Solar magnetogram

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A little history

Magnetic fields are important in many and varied contexts in astrophysics; for example, in active galactic nuclei, neutron stars, the black holes that populate the Universe, star formation regions, the atmospheres of the Sun and other stars, etc.
So great is the fascination that they arouse and the mystery they hide that Henk van de Hulst wrote,
"Magnetic fields are to astrophysicists what sex is to psychoanalysts".
Another renouned physicist, R. Leighton, wrote some time ago,
"If the Sun did not have a magnetic field, it would be as uninteresting a star as most night-time astronomers believe it to be" (quoted by J.L. Linsky).

George Ellery Hale

Photo Obs Mt Wilson

In 1908 George Ellery Hale built the first spectroheliograph. It observes black filaments in the shape of a vortex around the sunspots. They resemble the motif drawn by the iron filings in the presence of a magnet. He suspected quickly the presence of a strong magnetic field in the sunspots.
In 1896 P.Zeeman had discovered the phenomenon of splitting of the spectral lines by the magnetic fields. Hale obtained spectra of sunspots through Nicol prism and observed the splitting of the lines. It is caused by circular polarizations of opposed directions on each Zeeman component. The intensity of the magnetic field observed was evaluated as 3500 gauss.
Hale and Seth. Nicholson discover the solar magnetic field. After systematic studies they stated the magnetic law of polarity of the spots (Hale-Nicholson law) and the changes of their characteristics during the solar cycle. They found that the periodic variation of the number of spots according to a 11 years cycle constitutes half of the 22 years cycle of the evolution of the solar magnetic field.The most outstanding aspect is the inversion of East-West polarity of the magnetic fields of the spots of the active areas which accompanies the 11 years cycle.


Photo Caltec

1D Magnetography
In 1951, Horace W. Babcock developed the photoelectric magnetograph whose principle can be described as follows.
The two exit slits of a highly dispersive spectrograph are placed with one on the red wing and the other on the blue wing of a magnetic sensitive line.The two longitudinal components of a Zeeman doublet widened by the magnetic field, circularly polarized in opposed directions, show alternatively linear polarization by the effect of the rotation of a quarter wave plate followed by Nicol prism. They vary periodically the photometric profiles read by two photomultipliers.The differences in intensity measured between these two photomultipliers placed on each wing of the line, behind the two exit slits , change sign to each rotation of 90° of the quarter wave plate. These variations of electric intensity of the signal are amplified and recorded.They are proportional to the intensity of the magnetic field in the explored solar area . By scanning one obtains a succession of magnetic profiles and one rebuilds a cartography of the solar magnetic field. The process is very sensitive but its implementation requires much time because of multiple sweepings necessary to exploration of line after line of the surface of the disc of the Sun.

Robert. B Leighton

Photo Caltec

2D Magnetography
The method that we used was developed in 1969 per Robert B. Leighton and was described in "Observations of solar magnetic fields in plage regions" ApJ, 1969, 130, 366.
This method is based on the subtraction of images. Photographic operation requires true “technical acrobatics” according to the word of J.C. Pecker in "La Structure de la Photosphère", C. de Jager, D. Reidel Publishing Compagny, Dordrech- Holland, 1965. It consisted of the point-to-point superposition of a negative image A and a positive counterpart of the negative image B of suitable gamma. The two images A and B come from two successive scans of the Sun with a spectroheliograph . This method is today much easier to use since one works with digital images treated on computer.
This method is detailed below.

3D Magnétography
Progress in spectropolarimetry and the development of modeling on computer make it possible today to obtain models in three dimensions of the solar magnetic field and to study dynamics of it. The computing powers necessary are very large.
The image on the right is the result of such a calculation with the layout of the lines of field around a sunspot.

Opposite on the left a magnetogram SOHO/MDI combined with Potential-Field Source-Surface (PFSS), which makes it possible to calculate a model of the lines of the magnetic field in the lower corona. When these models are compared with the visible loops on the images of TRACE imagery, a bad agreement (as is the case here) indicates that this area can generate eruptions (flares) in the next days.
A true solar "meteorology" is constituted to a prediction of the events.

