2 Observations and reduction

TRACE sequences.

We use two different TRACE data sequences in this paper, from May 12, 1998 and October 14, 1998, respectively. Both were downloaded from the public TRACE archive (URL http://vestige.lmsal.com/TRACE/). Details are given in Table 1; background information is available in the TRACE Analysis Guide (URL http://diapason.lmsal.com/~bentley/guides/tag/). During the first run (which was part of Joint Observing Program JOP72 in which most of us participated) TRACE was programmed to observe a rectangular quiet region near disk center sequentially in its three ultraviolet passbands. In the second run, TRACE observed an even quieter rectangular disk-center area with broad-band white light imaging added into the passband sequence. The white light images show (but do not resolve) the solar granulation. They are not used in this paper but may serve for photospheric piston searches in future analyses.

Following the TRACE Analysis Guide we subtracted the readout pedestal of 86 readout units from the images for the 12 May data. We did not apply flat-field corrections or bad-pixel eliminations since none are specified for this date. For the 14 Oct. data we used the nominal dark field and the flat field measured on 31 August. The top and bottom pixel rows of the May 12 images are very noisy and were discarded. Only two frames in each data set were affected by telemetry errors; they were replaced by the averages of the preceding and subsequent images. Minor effects from the data compression appear in the data, for example as a low-amplitude interference pattern in spatial frequency in Fig. 23.

 

 

Table 1: TRACE observations used in this paper.

date	May 12, 1998	October 14, 1998
program sequence	TDT.trnotsofast	TDT.any_frames
image size [px]	$256 \times 1024$	$512\times512$
number of images	354	612
$X_{\rm cen}, Y_{\rm cen}$ [arcsec]	-40, 308	-13,-82
$L_{\rm cen}, B_{\rm cen}$ [deg]	-2.51, 15.98	-0.77, 1.04
duration [UT]	14:30-16:00	08:12-12:00
cadence [s]	15.0573	21.8625
exposure 1700Å [s]	2.0479	2.0480
exposure 1600Å [s]	1.0239	1.0239
exposure 1550Å [s]	5.7919	9.7400
exposure white [s]	--	0.0064

Passbands.

Transmission curves for the three ultraviolet passbands are given by Handy et al. (1998) together with a numerical recipe to isolate the contribution of the C IV doublet at $\lambda = 1548$Å and 1550Å through optimised combination of images taken in the three ultraviolet passbands. The C IV lines dominate the 1550Å brightness in active areas, but in quiet areas contributions from C I lines, from other lines, and from the continuum dominate in the 20Å wide 1550Å passband. We display Fourier results for such C IV "constructs'' below in which the combination recipe was applied to the Fourier transforms of the three sequences, after Fourier demodulation to correct for the time delays between the sequentially exposed images.

Exposure timing.

The TRACE housekeeping data specify the exposure duration and the moment at which the shutter closed for each individual image. The nominal delay between successive images in a given passband was 15s for May 12 and 21s for October 14. Occasionally there were 1s longer intervals on May 12 and up to 10s longer intervals on Oct. 14; the cadence values in Table 1 are sequence averages. These erratic increments upset the use of standard Fast Fourier Transform (FFT) routines which assume equidistant spacing. We therefore defined an equidistant time scale for each dataset, combining the average interval with an optimum starting time, and then selected the image closest to each equidistant time step for FFT analysis. For the May 12 data, the offset from the actual mid-exposure time is always shorter than half the exposure duration. The slower cadence and longer 1550Å exposures of the October 14 data combine into larger offsets. However, worse effects result from the non-simultaneity of the imaging in the different passbands (Sect. 6).

Figure 1: Solar location of the fields observed with TRACE on May 12, 1998 (left) and October 14, 1998 (right). The grid shows heliocentric longitude and latitude for each date.

Figure 2: Sample image taken by TRACE on May 12, 1998, at 15:26:32 UT in the 1700Å passband. The upper half contains stronger network. Axes: solar X and Y in arcsec from disk center. The greyscale is logarithmic in order to bridge large contrast. The field was split into the four indicated subfields for this analysis.

Figure 3: Sample image taken by TRACE on Oct. 14, 1998, at 10:05 UT in the 1700Å passband. The observed area was very quiet. Axes: X and Y in arcsec from disk center, same scale (on the paper) as in Fig. 2. Greyscale: logarithmic. The field was split into two subfields as indicated. The horizontal striping at right marks incomplete sampling which results from solar rotation correction.

