S substantial long time-scale trends remain. These can either be removed by introducing a temporal filter or through the application of a model for the trends. Such a model is presented below in Sect. 6 and time series which retain components with periods shorter than about 80 days are derived. The remaining detrended signal is then converted to a velocity variation through the multiplication of the residual signal by a derived sensitivity function . These velocity time series have been placed in the GOLF/SOHO archive. The key steps and data products are summarized in Table 1.

Table 1. Sequence of data flow and data products

The approach we use here allows us to study the power spectrum shape over a wide range of frequencies. From this spectrum which is presented it Sect. 7.1 we identify a break in the slope at 25 µHz. Below this frequency the power appears to come from solar activity whereas above the break the power spectral shape more resembles that due to convection. This distinction may be helpful in the formulation of strategies to find low frequency modes of oscillation. In addition, the derived solar profile permits a conversion between the intensity variation and an equivalent velocity shift using a known factor which depends on the sun-spacecraft line-of-sight velocity. Thus the rms variations in intensity which are a consequence of both the rms velocity amplitude and the time dependent line slope can have the latter factor removed and we are able to study the variation of the rms velocity itself in the 5-minute band as a function of orbital velocity. Because the orbital velocity causes the height of formation of the GOLF working point to shift through the solar atmosphere, we can determine the height dependence of oscillation amplitude.

1.2. Velocity versus intensity

The question of intensity versus velocity sensitivity can be discussed directly in terms of the data using a comparison with other instruments having known characteristics. An important technique in this regard is the study of phase relations between various signals. Pallé et al. (1999) and Renaud et al. (1999) have determined phase angles for modes in the five-minute band and concluded the GOLF signal is predominantly due to velocity. Gabriel et al. (1995) shows a comparison between a one-wing power spectrum derived from the ground-based comparison calibration and the two-wing power spectrum. Ulrich et al. (1998) compares power spectra based on the S method, an alternative method and the two-wing power spectrum. All three of these comparisons show that the one-wing power is greater than the two wing power for frequencies less than the 5-minute band. Since the intensity contribution is significantly reduced for the two wing method, this comparison suggests that the balance between intensity and velocity depends on whether the variations are caused by coherent oscillations or by the solar noise.

While the issue of the intensity versus velocity contribution is of concern, the primary objective of this paper is to explicitly describe a series of steps which can convert the raw GOLF signal into a quantity which has units of velocity and present some results based on this analysis. The first 6 months of the resulting data sets are now publically available on the web at: http://www.medoc-ias.u-psud.fr/golf/ . The remainder will be released shortly. The method described here is unable to make a distinction between these two components and treats the conversion as if the signal variations are caused by velocity changes alone. Extensions of this treatments utilizing additional data may provide a distinction between the intensity and velocity components of the GOLF signal and will be discussed in future papers. However, it must be recognized that the GOLF signal reduced to the S quantity inherently contains a contribution from intensity which cannot be evaluated based on the GOLF data alone. This intensity is for a point relatively close to the core of a strong resonance line and differs considerably from the continuum intensity so that its role in the oscillations is difficult to estimate theoretically. However, correlation with magnetic activity indicies provides a method of estimating the effects of this component of non-velocity signal.

1.3. Interaction of the instrument and solar line radiation

Preliminary discussions of the reduction of the GOLF data have been given by García et al. (1998), Robillot et al. (1998), and Ulrich et al. (1998) while García et al. (2000) provide details of another method of velocity scaling the GOLF signal. The first of these papers describes the development of a model data stream composed of contributions from oscillations and supergranular convection. The second describes corrections to the raw intensity and presents some alternate formulations to treat the single wing data. The third gives a summary of two data reduction methods and compares the implied velocity output for these two methods. A related paper to follow by Ulrich et al. (2000) extends the method developed here to incorporate data from spatially resolved images from the MDI experiment on SOHO.

We consider the scattered light signal from the system to be governed by two tunable parameters: a) the wing selection polarizing elements, which we denote by subscripts b and r for red and blue wings, and b) the modulation state of the electromagnet, which we denote by a superscript + or -. For parts of the time sequence during the two-wing mode of operation two additional parameters: a second rotating polarizing element and a 180^o redundancy in one retarding polarizer element, played a role in the data. For the two wing analysis we combine and average the separate data streams from these parameters.

The GOLF instrument system utilizes both D₁ and D₂ lines. Due to telluric absorption components near the working point on the red wing of D₂, no meaningful groundbased tests of the integrated system were possible and the evaluation of the properties of the instrument must be carried out using the operational data from space. The use of both members of the doublet complicates the interpretation of the GOLF signal due to fact that at any moment three separate wavelength bands are scattered into the detection chain. We designate as , and the longitudinal Zeeman components which are offset from the non-magnetic wavelengths nm and nm (Reader & Corliss 1950) to wavelengths of

For a permanent magnetic field of strength and an electromagnet modulation of the wavelength increments are:

and following Boumier (1991) we have used the notation . The magnetic conversion factor A is 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.

The design of the GOLF magnet provides a field at the sodium cell which is sufficiently uniform that can be taken as a constant for all scattered photons. The scattering process is broadened by the presence of hyperfine states in the upper and lower atomic states and by the thermal motions of the sodium atoms in the cell. These later processes dominate over the magnetic field non-uniformities and each scattering component is roughly described by a gaussian with a width parameter of about 1.3 pm while the values range between 8.0 and 13.8 pm. Thus the sampled portions of the solar spectral lines are well separated from each other. Through the use of the modulated electromagnet the magnetic field at the cell has two values: and . The values of and are inferred by Gabriel et al. (1995) from prelaunched subsystem measurements of the wavelengths of the scattering components from the actual flight system. In addition, the value of is determined below from an analysis of the flight data.

