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

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1. Introduction

The Global Oscillations at Low Frequency (GOLF) instrument on board the ESA/NASA sponsored Solar and Heliospheric Observatory (SOHO) measures solar velocities in integrated sunlight using a sodium resonance scattering system. Details of the instrument and its initial results have been given by Gabriel et al. (1995, 1997). A series of papers describing the conversion of the instrument signal into a quantity related to velocity is in preparation (García et al. 2000, Ulrich et al. 2000). Preliminary reports of these studies have been given by Ulrich et al. (1998) and Robillot et al. (1998). This paper describes an extension of the integrated sunlight analysis to an analysis of the dependence of the integrated signal on spatially resolved velocities such as can be obtained from the Michelson Doppler Imager (MDI) instrument which is also on board SOHO.

The formalism presented in this paper is applied to the GOLF instrument operating in the single-wing mode. The extension to similar instruments in dual or multiple wing modes is straightforward and indeed the original version of this model was intended for application to GOLF operations in the two-wing mode. At a fundamental level, one would wish to track the effect of a velocity displacement of the solar surface through to a signal detected by some instrument like those on SOHO. Intermediary effects include the displacement of spectral lines, the alteration of line profiles and changes in the continuum intensity. In addition, one would like to understand the effects of non-velocity perturbations such as might be caused by magnetic fields. Although it is possible to estimate the magnitude of such effects and we provide here a set of functions which allow their estimation, there is no possibility of compensating for them in the GOLF signal unless there is a data set providing a magnetically sensitive parameter on essentially the same time base as is available for the GOLF data. Although one parameter from the MDI instrument, the line strength parameter, is recorded as part of the MDI structure program, up to this time it has not been used thus far as a tool for the study of magnetic effects in the GOLF data. As a first step we concentrate on the effect of spectral line shift as the mechanism which produces the dominant signal in velocity sensitive instruments and report an approximate approach which can be used for the treatment of data during periods of high solar activity.

The need for a detailed understanding of the sensitivity of an integrated-sunlight instrument like GOLF to the spatial distribution of line-of-sight velocities over the solar surface comes from the advantages to be gained through the intercomparison of signals from several instruments. In the case of the helioseismology instruments on SOHO, our objective is to prepare data sets from the GOLF and MDI instruments which most closely resemble each other so that the different effects of solar noise in the two instrument data streams can be reduced by means of a cross-correlation technique. Our approach does not aim for an exact reproduction of the GOLF signal from the MDI images since both contain contributions from the largely random convective processes. Rather we seek to maximize the common coherent components of each so that the cross correlation method can achieve its best possible performance. The height of formation of the spectral lines used by GOLF and MDI differs with the Ni line used by MDI being formed closer to the photosphere than the points on the Na line used by GOLF. Because signals due to convection are a stronger function of height in the solar atmosphere than the coherent, global oscillations, we can enhance our ability to distinguish between these processes by carefully determining the spatial weighting function to be applied to the resolved data in order to create a simulation of the integrated sunlight signal. Indeed, results from this approach, which include the identification of modes having frequencies as low as 535.75 µHz, are described in a series of papers (Henney 1999, Henney et al. 1999, Bertello et al. 2000a, 2000b). An ultimate goal from an approach like ours would be to determine a convective and active region signal from spatially resolved observations by MDI and subtract this signal from the GOLF signal. We refer to such an approach as a signal subtraction method as opposed to the signal cross-correlation method which we use. If the method works, the rms variation in the subtracted signal should be less than that in either of the time series forming the difference. Unfortunately due to the combined effects of shutter noise in the MDI instrument and the single wing mode of operation by GOLF, the signal subtraction method was not successful in our studies.

