Steps toward a high precision solar rotation profile: Results from SDO/AIA coronal bright point data

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1 Astronomy&Astrophysics manuscript no. Rotaon c ESO 215 January 6, 215 Steps toward a high precision solar rotaon profile: Results from SDO/AIA coronal bright point data D. Sudar 1, I. Skokić 2, R. Brajša 1, and S. H. Saar 3 1 Hvar Observatory, Faculty of Geodesy, University of Zagreb, Kačićeva 26, 1 Zagreb, Croaa 2 Cybrotech Ltd, Bohinjska 11, 1 Zagreb, Croaa 3 Harvard-Smithsonian Center for Astrophysics, 6 Garden Street, Cambridge, MA 2138, USA Release January 6, 215 ABSTRACT Context. Coronal bright points (CB) are ubiquitous small brightenings in the solar corona associated with small magnec bipoles. Aims. We derive the solar differenal rotaon profile by tracing the moons of CBs detected by the Atmospheric Imaging Assembly (AIA) instrument aboard the Solar Dynamics Observatory (SDO). We also invesgate problems related to detecon of coronal bright points resulng from instrument and detecon algorithm limitaons. Methods. To determine the posions and idenficaon of coronal bright points we used a segmentaon algorithm. A linear fit of their central meridian distance and latude versus me was ulised to derive velocies. Results. We obtained 96 velocity measurements in a me interval of only 2 days. The differenal rotaon profile can be expressed asω rot = (14.47±.1+(.6±1.) sin 2 (b)+( 4.7±1.7) sin 4 (b)) day 1. Our result is in agreement with other work and it comes with reasonable errors in spite of the very short me interval used. This was made possible by the higher sensivity and resoluon of the AIA instrument compared to similar equipment as well as high cadence. The segmentaon algorithm also played a crucial role by detecng so many CBs, which reduced the errors to a reasonable level. Conclusions. Data and methods presented in this paper show a great potenal to obtain very accurate velocity profiles, both for rotaon and meridional moon and, consequently, Reynolds stresses. The amount of coronal bright point data that could be obtained from this instrument should also provide a great opportunity to study changes of velocity patterns with a temporal resoluon of only a few months. Other possibilies are studies of evoluon of CBs and proper moons of magnec elements on the Sun. Key words. Sun: rotaon - Sun: corona - Sun: acvity 1. Introducon We present a new solar rotaon profile obtained by tracing the moons of coronal bright points (CBs) observed by Atmospheric Imaging Assembly (AIA) instrument on board the Solar Dynamics Observatory (SDO) satellite (Lemen et al. 212). The most frequently used and oldest tracers of the solar differenal rotaon profile are sunspots (ewton & unn 1951; Howard et al. 1984; Balthasar et al. 1986b; Brajša et al. 22a). One of the advantages of using sunspots is very long me coverage. On the other hand, there are numerous disadvantages: sunspots have complex and evolving structure, their distribuon in latude is highly non-uniform and it does not extend to higher solar latudes. The number of sunspots is also highly variable during the solar cycle which makes measurements of solar differenal rotaon profile almost impossible during solar minimum. CBs are more uniformly distributed in latude and are numerous in all phases of the solar cycle. They also extend over all solar latudes. They have been used as tracers of solar rotaon since the beginning of the space age (Dupree & Henze 1972). In recent years there are numerous studies invesgang solar differenal rotaon by using CBs as tracers. Kariyappa (28); Hara (29) used Yohkoh/SXT data while Brajša et al. (21, 22b, 24); Vršnak et al. (23); Wöhl et al. (21) used SOHO-EIT observaons in 28.4 nm channel and Karachik et al. (26) used Send offprint requests to: D. Sudar, :davor.sudar@gmail.com 19.4 nm SOHO/EIT channel. Kariyappa (28) also used Hinode/XRT full-disk images to determine the solar rotaon profile. Other tracers are used as well: magnec fields (Wilcox & Howard 197; Snodgrass 1983; Komm et al. 1993) and Hα filaments (Brajša et al. 1991). Apart from tracers, Doppler