Section 34–4 Cosmic synchrotron radiation

 (Continuous spectrum / Light polarization / Magnetic field)

In this section, Feynman discusses the continuous spectrum, light polarization, and magnetic field of the Crab Nebula. With the use of space-based telescopes and new observatories (e.g., James Webb Space Telescope, Hubble Space Telescope, and Chandra X-ray Observatory) that provide high-resolution imaging, spectroscopic data, and polarization measurements, the discussions in this section are outdated to a certain extent.

 

1. Continuous spectrum:

“On the outside is a big mass of red filaments, which is produced by the atoms of the thin gas “ringing” at their natural frequencies; this makes a bright line spectrum with different frequencies in it. The red happens in this case to be due to nitrogen (Feynman et al., 1963, p. 34–6).”

Feynman’s statement about the red filaments of the Crab Nebula being due to nitrogen is outdated. The word “filament” has been traditionally used to refer to the macroscopic structures of the Crab Nebula observed by ground-based telescopes (Sankrit et al., 1998). With the higher resolution of Hubble Space Telescope, it magnifies the previously known filaments into many smaller substructures. By astronomy conventions, the optical features seen in the synchrotron nebula are called wisps, whereas the structures observed in the light of emission lines from thermal gas are now known as filaments (Hester, 2008). The filaments or wisps are quasi-stationary on time-scales of a few days or longer because they may move outwards at relativistic speeds.

“On the other hand, in the central region is a mysterious, fuzzy patch of light in a continuous distribution of frequency, i.e., there are no special frequencies associated with particular atoms. Yet this is not dust “lit up” by nearby stars, which is one way by which one can get a continuous spectrum. We can see stars through it, so it is transparent, but it is emitting light (Feynman et al., 1963, p. 34–6).”

Feynman explains that the continuous spectrum of Crab Nebula is not due to the dust “lit up” by nearby stars because we can see stars through it. However, the absorption spectrum of Crab Nebula is also reported (e.g., Sollerman et al., 2000), but it could be related to the interstellar dust or supernova remnants. Furthermore, the Crab Nebula’s spectrum has been studied from radio waves to gamma rays after the discovery of pulsating radio sources near the Crab Nebula (Staelin & Reifenstein, 1968). In 2021, there have been observations of light particles with energies exceeding a quadrillion electron volts (1 PeV) from the Crab Nebula (Cao et al., 2012). More research and observations are needed to refine and improve our understanding of the emission processes within the nebula.

The Crab Nebula seen in radio, infrared, visible light, ultraviolet, X-rays, and gamma-rays (8 March 2015).
 Image Credit: By Based on File:Crab Nebula in multiwavelength.png by Torres997: Public domain, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=38800932

2. Light polarization:

“…in this case, also, polarizers have been put on the telescope, and the two views correspond to two orientations 90∘ apart. We see that the pictures are different! That is to say, the light is polarized. The reason, presumably, is that there is a local magnetic field, and many very energetic electrons are going around in that magnetic field (Feynman et al., 1963, p. 34–6).”

Feynman suggests that the observation of polarized light is due to the presence of a local magnetic field and it results in many electrons going around the magnetic field. On the contrary, one may consider the cause to be the rotation of charged particles (including electrons) and it generates the magnetic field. Theoretically, there are also particles accelerated to relativistic speeds by the shock wave created by the supernova, and they emit radiation as they interact with the gas and dust in the nebula. Currently, the source of magnetic field is still a mystery, but it can be related to the rotating neutron star. Feynman did not specify the magnetic field is toroidal, but this was proposed by Rees and Gunn (1974) more than 10 years after this lecture of Feynman was delivered.

“Putting these two facts together, we see that in a region where one picture is bright and the other one is black, the light must have its electric field completely polarized in one direction (Feynman et al., 1963, p. 34–6).”

It may not seem appropriate for Feynman to say that light must have its electric field completely polarized in one direction. The degree of polarization of electromagnetic radiation emitted by the Crab Nebula varies with the wavelength of the radiation. For example, the average degree of X-ray polarization in the Crab Nebula is low, typically measured to be only around 20% (Bucciantini et al., 2021). On the other hand, the maximum degree of polarization could be as high as 45-50% in certain regions, but the overall polarization indicates a toroidal magnetic field (See figure below). However, instrumental limitations, calibration uncertainties, and background noise contribute to the observed polarization and introduce systematic errors that may impact the measured degree of polarization.

Diagram schematically representing the morphological features observed in the Crab Nebula in the optical and X-ray bands (Cerutti & Giacinti, 2021)

3. Magnetic field:

“This means that there is a magnetic field at right angles to this direction, while in other regions, where there is a strong emission in the other picture, the magnetic field must be the other way. If we look carefully at Fig. 34–8, we may notice that there is, roughly speaking, a general set of “lines” that go one way in one picture and at right angles to this in the other. The pictures show a kind of fibrous structure (Feynman et al., 1963, p. 34–6).”

