The Rotation of the Sun


Active Region AR 9393 3/27 to 4/2 2001.
Image from Astronomy Picture of the Day, 4/11/2001

Goals of this project

Prior to starting this lab, you should understand solar physics at the AST101 level. Check the references, or other Solar references you may find in the library. The introductory quiz will be based on basic knowledge of the Sun.

Grading Policy
You must complete the analysis of 6 weeks worth of recent YOHKOH images, up through the last data available at the time of the penultimate lab class. You should observe the Sun optically on at least 4 days during class. If you wish to observe outside of class time, you will need to coordinate with a TA. An observation should take no more than 15 minutes. Keep an observing log: if the sky is cloudy you will not be penalized for not making the optical observations.

Grading is based on the quality of the data analysis, the discussion of the uncertainties, and the answers to the questions at the end of this page. The actual rotation period you measure is not important for your grade.

I. An Introduction to the Sun

The Sun is a typical star. Its mass, luminosity, and radius are near the logarithmic mean of the range of stellar properties. The Sun is 4.6 Gyr old, about in the middle of its H-burning main sequence stage. Aside from its obvious role as source of energy for the Solar system, the Sun is useful to astronomers because it is the only star which we can see close up, and the only star for which we can directly resolve its surface features. All stellar models are dependent upon the sun, for any stellar structure code must reproduce the solar luminosity and temperature at the solar age. Models of the spindown of stars must reproduce the Solar rotation rate at the solar age.

The Sun and its atmosphere are a testbed for plasma physics, atomic physics, and nuclear physics. Solar nuclear reactions, and the solar neutrino problem, provided the first observational eevidence that there might be phase-mixing among neutrinos, and spurred the development of neutrino observatories. Observations of the Solar atmosphere provide a wealth of information on atomic physics that is difficult to obtain in the laboratory. Helium was discovered in the Solar atmosphere before it was found on Earth. The Solar corona, with its low densities, high temperatures, and magnetic fields, offers a marvelous site to undertake (uncontrolled) experiments in plasma physics. The more we observe the Sun, the more detail we see, and the more complicated our star becomes.

Facts about the Sun:

Solar and Stellar Rotation

The Russell-Vogt theorem states that the complete structure of a star depends only on its mass, chemical composition, and age. In reality, stars are not quite so simple. The stellar magnetic fields and their manifestation, stellar activity, depend crucially on the stellar rotation rate (e.g., Hartmann & Noyes, 1986, ARAA, 25, 271). The surface abundance of Lithium appears to be enhanced in rapidly rotating stars, perhaps because rapid rotation supresses convection.

Low mass (solar-like) stars initially spin with rotation periods of about 8 days (Edwards et al 1993, ApJ, 106, 372) when they become visible as T Tauri stars. This period appears to be a consequence of magnetic torquing of the star by the inner disk. After the accretion disk dissipates, the star is free to spin up as it contracts towards the main sequence. Solar-like stars appear to land on the main sequence with rotation periods between 8 hours and a day or two. After that the stars slowly spin down. The angular momentum loss is thought to be due to magnetic torquing of the stellar wind.

The Solar rotation rate is ill-defined because the Sun is a fluid body which rotates differentially. The rotation rate varies from about 25 days at the equator to 29 days at the poles.

An excellent place to start, if you want to look at the state of solar activity today, is the Solar Data Analysis Center (SDAC). The SOHO synoptic database contains a good sampling of daily images. A good public outreach site is the YOHKOH Public Outreach page.

To see a movie of the X-ray Sun rotating, start IDL on one of the lab computers and type .run c:/phy515/sunmovie/sole
A movie of the large sunspot group AR 9393 of March 2001 crossing the Solar disk is available at this website (this is the same image as displayed at the top of this page).


II. The Laboratory Exercise

The goal of this lab is to measure the solar rotation. To do so, you need to observe a feature on the solar surface. As a fluid object, the Sun does not have permanent markings like the planets do, but it does (usually) have long-lived magnetic structures. The magnetic fields manifest themselves as photospheric sunspots, or as magnetic loops in the chromosphere and transition region. A secondary goal is to observe the relation between the coronal active regions and the photospheric spots.

You have two options in this lab. Both options involve archival data analysis. Option A also involves visual observations.

You will then analyze the sequence of images to determine the stellar rotation rate. You should do this for both sets of data, and compare the results. In addition, you will determine the relation between the features seen in the X-ray images and the photospheric sunspots.

III. How to Proceed


You should try to get at least 45 days worth of data. Start with data about 1 month old, and then add data obtained through the penultimate lab meeting. You will likely find many SOHO images on every day; you need not use them all.

The SOHO data archives are accessible on the web. Go to the SOHO EIT Catalog Interface. Enter the following catalog selection criteria:

Then submit your query.

The catalog search results will be returned. Each image is labeled by Date, Exposure Time, Filter, Wavelength, and image size. Select the images you want to download. Do not download more than the disk can hold!. You should download a uniform set of images, with the same wavelenth and filter and similar exposure times. You will not need more than one image per day. Enter the requested information at the bottom of the page, and submit your request. It will be fulfilled within a few minutes. The data will be written into a gzipped tar file. Go to the indicated ftp site and download the data. Unpack the data using gunzip and wtar (note that the data will be written into a subdirectory). These are FITS format files, even though the extensions are not '.fits' (the extensions are the universal time at the start of the exposure).

