Computer-aided measurement of the heliographic coordinates of sunspot groups
NNoname manuscript No. (will be inserted by the editor)
Computer-aided measurementof the heliographic coordinates of sunspot groups
H. C¸ akmak
Received: date / Accepted: date
Abstract
Heliographic coordinates are used to identify the positions of so-lar features, especially the sunspot groups on the Sun’s surface. Tracking thepositions of sunspot groups provides information about solar rotation and themovement behavior of sunspot groups over Solar Cycles. Two heliographic co-ordinates are defined: Carrington and Stonyhurst. The calculations used heredepend on three solar parameters, position angle P , latitude angle B andthe starting longitude L . These values are calculated by using AstronomicalAlmanac for the observation time. In this study, a computer program called
Computer Aided Measurement for Sunspots (CAMS) is presented. The mainaim of the program is to determine the heliographic latitude and longitude ofthe sunspot groups besides other features like the latitudinal and longitudinallength, rectangular area and the tilt angle. This is accomplished by generat-ing the corresponding Stonyhurst disk for the P and B angles of the timeof observation and superimposing it onto the scanned drawing. Since 2009,CAMS is being used to process daily solar drawings at the Istanbul UniversityObservatory. Keywords computer-aided measurement, heliographic coordinates, sunspots
Sunspots are the first noticeable feature on the visible surface of the Sun. Thenumber of spots on the Sun’s surface increase and decrease during a specifictime range which is 11 years on average. This period is known as Solar Cycleor Sunspot Cycle. During the minimum phase of a cycle, no sunspots areseen, but, at the maximum phase, many sunspots can be observed on the
H. C¸ akmakIstanbul University Science Faculty, Astronomy and Space Science Department34119 Beyazıt / Istanbul - TurkeyE-mail: [email protected] a r X i v : . [ a s t r o - ph . S R ] J u l H. C¸ akmak
Fig. 1
Two typical views of a Sunspot Cycle.
Left : Minimum,
Right : maximum phase.Images were taken from the SOHO (Solar and Heliospheric Observatory) archive.
Sun’s surface (Fig. 1). Sometimes big-sized spots are visible to the naked-eyeunder proper conditions. These sunspots have attracted attention through thecenturies. Therefore, since the 17th century, sunspot observations are beingcontinued without interruption.One of the most known Sun observers, Galileo showed that movement ofthe sunspots across the apparent disk of the Sun is similar to rotating acrossa spherical surface, rather than a flat disk. This concept made it possible todevelop a spherical coordinate system of solar latitude and longitude, similarto the latitude and longitude system on Earth. Today, two heliographic coor-dinates are defined: Carrington and Stonyhurst. They differ on whether thelines of longitude are fixed for the Sun’s rotation (in Carrington) or fixed forthe observer (in Stonyhurst) [1–4]. More explanations about both heliographiccoordinates can be found in the articles of Thompson [3] and Sanchez-Bajo &Vaquero [4].More properties about the positions of the sunspot groups were discoveredwith increasing solar observations in the past. German astronomer ChristophScheiner showed that the solar rotation rate varied with latitude. This meantthat the Sun does not rotate as a solid body. Carrington published his observa-tions of sunspot positions in 1863. And, he estimated the correlation betweensolar rotation rate and latitude [4]. In 1904, Edward Maunder showed thelatitude of sunspot emergence changes from the beginning to the end of thesunspot cycle in a diagram called butterfly . All these movement behaviors ofsunspot groups provide information about the Sun: e.g. the rotation period ofthe Sun, the nature of the solar cycle and the existence of differential rotation.Most of observatories spread around the world are continuing to draw thesunspots manually. But, on the other hand, technological developments aremaking it also necessary to process these sunspot drawings in computer envi-ronment. Some of the observatories transferred their old drawings into digitalenvironment via scanners to process them later. Some studies are done on de- omputer-aided measurement of the heliographic coordinates of sunspot groups 3 termining the positions of sunspot groups from sunspot drawings. The mostknown applications are the Helio programs developed by Peter Meadows [5].These are sufficient in some extents, but not adequate for our own needs.Moreover, similar programs are developed by different people: the programHSUNSPOTS is developed by Cristo et al. [6] to analyze ancient solar draw-ings and the program DigiSun is used in the SIDC of the Royal Observatoryof Belgium [7].The CAMS program which will be introduced here has been developed witha different perspective from the others. It aims to obtain as many features ofthe sunspot groups as possible. Moreover, not only the