Lab 9: Sunspots

1. Student Preparation which includes Quiz Preparation.
2. Special Instructions For Instructors
3. Startup Presentation
4. Post Mortem

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Student Preparation

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Caption: The Sun in visible light with sunspots including a rare spiral one.

Credit/Permission: NSO/AURA/NSF, © NOAO/AURA, 1982 / NOAO/AURA Image Library Conditions of Use.

Download site: NASA Image Gallery: White light, February 19th 1982.

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Required Lab Preparation:

1. Read Lab 9. It is hard to understand software/equipment without first seeing and playing with it, but insofar as possible you should be ready.
2. Read the Startup Presentation.
3. Read the Post Mortem. Better before than after actually.
4. Read a sufficient amount of the articles linked to the following lab keywords so that you can define and/or understand the terms etc. at the level of our class: Julian day, orbit, orbital period, photosphere, revolution, rotation, sidereal period, sidereal time, solar cycle, solar photosphere, sunspot, sunspot group, sunspot number, synodic period.
5. Write out the definitions required in Part A of Lab 9.

Supplementary Lab Preparation: The items are often alternatives to the required preparation.

1. Bennett (2008 edition): p. 507--513 on sunspots and the solar cycle or the corresponding pages in similar books.

Quiz Preparation:

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Caption: St. Nestor the Chronicler (c. 1056--c. 1114), St. Vladimir's Cathedral, Kiev, Ukraine.

At his studies.

Credit/Permission: Viktor Vasnetsov (1848--1926), 1919 (uploaded to Wikipedia by User:Butko, 2006) / Public domain.

Image linked to Wikipedia.

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The quiz might be omitted if it's not feasible or convenient. The students may or may not be informed ahead of time of quiz omission depending on the circumstances.

The quizzes in total are 40 % of the course grade. However, only the top five quiz marks are counted.

In preparing for a quiz, go over the Required Lab Preparation.

The Supplementary Lab Preparation (see above) could help, but is only suggested if you feel you need more than the required Required Lab Preparation.

There is no end to the studying you can do, but it is only a short quiz.

One to two hours prep should suffice.

There will be 10 or so questions and the time will be 10 or so minutes.

The questions will range from quite easy to challenging.

Some of the questions will be thinking questions. You will have to reason your way to the answers.

There may or may not be a prep quiz to test yourself with ahead of the lab period.

The solutions might be posted at Sunspots: Quiz Solutions after the quiz is given. Whether they are or not depends on the circumstances of each individual semester.

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Caption: Plato (428/427--348/347 BCE) and Socrates (circa 469--399 BCE) in a Medieval image.

Here the disciple seems to be instructing the master/mentor using the Socratic method.

The basic pose is much like in intro labs.

Credit/Permission: Medieval artist, Middle Ages (probably 1000--1400) (uploaded to Wikipedia by User:Tomisti, 2007) / Public domain.

Image linked to Wikipedia.

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Special Instructions For Instructors

1. Check as needed:
   1. Usual Startup
   2. Usual Shutdown

2. As always with software labs you should be as prepped as possible.

   There are all kinds of little finicky things about the controls to remember.

   In situ, you can always run to other instructors for help with showstopper.

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Startup Presentation

1. Hand back old reports and quizzes.

2. Start 7:30 pm sharp.

3. Give tonight's agenda: quiz, post mortem on the last lab, Startup Presentation, lab. Be brief.

4. Then give the quiz. It will be 10 minutes or so. Late arrivals have to write the quiz at the tables in the hall.

5. Give the post mortem of the last lab. Be brief.

6. Then tell them to form new groups, report to a computer, launch Firefox, click down the chain Jeffery astlab on bookmarks, Lab Schedule, tonight's lab, and srcoll down past the foxes.

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   Caption: "Red foxes (Vulpes vulpes) at the British Wildlife Centre, Horne, Surrey, England." (Slightly edited.)

   Credit/Permission: © Keven Law, Photo 2008 Aug17 / Creative Commons CC BY-SA 2.0.

   Image linked to Wikipedia.

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7. Objectives: Lab 9 illustrates how the the solar rotation is measured using sunspots. It also teaches the students something about the nature of sunspots, the solar photosphere, and the solar cycle.