measurements can also be used (Howard & Harvey 197; Ulrich et al. 1988; Snodgrass & Ulrich 199). Helioseismic measurements also show differenal rotaon below the photosphere all the way down to the bottom of the convecve zone (Kosovichev et al. 1997; Schou et al. 1998). Further down, the rotaon profile becomes uniform for all latudes (cf. eg. Howe 29). For further details about solar rotaon, its importance for solar dynamo models, and comparison of rotaon measurements between different sources, see the reviews by Schröter (1985); Howard (1984); Beck (2); Ossendrijver (23); Rüdiger & Hollerbach (24); Sx (24); Howe (29); Rozelot & einer (29). In this work we use CB data obtained by SDO/AIA over only two days to assess the quality of the data, idenfy sources of errors and calculate the solar differenal rotaon profile. We will also invesgate the possibility of using CB data from SDO/AIA for further studies of other related phenomena (meridional flow, rotaon velocity residuals and Reynolds stress). CB data from SDO/AIA were also used in other works. Lorenc et al. (212) discussed rotaon of the solar corona based on 69 structures from 674 images detected in 9.4 nm channel Arcle number, page 1 of 6page.6

2 A&A proofs: manuscript no. Rotaon We have used data from the AIA instrument on board the SDO satellite (Lemen et al. 212). The spaal resoluon of the instrument is.6"/pixel. For comparison, SOHO/EIT resoluon is 2.629"/pixel while Hinode/XRT has a resoluon of 1.32"/pixel. To obtain posional informaon for the coronal bright points (CBs), we employed a segmentaon algorithm which uses the 19.3 nm AIA channel data to search for localized, small intensity enhancements in the EUV compared to a smoothed background intensity. More details about the detecon algorithm, which is similar to the algorithm by McIntosh & Gurman (25), can be found in Martens et al. (212). This resulted in measurements of posions of individual CBs covering two days (1st and 2nd of January 211). The me interval between two successive images was 1 minutes. In top panel of Fig. 1 we show the distribuon of detected CBs and compare it to the full disk image of the Sun in the 19.3 nm channel obtained on 1st of January 211 (bottom panel of the same Figure). In the bottom panel, white circles show CBs that were detected on one image by the segmentaon algorithm. We can see that CBs are scarce in acve regions, partly because of difficules in detecng them against such bright and variable backgrounds. The segmentaon algorithm provides coordinates in pixels (centroids of CBs on the image) and we converted them to heliographic coordinates taking into account the current solar distance given in FITS files (Roša et al. 1995, 1998). osions of objects near the solar limb are fairly inaccurate. Liming the data to ±58 from the centre of the Sun or.85r of the projected solar disk removes this problem (cf. Stark & Wöhl 1981; Balthasar et al. 1986a). As can be seen from Fig. 2, the calculated velocies show some scatter. This scatter arises because the shifts are fairly small at our 1 min cadence, and there can be significant variaons in brightness and structure of CBs which influences calculaon of the centroid points. evertheless, trends are visible, especially in azimuthal moon which is known to be a significantly larger effect. The dominant azimuthal moon led us to approximate the CB moon with a linear fit to calculate the velocies: li ωmer = 2 bi 2!2 bi li ω syn =!2 (1),, (2) where ω syn is a synodic rotaonal velocity, ωmer is a meridional angular velocity, li is central meridian distance (CMD) and bi Arcle number, page 2 of 6page Data and reducon methods 15 y [pixels] using an interacve method of detecon. Dorotovic et al. (214) presented a hybrid algorithm for detecon and tracking of CBs. McIntosh et al. (214b) used detecon algorithm presented in their previous paper (McIntosh & Gurman 25) to idenfy CBs in SDO/AIA 19.4 nm channel and correlate their properes with those of giant convecve cells. Using more SDO/AIA data and extending analysis back to SOHO era, McIntosh et al. (214a) concluded that CBs almost exclusively form around the verces of