Data Acquisition and Reduction

Observations

We selected the CaI 6122 Å line to derive the vector magnetograms and the photospheric Doppler maps. With an effective Landè factor of 1.75 this line is only moderately sensitive to Zeeman splitting but is relatively broad and better suited to the 160 mÅ bandpass of our Fabry-Perot etalon.

A full set of Stokes images was obtained by sequentially recording six filtergrams at the polarization states I+Q, I-Q, I+U, I-U, I+V, I-V, in both the blue and the red wing of the CaI line. The integration time for each filtergram was 30 ms. Approximately 130 s were needed to acquire and store the full set of vector polarimetric measurements (12 images). A series of 12 chromospheric filtergrams was recorded after recording two vector polarimetric sets. The Fabry-Perot bandpass was positioned at 6562 Å, i.e. 1 Å bluewards off-band of the Ha line core. The integration time for the chromospheric filtergrams was 125 ms. The sequence of two vector polarimetric sets followed by 12 Ha-1 Å filtergrams was completed in approximately 7.5 minutes. It was repeated for four hours, during which a total of 56 vector polarimetric sets and 324 chromospheric filtergrams were recorded.

 

Basic data reduction

First, the raw images were corrected for the CCD dark current offsets and flat fielded to account for the pixel-to-pixel gain variations introduced by the detector electronics and optical system imperfections. To improve the signal to noise the images were resized to 512 × 512 pixels with a scale of 0.18 arcsecs per pixel, corresponding to a field of view of 92.2 × 92.2 arcsecs (66.3 × 66.3 Mm). The images were then carefully co-aligned to account for image motions caused by the residual telescope pointing errors and drifts.

The telescope telemetry did not provide a very accurate position in latitude and longitude of the region observed. We determined its exact location by comparing a longitudinal magnetogram acquired by FGE at 16:44 UT on January 25, 2000 with a Kitt Peak synoptic magnetogram recorded between 16:21 UT and 17:16 UT of the same day. The region coordinates for this time were used as reference. We derived the region location for other times by measuring their time difference with respect to the reference time 16:44 UT and subsequently calculating the longitudinal distance from the reference location. We assumed a differential rotation in the photosphere of 13.39° - 2.7° · sin2(longitude) per day.

 

Vector magnetograms

The Stokes images Q/I, U/I, and V/I were obtained by calculating the normalized difference between measurements of opposite polarization states. For example:

V/I = [(I+V) - (I-V)] / [(I+Q) + (I-Q)].

The magnetic field components longitudinal () and transversal () to the line of sight (LOS) were calculated following Ronan et al. (1987):

where L and T are two constants that depend on the magnetic sensitivity of the spectral line used, on the exact location of the Fabry-Perot passband, and on the instrument polarimetric efficiency. We derived L and T by comparing the FGE data with vector magnetograms obtained with the Imaging Vector Magnetograph (IVM) of Hawaii (see Mickey et al. 1996 for a description of the instrument) that was observing the same active region at the same time. The IVM has a lower spatial resolution but it records full Stokes profiles and the longitudinal and transversal field components are derived by means of an inversion code that fits the Stokes profiles. The FGE vector magnetograms needed to be resized to match the IVM image resolution, and rotated and co-aligned before comparing the two datasets. From the comparison we derived the following calibration factors: L = 26100 ± 450 Gauss, T = 4500 ± 100 Gauss.

The magnetic field inclination (or azimuth angle) g(gamma) and azimuth c(chi) were calculated as follows (see Ronan 1987):

c has another possible solution: c1 = c + 180°, because of the 180° ambiguity introduced by the symmetry properties of the transverse Zeeman effect.

The 180° ambiguity is not a straightforward problem to solve. Many techniques have been proposed (see Metcalf 1994 and references therein; Skumanich and Semel 1996). However, most of them work well only for active regions that do not deviate too much from a potential field configuration. Active region AR 8844 has several areas where the field structure appears to be highly complex and non-potential. Therefore, a totally automated algorithm would not be capable to properly resolve the 180° ambiguity for those areas. We adopted an approach that combines a potential field solution with an empiric estimation of the correct field orientation based on simple geometrical considerations.

