Tilts in Coronal Holes

Transcription

1 Tilts in Coronal Holes B. T. Welsch Space Sciences Laboratory, University of California, Berkeley, CA L. W. Acton Department of Physics, Montana State University, Bozeman, MT H. S. Hudson Space Sciences Laboratory, University of California, Berkeley, CA ABSTRACT We report Yohkoh/SXT observations of a low-latitude coronal hole in April 1992 that exhibited an apparent tilt toward the West, in the prograde direction relative to the Sun s rotation, opposite to the direction of the Parker Spiral in the heliosphere beyond the low corona. Such tilts might result from a back-reaction on the magnetic field from solar wind acceleration, or from an l = 1, m = 0 mode in the photospheric magnetic field. We also discuss SXT observations of other coronal holes that exhibited some indications of prograde tilts. To quantitatively investigate properties of these coronal holes, we implemented an automated procedure that can identify, track, and characterize segments of coronal holes. Unfortunately, the intrinsic variability in coronal emission structures hampers our ability to unambiguously quantify the geometries of the holes we have studied. Further effort will be required to determine if prograde tilts are common in coronal holes. 1. Introduction Loren noticed that many low-latitude coronal holes (CHs) in Yohkoh SXT images appeared fuzzy when they were viewed on the western disk, as opposed to their sharper appearance on the eastern disk. He interpreted this fuzziness along west-disk lines of sight as arising from diffuse soft X-ray emission that was not present along east-disk lines of sight. Assuming this diffuse emission originates from closed fields, which bracket low-latitude coronal holes to the east (E) and west (W), the E-W asymmetry in observed intensity implies there are fewer intervening closed fields along east-disk lines of sight. This, in turn, implies

2 2 that the open fields of these coronal holes must run parallel to these east-disk lines of sight and therefore that these open fields are tilted toward the west, in the prograde direction. Hugh has pointed out that effects other than magnetic geometry could produce apparent tilts. For instance, asymmetries in temperature or density between the E and W edges of coronal holes could lead to differences in observed emission at the leading and following edges, mimicking the effects of tilts. Brian has tried to develop automated and therefore objective ways to quantify observational properties of coronal holes as the holes rotate across the disk. It is hoped that by studying the evolution of apparent hole properties e.g., their apparent longitudinal width, or perhaps the sharpness of their E-W boundaries as they move from east to west, aspects of their true, underlying structure can be determined. This approach assumes that the gross properties of this underlying coronal hole structure do not change significantly while the hole crosses the disk. Apparent changes in coronal hole structure, however, are subtle the signal is weak and the noise is strong so constraining hole properties has proven challenging. Below, we outline how we have approached this problem. We first briefly discuss the data we use ( 2), then review how segments of low-latitude coronal holes are automatically identified in individual SXT images, and then how these segments are automatically tracked as they move across the disk ( 3). Next, we present a simple model of how coronal hole geometry should affect the apparent properties of coronal holes as they move across the disk ( 4). Finally, we assess what we ve learned, and where to go from here ( 5). 2. Data We use SXT images from the Yohkoh Legacy data Archive (YLA). 1 While the SXT browse images have been co-aligned and are cosmetically appealing, they are not appropriate for quantitative analysis. Accordingly, we used half-resolution (4.91 pixels) Level 2 FITS data, which we co-aligned ourselves. We anlayzed SXT images made using the AlMg filter, as these were ubiquitous over the course of the Yohkoh mission, while Al filter images were more rare toward the end of the mission. The time difference between frames was required to be at least two hours, because evolution due to rotation is so slow that it does not require faster cadence, and including more data can substantially slow the process of tracking holes as they cross the disk, as discussed below. 1

3 3 3. Identifying & Tracking Coronal Holes To investigate the properties of coronal holes as the rotate across the solar disk, it is worthwhile to develop an automated method to identify coronal holes in individual SXT images, and to associate identified holes with holes in preceding and subsequent frames. This allows efficient and objective characterization of hole properties, and, in principle, enables the investigation of SXT s large image database. Fortunately, much of the necessary software had already been implented, in the YAFTA feature tracking suite, 2 developed for tracking photospheric magnetic features Welsch and Longcope (2003). Fig. 1. Identified and tracked coronal hole segments are overlaid on an SXT image of a narrow, low-latitude coronal hole from April The white curves enclose pixels identified as coronal hole segments by our algorithm. The colored curves enclose narrow, low-latitude hole segments that were tracked across the disk. The influence of the (10 10)-pixel dilation element is clearly seen in the structure of identified coronal holes. As a starting point in identifying coronal holes, we identify regions that appear dark 2 welsch/public/software/yafta/