giant convecve cells x [pixels] 1 2 Fig. 1. Distribuon of CBs detected by the segmentaon algorithm (top panel) and image of the Sun in the 19.3 nm channel obtained by SDO/AIA on 1st of January 211. White circles show detected CBs on this image (bottom panel). is latude of each measurement for a single CB. We have also removed all CBs which had less than 1 measurements of posion in order for linear fits to be more robust. This is equivalent to 1 minutes or about 1 at the equator. To obtain the true rotaon of CBs on the Sun we convert synodic velocies to sidereal using Eq. 7 from Skokic et al. (214). Trying to idenfy the same object on subsequent images with an automac method is bound to result in some misidenficaon. The resulng velocies are usually very large and can easily be removed by applying a simple velocity filter. Even the human factor can introduce such errors. For example, Sudar et al. (214) analysed solar rotaon residuals and meridional moons of sunspot groups from the Greenwich hotoheliographic Results and found that they had to use a filter 8< ωrot <19 day 1 for rotaonal velocity in order to eliminate these erroneous measurements. The Greenwich hotoheliographic Results catalogue is being invesgated and revised partly in order to remove such

3 D. Sudar et al.: Steps toward a high precision solar rotaon profile: Results from SDO/AIA coronal bright point data b [deg] σ(ω rot ) [deg/day] CMD [deg] t [days] t [days] Fig. 2. Moon of a single CB. Top panel: latude, b, over me, t; bottom panel: central meridional distance, CMD over me, t. problems (Willis et al. 213a,b; Erwin et al. 213). In this work we have also used a 8<ω rot <19 day 1 filter for rotaonal velocies to remove such outliers. In addion, we applied a meridional velocity filter of -4<ω mer <4 day 1 to remove further outliers. After compleng all the procedures described above, we obtained 96 velocity measurements by tracing CBs over just two days. Olemskoy & Kitchanov (25) pointed out that nonuniform distribuon of tracers can result in false flows. This effect is most notable for meridional moon and rotaon velocity residuals, but can easily be removed by assigning the calculated velocity to the latude of the first measurement of posion (Olemskoy & Kitchanov 25; Sudar et al. 214). Although the effect is negligible for solar rotaon, we nevertheless applied the correcon in this work. It is important to keep in mind that even when the tracers are uniformly distributed over the solar surface, the distribuon of tracers in latude will be non-uniform. As we move from equator to the pole, the area of each latude bin becomes smaller, so we observe progressively fewer tracers ( cos b). 3. Results In this work, we present an analysis of the moon of CBs observed by the SDO/AIA instrument. For a better understanding of the results and the potenal of future studies along these lines, it is very useful to analyse the accuracy and errors of the dataset Coronal bright point no. Fig. 3. Errors of rotaonal velocity,σ(ω rot ), for each of the 96 measurements. Heliographic latude [deg] Heliographic longitude [deg] Fig. 4. Distribuon of rotaon velocity errors (ω rot ) in heliographic coordinates. Error scale is in day 1. In Fig. 3 we show errors of the calculated rotaonal velocies,σ(ω rot ), for each CB, which resulted from errors in the linear fitng of longitude vs me measurements. Although the errors can go up to 3 day 1, the majority is below 1 day 1. In Fig. 4 we show these errors in heliographic coordinates to check their spaal distribuon on the solar surface. Larger errors are shown with brighter shades and we can see that these roughly correspond to the posions of acve regions shown in the bottom panel of Fig. 1. This correlaon with acve region is probably a consequence of the detecon algorithm design and difficules in detecon of CBs over a bright, variable background. In Fig. 5 we show the distribuon of CBs in heliographic coordinates with arrows indicang the velocity vector. As expected, the dominant effect is that of solar rotaon. The latudinal dependence of rotaonal velocity is usually expressed as (Howard & Harvey 197; Schröter 1985): ω rot (b)=a+ B sin 2 b+ C sin 4 b, (3) where b is the latude. arameter A represents equatorial velocity, while B and C depict the deviaon from rigid body rotaon. The problem with Eq. 3 is that the funcons in this expression Arcle number, page 3 of 6page.6