scanned solar drawingsbut also CCD and solar digital images can be used with the program byadjusting their size and resolution properly. In this program, a Stonyhurstdisk overlaying technique is used. This technique gives the opportunity forcalculating most of the properties of the sunspot groups easily. All operationsare carried out in two simple steps, superimposing Stonyhurst disk onto imageand, marking and classifying the sunspot groups separately. Most of the otherprocesses are performed automatically such as calculating the solar parametersat the time of observation, the heliographic coordinates and other measurableparameters of the sunspot groups and, altering and sorting the groups by theirlatitude and longitude.In the sunspot observations, the appearance of the Stonyhurst disk dependsmainly on the P and B angles. Therefore, the calculations of these solarparameters have a special importance and are introduced in detail in Section2. The algorithm for drawing the Stonyhurst disks is explained in Section 3.And, the basics of CAMS’s workings are given in Section 4. The advantages,importance and possible future developments of the CAMS are presented inthe Discussion Section. Any coordinate system used in astronomy must be set up using a plane and astarting point. For heliographic coordinates the plane in question is the equatorof the Sun, but the starting point is a little difficult to describe, because thereare no permanent features on the surface of the Sun, which can be taken as afixed point. Carrington defined this virtual point as a point occupied by theascending node of the solar equator on the ecliptic at noon on January 1st1854. By this assumption, heliographic coordinates of a point on the surfaceof the Sun are defined by the spherical definitions as shown in Fig. 2a [9].The line of sight is shown by the line towards the Earth in Fig. 2a and itshows the direction to the center of the apparent solar disk, which is labeled as E in Fig. 2b. Also, the rotation axis of the Sun is shown by E P N line and theangle between this line and the rotation axis of the Earth is P , the positionangle of the Sun. The angle (cid:92) F CE is the latitude angle B o and representsthe angular distance of the Sun’s equator from the center of the apparentsolar disk. In accordance with the definitions as shown in Fig. 2a, the starting H. C¸ akmak
Fig. 2 (a) Definition of the heliographic coordinates of a point X on the surface of theSun according to the spherical definitions. (b) Position of the rotation axis of the Sun withrespect to the rotation axis of the Earth and north & south line of the solar projection disk. longitude L o (point O ) and B o are calculated by [8] L o = arctan (tan( λ (cid:12) − Ω ) cos I ) + M,B o = arcsin (sin( λ (cid:12) − Ω ) sin I ) , where Ω is the angle between the ascending node of the Sun’s equator on theecliptic and the point of the vernal equinox ( Υ N angle), λ (cid:12) is the eclipticallongitude of the Sun, I is the inclination of the Sun’s equator with respectto the ecliptic plane and its value is 7.25 ◦ . M is the angular distance of theascending node of the Sun’s equator on the ecliptic from the starting longitude.Here, M is given by [9] M = 360 − M (cid:48) with M (cid:48) = 36025 .
38 ( JD − . M (cid:48) must be reduced to the range 0 - 360degrees. P is the angle between both rotation axis directions of the Sun and theEarth. But, this cannot be calculated directly. Therefore, both axis inclinationswith respect to ecliptic are calculated separately and P is the sum of both. So,let θ be the inclination of the Earth’s axis and let θ be the inclination of theSun’s axis. And, P is given by [8] P = θ + θ with θ = arctan( − cos λ (cid:12) tan ε ) ,θ = arctan {− cos( λ (cid:12) − Ω ) tan I } , where ε is the angular distance of the Earth’s rotation axis from the eclip-tic plane. More detailed explanations are given in the Textbook on SphericalAstronomy of Smart & Green [8]. omputer-aided measurement of the heliographic coordinates of sunspot groups 5
In general, Ω , λ (cid:12) and ε are changing with time. Therefore, these param-eters should also be calculated at the time under consideration and they aregiven by [9] Ω = 75 ◦ (cid:48) + 84 (cid:48) T,ε = 23 ◦ (cid:48) . (cid:48)(cid:48) − . (cid:48)(cid:48) T − . (cid:48)(cid:48) T + 0 . (cid:48)(cid:48) T ,λ (cid:12) = 360365 . T + 360 π e sin (cid:26) . T + ε g − (cid:36) g (cid:27) + ε g , with ε g = 279 . . T + 0 . T ,(cid:36) g = 281 . . T + 0 . T ,e = 0 . − . T − . T , where T is the number of Julian centuries since the epoch 2000 January 1.5, ε g is the mean ecliptic longitude of the Sun at the epoch, (cid:36) g is the longitudeof the Sun at perigee and e is the eccentricity of the Earth’s orbit around theSun. In order to form a Stonyhurst disk on an image, it is necessary to form atwo-dimensional projection of a three-dimensional sphere. But only half of thesphere or the visible side of the sphere must be taken into consideration. Letthis sphere be indicated in Figure 