Teacher s guide CESAR Science Case The differential rtatin f the Sun and its Chrmsphere Material that is necessary during the labratry CESAR Astrnmical wrd list CESAR Bklet CESAR Frmula sheet CESAR Student s guide CESAR images f the Sun The sftware fr this Science Case Paper, pencil, ruler, calculatr, prtractr Intrductin This Science Case is separated int tw sectins. The first sectin is abut t understand hw the Sun rtates i.e. t understand that the Sun is nt a slid bdy and it mves faster clse t the equatrs and slwer as we get clse t the ples. That is the Sun s differential rtatin f the Sun. The ther sectin is abut visualizing the different structures f the Sun s chrmsphere. The students have t identify as much structures as they culd and understand what they are. This is an easier Science Case cmpared with the thers slar Science Cases, fr this reasn this ne is fcused in the understanding f the Sun and has nt many calculus r measurements. T d this Science Case a set f 3-7 images f the Sun separated by 24h (r mre) in the time f acquisitin has t be acquired with bth the visual telescpe and the h-alpha telescpe. Then the students have t calculate the heligraphic crdinates f at least tw sunspts that have t be as much separated in latitude as pssible. It will be all explained later. Then they have t track the selected sunspts using all the images, writing its crdinates. T get the crdinates it is highly recmmended t use the sftware that CESAR prvides but a general methd is ging t be included here fr yu (nte that is the methd included in the Science Case: Slar activity and the slar cycle fr calculating the sunspts crdinates). Using these crdinates, they will be able t see hw the angular velcity f the Suns depends n the latitude. T get the images there are tw pssible slutins. If the rbtic CESAR slar telescpe is available fr bservatin and image capturing, yu can dwnlad images frm the archive. If the CESAR slar telescpe is nt available r if yu dn t want t use it, the ther ptin is t dwnlad a set f preselected images frm the CESAR website fr this Science Case and use them. Obviusly part f the educatinal purpse is t apprach prfessinal telescpes t the students s they culd learn hw prfessinal bservatries wrks. Mrever they wuld be able t see hw remtely a telescpe mves as they want (pinting the Sun in this Science Case). It culd happen that the day f bservatin n sunspts are visible. In that case, it s impssible t d this labratry. Fr this reasn yu culd check if there are sunspts available befre at http://sh.nascm.nasa.gv/sunspts/. T achieve a gd knwledge f the Sun s surface give them the bklet. There are a lt f structures in the Sun s surface explained that they will have t identify n the h-alpha images. 1
Sunspts tracking Chsing the sunspts frm the set f images As mentined in the labratry descriptin, yur students need t get the images and its dates fr the bservatins. They need t name sme f the sunspts t keep them n track. What name it des nt matter, but each spt shuld have its individual name. Furthermre it s imprtant t chse thse spts that are clser t the centre f the Sun. It is preferable because it s easier t appreciate the displacement f a sunspt n the images if it is near t the centre and cnsequently it s easier t d the measures. After taking the images with the CESAR telescpe, decide if it s wrth t prcess the images r nt. It shuld nt be necessary since the quality prbably will be gd enugh. The sunspts must be clearly visible and nt blurred. If yu cnsider that sunspts are nt clearly visible, try t increase the cntrast with an image prcessing prgram in rder t distinguish them. A very imprtant thing that has t be mentined is that the images have t be aligned in E-W directin in the slar disk. This is the first requirement t determinate the rientatin f the Sun and its heligraphic crdinates. The CESAR images will already been aligned but if yu have cnsidered t d this Science Case using yur wn telescpe with an equatrial munt a trick t get the E-W directin is t take pictures while mving in Right-Ascensin. If yu take tw pictures fr example and superpse them int a single ne, draw a line that cnnect the same sunspt f the tw frames. That is the E-W directin, and yu can nw rtate the image t see the E-W directin parallel t the mark frame as shwed belw. Figure 1: Image shwing the E-W directin where tw pictures taken at tw separated dates where superpsed. Credit: CESAR Until nw, we have a set f images n visible and h-alpha captured at different times and riented n E- W directin. Nw we are ging t determinate the heligraphic crdinates fr the sunspts. 2
