Introduction

The following discussion and module were created as a course project in the Spring of 2013 for the Harvard Department of Astronomy course Ay201b: Interstellar Medium and Star Formation, taught by Professor Alyssa Goodman. The content of this page and the deeper discussion have been edited and published as "An Essay On Interactive Investigations Of The Zeeman Effect In The Interstellar Medium" in the Spring 2015 issue of the Journal of Astronomy & Earth Science Education (Volume 2, Number 1).

This is meant to be used as a learning tool for general audiences, but I have also created a more in-depth discussion of these topics, which can be found at the link at the end of this section. I recommend that all readers view this write-up, as it contains many more examples of Zeeman Effect observations than I include in the short description on this page. Any are welcome to send me an email to ask further questions or to let me know if this information was helpful in your understanding of the physics behind and importance of this process; my current email address can be found by clicking the "Contact" tab at the top of the page. Enjoy!

Link to Deeper Discussion of the Zeeman Effect

Zeeman Effect

Lauren
		  Woolsey In 1896, Pieter Zeeman discovered that, when light was in the presence of magnetic fields, individual absorption lines or emission lines in the electromagnetic spectrum were split into many lines. This is due to the interaction between the magnetic field and the inherent magnetic moment of the atom, ion, or molecule. A deeper discussion of the effect would be covered in a college-level quantum physics course, but a short overview of the equations behind this effect are also presented on Wikipedia, which serves as a decent starting point for anyone interested in learning more of the detailed physics that describes this effect.

The figure to the right shows a photograph that he took in his laboratory. The top half of the picture is what the lines looked like without a magnetic field present, and the bottom shows the result of adding in the strong magnetic field. This work won Pieter Zeeman and Hendrik Lorentz the Nobel Prize in Physics in 1902, "in recognition of the extraordinary service they rendered by their researches into the influence of magnetism upon radiation phenomena."

To view this on the Sun, my favorite example of the Zeeman effect, check out Helioviewer using magnetograms from the Helioseismic and Magnetic Imager (HMI) instrument on Solar Dynamics Observatory (SDO). The image at the top of this page is the magnetogram data for the same observation time and date as the ultraviolet image on the other pages of this website! White spots and dark spots represent strong magnetic fields in opposite directions, i.e. into and out of the Sun's photosphere. The Sun has incredibly strong magnetic fields (up to 100 Gauss) compared to the interstellar medium (ISM), so Zeeman splitting is easy to observe in this case.

In the ISM

Magnetic fields are potentially very important in the process of star formation. Because they are so difficult to detect, researchers have had a hard time pinpointing the specific contributions magnetic fields make to star formation, but we do have a general sense of the effects. Magnetic fields can drive turbulence, which can allow small pockets of a gas cloud to collapse and form stars. Strong fields can alternately prevent large clouds from collapsing by providing a force to combat the pull of gravity.

There are only a few methods for observing magnetic fields in the ISM. The first involves measuring the direction of linear polarization of starlight or scattered light from dust. This provides the orientation of the components of the magnetic field in the plane of the sky, but does not give "arrowheads" on the vector, so the true direction is not known. This is a problem because there are many physical processes that can create random field directions, that when squashed together, may look aligned but are actually in opposite directions, like the lanes of a small road. However, scientists are much more interested in regions where the magnetic field direction is coherent, which is to say that the field actually points in the same direction over a wide distance, like one side of a major highway. In these regions, the magnetic field can have a significant influence on the physics.

The remaining two methods can both provide the real direction of the magnetic field and observe whether neighboring field lines point in the same or opposite directions. One of these two methods is Faraday Rotation, which is an extremely useful tool for measuring the line-of-sight magnetic field for parts of the ISM with a strong linearly polarized source in the background. For an excellent talk on this subject, please see Bryan Gaensler's colloquium from March 21, 2013 (link may eventually expire). The final method is the one we've been talking about here: Zeeman splitting. We can use this to measure the line-of-sight strength and direction, and for the strong Zeeman effect, we can measure the total strength of the magnetic field! The only problem with this method is that it requires atoms or molecules with large magnetic moments to be in regions that are dense enough to observe a signal. The ISM has magnetic field strengths typically from a microgauss to tens of milligauss (0.000001 to 0.01 Gauss - compare this to the Sun's magnetic field!), and Zeeman splitting can only probe the higher end of this range. Bryan Gaensler in the talk linked above summarizes the issue well: "It’s a really weak effect ... when you can use it, it’s gold, but there are only very limited places in the universe where Zeeman splitting actually works."

There are two distinct regimes of Zeeman splitting. The first is when the magnetic field strength is strong enough to produce multiple lines, as is the case for Zeeman's original laboratory measurements, the Sun's photospheric magnetic field, and very dense regions of the ISM called masers (these are very interesting phenomena and are discussed in more detail on Wikipedia. A rough explanation for masers are "lasers in space!"). In such a strong Zeeman effect regime, the splitting will appear in the observed total intensity of the spectrum. However, the other regime is when the magnetic field strength is not high enough to fully split the spectral line into multiple lines. The way these observations are actually made is reflected in the module below. Astronomers measure the Stokes Parameters I and V. The Stokes I is a sum of left and right circular polarization, and the Stokes V is the difference between these. In the presence of a magnetic field, the Stokes V can be fit to a derivative of the Stokes I which has been scaled up by the line-of-sight magnetic field strength. If you've read this far, please consider going through the deeper discussion of the Zeeman effect to understand more of the physical processes and equations included in the module.

Interactive Module

You may need to download the Free Wolfram CDF Player to see the content below. To download the source code as a Mathematica notebook, right-click here and select "download linked file." This module has been published through the Wolfram Demonstations Project and can be found at this website.

I have also made a short worksheet for interested educators and students, which provides three specific scenarios to investigate. If you use this worksheet, please send me an email with comments or suggestions!

The module has a pull-down menu and five slider bars:

  • Lines: the spectral line to be observed, species and frequency are listed.
  • Temperature: a hotter environment produces thermally broadened spectral lines.
  • Turbulent Velocity: turbulence adds non-thermal Doppler broadening to lines.
  • Line-of-Sight Magnetic Field: the key parameter to change the magnitude of the observed Zeeman effect. In the ISM, it is common to see fields of 40 to 400 microGauss, so be careful when using the slider, which extends to the special case of 50 milliGauss (50,000 microGauss) for some maser observations.
  • Y-axis Bounds for Stokes V: the magnitude of the Zeeman effect ranges depending on inputs, so the user can “zoom in” to a range where the effect is observable.
  • Signal-to-Noise Ratio: Longer observations on a telescope produce higher signal-to-noise, so the exposure time we need to see a clear signal for given inputs may differ.