4 A&A proofs: manuscript no. Rotaon 6 Table 1. Coefficients of the solar rotaon profile. Heliographic latude [deg] Type A [ day 1 ] B [ day 1 ] C [ day 1 ] n A, B, C 14.47±.1 +.6± ± A, B = C 14.59± ± ± A, B, C = 14.62±.8-2.2± orthern hemisphere A, B, C 14.43± ± ± A, B = C 14.55± ± ± A, B, C = 14.57± ± Southern hemisphere A, B, C 14.5± ± ± A, B = C 14.65± ± ± A, B, C = 14.69± ± Heliographic longitude [deg] Fig. 5. Distribuon of CBs in heliographic coordinates with arrows showing the direcon and strength of the velocity vector A, B, C B=C C= ω (deg/day) Fig. 7. Comparison of three different fitng procedures for the solar differenal rotaon profile. Average values ofω rot in 5 bins in latude, b, are also shown with their respecve errors b (degrees) Fig. 6. Solar differenal rotaon profile obtained with data from SDO/AIA. Open circles are individual measurements, while the solid line is the best fit defined by Eq. 3 for the A B C case. are not orthogonal, so the parameters are not independent of each other (Duvall & Svalgaard 1978; Snodgrass 1984; Snodgrass & Howard 1985; Snodgrass & Ulrich 199). This crosstalk among the coefficients is parcularity bad for B and C. The effect of crosstalk does not affect the actual shape of the fit (ω rot (b)), but it creates confusion when directly comparing coefficients from different authors or obtained by different indicators. There are various methods to alleviate this problem. Frequently C is set to zero since its effect is noceable only at higher latudes. This is almost a standard pracse when observing rotaon by tracing sunspots or sunspot groups because their posions do not extend to high latudes (Howard et al. 1984; Balthasar et al. 1986b; ulkkinen & Tuominen 1998; Brajša et al. 22a; Sudar et al. 214). Another method to reduce the crosstalk problem is to set the C/B rao to some fixed value. Scherrer et al. (198) set the rao C/B=1 while Ulrich et al. (1988), after measuring the covariance of B and C, set the rao to C/B= In Fig. 6 we show individual measurements of rotaonal velocies,ω rot, with respect to latude, b, as open circles. We indicate, with a solid line, the best fit to the data using a funconal form given in Eq. 3. Coefficients of the fit are given in Table 1. We also fitted the rotaon profile for orthern and Southern solar hemisphere separately because of possible asymmetry (cf.eg. Wöhl et al. 21) and show the results in the same table. Coefficient A shows a larger value in the Southern hemisphere for all 3 fit funcons. Jurdana-Šepić et al. (211) reported that coefficient A is larger when solar acvity is smaller. According to the SIDC data (SILSO World Data Center 211) we can see that orthern hemisphere is more acve both when looking at the monthly smoothed means and daily sunspot data, consistent with Jurdana- Šepić et al. (211). However, judging by the errors of the coefficients, the difference between South and orth is stascally low and the hypothesis that this is a result of asymmetric solar acvity needs to be verified with a larger data sample. In Fig. 7 we show a comparison between different fitng techniques: A B C(solid line), A B=C(dashed line) and A B, C= (dotted line). In the same figure we also show average values ofω rot in bins 5 wide in latude, b, with their respecve errors. 4. Discussion In Table 2 we show a comparison of the solar differenal profile (Eq. 3) from a number of different sources, including the results Arcle number, page 4 of 6page.6