A similar analysis of instrument sensitivity has been given by Christensen-Dalsgaard (1989) and applied to the instrument configurations of the IRIS and BISON systems. That analysis did not include the treatment of multiple components necessary for the GOLF system nor did it include explicitly measured center to limb effects on the line profile nor did it use explicitly measured differential rotation and limb shift factors appropriate to the Na D lines. In another simulation study García, Roca Cortés and Régulo (1998) have used an approach similar to that by Christensen-Dalsgaard (1989) to calculate the response of the GOLF instrument to two 12-month series of simulated solar velocity fields. This study represented the solar D lines as gaussians whose slopes in the spectral range covered during GOLF operations differ substantially from those of the solar D lines, and did not use limb darkening, limb shift and solar rotation curves appropriate for the D lines. This formulation has not been used with actual solar data from MDI so we cannot determine the effects of these approximations on our ability to carry out the cross-correlation analysis. While these details do not alter the overall nature of the sensitivity functions derived by Christensen-Dalsgaard (1989) and García, Roca Cortés and Régulo (1998), the unique opportunity presented by the space-based helioseismology instruments on SOHO requires that we treat the observations using the best possible model. This paper is one step in that process.

Although the focus of the present work is to describe the sensitivity of the GOLF instrument to velocity variations on the solar surface, additional functions needed to describe the sensitivity of the GOLF instrument to magnetic effects are defined and evaluated in an approximate fashion here. While the method can be extended by the evaluation of these additional terms using additional data to include the effects of active regions, magnetic data of adequate precision and with appropriate temporal and spatial resolution has not yet been extracted from the available instrument systems to permit an application of these terms to the correction of the GOLF time series. Consequently, we concentrate in this and subsequent papers on the spectral band between 200 and 1000 µHz where the active region induced signal is only a fraction of the total non-coherent variations. The GOLF signal used in this series of papers is obtained with the method described by Ulrich et al. (2000). As obtained from this method, the shape of the solar background power spectrum makes it clear that in the 200-1000 µHz range the solar noise is not dominated by the active region effects. Further discussion of the inter-relationships between solar signals, the signal subtraction method, global modes of solar oscillation and the GOLF and MDI instruments is given in the conclusions.

We seek here a function of position on the solar disk which when multiplied pointwise with the velocity on the solar disk will yield the change in the signal detected by GOLF. We call this the sensitivity function. For the case of a single scattering component in a spectral line, conceptually this sensitivity function is the difference between two spectroheliogram images taken through extremely narrow band-pass filters whose wavelengths bracket the working point of the GOLF instrument. An imaging system utilizing a sodium vapor cell as a band-pass filter which included a modulated magnetic field could obtain such images directly. However, there is at present no such system nor could there be a ground-based system measuring both the D1 and D2 lines simultaneously due to the problems of telluric contamination. Thus we have to approach this task indirectly utilizing available observing systems.

To model the system indirectly we note that it is possible to factor the sensitivity function into parts which are separately measurable with existing instrument systems: a line profile function and a center-to-limb intensity function. Line profiles are normally given as a ratio of the monochromatic intensity to the continuum intensity. Since only the product of these two functions is needed, we show here that the line bisector intensity can be used in place of the continuum intensity in defining the line profile and its slope at the GOLF working points. Since a Babcock (1953) magnetograph such as the one in use at the 150-foot solar tower on Mt. Wilson normally keeps the spectral line centered between its blue and red spectral sampling ports, the measured average intensity is inherently a bisector intensity. Thus if we reference the line profile to the bisector point defined by the Babcock magnetograph, utilize the center-to-limb bisector intensity from the magnetograms with a matching blue and red spectral port separation, and utilize a rotation and limb shift function appropriate to the spectral line in question, we can combine the two forms of data to recover the desired sensitivity function. Line profile functions are needed at several points on the solar surface and they can be measured with the facilities of the MWO 150-foot solar tower (Ulrich et al. 1991, 1993). Furthermore, we can obtain the measurements needed for all the components of the D lines and combine the sensitivity functions according to the measured scattering strength to obtain a net sensitivity function for the GOLF instrument.

The utilization of the Babcock magnetograph data and the line profile data for the analysis of the GOLF signal from both D1 and D2 lines requires the development of a notation which can clearly deal with multiple components. This notation is described in the next section. The Mt. Wilson line profiles are presented and described in Sect. 3. Next the velocities and limb darkening functions derived from the magnetograph observations are presented in Sect. 4. Finally the sensitivity functions are derived in Sect. 5 and compared to the integrated sensitivity function derived directly from GOLF.

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© European Southern Observatory (ESO) 2000

Online publication: January 29, 2001