4 4 in soft X-ray emission, the defining characteristic of coronal holes. In practice, this is done with negative log 10 -scaled images, offset by a positive pedestal of 10; low-value pixels correspond to bright regions. We smoothed the images with a (3 3) pixel boxcar filter, to ameliorate substantial pixel-scale intensity variations, due to noise and low-number statistics where emission is weak. Remaining pixel-scale structure precluded simply imposing a single intensity threshold and rejecting pixels that were too bright: either the threshold was too strict, and individual bright pixels surrounded by hole pixels were not identified with the hole, or the threshold was too weak, and regions of faint, closed-field emission were improperly identified as holes. Accordingly, we employ a dual-threshold technique, after DeForest et al. (2007): each hole pixel must be both above a weak threshold (0.5), and at least one of its contiguous weak-threshold pixels must also exceed a strict threshold (0.75). The resulting threshold mask was then dilated with a (10x10)-square image structuring element (see IDL s dilate.pro) to blend nearby hole regions separated by small patches of relatively weak emission together. The white boundaries in Figure 1 show the regions identified in the resulting hole mask. In subjective tests with a variety of images, this rather convoluted procedure seemed a robust way to identify coronal hole regions. Because rotation most strongly affects the properties of low-latitude coronal holes, we restricted our attention to coronal hole segments lying within ±30 latitude of disk center. Because we are primarily interested in the evolution of coronal hole edges as they move across the disk, and edge properties can vary substantially over this latitude range, we opted to subdivide identified hole pixels into segments 10 wide in latitude. We further required that the hole segments be narrow: eastern- and western-most pixels of hole segments could not be separated by more than 100 pixels. This narrowness requirement is discussed further below. An IDL structure is created for each hole segment that is identified in a given frame, and its frame number, total number of pixels, pixel addresses (as a single, space-delimited string variable), and average position (both in pixels, and in central meridian distance and latitude) are recorded. (A lot of other stuff is recorded, too.) Once hole semgents were identified in an individual frame, they had to be associated with hole segments that identified in preceding and subsequent frames. The basic approach is to compare the shifted pixel locations of hole segments from a previous frame with the pixel locations of hole segments in the current frame, to see if there is any overlap between the two. This is relatively straightforward for the case that drove the development of YAFTA, tracking photospheric magnetic features, since the features persist between frames. In contrast, as a given coronal hole crosses the disk, intensity fluctuations due, for instance, to transient brightenings and flares can prevent identification of a segment of that hole in a few

5 5 (random) individual frames. Consequently, each hole segment identified in a given current frame had to be checked against the rotated locations of holes in many previous frames, which adds complexity to the tracking algorithm, and slows the tracking process. To ensure that hole segments were tracked over a sufficient range of longitudes to discern evolution in their apparent structure from the change in viewing angle, we required that each segment be followed over at least 60 in central meridian distance. For the April 1992 coronal hole, five 10 -latitude segments met this criterion. 4. Inferring Coronal Hole Geometry Our pixel classification scheme is binary: a coronal hole is either visible in a given pixel, or not. Because sufficient foreground emission will preclude observing a coronal hole along a line of sight toward that hole, our approach effectively treats SXR emission as optically thick, even though in fact it is not. Making this assumption explicit allows creating a simple model of tilted coronal hole visibility, which can be used to quantitatively characterize the hole s geometry as the hole moves across the disk SXT. We must also assume that the hole s structure does not evolve significantly during its disk passage. Figure 2 illustrates the geometry of an idealized, narrow coronal hole that is tilted to the west (toward the right), when viewed in cross section, looking from south to north (into the page). The gray shaded areas represent closed- field regions of the corona that are visible in SXR emission, and the thick black line represents the base of the corona. The hole is assumed narrow enough that its width is very small compared to the Sun s radius, so curvature of the coronal base across the hole s width is negligible. The upper left panel illustrates the geometry of the hole: its east (E) and west (W) edges are assumed to make the same angle φ T < 0 with respect to the vertical (dashed line); the SXR emission is assumed to originate from the atmoshperic volume below height h; and the hole s width w is assumed uniform with height. The three parameters {w, h, φ T } fully characterize the hole s structure in this simple model. The distance x 0 appears in several expressions derived below, and is given by x 0 = h tan φ T, (1) where the minus sign reflects the fact that the tilt angle is assumed negative. The remaining panels of Figure 2 illustrate how much of the coronal hole is visible from various lines of sight (dotted lines). Lines of sight toward the observer (assumed to be at 1 AU) are approximated as parallel. For a given point on the base of the corona, an angle defined from the vertical, with west negative, corresponds to the angular central meridian distance (CMD) of that point to an observer, with east and west CMDs being negative and