Once the file sohodata.fits is safely on disk, you can read it using IDL. The command is
The header information will be placed in variable h, the data array is in variable d. A sample SOHO header follows:

SIMPLE  =                    T / Written by IDL:  25-Aug-2003 15:12:11.00
BITPIX  =                   16 / Short integer (2 bytes/word)
NAXIS   =                    2 /
NAXIS1  =                 1024 / Number of columns
NAXIS2  =                 1024 / Number of rows
DATE    = '2003-08-01'         / Date of file creation
TIME-OBS= '00:00:10'           /
DATE-OBS= '2003-08-01T00:00:10.638' / UTC at spacecraft
ORIGIN  = 'Rocket Science'     / Rocket Science = NASA GSFC
DATASRC = 'LZ file           ' /
TELESCOP= 'SOHO'               /
INSTRUME= 'EIT'                /
OBJECT  = 'full FOV'           /
BSCALE  =                   1. /
BZERO   =                   0. /
BUNIT   = 'counts / pixel    ' /
WAVELNTH=                  195 / 171 = Fe IX/X, 195 = Fe XII,

FILTER  = 'Al +1             ' /
DATE_OBS= '2003-08-01T00:00:10.638Z' /
SCI_OBJ = 'CME WATCH 195     ' /
OBS_PROG= '195_10S_AL_1.000  ' /
CMP_NO  =                    1 / Unique campaign instance (1 = synoptic)
EXPTIME =               12.697 / s (total commanded + shutter close)
EXPMODE = 'backside          ' /
FILENAME= 'efz20030801.000010' /
CFTEMP  =               -67.57 / CCD cold finger temperature (C)
CCDTEMP =                 7.37 / CCD temperature (DN/100)
CTYPE1  = 'Solar-X '           /
CTYPE2  = 'Solar-Y '           /
CRPIX1  =               507.19 / Sun center x, EIT pixels
CRPIX2  =               517.80 / Sun center y, EIT pixels
CRVAL1  =                 0.00 /
CRVAL2  =                 0.00 /
CDELT1  =                 2.63 / Pixel scale x (arc sec, fixed)
CDELT2  =                 2.63 / Pixel scale y (arc sec, fixed)
SOLAR_R =               362.76 / Solar photospheric radius, EIT pixels
SOLAR_B0=                 5.75 / Degrees
SC_X0   =                 0.00 / s/c yaw (arc sec)
SC_Y0   =                 0.00 / s/c pitch (arc sec; -109.14 after 1996/04/16)
SC_ROLL =               180.00 / s/c roll (deg., Solar north + CCW from nominal
HEC_X   =          92913560.00 / s/c heliocentric ecliptic x (km)
HEC_Y   =        -118435048.00 / s/c heliocentric ecliptic y (km)
HEC_Z   =             59165.79 / s/c heliocentric ecliptic z (km)
CAR_ROT =              2005.00 / Carrington rotation at earth
COMMENT   CORRECTED DATE_OBS = '2003-07-31T23:59:59.539Z'
COMMENT   IMAGE_OF_SEQ =                    0
COMMENT   NUM_LEB_PROC =                    3
COMMENT   LEB_PROC = 27 (no occ mask)
COMMENT   LEB_PROC = 12 (Rice)
COMMENT   P1_X =           1
COMMENT   P2_X =        1024
COMMENT   P1_Y =          20
COMMENT   P2_Y =        1043
HISTORY   Version 4.0, 2001 December 10
This is a 195 Angstrom image of the Sun obtained on August 1 2003. The exposure time is 12.7 seconds. The image was obtained through the Al+1 filter. The image is 10242 pixels square, and the sun is nearly centered. The angular scale is 2.63 arcsec per pixel, and the solar radius is 363 pixels. Most of the information is self-explanatory.

III B. Taking the Optical Data

You will use one of the 8" Celestron telescopes with a mylar filter to observe the white light image of the Sun. Read the document on basic telescope safety.
NEVER LOOK DIRECTLY AT THE SUN. Always look in projection. You will use a Mylar filter on the 8" telescope. Before using the filter, hold it up to the Sun to ensure that there are no holes in it. After placing the filter over the end of the telescope, point it at the Sun. Verify that there are no leaks in the filter by placing your hand (or a piece of paper) behind the eyepiece. If it has a bright spot, or gets very warm, the filter may have a pinhole, DO NOT LOOK THROUGH THE TELESCOPE IF THE FILTER IS FAULTY.

You will undertake visual observations: look at the Sun though the telescope eyepiece, and sketch what you see in your lab book (click here to download a template for your drawing). Find and mark North and East. In a few observations over a 2-3 week span, you should be able to see the Sunspots moving.

If it is very cloudy, you can download white light images from the Mees Solar Observatory at Haleakela or from the Big Bear Solar Observatory at Big Bear City, CA. These images are in JPEG format.


