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Manual for the
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Measuring magnetic fields in sunspots
1 Task
The goal of this experiment is to measure the magnetic field in sunspots with methods of spectroscopy. Following steps will be done:
• Operation of the telescope
• Observation of a sunspot
• Data analysis with IDL
• Writing a report
2 Report
Your report should contain following information / answer following questions:
• Description of the experimental setup.
• What are sunspots?
• What is birefringence? How does a polarimeter work?
• The Zeeman effect.
• Describe the observation and the data analysis.
• Discuss your results.
• Analyse your errors. How accurate is the measurement?
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3 Theoretical background
3.1 Sunspots
Sunspots (cf. Fig. 1) can be seen as relatively dark areas visible on the solar disk. Sunspots can
have a sizes of around 10 to 100 megameters. They appear alone or in small groups called active
regions and have lifetimes between several hours and multiple weeks. Sunspots consist of a dark
inner part, the umbra and a filamentary surrounding, the penumbra. The average number of
visible spots changes with an eleven year period, the solar cycle.
In the inner layers, the energy produced by nuclear fusion in the solar core is transported outwards by radiation. In the outer 30% of the sun the energy transport is dominated by convection.
This can be seen as the so-called solar granulation, a pattern of bright patches and dark lanes on
the solar surface (quiet sun, solar surface). Only the very best atmospheric seeing condition allow
the observation of granulation at the Schauinsland Observatory.
Sunspots are dark because they are cooler than the surrounding quiet sun. The reason for
their lower temperature is that the magnetic field in sunspots suppresses the convective energy
transport in the outer layers of the sun. The plasma can only move along field lines due to the
Lorenz force. After the plasma is cooled by radiation, hot plasma from the inner layers can not
move upwards as fast as it can in the quiet sun.
Figure 1: Close up view of a sunspot. The central dark area is called umbra, the filamentary
greyish area penumbra. The surrounding of the sunspot shows granulation in the quiet
sun. Large sunspots can have diameters of the order of up to 100 000 km, for size
comparison the earth is included in the image. The quality of the right hand side is the
result of image reconstruction.
3.2 The Zeeman effect
To measure magnetic fields we need to observe magnetic sensitive spectral lines. This experiment
will make use of the iron absorption lines at 630.15 nm and 630.25 nm. Figure 2 shows the solar
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Magnetic Fields in Sunsposts
spectral line [nm]
FeI 630.15
FeI 630.25
geff
1.67
2.5
Table 1: Effective Landé factors of the iron lines used in this experiment.
spectrum and some prominent Fraunhofer lines.
Figure 2: The visible solar spectrum with famous Fraunhofer lines.
The strong magnetic field in sunspots can be measured using the Zeeman effect. In case of the
regular Zeeman effect a spectral line splits in presence of a magnetic field into three equidistant
lines. The distance of those lines depends on the strength of the magnetic field, following the
Zeeman formula. The sigma components of the spectral line shift by:
e
λ − λ0 =
geff λ2 B
(1)
4πcme
This gives a line sparation between left and right line of ∆λ = 2(λ − λ0 ).
B=
∆λ
2 · 4.67 · 10−12 · λ2 geff
(2)
∆λ and λ in nm, B in Gauss (G). 1Gauss = 10−4 Tesla. c is the speed of light, e the electron
charge, me the electron mass and geff is the effective Landé factor, calculated from the quantum
numbers of the energy levels of the transition. geff defines how magnetically sensitive a spectral
line is. The FeI 630.25 nm line has the higher geff and is therefore better suited to measure
magnetic fields and should be used in the data analysis (table 1).
The Zeeman effect not only induces a shift in energy levels, but also polarizes the light. In this
experiment we measure parallel to the magnetic field lines - this corresponds to the longitudinal
Zeeman effect. We are going to observe both σ components which are circular polarized, while
the unshifted π component will not be visible. See also figure 3 and table 2.
3.3 Stokes formalism
The Stokes parameters I, Q, U, and V can be used to describe the linear polarized light. I gives
the total intensity, V the circular polarized light and Q and U represent linear polarized light in
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Figure 3: Zeeman transitions.
transition
∆m = 0
∆m = 1
∆m = −1
comparison to the field free case
no change in energy
energy enhanced
energy decreased
polarization
linear in direction of the field
circular in direction of the field
circular in direction of the field
term
π -component
σ + -component
σ − -component
Table 2: Components of the regular Zeeman effect.
different planes. We focus on Stokes I and V in this experiment.
In practise we measure the Stokes parameters as the intensity after the light has passed various
optical elements. In this setup we make use of a quarter wave plate (λ/4) and a polarimeter build
of two birefringent calcite crystals. The λ/4-plate transforms the circular polarized light in two
orthogonal linear polarized components. The first calcite separates the two polarisation states
spatially (Fig. 4). To compensate the different travel distances the light passes a second calcite
(Figure 5).