3D model of a solar magnetic field .


Inverse Zeeman effect (spectral lines in absorption).
1: Sun surface seen by the observer. Two sunspots of opposite polarity, N and S.
2: image of the Sun on the slit of entry of the spectroscope.
3: fine band cut out by the slit of entry and transmitted to the spectroscope.
4 and 5: circular state of polarization of the incidental light (cw=right, ccw= left).
N on sunspot drawing : Northern polarity.
S on sunspot drawing : Southern polarity.
6: quarter wave plate, Ox faster axis, Oy slower axis.
7:linear polarizer with 45° of the axes of the quarter plate.
8: resulting spectrum recorded by the sensor. Violet is on the left wing, red on the right wing of the line.

The light cone of the telescope goes into the entrance slit of the spectroheliograph. The slit cuts out a fine strip, which is treated by the spectroscope. One sees on the figure that two sunspots of opposite polarity were bisected by the slit. The top vector field is plunging towards the interior of the Sun (red arrow) whereas the bottom one is emerging (blue arrow) .When the vector field comes towards the observer, i.e., it is emerging (blue case) then the component of shorter wavelength of the Zeeman doublet is constituted by circular vibrations of the same direction as the magnetizing current, which would produce this vector ( counterclockwise, or left). It is the opposite for the red case (clockwise, or right) . The light then meets a quarter wave plate of which we will the fast axis carried by Ox. The reference mark xOy is direct in its plan by the direction of the light . If the incidental light is right circularly polarized (clockwise) its Jones vector is written . The Jones matrix of the quarter wave plate is written: . At exit of the quarter wave plate the transmitted vibration is described by the Jones vector: .
If it is received by a linear polarizer whose axis forms an angle of +45° with Ox and thus from matrix which is written , then at exit the Jones vector of the luminous vibration is. The vibration is thus transmitted with an intensity equal to the intensity of the incidental vibration.
If on the contrary, it is received by a linear polarizer whose axis forms an angle of -45° respect to Ox and thus from matrix which is written then at exit of this one the vibration is described by the vector . It is stopped.

Let us take again this calculation on the assumption of a left circular vibration arriving on the quarter wave plate which remains directed with its fast axis carried by Ox.
At the exit of the quarter wave plate plus linear polarizer with +45° respect to Ox, the luminous vibration has as a vector of Jones: =.
It is stopped.
At the exit of the quarter wave plate plus linear polarizer with -45° respect to Ox, the luminous vibration has as a vector of Jones: =

. The vibration is transmitted with an intensity equal to the intensity of the incidental vibration.

It is completely equivalent to make a turn of 90° of the quarter wave plate or of the polarizer as one can check it easily.
It appeared mechanically easier to choose a rotation of the quarter wave plate because of its situation and of natural axial symmetry . It is thus this solution which was adopted for our assembly.


Our quarter wave plate results from the cleavage of a mica sheet, which is almost equal to the optical quality of a quartz plate but its cost is quite lower . Mica optical quality is good . It is rigorously quarter wave for 633nm . However it can be used without problem in a broad vicinity of the wavelength (between 400 and 700 Nm) because of its optical properties. I chose to use mainly the line of iron Fe I 6302.5Å, which offers a favorable factor of Landé g=2.5, or the line Fe I 5250.2Å (g=3.00) classically used in magnetography, for instance, with the Mount Wilson magnetograph (Mt. Wilson 150-Foot Solar Tower).

The polarizing device for solar magnetometry.


The adopted optical diagram. The revolving quarter wave plate is carried by the brassplated ring.
1: CW and CCW circular polarization.
2: quarter wave plate.
3: polarizing cube beamsplitter.
4: nonpolarizing cube beamsplitter.
5: s-polarized light.
6: spectroscope entrance slit.
7: filter.
8: auxiliary focal point.
9: filter.