The fibrous structures in the Crab Nebula are now interpreted as showing the local direction of the magnetic field (Hester, 2008). Based on NASA research, the polarization pattern shows that the Crab Nebula’s magnetic field is donut-shaped as shown below. In short, astrophysicists analyze the nature of Crab Nebula using the observed light polarization and inferred magnet field. Specifically, the Crab Nebula has a complex magnetic field structure, i.e., the magnetic field lines within the nebula could be twisted and tangled, leading to variations in their orientation and strength across different regions. However, the interpretations of magnetic fields in the Crab Nebula are dependent on theoretical models, such as the synchrotron model, magnetic dipole model, pulsar wind model, or core-collapse supernova model.

Credits: Magnetic field lines: NASA/Bucciantini et al; X-ray: NASA/CXC/SAO; Optical: NASA/STScI; Infrared: NASA-JPL-Caltech

“What keeps the electron energy so high for so long a time? After all, it is 900 years since the explosion—how can they keep going so fast? How they maintain their energy and how this whole thing keeps going is still not thoroughly understood (Feynman et al., 1963, p. 34–6).”

Feynman did not use the term supernova or relate the magnetic field and electron energy (or radiated power) to the supernova remnants. In his advanced lectures on gravitation, Feynman questioned whether the radiated power of a radio source could be due to annihilation of 10⁶ to 10⁸ stars or nuclear processes. In Feynman’s words, “[e]ven exploding all the stars in an ordinary galaxy would hardly produce that much power. The only way to have such power radiated away from luminous objects would seem to be to have a million stars annihilate a million stars of antimatter. Alternative explanations involve some kind of structure at the center of these galaxies, some monster superstars in which the generation of energy follows paths very different from those of the ordinary star… (Feynman et al., 1995, pp. 186-187).” Feynman suggested that the preferred direction of nuclear processes might be toward inverse beta decays of the protons, i.e., p + e ® n + n, at sufficiently high pressures.

 

Review Questions:

1. Do you agree with Feynman that the continuous spectrum of Crab Nebula is not due to the dust “lit up” by nearby stars?

2. Do you agree with Feynman that the light emitted by the Crab Nebula must have its electric field completely polarized in one direction?

3. How would you describe the magnetic field of Crab Nebula?

 

The moral of the lesson: The degree of light polarization varies with the wavelength and location of radiation emitted by the Crab Nebula, but it is related to the direction and intensity of the magnetic field.

 

References:

1. Bucciantini, N., Ferrazzoli, R., Bachetti, M. et al. (2023). Simultaneous space and phase resolved X-ray polarimetry of the Crab pulsar and nebula. Nat Astron 7, 602–610.

2. Cao, Z., Aharonian, F., An, Q., Axikegu, Bai, L. X., ... & Qi, M. Y. (2021). Peta–electron volt gamma-ray emission from the Crab Nebula. Science, 373(6553), 425-430.

3. Cerutti, B., & Giacinti, G. (2021). Formation of giant plasmoids at the pulsar wind termination shock: A possible origin of the inner-ring knots in the Crab Nebula. Astronomy & Astrophysics, 656, A91.

4. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.

5. Feynman, R. P., Morinigo, F. B., & Wagner, W. G. (1995). Feynman Lectures on gravitation (B. Hatfield, ed.). Reading, MA: Addison-Wesley.

6. Hester, J. J. (2008). The Crab Nebula: an astrophysical chimera. Annu. Rev. Astron. Astrophys., 46, 127-155.

7. Rees, M. J., & Gunn, J. E. (1974). The origin of the magnetic field and relativistic particles in the Crab Nebula. Monthly Notices of the Royal Astronomical Society, 167(1), 1-12.

8. Sankrit, R., Hester, J. J., Scowen, P. A., Ballester, G. E., Burrows, C. J., Clarke, J. T., ... & Westphal, J. A. (1998). WFPC2 studies of the Crab nebula. II. Ionization structure of the Crab filaments. The Astrophysical Journal, 504(1), 344-358.

9. Sollerman, J., Lundqvist, P., Lindler, D., Chevalier, R. A., Fransson, C., Gull, T. R., ... & Sonneborn, G. (2000). Observations of the Crab Nebula and Its Pulsar in the Far-Ultraviolet and in the Optical. The Astrophysical Journal, 537(2), 861-874.

10. Staelin, D. H., & Reifenstein III, E. C. (1968). Pulsating radio sources near the Crab Nebula. Science, 162(3861), 1481-1483.