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 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 exerted by the Sun star and those exerted among them, the electrons of the atom will have specific orbits based on the magnetic forces exerted by the nucleus and those exerted 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, alternative orbits will be spaced further away (Figure 3, middle).

The Zeeman effect is the splitting of energy levels of atoms and molecules upon the presence of a magnetic field (Figure 1). The effect describes the splitting of spectral lines by a magnetic field into multiple closely spaced lines, with the spacing of the lines being dependent on the strength of the magnetic field. Due to this, the spacing can be used to measure the magnetic field of distant bodies such as the Sun and other stars, the Earth and also plasmas.

It is noted that spins couple to the magnetic field through the Zeeman interaction: 

H= -μ * B (t)

A Zeeman-effect demonstration is provided in a video by the by the European Southern Observatory (ESO). It is featured in Wikipedia article on the Zeeman effect and can be also found at the following YouTube link: https://youtu.be/SRTP-Obia0w. A composite figure based on this video is presented in Figure 4.

Technical details:

The dependence of the sublevel energies to the magnetic field is described by the Breit-Rabi formula:

https://en.wikipedia.org/wiki/Zeeman_effect & https://commons.m.wikimedia.org/wiki/File:Breit-rabi-Zeeman.png

http://demonstrations.wolfram.com/BreitRabiDiagram/

An example demonstrating how to calculate the solar magnetic field from spectroscopic data is provided at this reference.

Figure 4: Demonstration of the Zeeman effect via a composite figure created from captures of ESO video. Initially (left panel), there is one spectral line and as the strength of the magnetic field increases it splits in three components (middle and right panel). At the highest magnetic field strength increase (right panel), the distance between the three spectral lines becomes greater.

A Zeeman-effect demonstration is also provided in a video by Synctrotron SOLEIL. It is represented by a 20-second excerpt in this video starting at time stamp t=120. As mentioned in the video (translation): "By approaching a magnet to the sodium lamp, the characteristic yellow line of sodium is subdivided, proving that the electron experiences an electromagnetic force that modifies its energy levels." A representative figure is provided at time stamp  t=124

A related transcript excerpt (translated) starting at time stamp t=54 is provided below.

(In 1913) "Bohr's atomic model was describing correctly the hydrogen atom. The electron was rotating in circular orbits corresponding to authorized energy levels. By describing the orbits with positive integers, 1, 2, 3 etc. Niels Bohr was introducing the first quantum number of modern physics. As his model was struggling to describe multi-electron atoms, the German physicist Arnold Sommerfeld improved it in 1916 by providing electrons with two additional degrees of freedom: being able to rotate on elliptical orbits like the planets of the solar system as well as modify their trajectory in the presence of a magnetic field. Sommerfeld was thus adding two numbers: "l" the "orbital quantum number" and "m" the "magnetic quantum number". "

"Magnetic because the electrons behave like a small electrical circuit that is sensitive to external magnetic fields. This is the Zeeman effect, named after the Dutch physicist that discovered it twenty years ago when he studied the sodium spectrum. By approaching a magnet to the sodium lamp, the characteristic yellow line of sodium, is subdivided, proving that the electron experiences an electromagnetic force that modifies its energy levels."

In other cases, it is possible that the emitted photons have a polarization state which varies with the specific transition linked to the strength of magnetic field. In other words, the polarization of the emitted light may change depending on the strength of the magnetic field. 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 5 [*].

Figure 5: Magnetically-sensitive spectral lines (Table 2 from [*]).

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

More details in the document below.

Magnetographs

Magnetographs are scientific instruments that measure magnetic fields by analyzing the spectral and polarization characteristics of emitted or reflected electromagnetic radiation, often using the Zeeman effect. While traditionally used to map magnetic fields on the Sun’s surface, the principles of magnetography are also applied in studying stars, planets and laboratory plasmas. The output of a magnetograph is a magnetogram, which is a visual representation of magnetic field intensity and direction. A typical filter-based magnetograph comprises a polarimeter, a narrow-band spectrometer (filter), and a charge-coupled device (CCD) camera for image acquisition. 