Image processing

Certain absorption lines of the solar spectrum, like those quoted above and illustrated low, are sensitive to the longitudinal component of the ambient magnetic field in the area where they occur (i.e., in photosphere or the lower chromosphere). This sensitivity is given by the value of the Landé factor, noted g, ranging between 0 and 3.
Under the effect of this magnetic field the initial line is duplicated in two components G and D (Gauche, CCW ; Droit, CW ) equally moved on both sides this line (see the spectral profiles simulated below). Their intensities are equal and equal to half of the intensity of the initial line.If the observation is carried out using a circular analyzer (i.e., a quarter wave plate followed by a linear polarizer at 45° of its neutral axis), it is noted that one of the two components can always be extinct by the analyzer. This component is restored and the other extinct when the analyzer is turned 90°. The two components are thus circularly polarized and in opposite directions.The component of shorter wavelength is consisted of the same vibrations of the magnetizing current which would create the field . The shift in wavelength of each of the two components is the double of

(For more details, click here)

It is supposed that the lines have a Gaussian spectral profile

the Stokes parameter V is given by:

The two components observed for the two positions of extinction of the analyzer are D=I +V and G=I - V . They make it possible to find et .

The two images below illustrate the two stages of the manipulation.On the left one finds the principle of operation of the “quarter wave plate" plus " linear polarizer" with axis at 45° to the axis of the plate. That makes it possible to separate two circular polarizations from opposite directions and to filter them as indicated in the preceding paragraph.
One will acquire two series of spectral images corresponding to each of the two directions of circular polarization. One, image areas of outward magnetic flux (blue on the image).The other, those of magnetic flux inward (red on the image).

The image of the right-hand side illustrates the exploration of these two series of spectral images. One applies to each one the usual processing of rebuilding of a monochromatic solar image.
One chooses one of the wings of the selected line. For instance the blue wing as on the drawing below.
Finally it remains to carry out the difference in these two images, which gives the final magnetogram.

Spectroheliogram recording.

1:sunspots group of opposite magnetic polarities.
2: solar spectrum circular polarity and zeeman line splitting.
3: mica 1/4 l.
4: linear polarity light
5: fixed polaroid.
6: recording spectrum

Image processing.

7-8: in dot line the column uses for spectroheliogram construction.
To see
9: BI or BII image in the blue wing.
10: RI or RII image in the red wing.
11: (BI - RI) image, (9) minus (10).
12: (BII - RII) image, (9) minus (10).
13: magnétogram (BI - RI) - (BII - RII), (11) minus (12).

Normal spectrogram by webcam.
Animation of the two positions of the mica 1/4 l .
Notice the insensitivity of the atmospheric lines to the position of the quarter wave plate.

To calculate images BG, RG,BD,RD we consider the values of the intensity of the spectral line on both sides of its axis: I(-3), I(-2), I(-1) in the blue wing, I(0) at center, I(1), I(2), I(3) in the red wing.These points of measurement are represented on the spectral profiles below for the left wing of the Zeeman doublet or for the right wing of this one.

One simulated below a spectral profile of the line FeI 5250Å such as it is observed in our SHG where 1 pixel corresponds to 0.0037 angström. The profile can be compared to Gaussian curve of following equation:

Is the intensity of the line to the wavelength l.
is the intensity of the continum.
is the depth of the line i.e. the ratio : (Ic-I0)/Ic
is the side shift of the center of the line respect to the pixels.
is the half-width of the line at the point of inflection of this one.

On the image below on the left, the line (in black) is centered perfectly on pixel 20. On that of right-hand side on the contrary there is a shift of 0.010 angström respect to the axis of pixel 20.The problem is of knowing which is the impact of this shift on the value of I(-3)+I(-2)+I(-1)-I(1)-I(2)-I(3) =Blue - Red, who measures on each of the two Zeeman components this shift respect to pixel 20. This one is directly proportional to the value of the magnetic local field B.