The setup can be justified theoretically. Stokes V can be measured as followed (see ZULA):
V
= INT0 (45◦ , 90◦ ) − INT0 (45◦ , −90◦ )
1
1
=
(I + V) − (I − V)
2
2
(3)
(4)
The first entry corresponds to the fixed position of the λ/4-waveplate of 45◦ . The second entry
describes both different configurations of a polariser. The equation states that one should measure
the intensity for two different states of the polariser, than subtract both resulting images. This
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Figure 4: Dependence of the refraction of light on its polarisation state in a birefrigent calite
crystal.
Figure 5: Optical setup of the ordinary and extraordinary beam in the calcite. Upper panel: In
case of a single calcite both beams have a phase difference. Lower panel: In case of two
crystals the beams are in phase again.
way one gets Stokes V, the intensity of the circular polarized part of the light. Using a polarimeter
makes it possible to acquire both images simultaneously.
Figure 7 shows the resulting Stokes I and V profiles for different magnetic field strengths.
The spectral line broadens with increasing field strength until it separates completely. The data
analysis should result in such Stokes V profiles. The magnetic field strength can be calculated
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from the position of the two lobes using equation 2.
Figure 6: Stokes I, B=1100, 1300, 1500,
1700 Gauss
Figure 7: Stokes V, B=1100, 1300, 1500,
1700 Gauss
4 Experimental Setup
Knowledge of the telescope and the spectrograph is required. Figure 8 shows a schematic the
setup of the experiment.
Figure 8: Schematic setup. The spectrograph is locaded in a different room, separated from the
rest of the experiment.
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Magnetic Fields in Sunsposts
Figures 9 and 10 show the polarimeter in the metal tube and the polarimeter with its different
pieces respectively.
Figure 9: the polarimeter as it is put into
the metal tube
Figure 10: Image of the polarimeter. The
λ-4 waveplate and the calcite
crystals can be rotated.
The experiment consists basically of the following steps:
1. Selection the iron lines at 630 nm with the spectrograph.
2. Installation the polarimeter if not already done.
3. Pointing of the telescope at a sunspot.
4. Adjustment of the camera.
5. Calibration of the polarimeter.
6. Recording sprectra of a sunspot.
4.1 Selection of the iron lines
Search for the iron 630 nm lines. To do so, first install the 630 nm prefilter, then use the ocular
and rotate the spectrograph until the two iron lines at 630.25 nm are visible. Select the lines in a
high spectral order (4 or 5). Take care that both iron lines and both terrestrial oxygen lines are
visible in the field of view. Hint: It may be easier to find the iron lines without the polarimeter.
Focus the spectrograph once the polarimeter is mounted.
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4.2 pointing the telescope at a sunspot
Move the telescope mirror (M2) until a sunspot is on the slit. A piece of paper can be used for
the rough adjustment until the spot is visible on the slit jaw camera. The life image can be used
for fine tuning and moving the spot on the slit. Focus the telescope until the image of the spot is
sharp.
4.3 adjustment of the camera
The camera might be tilted, as a result the spectral lines are not vertical on the screen. Rotate
the camera a little until they are vertical. Hint: the hair which is taped across the slit is exactly
horizontal. It can be used as reference. This step is important because it simplifies the data
analysis significantly when the image does not have to be rotated.
4.4 Calibration of the polarimeter
Rotate the calcite until the two sub images are exactly above each other. Figure 10 shows how
they can be rotated.
When the polarimeter is set up correctly, one image shows Stokes I+V, the other I-V. This
means that we can see two lines next to each other in the sunspot umbra (see Fig 11). In case of
a weak field only a bump in the line is visible.
Figure 11: Image of the solar iron lines after transmitting the polarimeter. The influence of a
small sunspot is visible .
Rotate the λ/4 wave plate until the upper image shows a bump to the left, and the lower image
a bump to the right.
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5 taking data
5.1 science data
Save one burst (100) of polarimetric images with the sunspot across the slit. If the seeing conditions are variable try to capture a moment where the seeing is particularly good (where the slit
jaw image is sharpest). Move the telescope a little and repeat. If there are multiple sunspots you
can repeat the measurement on another spot as well.
Make sure that the light is switched of and that nobody is walking in the telescope tower during
observations.
5.2 flat field data
A flat field is an equally illuminated image. Since it does not contain any information of the target
all structure seen in it corresponds to some contamination in the optical system. Most prominent
is the visible dirt on the CCD of the camera, it is also contains vignetting and other unwanted
errors.
It is important that the flatfield is taken with as little changes in the optical setup as possible.
Do not change the focus of the telescope, the focus of the spectrograph, the prefilter, the position
of the grating and do not change the polarimeter. Flat fields should be taken close in time to the
science data. The integration time should be the same as in the science data.
To take flatfields, position the slit on the center of the sun (by moving M2). Shake the telescope
a little so the so the image moves on the slit jaw camera. This can be done easily from the ground
floor inside the tower.
Acquire 10 bursts of 100 images each. Averaging those should result in a sufficient flat image.
