# Magnetometry with magnetically-sensitive lines

## Remote magnetometry using magnetically (Zeeman)-sensitive spectral lines and measurement of the polarization of their emission (polarization radiative transfer)

How do we measure the magnetic field of the Sun and stars found many light years away?

The Sun and other stars radiate energy that is produced by nuclear fusion in their core. Most of the radiation of the Sun is in the optical spectrum, although practically the entire electromagnetic spectrum is covered. The atmosphere of the Sun and other stars contains various elements in gas form which absorb different wavelengths of that radiation. As a result of this energy absorption, the electrons of atoms and molecules of those elements get excited and change energy levels ("orbits"). Specific spectral lines corresponding to energy absorption and subsequent transition to these new energy levels appear in the spectrum as dark lines (Figure 1). These are spectral absorbance lines. In the case of the Sun, they are known as Fraunhofer lines (Figure 1)

Figure 1: Solar spectrum with absorbance lines (Fraunhofer lines) (Wikipedia).

Following the discovery of the Fraunhofer lines, it was found that some of these lines corresponded to the emitted radiation from specific atoms or molecules when they are heated (Figure 2). For instance, when we heat sodium powder, we obtain a yellow light which has a wavelength of approximately 589 nm. It was concluded that the D line of the solar spectrum (Figure 1) corresponded to sodium. Further analyses, showed that this is a double line (Figure 1 and 2). The two individual lines were named D1 and D2.

Figure 2: Emission lines of elements H, He and Na.

An interesting discovery was made by the scientist Pieter Zeeman. He used a magnet and a sodium lamp, which emits yellow light. He first noticed that there was what would appear as one emission line for sodium (Figure 3, left). When he approached the magnet to the sodium lamp, he noticed that the line was split into two (Figure 3, middle). This was termed "Zeeman splitting". Interestingly, as he further approached the magnet, the spacing between the lines would become greater (Figure 3, right). The distance between the lines would be proportionate to the magnetic field. This meant that the sodium spectral lines could be used to measure the ambient magnetic field.

Figure 3: In a low magnetic field, we observe one spectroscopic line corresponding to a transition from 3s to 3p. In a medium strength magnetic field, as the 3p energy level is split into two sublevels, we observe two transitions and two spectroscopic lines. In a high strength magnetic field, the spacing of the lines is increased. By analysing the spacing, we can determine the magnetic field strength.

The experimental results can be explained if we consider that the ambient magnetic field exerts an external magnetic force on the atom. The combination of the external magnetic force and the internal magnetic forces of the atom will give a net force that that will determine the orbits or energy levels of the electrons. Similarly to the planets of our solar system which have specific orbits based on the gravitational forces among them, the electrons of the atom will have specific orbits based on the magnetic forces among them.

As a result, in a low magnetic field, the outer electron of sodium is found in one specific orbit or energetic level and exhibits one spectral line (Figure 2, left). In a higher magnetic field, given the new force equilibrium, determined by the sum of the internal and external forces, the electron can assume either one of two alternative orbit configurations or energetic levels, in which case it will exhibit two spectral lines (Figure 2, middle). In an even higher magnetic field, the two alternative orbits will be spaced further away (Figure 3, middle).

In other cases, the polarization of the emitted light could change. Analysis of the emission and specifically of its linear and circular polarization can provide the strength and the direction of the ambient magnetic field.

There are specific electron transitions in atoms and molecules which are sensitive to the magnetic field and which are therefore providing magnetically-sensitive spectral lines. Such lines include those mentioned in Figure 4 [*].

Figure 4: Magnetically-sensitive spectral lines (Table 2 from [*]).

## The magnetic field of stars is detected and characterized using the Zeeman effect

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## Magnetographs

The magnetism of the solar atmopshere can be probed using the polarimetric signatures of the corresponding spectral lines [*]. Magnetographs are instruments that conduct these analyses. A most important one is NASA's Marshall Space Flight Center (MSFC) Vector Magnetograph  [*]. As mentioned by NASA [*] the "MSFC vector magnetograph works by measuring the amount of polarization in the light which originates from sunspots at one specific wavelength, 5250.2 Å" which corresponds to the Fe I absorption line [*].

Also, the NASA Solar Dynamics Observatory (SDO) [*] satellite carries the HMI instrument [*] which examines the 6173 Å Fe I absorption line and produces daily magnetograms available on the SDO site [*] under "HMI Magnetogram". In the same section, we can appreciate how different spectral lines allow the study of different scientific subjects.

As mentioned in this source [*], the HMI obtains filtergrams in various positions in the Fe I 617.3 nm spectral line and a set of polarizations at a regular cadence. Several higher levels of data products are produced from the filtergrams, including line-of-sight magnetic flux, and vector magnetic field at a 45-second cadence. Additional estimates are generated for the line width and line depth.

It is noted that the propagation of radiation through a medium, termed radiative transfer, is affected by absorption, emission and scattering. The polarization of the radiation can be affected during the propagation. Its analysis in the frame of polarization radiative transfer studies can provide information on the magnetic nature of the medium.