The problem of the magnetic field gradients in sunspots

Organisateur : Veronique BOMMIER

Date prévue : 3-5 October 2016
Date définitive : 2016-10-03

SOC: V. Bommier, H. Balthasar, E. Landi Degl’Innocenti, J.M. Malherbe

In sunspots, the measured gradients respectively vertical (dBz/dz) and horizontal (dBx/dx+dBy/dy) largely differ in the observations, whatever the methods, instruments or spectral lines are. All the measurements agree on a vertical gradient of about 3 G/km on the one hand, and an horizontal gradient of about 0.3 G/km on the other hand, which surprisingly questions the vanity of the apparent divB computed from these values. Thus S. Solanki wrote in a review devoted to sunspots in 2003, p. 184 (S. Solanki, Astronomy and Astrophysics Review, 2003, 11, 153): "No satisfactory solution has been found as yet for the unexpectedly small vertical gradients obtained by applying the divB=0 condition”.

The workshop is devoted to investigate the following question: do these measurements enable us to conclude about the local divergence of the magnetic field, and, if not, what effect explains the departure from zero of the observed value corresponding to a larger scale ?

The workshop will be organized as follows: after presentation (V. Bommier), reports on the problem itself as observation result (H. Balthasar) and Stokes inversion and radiative transfer (E. Landi Degl’Innocenti), the discussion will remain free and open around a table, for together investigation of possible solutions or artifacts. Any other contribution prepared in advance is welcome.

Depending on the conclusions, the workshop would eventually be followed by a second one more aimed towards theory, in the following year.

Open Access paper by V. Bommier about this question

If you wish to participate, send an e-mail to with the following informations:
Name, Surname:
I wish to participate to the divB workshop 3-5 October 2016 in Meudon.
Eventually: proposed oral contribution: (title, + eventually a short abstract)

Lunches in the Meudon canteen (and coffee breaks) will be offered. There are no fees.


Concluding remarks after the workshop “The problem of the magnetic field gradients in sunspots”
CIAS, Chateau, Observatoire de Meudon, France
3-5 October 2016

After having listened to an introduction to “Solar Magnetometry” by Egidio Landi Degl’Innocenti, and a very detailed review of gradient observations in sunspots (found on the order of 3 G/km along the vertical direction and 0.3 G/km along the horizontal direction) by Horst Balthasar, the group agrees that the following sentence derived from Solanki (2003) describes our global opinion: “No satisfactory solution has been found as yet for the unexpectedly large observed vertical gradients with respect to those obtained by applying the divB=0 condition”. Several scenarios were discussed and finally nearly all discarded:

- the existence of smaller than unity magnetic filling factors in sunspot umbrae was suggested, but finally discarded because the flux conservation would imply a widening of the spot umbra with height, which is not observed. Pascal Démoulin showed also that a smaller than unity magnetic filling factor would decrease the magnetic field gradient instead of increasing it as required for explaining the observations within this model.

- this is a kind of unresolved structure. Obviously, the existence of unresolved structures is often suggested as a possible cause. However, it can be easily shown in the Fourier space that spatial derivation and spatial averaging commute, which would discard the effect. It has been remarked that the numerical tests suggested by Jean Heyvaerts by sophisticated averaging on more or less unresolved structures, would lead at best to scattered insignificant values of divB (in fact very small values are obtained when running the code), whereas the apparent observed departure from zero is always of the same sign: there is a vertical magnetic flux loss with increasing height in the atmosphere, which is not compensated for by an horizontal flux (which is also determined because the full magnetic field vector is measured). However, one of us, Silvano Bonazzola, is presently investigating an idea for a bias effect in the spatial averaging, which would explain the observed departure.

- Our evaluation of the noise level in the present observations leads to a much smaller value than the observed gradient difference. In addition, an eventual noise effect would also produce scattered insignificant values, in contradiction with the systematic sign of the observed gradient (flux loss with increasing height).

- The departure between the induction (usually denoted as H) and the magnetic field (usually denoted as B) was evaluated in the photosphere conditions. This departure is due to magnetization. Due to the fact that the solar photosphere is a weakly ionized medium, with a neutral atom density four orders of magnitude larger than the charged particle density, the susceptibility due to the free charge gyration about the magnetic field (computed with the charged particle density) is four orders of magnitude lower than the plasma beta (computed with the neutral atom density), which is about unity. As a consequence, B=µ0*H within 1e-4.

- refraction was suggested as a possible source of localization errors because the radiative transfer does not presently account for it. However, some participants know that refraction in solar atmosphere was previously studied and found negligible. It is also remarked that sunspots are generally observed close to disk center and then along the density gradient direction, whereas the refraction effects (mirages) occur when observing perpendicularly to the density gradient direction.

New observations are suggested, with a better spatial resolution. It is suggested to provide observed values of the vertical gradients at different altitudes. When the inversion code is of the SIR type (based on response functions) with depth nodes, it is suggested that the results be provided for all the nodes. V. Bommier has THEMIS observations of sunspots in two couple of spectral lines, thus able to provide the vertical gradient at two altitudes: one photospheric (Fe I lines) and one at the basis of the chromosphere (Na I D lines). Investigation outside sunspots would also be interesting, but this require ambiguity resolution.

Test inversion of theoretical Stokes profiles built of sophisticated magnetic field lines, eventually issued from MHD models, would also be desirable.

In addition to the concluding sentence agreed by all the participants and cited at the beginning of this document, it may be remarked that the Sun offers interesting and unresolved problems of physics, in addition to its role in the Space Weather.

The solar photosphere is a strongly stratified medium and an anisotropic plasma. Should the magnetic field vector reflect this anisotropy ?

No following workshop was determined.

V. Bommier, on behalf of the workshop participants:

1 Balthasar Horst (Potsdam, Germany)
2 Belmont Gérard (LPP, Palaiseau, France)
3 Janvier Miho (IAS, Orsay, France)
4 Landi Degl’Innocenti Egidio (Florence, Italy)

Paris Observatory staff:
5 Aulanier Guillaume (LESIA)
6 Bommier Véronique (LESIA)
7 Bonazzola Silvano (LUTH)
8 Démoulin Pascal (LESIA)
9 Klein Karl-Ludwig (LESIA)
11 Mein Pierre (LESIA)
12 Mottez Fabrice (LUTH)
13 Schmieder Brigitte (LESIA)