If you are undertaking option B, you will download YOHKOH SXT images taken once every solar rotation over the full span of the YOHKOH data. Since you won't have time to determine the rotation period (that's option A of this lab), assume a 27 day period.

The YOHKOH SXT data are stored in FITS format, and are accessible via this ftp site. The most recent data are in the main directory; earlier data are in subdirectories labelled by year. File names are of the form sfdyymmddhhmm.fits, where yymmddhhmm are the year, month, day, hour, and minute at the start of the image. (Some of the earlier data are named sf_fitsyymmddhhmm.fits, and may be in a smaller 256x256 format.)

Right-click on the file name to download.

Once the file yohkohdata.fits is safely on disk, you can read it using IDL. The command is
The header information will be placed in variable h, the data array is in variable d. A sample YOHKOH header follows:

 SIMPLE  =                    T /
 BITPIX  =                    8 /
 NAXIS   =                    2 /
 NAXIS1  =                  512 /
 NAXIS2  =                  512 /
 DATE-OBS= '02/03/98'           / DD/MM/YY  [UT]
 TIME-OBS= '06:59:51'           / hh:mm:ss [UT]
 CRPIX1  =              272.185 / sun E/W center (pixels 1-NAXIS1)
 CRPIX2  =              293.355 / sun N/S center (pixels 1-NAXIS2)
 CROTA   =             0.929276 / Degrees CCW:  PREDICTED (Error +/- .3 Deg)
 RADIUS  =            197.20098 / Radius of sun (pixels)
 FILTER-A= 'Open    '           / 1=Open , 2=NaBan, 3=Quart
 HISTORY                          4=Diffu, 5=WdBan, 6=NuDen
 FILTER-B= 'AlMg    '           / 1=Open , 2=Al.1 , 3=AlMg
 HISTORY                          4=Be119, 5=Al12 , 6=Mg3
 RESOLUT = 'Half    '           / Full=2.46 arcsec pixel, half=4.92, qrtr=9.84
 EXP-TYPE= 'Norm    '           / Normal, dark, calibration
 EXP-DUR =              5369.04 / Exposure duration in milliseconds
 EXP-LEV =                   25 / DPE (commanded exposure level 0 to 32)
 DP-MODE = 'Quiet   '           / S/C Data Processor (DP) Science Mode
 DP-RATE = 'High    '           / S/C Data Processor (DP) Telemetry Rate
 DATEOBS = ' 2-MAR-98 06:59:51' / Start CCD Integration [UT]
This is a 5.4 second integration in the ALMg filter taken on 2 March 1998. The image is 512X512 pixels in size. Most of the information is self-explanatory.

There is a YOHKOH Analysis Guide available. The Instrument Guide is particularly useful. While it is instructive to read the rest of the manual, we have not installed the software described in these guides on the PCs.

III D. Measuring the Features

The bright regions in the SOHO or YOHKOH images are active regions; the dark regions in the white light images are Sunspots. Your task is to determine the positions of these features as a function of time. Using that data, it should be easy to determine the solar rotation rate. Hint: the Sun is a sphere; you will have to convert from the projected position to the surface latitude and longitude. Unless your data shows otherwise, you may assume that the features do not move relative to each other.

Note that the features you want to measure in the X-ray images are fuzzy. This is because the corona is an optically thin three-dimensional object, whereas the sunspots are features on a two-dimensional surface. The X-ray-emitting loops are anchored to the solar photosphere at the sunspots, but diverge with height. Usually, the tops of the loops are hotter (and brighter in X-rays) than are the footpoints of the loops. The images to the left show the relation between the two levels of the atmosphere. As part of this lab, you will need to determine a justifiable method of determining the location of the active regions in the coronal X-ray images.

Left: Three images of the Sun taken on March 29 2001. The prominent active region near the center is AR 9393 (the same active region featured in the movie at the top of the page).

  • Upper image: A visible light image of the solar photosphere at a wavelength of 6767 Angstroms, obtained by the SOHO Michelson Doppler Imager.
  • Middle image: The solar chromosphere, in the light of Helium II (304 Angstroms). This image was obtained with the SOHO Extreme Ultraviolet Imaging Telescope (EIT). He II gas has a temperature of about 20,000 K.
  • Lower image: The solar corona in soft X-rays, as viewed by the YOHKOH observatory. This is 1-2 million K gas.
This picture is the Astronomy Picture of the Day for April 19, 2001.

Questions to be answered

  1. Why do sunspots appear dark? If the solar photosphere were to turn into one large sunspot, how much fainter would the sun appear?
  2. What is the inclination of the solar equator to the ecliptic? How do we know? Why are they not co-aligned?
  3. How well do the active regions, prominent in the SOHO images, line up with the Sunspots? Are there spots without prominent active regions, and vice-versa? (Option A)
  4. Comment on changes in the morphology of the sunspots and sunspot groups or active regions.
  5. Characterize the variation in the X-ray flux in the active regions with the solar cycle. (option B)
  6. Comment on the lifetimes of the active regions (option A).

Return to top

Return to PHY 445/515 Astronomy page