Ideal case of a line (in black) centered on the column of pixels number 20 and its two wings of Zeeman duplicated by a local magnetic field of 1000 gauss.

Case of a line (in black) shifted of 0.019 angström compared to the column of pixels number 20 and its two wings of Zeeman duplicated by a local magnetic field of 1000 gauss.

One thus simulated the variations of this measurement I (- 3) +I (- 2) +I (- 1) - I (1) - I (2) - I (3) = Blue-Red according to the values of the magnetic field B for various values of the off-centring of the axis of the line respect to pixel 20 . The values of between 0, 0.005, 0.010 and 0.015 angström are considered below.

B-R versus B for various values of off-centring.

Stokes's parameter calculated starting from the measurements simulated for a centered line (black) and for an shift of the line of 0.010 angström with a magnetic field of 1000 gauss.

One notes the conservation of the linearity, with one slope independent of the shift of the line respect to the lines of pixels. On the other hand, this shift varies the ordinate at the origin of the approximations closely connected of these “curves” in a range from -30 to 30 ADU for a side shift of the line varying of -1/2 pixel to 1/2 pixel.
It will be enough to correct such an off-centring to bring back to zero the values of I (- 3) +I (- 2) +I (- 1) - I (1) - I (2) - I (3) measured on a portion of the magnetically quiet solar image by addition of a suitable constant . This operation will be carried out on each difference before calculating this sum.

Result of the calculation of the sums of differences BG-RG and BD-RD. I (- 3) +I (- 2) +I (- 1) - I (1) - I (2) - I (3) according to the various values of the magnetic field B.

The two blue dotted lines show the level of average noise on the final image of about 30 ADU what seriously limits the detection of fields of less than 100 gauss.

Intensity of the final image versus the value of the field.

Note: ADU (Analogic Digital Unit) ,"pas codeur" in French.
Here some lines classically used for the study of the solar magnetic field and obtaining magnetograms.

They are characterized by their intensity, and their large Landé factors.

Spectrograms availables in Lunette Jean Rösch site:

Our observations with the spectroheliograph

The differential of circular polarization is quite perceptible in the middle of the spot
but it is also visible out of this one, which is of good omen for the continuation…
Line Fe I 6302.5Å (g=2.49).

1: normal spectrogram by webcam.
P: penumbra.
U: umbra

2: spectrogram with mica 1/4 l in position I minus spectrogram with mica 1/4 l in position II.

In the images below one tries to illustrate the principle and the sensitivity of the method of the differences.

The image of left is obtained by making the difference of spectral image of the line 5250.2Å and its symmetrical respect to a vertical axis for left linear polarization. One thus obtains the blue minus red profile noted BI-RI for the area of the spot NOAA0898b on July 5, 2006. On the right the same difference in right linear polarization BII-RII. Note the inversion of intensity right/left after 1/4 l mica rotated 90°.
In the center, photometric profile of this difference.
On the right this same difference for a zone except spot (more in the East).

BI-RI, blue wing of the left linear polarizing component minus red wing of of the left linear polarizing component.
Note: BII-RII, blue wing of the right linear polarizing component minus red wing of the right linear polarizing component.

The image of left is obtained by making the difference of spectral image in left polarization and in right polarization: I-II. On the right the image II-I. This is for the area of the spot NOAA0898b on July 5, 2006.
On the right, photometric profile of this last difference for the line FeI 5250.2Å.

R.B.Leighton announced the difficulty in the center of the spots (in the umbra) with images as strongly underexposed . The signal becomes of the same order as the noise, and the difference R-B give a uniform plage . In these areas of the magnetogram, the magnetic field is not correct any more, detected in spite of its great intensity .All must return in order if one wants the exposed images to be correctly exposed.
Area of the correctly exposed spot. The umbra shows the same polarity well as the penumbra .The outside of the spot is over-exposed. See on the right the image difference R-B of the spectrum in the line Fe I 6302.5Å for the position of the slit indicated by the red vertical line..