We started by selecting one vector magnetogram out of the 56 recorded, which will be kept as reference, and we solved the 180° ambiguity for it. First, we compared the field vectors with a simple potential filed model derived by the longitudinal magnetograms. In this model we just considered the two main polarities in the active region and neglected the magnetic flux in-between. The field azimuths were chosen such that their angular difference with the model azimuths was the smallest. The resulting vector magnetogram was subsequently filtered with a "smoothing algorithm" that checks for maximum continuity between adjacent vectors to create a smooth azimuthal distribution of vectors across the entire region. The azimuth map was then visually inspected to correct for local geometrical inconsistencies. Finally, the vector field map was transformed from the LOS reference system to the local, heliographic reference system. In it, the zenith angle is expressed with respect to the local vertical and the azimuth with respect to the local N-S / E-W directions. The transformation into the heliographic reference system helps in revealing vectors that were incorrectly chosen due to the non-vertical viewing angle of the region (see Gary and Hagyard 1990 for a discussion on the effects of perspective). Therefore, the vector magnetogram was again visually inspected and corrected for local geometrical inconsistencies.

The rest of the vector magnetograms in the time sequence were corrected sequentially by comparison with the preceding vector magnetogram in the time sequence, starting with the reference vector magnetogram. Our assumption was that during the time interval between consecutive vector magnetograms the vector directions changed less than 90°. After this sequential comparison process, a few vector magnetograms still needed some manual correction to account for isolated local errors.

The results are two time sequences of 56 vector magnetograms corrected for the 180° ambiguity. One with the vectors expressed in the LOS reference system, and one in the heliographic reference system. The sequences cover a time span of approximately 4 hours, with an average time gap between consecutive vector magnetograms of about 3.5 minutes.

 

Photospheric Doppler maps

The photospheric Dopplergrams were obtained by calculating the difference between filtergrams recorded in the two wings of the CaI 6122 Å line of the vector polarimetric sequences.

We averaged all the images recorded in each wing during two consecutive vector polarimetric measurement sets:

,

,

where b,r means blue-,red- wing respectively. This was done to improve the signal to noise ratio, to remove some of the 5 minutes oscillations effects, and to cancel out image to image intensity variations introduced by the vector polarimetric measurements. The Doppler image was then obtained as follows: D = Db - Dr. A positive value in D corresponds to a red shift.

To remove some residual contribution of the 5 minutes oscillation and to reduce image-to-image noise, we applied a space-time Fourier filter. The filter combined a high-pass filter, for the noise, with a bandpass filter, for the intensity oscillations.

The Doppler image D in reality is just a map of the intensity difference between the blue and the red wings of the CaI 6122 Å line for a specific location. To obtain an estimation of the effective longitudinal velocities we assumed a linear relationship between the difference maps and the effective Doppler velocity, i.e.: V = c · D, where c is a calibration constant. We derived c by comparing the FGE Doppler images with the velocity maps provided by the inversion of the IVM data: c = 22 ± 1.5 km/s.

We want to emphasize that the so derived Doppler velocity maps are just a rough estimation of the effective Doppler velocities. Only a line fit through multiple points across the spectral line can provide accurate velocity values.

 

References

Gary, G. A., & Hagyard, M. J. 1990, Sol. Phys, 126, 21

Metcalf, T. R. 1994, Sol. Phys, 155, 235

Mickey, D. L., Canfield, R. C., Labonte, B. J., Leka, K. D., Waterson, M. F., & Weber, H. M. 1996, Sol. Phys., 168, 229

Ronan, R. S., Mickey, D. L., & Orrall, F. Q. 1987, Sol. Phys., 113, 353

Skumanich A., & Semel, M. 1996, Sol. Phys., 164, 291


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