8. The earliest record of sunspots was made by Chinese astronomer Gan De (4th century BCE) in 364 BCE.

   Sunspots were occasionally recorded thereafter without their existence becoming common knowledge (Wikipedia: Sunspots: Early observations; J.M. Vaquero, 2007, astro-ph, Historical Sunspot Observations: A Review).

   The early, occasional observations were probably mostly done when there was a large sunspot and the Sun was very close to the horizon (i.e., at sunrise and sunset) so that its intensity was strongly reduced by the thicker air mass at those times or when the Sun was viewed through smoke or mist.

   One should NEVER observe the Sun this way. It is damaging to the eyes although a few such fleeting observations MAY cause only marginal damage.

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   Caption: Pinhole projection.

   Actually this figure is incorrect for partial solar eclipse since the Moon really gives convex bite, not a concave bite as in the figure.

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   Eventually, pinhole projection (see also Wikipedia: Camera obscura) was used for safe observation. This seems to have been after the discovery of the telescope.

   Pinhole projection uses an opaque covering with a small aperature that allows pinhole projection on a background screen.

   A point inverted image of the object is cast on the screen. Pinhole projection is easily understood using light ray tracing.

9. Sunspots became common knowledge with their telescopic discovery by Galileo (1564--1642) (not first, but among the first) and his contemporaries using the first telescopes (Wikipedia: Sunspots: 17th and 18th centuries).

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   Caption: Galileo Galilei (1564--1642). Portrait in crayon by Ottavio Leoni (1578--1630).

   Credit/Permission: Ottavio Leoni (1578--1630), 1624 (uploaded to by User:Pseudomoi, 2005) / Public domain.

   Image linked to Wikipedia.

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   The first telescopic observations seem to have been direct ones with the Sun very close to the horizon. This was probably very bad for eyes. However, Galileo's blindness late in life seems to have been unrelated to his solar observations (see The Enigma of Galileo's Eyesight).

   Benedetto Castelli (1578--1643), a protege of Galileo, developed a projection technique for the telescope to allow safe observation of the Sun at any time (see The Galileo Project: Sunspots (scroll down about 50 % or search on "Castelli")).

   Castelli's setup may have been a lot like the one in the figure below---without the wife and kids---he was a monk.

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   • The early telescopic observers quickly established that individual sunspots were ephemeral and varied in shape and size. They typically last a few days to tens of days.

   • Sunspots proved the Sun rotated.

   • At some point, it was noticed that solar rotation is differential rotation.
     One of the "discoveries" of Lab 9 is that solar rotation this differential rotation: i.e., parts rotate at different rates.

     The Sun is a sphere of gas, and not a solid sphere. Sphere of gas and liquid can have differential rotation and non-rotational motions like convection and oscillations. The Sun (a sphere of gas) exhibits differential rotation and other non-rotational motions like convection and oscillions.

     The Earth, is in fact, not entirely a solid sphere. The outer core (2890--5150 km from the center) is liquid (primarily molten iron and nickel) (see Wikipedia: Structure of the Earth). The outer core probably exhibits both differential rotation and convection.

   • Modern sunspot measurements of solar photosphere rotation and helioseismology of interior rotation have established a pretty good picture of overall solar rotation.

     The figure below illustrates the current understanding of the overall solar rotation.

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     Caption: Internal-to-solar photosphere solar rotation for solar latitudes 0, 15, 30, 45, and 60 degrees.

     The horizontal axis is radius in units of the solar radius:

     1 R_☉ = 6.955*10**8 m = 0.0046491 astronomical units (AUs).

     This value may be a mean value: the sources are a bit unclear.

     It is sort of the radius of the solar photosphere---but the solar photosphere is usually defined to be a thin layer, and so it is NOT clear to yours truly what the given value is exactly.

     The vertical axis is frequency f=Ω/(2π) measured in nanohertz (1 nHz=10**(-9) Hz).