NOAA8998b, on July 1, 2006 12h 37 UT.
Spectral line used 6302.5A

7 files 060701_6302_x. avi recorded in this wavelength Fe I 6302.5Å center of line.
(9 files 060701_hax.avi in Ha line).
The magnetogram result obtained with our SHG is shown above on the first three images starting from the left.

The beautiful spot of NOAA0898 is ideally located today at the center of the solar disc, for a second test of magnetographic imagery.It is the ideal configuration to detect the line of sight component of the magnetic field.
The sky is slightly veiled per moment and the transparency is not uniform.
The image processing will be somewhat complicated and will oblige not to preserve some scans

Spectral line used: Fe I 5250.2Å (g=3.00).

4 scan 060704_5250_x.avi,
3 scans 060704_6302_x.avi
were recorded.
(2 files 060704_hax.avi in the Ha line).

A red left image(RG)

A blue left image(BG)

Sum of these images
(for information RG+BG)

Final result.

There is then composity of several magnetograms resulting from consecutive scans to obtain the final result.
Comparison SOHO image of reference with full resolution on the left, and the image obtained on our SHG in spectromagnetography in the center, and on the right (two images). One can note the good agreement.

SEIT 171Å NOAA0898

SHG Juillan, Ha center line

Two active areas arised on July 8, 2006

File 060708_6302_12
SHG Juillan 10h13m UT

File 060708_5250_3
SHG Juillan 10h13m UT

4 files 060708_5250_x.avi,
4 files 060708_6102_x.avi,
2 files 0607078_6173_x.avi,
4 files 060708_6302_x.avi (et 3files 060708_ha_x.avi).

Active area of July 24, 2006: NOAA0901.






One sees above the various stages of construction of a magnetogram by the method of the sums and differences derived from that of R.B.Leighton.
The scan in the line Fe I 5250.2Å is considered a NORTH-SOUTH to and from with 9 consecutive passages above area NOAA 0901 per one duration of recording of 6 minutes.
With each change of direction, the 1/4 wave plate rotated orientation of 90°. Scan of the south in north with an angle +45° respect to the polaroid analyzer (direction says Gauche on our figure) and scan of north in the south with an angle of the wave quarter plate of -45° respect to the polaroid (direction says Droit on the figure). The center of the line is on column 102 on the 1500 spectral images . One builds the dopplergram images; then make the difference of blue side minus red side of the line for each scan:

One finishes the procedure detailed higher in the presentation by making the differences of consecutive scans Left minus Right , i.e. (BG5-RG5)-(BD4-RD4) and (BG7-RG7)-(BD6-RD6). The sum of the four magnetograms thus obtained is shown opposite on the left with several made in black and white or false colors.

Above, on the left, comparative between the results which we obtained in the city of Juillan, France (four images top surrounded by red) and the reference documents of the professional observatories (GONG and Wilson Mount). Dimensions of our images were reduced to bring back them on a scale with those of the GONG and Wilson Mount. False colors with the same palette which the Observatory of the Wilson Mount shows the good agreement between the magnetogram obtained with Juillan and the magnetogram of reference of the Wilson Mount using the same iron line.
Note: Juillan (N 43°12'28" E 00°01'33") in the south of France. Close to the Pyrenees.

At the top of the images on the left, the magnetogram of reference of SOHO MDI on July 24, 2006 to 0h35 UT.

Opposite the result of the treatment of the alternative scans "right polarization"/ "left polarization" in the North-South direction in the line Fe 6302.5Å (filer: 060724-6302-5).
The 5 individual magnetograms obtained were added. The result is shown opposite at the top in black and white. Below the same image but with application of Mount Wilson's palette. The third image is obtained with part of the starting image by applying a Gaussian filter to s = 1 follow-up of return with Mont Wilson palette.

