E11 Special Relativity in Astrophysics

Topic

The key element in this model is the Lorentz factor—a quantity measuring the extent to which the velocity of a particle or flow of matter deviates from a state of rest. In high-energy astrophysics—such as in jets from active galactic nuclei, pulsars, cosmic rays, and relativistic supernovae—this factor can range from ten to as much as a million.

As the object's speed approaches that of light, the Lorentz factor increases; this causes a simultaneous rise in the object's effective inertial mass and a dilation of its proper time, while lengths measured along the direction of its motion undergo contraction.

The relationship between the object's energy and momentum simplifies to the well-known mass-energy equivalence when the object is at rest; at the opposite extreme—when the object is massless and travels exactly at the speed of light, as is the case with photons—the relationship becomes one of pure proportionality between energy and momentum.

The relativistic Doppler effect causes the object's radiation to shift toward the red end of the spectrum as it moves away from the observer and toward the blue end as it approaches; in the case of jets with very high Lorentz factors pointing almost directly at the observer, this same effect enormously amplifies the emission—far exceeding what the source would produce if it were at rest.

Synchrotron emission—produced by relativistic electrons (i.e., those with a high Lorentz factor) spiraling within a magnetic field—results in a power-law spectrum and dominates the radiation observed from radio galaxies, pulsar wind nebulae, and supernova remnants. Thus, from the Lorentz factor with which this document begins to the synchrotron emission with which it concludes—encompassing the relationship between energy and momentum and the relativistic Doppler effect—special relativity dictates that a single Lorentz factor determines the effective mass, the observed shift, and the final high-energy radiation spectrum, depending on the extremity of its value and the direction of the incident flow.

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