     To convert the plotted frequencies to sidereal period (i.e., period relative to the nearly inertial frame of the fixed stars) in days use the following formula:

      
           29.7888 ... days
      p = ------------------
            f_nHz/435 nHz 
     
     
              30 days
        ≅ ---------------   ,
           f_nHz/435 nHz
               

     where f_nHz is frequency in nanohertz and 435 nHz is a fiducial value for the internal solar rotation as the plot itself shows.

     The formula values obtained by casual inspection of the plot are probably not so good The plot gives a 0 degrees latitude surface sidereal period of 25.9 days, but the measured value is 24.47 days (see Wikipedia: Solar rotation: Sidereal rotation; Jurgen Giesen plot).

     The plot gives 31.3 days for 60 degrees latitude surface sidereal period. The measured value is more like 30.2 days (see Jurgen Giesen plot).

     But maybe the plot is meant to be extrapolated to the surface.

     The observed 90 degrees latitude limit surface sidereal period is about 34 days (see Wikipedia: Solar rotation: Using sunspots to measure rotation period with a conversion from synodic period to sidereal period; Jurgen Giesen plot)

     The plot clearly shows the differential rotation of the Sun.

     Remarkably, the rotation rate inward of about 0.65 R_☉ is nearly constant---the curves for the different solar latitudes converge to a nearly constant value of about 435 nHz.

     This means this region rotates nearly as if it were a solid sphere even though it is a sphere of gas.

     The radius 0.65 R_☉ approximately divides the inner solar radiative zone from the outer solar convective zone.

     The transition between these two zones is the tachocline.

     Credit/Permission: © Global Oscillation Network Group (GONG), 2008 (uploaded to Wikipedia by User:KeepOpera, 2010) / Creative Commons CC BY-SA 3.0.

     Image linked to Wikipedia.

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   • The (surface) solar rotation sidereal period as a function of solar latitude is given by the Jurgen Giesen solar rotation plot---NOT show in the figure below---but just a click away.

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     Caption: Click on the Alien image to see the Jurgen Giesen solar rotation plot.

     Credit/Permission: © David Jeffery / Own work.

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   • Just observing sunspots shift by position day-by-day allows one to measure their synodic rotation rate by dividing solar longitude change by time.
     By solar longitude, we mean what is usually called Carrington longitude in the heliographic coordinate system.

     The prime meridian of heliographic coordinate system is just "the north-south centerline on the visible solar disk" (Coordinate System: Center for Integrated Space Weather Modeling (CISM)).

     This prime meridian is always moving because of the solar rotation and the Earth orbital motion.

     The solar longitude is negative/positive to the Sun's west/east (east/west on the sky).

     Given that the Sun has no permanent surface features, the solar longitude defined as above seems to be convenient.

     Then 360 degrees over that synodic rotation rate gives the synodic period.

     What is synodic period?

     It is the period as measured from Earth.

     But the Earth is moving relative to the nearly inertial frame of the fixed stars.

     So the synodic period is not the true physical period---which is the sidereal period (i.e., period relative to the nearly inertial frame of the fixed stars).

     The conversion formulae between the two kinds of periods is simple as long as we neglect the fact that the Sun's axis is inclined to the ecliptic plane by 7.25 degrees: i.e., we assume zero inclination.

     We give the quick derivation here.

     There is an object orbiting the Sun: it could be a planet or a sunspots.

     The object is rotating with rotation rate R and the Earth with rotation rate R_⊕.

     We use the Earth symbol ⊕ to identify Earth quantities.

     At time zero, the object is on the Earth-Sun line.

     By definition, one synodic period p_syn later, the object is back on the Earth-Sun line.

     The object has lapped the Earth, and so is now 360 degrees ahead of the Earth.

     Thus, we must have

                R*p_syn= R_⊕*p_syn + 360  ,
     
                    where R is the Sun's rotation rate---it's sidereal rotation rate.
     
                Now R=360/p and R_⊕=360/p_⊕, where
                p is the object's rotational sidereal period
                and
                p_⊕ is the Earth's orbital sidereal period.
     
                So, skipping obvious algebra, we get
     
                    1/p=1/p_⊕+1/p_syn   .
     