5.3 dark
A dark image is taken to correct the data for things like readout noise in the camera and dark
current.
Block the light (e.g. by closing the spectrograph slit cover) and take a burst of 100 images.
Integration time must be the same than for the science data.
6 data analysis
To gather information about the magnetic field following steps have to be done:
1. Calibration of the data.
2. Convertion of the images into Stokes V profiles.
3. Calculate the wavelength scale.
4. Calculation of the magnetic field strength with the Zeeman formula.
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6.1 Data calibration
First, the science data has to be corrected for dark and flatfield (gain table).
1. Read the dark data and average them. Save the averaged dark file.
2. Read the flatfield data and average them.
3. Substract the dark from the averaged flatfield data. Save the flatfield.
4. The flatfield still contains spectral lines. They should be removed in order to get a gain
table of the optical set up. Average over the spatial dimension in the flatfield to get an
average spectral profile. Save the average quiet sun profile.
5. Subtract this average spectral profile from each row of your flatfield. In the case of polarimetric data you might want to do this and the previous step for both subimages individually.
6. Your gain table should be an equally illuminated image. No spectral lines should be visible
any more, you should see the contamination of dirt on the CCD. Normalize this image to
its maximum and save it.
7. Calibrate the science data by subtracting the dark and dividing by the gain. You can
average each burst of science data first.
8. Save the calibrated data.
6.2 Conversion of calibrated data into a Stokes V profile.
1. Read the calibrated data.
2. Select the same region in both sub images and subtract those two. The oxygen lines and
the hair help to align the images.
3. Save the Stokes V map.
4. Select a spectrum (row) in the sunspot umbra. If the spot is large you can average over a
couple of rows to get a better signal to noise.
5. Save the Stokes V profile.
6.3 Conversion of the image scale into a wavelength scale
1. Load the average quiet sun profile. Find the position of the oxygen lines with a parabola
fit. Make sure to fit only the very line core.
2. Calculate the wavelength scale. The separation of the oxygen lines is 0.0761 nm.
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6.4 Calculation of the magnetic field strength.
The Zeeman formula allows to calculate the magnetic field strength in the sunspot. If the field
is strong enough the two components of the spectral line should be separated so far that we
can assume that the extrema of the Stokes V profile correspond to the positions of the sigma
components.
1. Load the Stokes V profile.
2. Find the positions of the extrema of the two lobes with parabola fits.
3. Calculate their spectral separation.
4. Calculate the magnetic field strength using the Zeeman formula.
6.5 Export some figures for your report.
You should include an image of your raw data, the gain table and your calibrated data in the
report. Show the quiet sun profile with the fits for the wavelength calibration and the Stokes V
profile with parabola fits.
7 Useful IDL commands
This chapter contains some IDL commands which are necessary for the data analysis in this
experiment. See the IDL first steps for a introduction to IDL.
Starting IDL
IDL can be started from the command line with the command IDL.
Reading .fits data.
First, the file containing the data has to be specified. Then the data in this file can be read into
a variable.
path=’/Pfad 1/Pfad 2/.../Bildordner’
file=’test.fits’
raw = readfits(path+file)
The variable raw is multidimensional. Its structure can be determined with:
s = size(raw, /dim)
print, s
Displaying data
One dimensional arrays can be plotted via
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plot, data
for two dimensional arrays there is the command
tvscl, data
Averaging Data
For a better signal to noise ratio, to even out statistical variations it is sometimes usful to average
data. The function total can be used here to integrate over one dimension.
meanimage=mean(raw,dim=1,/nan)
Cutting out data
Subsets of an array can be addressed as follows:
sub = meanimage[x0:x1,y0:y1]
"*" is a wild cart and selects all entries in a particular dimension. It is also possible to select
just one row (or column). the command reform is needed here to decrease the dimensionality.
spectrum = reform(meanimage[*,y0], [x1-x0+1])
Parabola fit
There are multiple functions to fit curves to data in IDL. For a parabola fit poly_fit is useful.
y = spectrum[x0:x1]
x = findgen(n_elements(spectrum)
p = reform(poly_fit(x,y,2))
fit = p[0] + p[1] x + p[2] x^2
plot, x, y
loadct, 2
oplot, x, fit, color = 100
Saving and restoring data
It is possible to save data into a file (.sav) this data can later be restored in another IDL session.
data = findgen(100)
save, data, filename = ’test.sav’
IDL can be closed now. In a new session the variable can be restored via:
restore, ’text.sav’
Exporting plots and Images.
Alternatively to plotting data into the x-window the .eps format can be chosen as well. Be careful
and double check your plot. x-window and .eps figures do not look the same.
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x = findgen(10)
set_plot, ’ps’
device, filename = ’test.eps’, /encapsulated, /color
plot, x
device, /close
set_plot, ’x’
One might want to convert the result into .pdf later. This can be easily done from the linux
promt with the comand epstopdf test.eps.
Two dimensional arrays can be saved as .png.
image = dist(300)
write_png, ’test.png’, bytscl(image)
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