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Astron. Astrophys. 346, 633-640 (1999)

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3. Conversion of coordinates

It was our aim to follow physically the same areas on the Sun for the whole observing period of 17 hours. This is best possible with a selection of arrays that are equidistant in the heliographic coordinates. For the conversion of the [FORMULA] coordinates to heliographic coordinates in general the solar radius, the tilt P of the solar axis, and the latitude [FORMULA] of the disk center are necessary. The solar axis tilt P had not to be taken into account, since this was compensated automatically on board of SOHO. For the solar equator position on the observing day [FORMULA], with a small increase of [FORMULA]/h, was taken into account.

The velocity of the solar differential rotation was fitted for each hour to the formula


where [FORMULA] and [FORMULA] are the latitude and longitude (central meridian distance), respectively, and [FORMULA], A, B, and C are velocities. The data of the array v are the measured velocity values averaged over one hour and selected for central meridian distance larger than 30o. The constants A, B, and C are the fitted parameters of the differential rotation; their mean values for the whole period of investigation are 1790 m/s, -202 m/s, and -342 m/s, respectively.

It should be mentioned that the equatorial rotation velocity obtained here is about 10% smaller than the equatorial rotation velocity measured spectroscopically (e.g., Schröter 1985). To our knowledge no detailed discussion of this discrepancy exists in the literature. Scattered light from the disk center would indeed cause an apparent decrease of the rotational velocity. However, according to R.S. Bogart (1998, private communication) the effect of scattered light had been investigated and virtually ruled out as an explanation. Since the discrepancy is evidently caused by MDI, this problem should be investigated further. For the analysis below, the rotation velocity is unimportant, since we investigate small-scale oscillatory motions and a field-independent velocity offset would not affect the diagnostic diagrams. Only the compensation for the field displacement due to the rotation may be slightly incorrect. The variation of the line-of-sight component of the spacecraft velocity is only a few m/s per day and can be ruled out as an explanation for the measured rotation law.

Within each selected area the x and y coordinates of all pixels were transformed to heliographic coordinates, i.e., distance [FORMULA] from the central meridian and latitude [FORMULA]. The longitude values were corrected for the rotational displacement since the beginning of the observation by means of Eq. (1). For computational reasons the coordinates were then multiplied by a factor 5; the result were [FORMULA] arrays with integer coordinate values, corresponding to fields of [FORMULA] in heliographic coordinates. Within each subfield of [FORMULA] all existing data were averaged. Near the solar limb an increasing amount of subfields appeared without any data. In these cases values were interpolated from adjacent subfields with data. With this procedure we constructed data sets of [FORMULA] spatial and 1000 temporal elements, corresponding to [FORMULA] min.

For the study of the center-to-limb variation we used a series of these 3D-arrays, centered at latitudes [FORMULA], [FORMULA], [FORMULA], ..., [FORMULA], and located along the meridian at the beginning ([FORMULA]). Both hemispheres were analyzed independently.

In order to improve the sampling at intermediate latitudes, additional data sets at [FORMULA], [FORMULA], [FORMULA], and [FORMULA] (both North and South) were constructed and analyzed. Although these data sets did not contain independent information (due to the complete overlap with the data sets located at "even" latitudes), they were useful to verify the slope of the resulting curves.

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© European Southern Observatory (ESO) 1999

Online publication: May 21, 1999