One of the most historically significant solar observatories, the Mount Wilson Observatory (MWO) 150-foot Solar Tower, constructed in 1912, was equipped in 1957, with a next-generation magnetograph based on Horace Babcock’s pioneering design, allowing for daily full-disk magnetic field observations. Managed by UCLA in its later years, the tower continued producing magnetograms until 2013, contributing over half a century of continuous data to solar physics. Spectral lines examined by the magnetograph included the Ca II K line (3933.7 Å) for chromospheric diagnostics; Cr II (5237.325 Å) and Fe I (5250.2 Å) for high-sensitivity Zeeman analysis; Na I D1 (5895.9 Å) and D2 (5890.0 Å) for velocity and field gradients; and Ni I (6767.8 Å and 6767.782 Å) for advanced Doppler and magnetic field studies.

A most important magnetograph 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 [*] (pictures indicating "HMI"). On this site, 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.

Magnetic sensing capabilities using the Zeeman effect

How will the Zeeman spectrometer of the NASA EZIE mission measure the magnetic field of the electrojet?

Reference: https://ezie.jhuapl.edu/mission/ezie-spacecraft/

In atoms and molecules, we may encounter electronic transitions, where electrons move from higher energy orbitals to lower energy ones with simultaneous energy release. 

Some molecules, such as oxygen, which is a magnetic dipole, are rotating. They may rotate in different configurations, occupying different energy levels, i.e. higher energy or lower energy level configurations. We may have rotational transitions, where an oxygen molecule transits from a higher rotational energy level (equivalent to a faster rotating speed), to a lower one (equivalent to a slower rotating speed) with simultaneous energy release. This energy release, occurring while the molecule is slowing down, is in the microwave range (and the GHz range). It is captured by spectrometers and is shown to correspond to a (spectrophotometric) line.

When near a strong magnetic field like that of the electrojet, the line splits into two different lines. This phenomenon is called the Zeeman effect. The stronger the magnetic field, the farther the lines split apart.

Remote sensing of magnetic fields - Microwave magnetogram

Microwave radiation is processed to calculate magnetic field strength globally at different locations simultaneously.

The Electrojet Zeeman Imaging Explorer (EZIE) mission.

From https://ezie.jhuapl.edu/content/News/EZIE_Factsheet_Web.pdf

"EZIE’s MEM instruments can simultaneously collect polarized microwave light from multiple angles before passing it into a spectrometer to collect information about the magnetic disturbances that the electrojets induce."

From https://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=5313&context=smallsat

The sensor is a radiometer (RF receiver) with a heterodyne spectropolarimeter. It measures both horizontal and vertical polarizations of the incoming signal. 

(The front-end of the polarimeter collects the incoming signal and non-linearly mixes it with the signal generated by an oscillator.)*

"The digital backend ingests the two polarizations and digitally computes all four polarization states of the incoming signal (H,V,3rd,4th). The digital backend also computes the spectra of the signal, allowing the ability to measure spectral distances of the Zeeman split. Thus MEM is able to measure residual current-induced magnetic fields in addition to the geomagnetic background fields."

*From https://science.nasa.gov/science-research/science-enabling-technology/technology-highlights/new-compact-remote-sensor-to-image-ionospheric-currents-spatial-structure-from-space/

"Microwave receiver system that consists of multiple heterodyne full-Stokes spectro-polarimeters".

"Array receiver capable of remotely imaging the ionospheric current structure". 

"Each element of this MEM sensor spectrally resolves the three Zeeman-split O2 thermal lines".

"Provides measurements of the current-induced magnetic field globally at multiple locations simultaneously under all solar and atmospheric illumination conditions."

From https://ieeexplore.ieee.org/document/9884004

"The technique has been used extensively to derive the Sun's magnetic field. EZIE now applies this technique to the Earth system."

From https://cgms-info.org/html/iww16_html/posters/Poster_Monday_1615_IWW16_Dong_Wu.pdf

Microwave Doppler Techniques for Mesospheric Winds: MLS and EZIE