6 6 Fig. 2. These images show the cross section of an idealized coronal hole that is tilted to the west (toward the right) when viewed from south to north, looking into the page. The gray shaded areas represent closed- field regions of the corona that emit in SXR, and we assume that the coronal hole is not visible along lines of sight that intersect these emitting regions. See text for explanation of variables. positive, respectively. Because we assume that the coronal hole cannot be observed along line of sight angles φ L that intersect the gray regions, the coronal hole is not visible along any line of sight more negative than φ E (middle left panel), where or more positive than φ W (lower left panel), where φ E = tan 1 ( (w + x 0 )/h), (2) φ W = tan 1 ((w x 0 )/h). (3) The maximum apparent width w a occurs when the line of sight angle φ L matches the tilt

7 7 angle φ T (upper right panel), with w a = w cos φ T. (4) In principle, finding the longitude at which the coronal hole s width is a maximum determines both φ T and w. Then a measurement of either φ E or φ W can be used to determine h. In practice, measurement uncertainties and systematic biases (e.g., the minimum size criterion in our algorithm for identifying coronal hole segments), as well as transient brightness variations, introduce errors into each measurement of a hole segment s true width and location. Consequently, our characterization of the hole s geometry will be improved if we determine the functional form of w a, the apparent width of the segment of the coronal hole that is visible, as a function of CMD φ L. Then we can use every observation of the hole as it crosses the disk to characterize {w, h, φ T } statistically. For line-of-sight viewing angles φ L more negative than φ T (middle right panel), the visible segment w v is which an observer sees as the apparent width w v = w x E (5) = w ( h tan φ L x 0 ) (6) = w + h(tan φ L tan φ T ) (7) = w + h sin (φ L φ T ) cos φ L cos φ T, (8) w a = w v cos φ L (9) = w cos φ L + h sin (φ L φ T ) cos φ T. (10) For line-of-sight viewing angles φ L less negative than φ T (bottom right panel), the visible segment w v is which an observer sees as the apparent width w v = w x W (11) = w (x 0 + h tan φ L ) (12) = w ( h tan φ T + tan φ L ) (13) = w + h sin (φ T φ L ) cos φ L cos φ T, (14) w a = w cos φ L + h sin (φ T φ L ) cos φ T. (15)

8 8 We can now write the apparent width of a hole as a function of the hole s angular distance from central meridian φ L and the parameters {w, h, φ T } that characterize the hole s structure, w a = w cos φ L + h sign(φ T φ L ) sin (φ L φ T ) cos φ T. (16) In Figure 3, we plot a family of curves showing the apparent width w a, in pixels, for a model Fig. 3. This family of curves shows the apparent width w a, in pixels, for a model coronal hole that is w = 30 pixels wide, and tilted 15 (toward the west), under varying assumptions regarding the height h below which most closed field emission originates. (The ratio h/w decreases from the bottom curve to the top curve.) The tilt angle is shown with the vertical dashed line. Note that the longitude of peak width becomes hard to discern for small h/w. coronal hole that is w = 30 pixels wide, and tilted 15 (toward the west), under varying assumptions regarding the height h below which most closed field emission originates. Work by Hudson et al. (1998) suggests most SXR emission tends to originate within 6 SXT halfresolution pixels of the limb, implying the upper two curves (corresponding to the smallest h/w) might best describe the E-W intensity evolution of a CH that is 30 half-resolution pixels wide. We remark that, in general, the variation in apparent width CMD decreases as the ratio of h/w decreases (going from lower to upper curves in this figure), suggesting that width variations would be difficult to detect in wide coronal holes hence the narrowness requirement imposed on identified hole segments ( 3). The simplified model of the coronal hole geometry shown in Figure 2 had unrealistic sharp corners on the boundaries between closed and open field regions. Since SXR structures in the actual corona appear more rounded, observed intensity variations as CHs move across the disk are expected to be more smooth than the hypothetical curves shown in Figure 3. In Figure 4, we plot actual width vs. CMD curves for five segments of the April, 1992, coronal hole as it crossed the disk. Labels for each tracked hole segment are overplotted at