Some care with notation is required in describing the GOLF system because of the variety of varying parameters: the multiple scattering wavelengths, the two distinct spectral lines, the magnetic modulation and the red or blue wing selection. In addition, we need to refer to actual intensities for a particular configuration and to spectral line profiles which are functions of a wavelength difference. The sub and superscript notation was given above. In order to make a clear distinction between a realized intensity and a line profile function, we use math italic for the intensities as refers to the intensity in the blue wing with the positive state of the electromagnet. This intensity will generally depend on the sun-spacecraft velocity but we do not explicitly designate this dependence. For a line profile function we use bold face and explicitly give the function on which it depends: is such a profile function for spectral line j depending on w which has dimensions of wavelength. The indicated time dependence comes primarily from the transit of active regions across the solar disk and is neglected for most of this discussion.

The GOLF system avoids the need for a filter to separate the two sodium D line components by measuring both lines. The absence of such a filter improves system stability but comes at the price of introducing some uncertainty in knowledge of the balance between the three scattering components. Boumier (1991, see also Boumier & Damé 1993) has modelled the transfer of radiation within the sodium cell and successfully simulated the wavelength dependence of the scattered light as a function of cell gas temperature. Subsequent subsystem tests described by Boumier et al. (1994) have validated his simulation. Fig. 1 shows two measured scattering profiles from these prelaunched tests, , at gas temperatures of about 155^o and 163^o C. The scale shown for is based on the comparison of the photomultiplier outputs for the straight-through beam to the scattered beam and is uncertain on an absolute basis. However, the relative intensities between the different scattering components has an uncertainty of 5%. For comparison the observed integrated sunlight profiles measured by Delbouille et al. (1973) are shown in Fig. 1 shifted in such a way that they both coincide with the scattering functions. The solar line is shifted from this position by a combination of orbital motion, Einstein shift and a third effect known as the convective correlation shift which is caused by the enhanced brightness of the hotter, rising convective cells relative to the cooler, sinking cells. The convective correlation shift depends on altitude in the solar atmosphere and can alter the spectral line shapes. The details of this process are not well enough understood to permit a reliable calculation of the shifts.

Fig. 1. Comparison of the sodium cell scattering functions, , to the observed integrated-sunlight line profiles of the two sodium D lines. The scattering functions for D2 are shown as solid on the blue wing while the scattering function for D1 is shown on the red wing. Both the observed solar line profiles and the scattering functions have been shifted so as to have their central wavelengths coincide. The scattering functions in fact are both selected to be on the blue or red wings by the alignment of the rotational orientation of the polarizer optics. They are shown here on opposite wings for clarity.

At low cell gas temperature all scattering components increase in strength in proportion to the gas density and maintain a constant relative ratio. However, at cell gas temperatures above about 140^o C, the component which has the largest scattering cross-section progressively saturates and makes a reduced relative contribution to the detected signal. This effect is evident by comparing the scattering profile at in Fig. 1. Because the solar line slope differs at each of the scattering wavelengths, the balance between the three scattering components influences the conversion factor between intensity variations and velocity. Consequently, we need to know the cell gas temperature in order to properly analyze the GOLF signal. A platinum temperature probe near the sodium cell stem provides an important indication of the critical temperature but there is a poorly known offset between this measurement and the actual gas temperature.

Two instrumental quantities necessary for a full interpretation of the GOLF data are the on-orbit magnetic field modulation amplitude and the temperature of the gas in the sodium cell. Preflight subsystem tests were carried out to obtain these quantities. The early two wing observations between Jan. 19 and Apr. 1, 1996 are used here to determine the magnetic modulation based on the known variation in the sun-spacecraft velocity. The same observation period permits an estimation of the cell gas temperature by comparison of the observed intensity ratios as a function of orbital velocity to the average of integrated sunlight line profiles weighted by factors dependent on the cell gas temperature.

In this paper we utilize the magnetic modulation to deduce the average solar line profile as a function of orbital velocity and thus reduce the observed signal to photometric quantity independent of the orbital velocity induced variations. This method is directly dependent on all instrumental drifts and decays in sensitivity. Although it is necessary to estimate the long term trends in the instrument, because no other smoothing is done during the reduction, it is possible to preserve phenomena on longer time scales. The range of frequencies preserved in the analysis is limited primarily by the detrending process which does not include a formal temporal filter but instead utilizes a somewhat complex functional fitting procedure. In some cases it is desireable to impose an additional hard frequency cutoff with a high-pass filter. The detrending strongly reduces the spectral power on time scales longer than 60 days but leaves it largely unchanged for time scales shorter than 45 days. A hard cutoff of 60 days is generally used to assure that the poorly fit spectral components with time scales longer than this do not leak into the higher frequency spectra. Furthermore, since each phase of the magnetic modulation is treated independently, the analysis yields four independent data sets - two for each photometer channel.

The remainder of this paper consists of five parts: Sect. 3 uses data from the two-wing period of operation to determine the amplitude of magnetic modulation; Sect. 5 describes our method of converting the photomultiplier output into a velocity result; next, a Sect. 6 applies the method to the GOLF data and presents time series analysis based on the detrended velocity data set; and finally a Sect. 7 presents results for the deduced power spectra extending from Hz to Hz and the time dependence of the rms velocity in the 5-minute band.

© European Southern Observatory (ESO) 2000

Online publication: January 29, 2001
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