                We rearrange this into the convenient conversion formulae
     
                    p=p_syn/(1+p_syn/p_⊕)=p_syn/(1+p_syn/365.25)
     
                    and
     
                    p_syn=p/(1-p/p_⊕)=p/(1-p/365.25)  ,
     
                       where we have  approximated the Earth's orbital sidereal period 
                       by the Julian year of exactly 365.25 days.
               

     The formula for p is the one of interest for this lab since we measure p_syn directly and have to calculate p.

     The formula for p has some interesting features as a function:

     1. For p_syn=0, p=0. This is the limit where the object is racing so fast that the rotational period p is negligible compared to the orbital period p__⊕.

     2. For p_syn ∈ (0,∞), p strictly increases with p_syn, but obeys the rule p < p_syn.

     3. For p_syn=∞, p has its maximum value of p_⊕. This just means that if the rates of the object and Earth are equal, then the synodic period p_syn becomes infinite since the object never laps the Earth.

     4. Negative p_syn values have meaning too, but let's not go into that.

     As an exmaple calculation with the formula for p, say we measure p_syn=25.00 days, then p=25.00/(1+25.00/365.25)=23.40 days.

     And that is the whole story for sidereal period and synodic period.

   • For the lab, just follow the instruction line-by-line. They are complete and correct.

   • For measuring the solar rotation rate---which is NOT the first thing---you need to measure three sunspots as they rotate across the Earth-facing side of the Sun:
     1. The sunspots move left to right. Measure them at 1 day intervals as they move from leftmost to rightmost observable position: this will be about 13 days.

     2. You measure them one at time. It is convenient if they are all from about the same time interval in 2002 January. Then they can all be plotted on one graph.

     3. The sunspots are labeled A, B, C.

     4. For sunspot A, I require you to use the sunspot that traverses the Sun in the time period Jan08 to Jan18 that is at about 29 degrees north latitude.

        This sunspot is the only significant one at a latitude as high as this on the Sun in our data set.

     5. For sunspot B, use a sunspot at an intermediate latitude (i.e., about 14 degrees).

     6. For sunspot C, use a sunspot at zero latitude (i.e., on equator).

     7. Sunspots B and C should be good clear sunspots that are easily followed that don't disappear before going all across the Sun.

   • Students will need to consult a record of sunspot numbers. The following sources are available online:
     1. Australian Government: Bureau of Meteorology: Monthly Sunspot Numbers.
     2. Spaceweather.com: The Sunspot Number
     3. Wikipedia: Sunspot number

     The Australian site has the actual sunspot number data for 2002 that is needed to answer one of the question on sunspot number.

   • That's all and for the Startup Presentation.



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Post Mortem

Below are some generic comments for Lab 9: Sunspots that may often apply.

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Caption: Film poster for the TheMummy (1932) starring Boris Karloff (1887--1969).

Credit/Permission: Employee or employees of Universal Pictures attributed to Karoly Grosz (fl. 1930s), 1932 (uploaded to Wikipedia by User:Crisco 1492, 2012) / Public domain.

Image linked to Wikipedia.

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Any that are semester-section-specific will have to added as needed.

1. Some terms have many definitions.

   The definitions required for the reports are those that are relevant to astronomy and NOT other topics.

   The links given with the lab keywords in Required Lab Preparation are usually better sources than just googling for a term definition. Often googling will lead to the plain wrong definition or a definition by a person who doesn't really understand the term themself and is just paraphrasing someone else's definition.

   Such a person is a lexicographer:
   Lexicographer: A writer of dictionaries; a person who busies himself in tracing the original, and detailing the signification of words; a harmless drudge. (Slightly edited.)
   ---Samuel Johnson (1709--1784) (see Some Definitions from Johnson's Dictionary).

2. Answer questions that require sentences with sentences. Usually it is obvious what those questions are. Sometimes maybe not. Err on the side yes sentences are needed.

   Sentences begin with a capital letter letter and end with a period. Usually there is a subject and a verb. Not always.

   Since you are working in groups, you should have different group members read over the sentence answers to see if they are correct and comprehensible. Read them out loud.

3. There are questions that imply that an explanation must be given and NOT just a bare yes or no. So give the explanation NOT just yes/no.

   Usually it is obvious what those questions are. Sometimes maybe not. Err on the side yes an explanation is needed.