5 D. Sudar et al.: Steps toward a high precision solar rotaon profile: Results from SDO/AIA coronal bright point data Table 2. Comparison with some other results. Method/object me period A [ day 1 ] B [ day 1 ] C [ day 1 ] A G [ day 1 ] B G [ day 1 ] C G [ day 1 ] Ref CBs ± (1) CBs ± ± ± (2) CBs ± ± ± (3) CBs ± ± ± (4) CBs 1-2 Jan ±.1 +.6± ± (5) CBs 1-2 Jan ± ± ± (5) CBs 1-2 Jan ±.8-2.2± (5) sunspot groups ± ± (6) sunspot groups ± ± (7) sunspot groups ± ± (8) sunspot groups ± ± (9) sunspots ± ± (1) sunspot groups ± ± (1) Hα filaments ± ± ± (11) magnec features ± ± ± (12) magnec features ±.2-2.± ± (13) Doppler (14) Doppler (15) Helioseismology (16) Helioseismology Apr (17) References. (1) Dupree & Henze (1972); (2) Hara (29); (3) Brajša et al. (24); (4) Wöhl et al. (21); (5) this paper; (6) ulkkinen & Tuominen (1998); (7) Balthasar et al. (1986b); (8) Sudar et al. (214); (9) Brajša et al. (22a); (1) Howard et al. (1984) (11) Brajša et al. (1991); (12) Snodgrass (1983); (13) Komm et al. (1993); (14) Howard & Harvey (197); (15) Snodgrass (1984); (16) Schou et al. (1998); (17) Komm et al. (24) from this paper (Table 1). Since we found no stascally significant difference between orthern and Southern hemisphere we only include the results for both hemispheres combined. Results in Table 2 come from a wide variety of different techniques, tracers and instruments. Snodgrass (1984) suggested that the rotaon profile should be expressed in terms of Gegenbauer polynomials since they are orthogonal on the disk. This eliminates the cross-talk problem between coefficients in Eq. 3. Using the expansion in terms of Gegenbauer polynomials solar rotaon profile becomes: ω rot (b)=a G T 1 (sin b)+ B GT2 1 (sin b)+ C GT4 1 (sin b), (4) where A G, B G and C G are coefficients of expansion and T 1 (sin b), T2 1(sin b) and T 4 1 (sin b) are Gegenbauer polynomials as defined by Snodgrass & Howard (1985) in their equaon (2). As Snodgrass & Howard (1985); Snodgrass & Ulrich (199) pointed out, the relaonship between coefficients A, B and C from standard rotaon profile (Eq. 3) and coefficients A G, B G and C G from Eq. 4 is linear. Therefore, it is not necessary to recalculate the fits using Gegenbauer polynomials, we can compute A G, B G and C G directly from A, B and C. We used the relaonship given in Snodgrass & Howard (1985) (their equaon (4)) since there seems to be a typo for a similar relaonship for coefficients C and C G in Snodgrass & Ulrich (199). In Table 2 we also show the values of coefficients A G, B G and C G. Our rotaonal profile results are roughly consistent with all the previously published work we surveyed (Table 2). The accuracy of our coefficients is lower when compared with other results, a consequence of our fairly small number of data points (n=96). Wöhl et al. (21), for example, had more than 5 data points spanning a me interval of 8 years. We have used data spanning only 2 days. It is therefore reasonable to expect that with AIA/SDO CB data we could reach 5 data points with only 4 months of data and achieve similar accuracy in solar rotaon profile coefficients. This means that with AIA/SDO data it should be possible to measure rotaon profile several mes per year and track possible changes in solar surface differenal rotaon directly with a very simple tracer method. This is also true for meridional moon and Reynolds stress, both of which probably vary over the solar cycle (cf. e.g Sudar et al. 214). 5. Summary and Conclusion Using 19.3nm data from the SDO/AIA instrument at 1 min cadence we have idenfied a large number of CBs, resulng in 96 rotaon velocity measurements. We obtained a fairly good differenal solar rotaon profile in spite of the fact that we used data spanning only two days. The large density of data points in me is a result of several factors. The instrument itself (SDO/AIA) has better spaal resoluon and is capable of high cadence (<5 min). For comparison, SOHO/EIT 28.4 nm channel had a cadence of two images every 6 hours (Wöhl et al. 21). In this work, the high cadence enabled us to track and measure velocies of short lived CBs which couldn t be detected or accurately tracked by the comparavely large me interval between successive images in the SOHO/EIT 28.4 nm channel. Coupled with the fact that short lived CBs are more numerous than long lived ones (Brajša et al. 28), this resulted in a very high density of data points in me. High data density necessitated the use of an automac procedure to detect and track CBs. The segmentaon algorithm used here proved to be completely adequate for the task, as similar algorithms have elsewhere (McIntosh & Gurman 25; McIntosh et al. 214a,b). The surface rotaon profile and its accuracy obtained by helioseismology is seldom given in a form suitable for comparison with those obtained by tracer measurements. We can esmate from the number of published significant digits in the results Schou et al. (1998); Komm et al. (24), given in Table 2, that Arcle number, page 5 of 6page.6