3a. If N is any point on this sphere and itsspherical coordinates in three-dimensional space are the radius of the sphere( r ), latitude angle ( θ ) and longitude angle ( ϕ ), its Cartesian coordinates ( x, y,z ) are given by [12] x = r cos θ sin ϕ,y = r sin θ,z = r cos θ cos ϕ, where the angle θ is selected between -90 ◦ and +90 ◦ and, the angle ϕ is selectedbetween 0 ◦ and 180 ◦ [8]. These three-dimensional (3D) coordinates have to beconverted to two-dimensional (2D) coordinates to draw the Stonyhurst diskdepending on P and B o parameters of the Sun. These are done with the wellknown transformation and projection equations [10–13]. Let us assume that anangle is rotated in the anti-clockwise direction of its positive and in clockwisedirection of its negative values. And also, let us assume that P and B o anglesare positive. First, the x axis is rotated B o degrees and x , y , z values are H. C¸ akmak(a) (b)
Fig. 3 (a)
Spherical ( r , θ, ϕ ) and Cartesian ( x , y , z ) coordinates of the point N in three-dimensional space. (b) Projection coordinates of the point N are expressed as x , y and z in the x (cid:48) y (cid:48) z (cid:48) projection system. Here, z axis (blue) is rotated P degree and x axis (blue) isrotated B degree. Also, blue colored circles represent the rotated planes of the point N . obtained, and then, the z axis is rotated P degrees and x , y , z values areobtained (Fig. 3b). These equations are specified as follows [10] x = x, x = y sin P + x cos P,y = z sin B o + y cos B o , y = y cos P − x sin P,z = z cos B o − y sin B o , z = z , Here, x and y are the 2D projection coordinates of the point N with respectto the sphere center. When these are rearranged, we get x = ( z sin B o + y cos B o ) sin P + x cos P,y = ( z sin B o + y cos B o ) cos P − x sin P, Since the zero point of the screen coordinates in the computer environmentsis the top-left corner, the x-axis’s value is increasing from the left to right ofthe screen and, the y-axis’s value is increasing from the top to bottom of thescreen, Therefore, the center of the any solar disk image on the screen doesnot coincide with the zero point of the screen coordinates. Hence, in order todraw the sphere onto solar image, the center of the sphere must be moved tothe center of the solar disk image. This is done by adding x and y-axis valuesof the screen coordinates of the center of the solar disk image to the x andy-axis values of the all points of the sphere separately. Let x p and y p be thescreen coordinates of the point N . The following equations are obtained withthe explanations above: x p = x + x , x p = x o + ( z sin B o + y cos B o ) sin P + x cos P,y p = y − y , y p = y o − ( z sin B o + y cos B o ) cos P + x sin P, where x and y are the coordinates of the disk image center in screen coor-dinates. The subtraction is carried out in y-values because of the increase in omputer-aided measurement of the heliographic coordinates of sunspot groups 7 the reverse direction contrary to the Cartesian system. With these projectionequations, Stonyhurst disk can be prepared with any values of P and B o . Asan example, the Stonyhurst disk for B o = 5 ◦ and P = 0 ◦ values is shown inFigure 4a. This is compared with the one used in the observatory (Fig. 4b)and their can be seen agreement in Fig. 4c. Also, other Stonyhurst disks (for B o = 0,1,2,3,4,5,6,7 ◦ ) were checked as well and exact fits were obtained. Fig. 4 (a) Stonyhurst disk prepared for B o = 5 ◦ in computer. (b) Plastic Stonyhurst diskwith the same B o . (c) Two disks superposed. CAMS is mainly designed to process the daily solar drawings, and the interfaceis presented in Fig. 5. All processes are performed in this window, such as a newprocess, checking the previous processes, calculation of the solar parametersand transferring the results of the process to the web. Processing the solardrawing has two stages. First stage is the transferring the drawing into theprogram and superposing the Stonyhurst disk onto it.The second stage is thedetermining the heliographic coordinates of each sunspot group besides otherfeatures like the group length and tilt angle.4.1 Transferring the solar drawing into program and superposing Stonyhurstdisk on itAfter all sunspots on the solar surface are drawn manually on the observationpaper, the processing stage starts with the calculation of the solar parame-ters by entering date and time of the observation in the parameter calculationwindow. Then, the drawing is transferred into the program by using the scan-ner interface. After this is done, the center and a point on the outer borderof the drawing disk must be marked, respectively. A circle representing thesize of the Stonyhurst disk is imposed spontaneously over the image (Fig. 6).Conformity between circle and disk is checked visually by changing the radius
H. C¸ akmak
Fig. 5
CAMS main window with an example of the transferred sunspot drawing. Thesolar parameter calculation and image quality selection windows are seen at the bottom,respectively.