Heligraphic crdinates Determine the heligraphic crdinates f the sunspts The heligraphic crdinates are the crdinates f the Sun. As well as a place in the Earth has a lngitude and a latitude in the Sun is exactly the same. A sunspt has a lngitude and latitude n its surface t. Its latitude is divided int 90 degrees nrth t the equatr, and 90 degrees suth t the equatr. Its lngitude is divided int 360 degrees t the West in the directin f the slar rtatin. The Sun as the Earth has a place frm which t start cunting the lngitude degrees. As well as the Earth has a rtatinal axis, the Sun t. It s well knwn that the Earth rtatinal axis is tilted 23,5 degrees while the Sun s rtatinal axis is tilted 7 degrees. If bth Earth and Sun rtatinal axis were parallel between them and perpendicular t the ecliptic, then the E-W directin that we mentined befre wuld be the equatr f the Sun. Figure 2: Inclinatin f the slar axis alng a year viewed frm Earth. Credit CESAR What we are ging t d nw is t calculate the heligraphic crdinates f the sunspts using the crdinates f the sunspts in the E-W and N-S crdinate system. In rder t d this, students first have t measure the psitin f the sunspts frm the center f the Sun using the first images, nt the h-alpha images. The center f the Sun has t be lcated because is the center f ur reference system. Students have t create a table like this: Sunspt X crdinate Y crdinate R m R 1 356 pixels 232 pixels 425 pixels 3115 pixels Where R! is X! + Y! and R is the diameter f the Sun that they have t measure t (nly nce). We need nw t calculate ther values using the X and Y crdinates f the sunspts. This values are the psitin angle f the sunspt measured frm N-S directin (that we call P! ) and the angle between the sunspt with the visual (that we call ρ). Their frmulas t are: 3
P! = arc tg( X Y ) (1) and ρ = arc sin (R!/R) α/2(r! /R) (2) Where α is de angular diameter f the Sun (n degrees). This values are ging t be autmatically calculated by the CESAR sftware fr this Science Case. As well as in the first table, the students have t nte the values f P! and ρ fr each sunspt in a table: Sunspt P m ( ) ρ ( ) 1 56,9 7,8 As we said, the Sun s axis is tilt s we see different angles with the N-S directin alng a year. Furthermre the center f the heligraphic crdinate system is nt the place where E-W and N-S lines crss each ther. Fr all f this, we need t take sme values which are: P: Is the psitin angle f the slar rtatin axis measured frm the N-S directin. Psitive when it s t the East and negative when it s t the West. B! : Heligraphic latitude f the slar disk center. L! : Heligraphic lngitude f the slar disk center. T make this Science Case easier, we culd take these values frm the Ephemeris. There are sme websites such as: http://alp-astrnmy.rg/slarblg/wp-cntent/uplads/ephems/ephem2015.html r http://bass2000.bspm.fr/ephem.php. Here there is a picture shwing all these values. Figure 3: Picture shwing all mentined values. Credit: CESAR 4
At this pint, the students will btain the heligraphic crdinates f any f the sunspts by filling the values: R!, R, ρ, P, P!, L! and B! in the gaps. The frmulas besides t calculate the crdinates are: sen B = sen B0 cs ρ + cs B0 sen ρ cs P Pm (3) sen(l L0) = sen(p Pm)sen(ρ)cs (B) (4) Where B is the latitude and L the lngitude. Nte that all f the values that are used in the frmula are expressed in degrees as well as the results. T sum up, the mst imprtant part is t write dwn all the data n a paper. The students shuld create a final table as the ne belw: Date/time Sunspt Lngitude( ) Latitude( ) Observatins 17/11/14 12:00 1 242,813-18,209 As we have said, the sftware at the website simply ask the students t d sme measurements f the sunspts and then autmatically calculate the heligraphic crdinates. It was said that the students have t chse at least tw sunspts at different latitudes. The reasn fr that is because the differential rtatin f the Sun is mre appreciable if yu cmpare the angular rate at the equatr with the angular rate f a sunspt clse t a ple. Fr example a gd chice wuld be t get a sunspt at 5-10 degrees and the ther at 20-25 degrees. It desn t matter if they are n different hemispheres, just cnsider the f latitude in abslute value. Grid alignment Align the images with a grid f heligraphic crdinates As it was mentined there is an easy way t estimate the crdinates. Using a grid f the Sun with the crdinates, a sunspt culd be easily lcated withut ding all the measurements that we explained befre. The first step fr this is t dwnlad the exact grid fr the day when the images were taken. Here is the website fr this: http://bass2000.bspm.fr/ephem.php At the website yu just have t select the date and time and select grid t cmpute. Once it has been dwnladed we need t superpse it t the image. There are tw ways t d this, the first ne is t print bth (the image and the grid) and draw the sunspt ver the grid. The ther ptin is t superpse the grid using sftware. With this Science Case we prvide sftware t d that. In bth cases, is essential t rtate the image the angle P t align the image with the nrth slar ple. Nw it s very easy t estimate the psitin f any f the sunspts. We are als able t determinate the size (in terms f heligraphic crdinates) f a filament (if fr example a h-alpha filter were used) r the size f a grup f sunspts as shwed in the Science Case: Sun s differential rtatin. 5