6 A&A proofs: manuscript no. Rotaon the accuracy is of the same order as better quality tracer measurements. Zaatri et al. (29) published the error for the coefficient B (see Eq. 3) and the value of.1 from that paper is in agreement with our esmate above. It is quite conceivable that errors in the differenal rotaon profile coefficients would drop significantly when more data is used. From our analysis, we can expect to obtain 4-5 velocity measurements per day from CBs using SDO/AIA. A me interval of 4 months seems adequate to obtain 5 velocity measurements, which should be sufficient to match the most accurate results obtained by tracer methods (for example Wöhl et al. (21)). CBs are also very good tracers since they extend to much higher latudes than sunspots. They are also quite numerous in all phases of the solar cycle while sunspots are often absent in the minimum of the cycle. This opens up an intriguing possibility of measuring the solar rotaon profile almost from one month to the next over an enre cycle. Such studies could provide new insight into mechanisms responsible for solar rotaon. We already know that meridional moon exhibits some changes during the course of the solar cycle, and the same is probably true for Reynolds stress. Sudar et al. (214) found by averaging almost 15 years of sunspot data that meridional moon changes slightly over the solar cycle and hinted that the Reynolds stresses are probably changing too. Here we have found a small asymmetry in rotaon profile for two solar hemispheres and suggested that this might be related to different solar acvity levels in the two hemispheres. This needs to be verified with a larger dataset though, as the difference in rotaon profiles was of low stascal significance. The planned SDO mission duraon of 5 1 years will cover a large poron of the solar cycle which should result in enormous amount of velocity data to assist in the understanding of the nature and variaon of solar rotaon profile. Having more detailed temporal resoluon and direct results (without the need to average many solar cycles) could prove to be very informave. A me interval of 1 minutes between successive images also offers a good opportunity to study the evoluon of CBs and possible effect this might have on the detected surface velocity fields. For example, Vršnak et al. (23) reported that longer lasng CBs show different results than short-lived CBs. Based on the promising results here, we will use larger datasets to further exploit the potenal of SDO/AIA CB data to determine meridional moons, rotaon velocity residuals, Reynolds stresses and proper moons in subsequent papers. Acknowledgements. This work has received funding from the European Commission F7 project eheroes (284461, ) and SOLARET project (312495, ) which is an Integrated Infrastructure Iniave (I3) supported by F7 Capacies rogramme. It was also supported by Croaan Science Foundaon under the project 6212 Solar and Stellar Variability. SS was supported by ASA Grant X9AB3G to the Smithsonian Astrophysical Observatory and contract S2H171R from Lockheed-Marn to SAO. We would like to thank SDO/AIA science teams for providing the observaons. We would also like to thank Veronique Delouille and Alexander Engell for valuable help in preparaon of this work. Brajša, R., Wöhl, H., Vršnak, B., et al. 24, A&A, 414, 77 Brajša, R., Wöhl, H., Vršnak, B., et al. 28, Central European Astrophysical Bullen, 32, 165 Dorotovič, I., Shahamatnia, E., Lorenc, M., et al. 214, Sun and Geosphere, 9, 81 Dupree, A. K. & Henze, Jr., W. 1972, Sol. hys., 27, 271 Duvall, Jr., T. L. & Svalgaard, L. 1978, Sol. hys., 56, 463 Erwin, E. H., Coffey, H. 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