Fig. 6
Defining the center and radius of the circle represent the size of the Stonyhurst diskover the image of the drawing. and by shifting the center of the circle. Also, the location of the North pointof the drawing is adjusted properly by the arrows of the positioning window. omputer-aided measurement of the heliographic coordinates of sunspot groups 9
After approval of conformity between circle and disk, the cleaning of the outerregion and the clipping process of the image is carried out and, the image istransfered into the measurement window.
Fig. 7 (a) Marking the sunspot group using an enclosed rectangular frame. The beginning,middle and last sequence of the stage. (b) The adjustment can be made easily by movingthe handles on the border of the frame. ◦ is encountered, point source measurement is fulfilled by touching to Fig. 8 (a) Selecting the type of the group and the number of the sunspot with the drop-down lists. (b) Measuring the point like sunspot and information about it. Fine adjustmentsare done using the arrow buttons. (c) Positioning the tilt line according to the tilt directionof the group.
Fig. 9
A finished observation process example that all the sunspot groups are measured.
Left : Calculated values for the sunspot groups.
Right : Rectangular frames of the groups withthe corresponding sequence number. the center of the group. No length, tilt angle and rectangular area for thegroup is calculated in this case (Fig. 8b).The tilt angle of the group is started to adjust by pressing the E symbol onthe top-left corner of the group’s frame. A line with two small handles at itsends appears in the middle of the frame. Then, the inclination of this line isadjusted by moving these handles in proper position to indicate the tilt direc-tion of the group (Fig. 8c). Adjusting the tilt is concluded by pressing again omputer-aided measurement of the heliographic coordinates of sunspot groups 11 Table 1
The comparative measurement values of a sample observation day. Left panelresults are calculated manually by using the plastic Stonyhurst disk (for B = 2), whereasright panel results are obtained with CAMS.Date 19.12.1989 P +8.06 +8.08Time 09:45 UT B -1.51 -1.52 L ∆ L L U B ∆ L L U UB TiltDAO 4 +09 72 W 345 7.5 +08.97 71.94 W 344.94 7.9 3.5 18.94AX 1 +34 70 W 343 - +32.84 69.48 W 342.48 - - -BXO 2 +30 63 W 336 4.0 +29.75 62.84 W 335.84 4.9 2.2 25.10FKC 43 +21 32 W 305 15.0 +20.85 32.86 W 305.86 14.7 9.3 24.25DKC 29 +27 03 W 276 10.0 +26.69 02.48 W 275.48 9.7 6.5 26.35CRO 6 +17 09 E 264 4.5 +16.88 09.54 E 263.46 4.7 1.5 10.92FKI 43 +26 11 E 262 18.0 +25.44 11.40 E 261.96 18.6 9.0 18.30EHI 9 +18 55 E 218 14.0 +17.27 54.47 E 218.53 13.3 3.2 1.45? 9 +22 74 E 199 11.0 +21.61 75.22 E 197.78 12.6 2.7 9.80CRO 6 -13 63 W 336 6.5 -13.21 63.83 W 336.83 6.8 1.6 13.59FKC 22 -33 51 W 324 17.0 -32.68 50.85 W 323.85 16.8 4.9 12.65DAC 16 -21 08 E 265 5.5 -21.35 08.20 E 264.80 5.8 2.2 12.15BXO 9 -23 15 E 258 4.0 -23.30 14.47 E 258.53 4.0 1.9 32.29 S : Spot number, B : Latitude, ∆ L : Apparent Longitude, L : Longitude, U : Length of thegroup, UB : Latitudinal Length, Tilt : Inclination of the group with respect to the solarequator. the E symbol again. After all the sunspot group are marked and processedindividually (Fig. 9), all data about the observation is saved into the databaseof the program and sent to web page server of the observatory. Detailed in-formation about the CAMS and steps of the processing the observations withCAMS are given in the C¸ akmak’s symposium proceeding [14].As an example of the precision of the CAMS, the comparative measurementvalues of a sample observation day is listed in the Table 1. Image of the solardrawing of this day is shown in Fig. 10. Old-dated solar observation is speciallyselected to show the capability of the built-in solar ephemeris of the program.In this table, the measurements of the both plastic Stonyhurst disk and CAMSare given for every sunspot group separately. The last two columns of the rightpanel are the values calculated with CAMS, latitudinal length and tilt angleof the sunspot group, respectively. Fig. 10
Solar drawing of the observatory taken in 1989.12.19. Stonyhurst disk is superim-posed for the time of the observation, 09:45 UT.