The picture result f superpsing the image and the grid shuld be similar t the ne belw: Figure 4: Heligraphic crdinates superpsed t an image f the Sun. Credit: CESAR/LEISA Sun s differential rtatin Different angular velcity depending n the sunspt latitude As we have said, the angular velcity f the Sun depends n the latitude. As we nw have the psitin f the sunspts fr all f the days students can calculate that different angular velcity. After the student has the change in angle written dwn fr each day and each sunspt, they can calculate the angular velcity f the Sun. Yu shuld first explain what angular velcity is. A brief explanatin can be that it is a measure f hw fast smething is mving n a sphere (r in a circle). It is the angle by which an bject turns in a specific time that is the rtatin rate. This is a pretty straightfrward exercise and the mathematics is nt cmplex. Nw t the calculatins. First the students have t calculate the perid f time between each pair f images i.e. the perid f time between the first and the secnd image, then the time between the secnd and the third and s n. They culd express that time in days r secnds. Once it has been dne, they have t calculate the number f lngitudinal degrees that the sunspt have been mving during each pair f images expressed in degrees. T make it easier, they culd create anther table with nly the necessary values and the intervals. Here is an example f that table that has t be filled fr each sunspt: 6
Sunspt 1 Latitude 16 Pair Lngitude difference ( ) Time difference (days) 1-2 12,325 0,987 2-3 12,380 0,991 They nw have t calculate the mean f the lngitude differences and the mean f the time difference and simply use the frmula: Angular vlcity = Lngitude difference Time difference [degrees/day r degrees/secnd] (5) T cmpare with the real angular velcity and see if they did well, here is a table: Sun's angular velcity Latitude ( ) Velcity ( /day) 0 14.71 5 14.69 10 14.64 15 14.54 20 14.41 25 14.23 30 14.00 35 13.73 40 13.42 45 13.07 50 12.69 55 12.30 60 11.91 65 11.54 70 11.20 75 10.92 80 10.71 85 10.58 90 10.53 7
It s very imprtant fr the students t understand that if the Sun were a slid bdy, all the surface shuld then rtate at the same angular velcity. That means that if the equatr rtates at 14.71 degrees per day, als the ples shuld be rtating at that rate but they actually mve slwer than the equatr. As we said the students had t try t measure at least tw spts at with very different latitudes but mst f the time it is difficult t find tw sunspts separated mre than 5-10 degrees s dn t be wrried abut that. Finally, they can cmpare the angular velcity f the Sun with the angular velcity f the Slar System planets. They shuld have a shrt discussin abut this and they can cmpare their results with this table: Planet's angular velcity Planet Velcity ( /day) Mercury 6,14 Venus 1,48 Earth 360 Mars 350,89 Jupiter 870,53 Saturn 818,96 Uranus 501,16 Neptune 536,27 Elements f the chrmsphere Find different structures f the Sun using CESAR h-alpha images Nw it is time t use the ther set f phts thse that were taken with the h-alpha telescpe. An h-alpha telescpe basically restricts the incming light f the Sun in the way that we culd nly see its chrmsphere instead f the phtsphere. Using an h-alpha telescpe we culd fr example watch the evlutin f a mass ejectin, the prtuberances and spicules. Mst f these structures have a very fast dynamic s they culd appear and disappear in the same day. This is the reasn why we prvide yu a whle set f images with the h-alpha telescpe instead f nly ne despite there is n sunspt tracking this time. Maybe the first day f bservatins the Sun seems t be calmed but the next days a lt f activity n its chrmsphere culd appears. The task fr the students is t identify these structures and get sme knwledge abut what they are. Fr this, there is a sample picture f the Sun in their Student s Guide with a shrt descriptin f each element n the chrmsphere. Fllw the instructins f the CESAR sftware r just tell the students that they have t cunt the number f each element and have a discussin fr each funded element. The teacher shuld have a gd clear knwledge abut the differences between each element. Fr example, a prtuberance may lks like a dark filament n the Sun s surface but when yu lk at them when they are in the limb they lks like a lp ut f the slar disk. 8
Here is an example f an h-alpha image where all the chrmsphere parts are indicated: Figure 5: Sun s characteristics. Credit: CESAR The labratry is nw dne. End by having a discussin abut what they have dne and summarize the labratry t see if every grup have understd the labratry. 9