9 9 Fig. 4. The measured width, in SXT half-resolution pixels, as a function of CMD, for five segments of a narrow coronal hole that crossed the disk in April, Labels for each tracked hole segment are overplotted at the maximum of each curve, which is plotted as a small box. Error bars were computed from the standard error in the mean from the average E and W edge locations. These curves are probably too spiky to be easily fit with the function in equation (16). the maximum of each curve, which is plotted as a small box. Error bars were computed from the standard error in the mean from the average E and W edge locations. The curves in Figure 4 are probably too spiky to be effectively fit with the function in equation (16). The rough shapes of the curves, which are essentially rounded humps, is consistent with a small h/w ratio. Readers with vivid imaginations might perceive indications of tilt angles φ T between 20 and 10, and peak widths near 25 pixels for the curves for features 1, 9, and 15. We suspect that much of the variation in the observed widths of hole segments arises from relatively short-lived intensity variations, probably due to transient brightenings and

10 10 flare emission. Smoothing of these curves, therefore, might enable fitting them with the function in equation (16). We implemented the smoothing with Gaussian- weighted longitudinal averaging, where the Gaussian width parameter σ = 15. The resulting curves are shown in Figure 5. How best to proceed from here? 5. Discussion I ve studied three other coronal holes, two from Nov and one from Oct None of the hole segments from Oct were tracked for more than 60 in longitude. If I recall correctly, this was one of the extremely narrow holes studied by Kahler and Hudson (2002). For the other two holes, both from Nov. 2000, I ve generated similar smoothed plots of hole width, but they don t clearly show prograde tilt: most hole widths on either side of disk center. For the first hole, this might be an artifact of the inability to accurately estimate peak hole width when holes are wide. Movies of the identified hole segments (white) and those tracked for more than 60 in longitude are online at: welsch/public/manuscripts/corhol/overlay apr92.gif welsch/public/manuscripts/corhol/overlay nov00a.gif welsch/public/manuscripts/corhol/overlay nov00b.gif So I could try to track other coronal holes. However, in light of the discrepancy between tilts that I, subjectively, see in movies of the tracked holes, but that aren t apparent from quantitative analysis of the tracked hole segments, I must also question the general approach of trying to quantify aspects of the tilts using the evolution of apparent width vs. latitude. I must also compute something like width center of gravity, which ought to be more statistically robust than the peak of a noisy curve, but haven t implemented anything along these lines yet. I ll keep you posted on that. Distinct from the analysis of hole widths vs. longitude that I ve undertaken, having automatically tracked the locations of hole segments was still a worthwhile effort: now have estimated locations of holes (as well as hole edges). We might therefore be able to quantify something like coronal hole fuzziness perhaps by computing changes in averaged intensity gradients across E-W hole boundaries vs. longitude, or average relative intensity ratios between hole segments and nearby closed field regions vs. longitude.

11 11 It is also true that the detection of tilt seems unambiguous in the April 1992 hole, so perhaps a paper on this hole alone would be worthwhile. But I suspect a study of just one hole probably isn t sufficiently interesting to merit publication. But something we should ponder regarding this tilted hole (and others that we find) is how (if?) to use source-surface potential field (PFSS) extrapolations. What does it tell us if tilts are present in these extrapolations? (How do we quantify tilts in the extrapolated fields?) Presumably that the origin of the tilt is in the large-scale photospheric magnetic field. This would, I think, be consistent with findings by Shrauner and Scherrer (1994). We thank members of the Yohkoh Legacy Project team, whose efforts created a database that greatly simplified this study. We also gratefully acknowledge??. REFERENCES DeForest, C. E., Hagenaar, H. J., Lamb, D. A., Parnell, C. E. and Welsch, B. T. (2007), Solar Magnetic Tracking. I. Software Comparison and Recommended Practices, ApJ 666, Hudson, H. S., Labonte, B. J., Sterling, A. C. and Watanabe, T. (1998), NOAA 7978: the Last best Old-Cycle Region, in T. Watanabe and T. Kosugi, eds, Observational Plasma Astrophysics : Five Years of YOHKOH and Beyond, Vol. 229 of Astrophysics and Space Science Library, pp Kahler, S. W. and Hudson, H. S. (2002), Boundary Structures and Changes in Long-lived Coronal Holes, ApJ 574, Shrauner, J. A. and Scherrer, P. H. (1994), East-west inclination of large-scale photospheric magnetic fields, Sol. Phys. 153, Welsch, B. T. and Longcope, D. W. (2003), Magnetic helicity injection by horizontal flows in the quiet sun: I. mutual helicity flux, ApJ 588. This preprint was prepared with the AAS L A TEX macros v5.2.

12 12 Fig. 5. Measured widths ( s) and Gaussian-weighted longitudinally-averaged widths (solid), with Gaussian width parameter σ = 15, of coronal hole segments in SXT half-resolution pixels, as a function of CMD, for five segments of a narrow coronal hole that crossed the disk in April, The maximum of each smooth curve is plotted as a small box. These curves might be more easily fit with the function in equation (16).