Nowadays, i.e. in the computer age, observation techniques, calculation stepsand archiving the obtained knowledge are important and essential. From thisperspective, the main purpose of CAMS is the shortening the time spent onprocessing the observation and to eliminate possible observer errors from thecalculations. Second purpose is calculating the heliographic coordinates, latitu-dinal and longitudinal length, tilt angle and the rectangular area of the sunspotgroups more precisely than manual measurements. Therefore, the measuredvalues are saved with two decimals. When working on the positions of thesunspot groups, increasing the numerical precision in the coordinates gives amore accurate approach in the calculations. For example, in the butterfly dia-gram, the distributions of the sunspot groups with latitudes will appear to bemore accurate instead of being concentrated on the latitude lines.Another point of the CAMS is that the Stonyhurst disks are drawn at thetrue angle of the latitude angle instead of the nearest integer value. That is tosay, it is drawn at the angle, for example, 7.12 ◦ or 7.25 ◦ or 7.57 ◦ or 7.92 ◦ , so notjust for 7.0 ◦ . The same is valid for the position angle, as well. Although CAMSis designed to process daily solar drawings, any digital solar image can be usedby the program. Two examples of this are shown in Fig. 11. One is a HMIIF(Helioseismic and Magnetic Imager Intensitygram - Flattened) image of theSolar Dynamics Obsevatory, and the other is the chromospheric H-Alpha imagetaken with CCD at the university observatory. The heliographic coordinatesof the sunspot groups can be measured more precisely with respect to the omputer-aided measurement of the heliographic coordinates of sunspot groups 13 Fig. 11
Examples of the using digital solar image with CAMS.
Left : A HMIIF (Helioseismicand Magnetic Imager Intensitygram - Flattened) image of the Solar Dynamics Observatory(SDO).
Right : A chromospheric H-Alpha image taken with CCD at the Istanbul UniversityObservatory. drawings. This can be done to obtain more accurate results or to eliminatethe drawing errors of the observers in their studies.The development of CAMS is still continuing and the integration withthe database is under development. After this is done, it will be possible toobtain any group’s evolution separately and all statistical information aboutthe positions and types of the sunspot groups. Also the daily, monthly changesand general trend of the sunspot relative number can be easily generatedgraphically. Since the relative numbers are archived by making a distinctionbetween the Northern and Southern, the variations of the relative number inboth will be also examined separately. After sufficient data is gathered, thewhole solar sunspot cycle will be analyzed in detail.
Acknowledgements
Thanks to Dr. Tuncay ¨Ozı¸sık from the Turkish National Observatoryto develop the CAMS and Assoc. Prof. Dr. Nurol Al Erdo˘gan from the Istanbul UniversityScience Faculty, Astronomy and Space Sciences Department for the idea to prepare andpublish this article. Also, thanks to Asst. Ba¸sar Co¸skuno˘glu for his contributions towardsimproving the language of the manuscript. Also, thanks to anonymous reviewer for his/hervaluable suggestions and comments improving manuscript This work supported by the Is-tanbul University Scientific Research Projects Commission with the project number 24242.
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