Figure 4: Network and internetwork masks for the top subfield of the May 12 data shown in Fig. 2. Upper left: 30-min average (15:00-15:30UT) for 1600Å, logarithmic greyscale, X and Y axes in arcsec from disk center. Upper right: histogram of the number of pixels per brightness bin in this average. Dotted lines: division into internetwork (left), intermediate (middle strip), and network (right) categories. Lower left: logarithmic average overlaid with white and black contours corresponding to the demarcations. Lower right: final mask resulting from three successive 30-min averages. Dark grey: internetwork. White: network. Light grey: intermediate category in all three averages. Black: pixels which switch category between averages, discarded. The left and right edges are sampled incompletely due to solar rotation tracking and are also discarded.

Observed fields.

The $(X_{\rm cen}, Y_{\rm cen})$ values in Table 1 specify the location of the center of the field in the TRACE coordinate system measuring distance from apparent disk center in arcsec on the sky along the solar meridian (north positive) and latitude circle (west positive) through disk center. The $(L_{\rm cen}, B_{\rm cen})$ coordinates specify the corresponding heliographic longitude and latitude of the field center midway the sequences. Figure 1 shows the field orientations. Figures 2 and 3 show sample 1700Å images from the May 12 and October 14 sequences, respectively. The intensity scaling is logarithmic in order to accommodate both network and internetwork variations; this is the case for all greyscale image displays in this paper. The May 12 field contained some active network. The October 14 field sampled an area that was very quiet. Both fields where divided into smaller subfields to fit our computer memory during the analysis.

Solar rotation causes a drift of the entire field during the observation period while differential rotation causes differential drifts within the field. The split of the May 12 field into four subfields and of the October 14 field into two subfields, each covering 256 px in Y, reduces the differential variation. Each subfield was "derotated'' by co-alignment through cross-correlation. This was done for the four May 12 subfield sequences by aligning each frame to the average of 10 mid-sequence frames. Direct comparison between different wavelengths was made possible by co-aligning each subfield sequence to the corresponding 1600Å one.

The longer duration of the October 14 subfield sequences (nearly four hours) and the consequent evolution of the solar scene necessitated a more elaborate three-step alignment procedure. It consisted of first aligning each sequence of 20 images to the last previously aligned image, then replacing image shifts above three-sigma rms value by the average shift of the preceding and subsequent images in order to reduce pointing jitter extremes, and finally co-aligning all images per sequence to the 1600 Å sequence. The resulting October 14 alignments are generally accurate to a few tenths of a pixel. The May 12 alignments show larger displacements and were smoothed through $3 \times 3$ pixel spatial boxcar averaging.

These alignments make fixed-pixel locations (X,Y) in each (X,Y,t) sequence correspond to fixed solar locations with respect to the local co-rotating solar frame. The rotation produces incomplete solar sampling at the east and west field edges where pixels rotated in or out of the field during the sequence. These are excluded from the measurements below by using edge masks as illustrated in Fig. 4.

Network/internetwork separation.

Each observed subfield was divided into network, internetwork, and remaining area called "intermediate''. The latter may (and indeed does) mix properties of the two regimes and was introduced at appreciable fill factor in order to achieve better isolation of characteristic properties of the network and internetwork, respectively.

The separation was defined in terms of the average 1600 Å brightness per pixel over periods of 30 min for May 12, 80 min for October 14. The more stably present network patches survive such averaging, whereas the faster varying internetwork emission is washed out (compare the sequential variations in Fig. 5 with the 30-min average in the first panel of Fig. 4 and with the 90-min average in the first panel of Fig. 14). The upper-right panel of Fig. 4 shows a sample 30-min brightness distribution in the form of a histogram. It is characteristic for all our data and shows a Gaussian peak with an extended tail towards large brightness. Network/internetwork masks were constructed from the three successive 1600Å histograms per subfield by assigning a pixel to be "internetwork'' if its average brightness was below the Gaussian peak location in all three histograms, to be "network'' if it belonged in all three histograms to the non-Gaussian high-intensity tail demarcated in Fig. 4, and to be "intermediate'' if it fell between these extremes in all three histograms. Pixels that changed category between the three histograms were excluded. The mask that resulted for the May 12 top subfield is shown at lower right in Fig. 4. It restricts the pixels labeled network to the brightest areas in the first panel of Fig. 14 and the internetwork to rather small "heartland'' regions relatively far from network, with a large zone of intermediate-category pixels (light grey) separating the two.