Lastly, below, the image of professional reference: The 150-Foot Solar Tower Current Magnetogram. Image magnetogram of today.

The complete image magnetogram of July 24, 2006 is available while clicking here.

Animations showing in alternation a magnetogram of SHG Juillan like above and the magnetogram of the Mount Wilson with the same palette but two adjustments from the thresholds of visualization.
NOAA0904 in the continum at 6301.5Å on August 13, 2006 , 10h00 UT.
Image sum of the three magnetograms obtained starting from the scan 060813_6302_1 , 10h00 UT.
Application of the standard Mt. Wilson palette on the image above.
Even images with Gaussian smooth and raising of contrast, it is noted that the fields of +/-150 gauss are detected perfectly. The limit of detection seems to be at the neighbourhoods from +/- 50 gauss, which is well in the limits estimated. In lower part of these values, the signal is drowned by the noise.
To compare with the magnetogram of reference of the Mount Wilson,
the complete image magnetogram of July 24, 2006, is available while clicking here

Comparison between our result with the SHG Juillan and the image of reference provided by the magnetogram SoHo MDI: satisfactory result.

The cloudy passages with which it was necessary to find attic windows of 6minutes in order to take these magnetographic images did not enable me to also make images of the same area in H alpha.

Sky very cloudy , poor transparency and frequent cloudy passages! Our magnetogram lacks contrast and clearness.

The situation near limb does not make work easy…

NOAA AR0905 is the only active area 29/08/2006.

Fields about +/- 100 gauss are detected. The image of reference SOHO MDI is in the center.

I tried today a complete observation of active area NOAA 0905. In addition to the usual magnetogram, I observed the area in Ca II K, around Ha and make a dopplergram and a spectroheliographic image in the continum near Ha. The results are presented below.

Only one really active area still, NOAA 0905b of which one follows the evolution 29 August and August 30, 2006.


Sun, on July 30, 2006, in white light.


The same area observed the same day in Ha and in Calcium CaII K3 (celestial north is at the top).

August 30, 2006, 13h17 UT, SHG Juillan: Exploration in wavelengths around line Ha.

SHG Juillan, August 30, 2006.
One drew the traces of the spots and the filaments in overprinting on our images.
Dopplergrams false colors: blue = towards the outside of the Sun (blueshift), red-yellow = towards the interior of the Sun (redshift).
On the image of the medium in bottom, the green indicates a null speed, translated by the white on the image into bottom on the left.

Translation of the dopplergram in speeds: One can measure the spectral shift and thus deduce speeds from them on the parts of the spectra corresponding to the green and red reference marks of the image dopplergram presented opposite in two versions: false colors on the left and B/W on the right.
The shifts observed are about 20 to 60 km/s towards the red or the blue according to the area.

On the left, median of 3 magnetograms SHG Juillan resulting from the file 061102_gd6302_3 to 10h18 YOU. On the right, the magnétogram of reference SoHo MDI smdi_maglc_fd_20061102_1605.gif


Results obtained

These results, which I did not dare to expect, confirm that solar magnetography is possible for amateur observers by using a spectroheliograph of personal construction.
I warmly thank FREDRICK VEIOof the U.S.A.who dreamed to see this goal to be carried out. I am happy to have taken part in the beautiful adventure that he has impelled and made live forthe past40 years.
The site of Fred Veio is of a rare wealth of information of many orders. To consult absolutely!
He had the extreme kindness to help me to translate this page into English.
Thank you Fred!
Today, August 16, 2006, SOLIS has just detected the first index of the beginning of the new solar cycle. The interesting targets thus will multiply!
Beautiful observations in prospect…




Polarisation theory :
Howard, Robert F., “The Mount Wilson Solar Magnetograph: Scanning and Data System”,Solar Physics, Vol. 48, June 1976.
Babcock, Horace W., “The Solar Magnetograph”, Astrophysical Journal, 118, 387 (1953)
The Magnetograph (Solar Physics, march 1963, pages 476 à 479)
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