One of the most intriguing phenomena in astrophysics is the apparent superluminal motion observed in the jets of quasars and other active galactic nuclei (AGN). Superluminal motion refers to the illusion that the components of a quasar's jet are moving faster than the speed of light, c. While this seems to violate the principles of relativity, it is actually an observational effect arising from the relativistic motion of jets and the geometry of their emission relative to the observer.
Quasars are known to eject relativistic jets of plasma, often aligned at small angles to our line of sight. The material in these jets can travel at speeds close to the speed of light. When such a jet is directed towards the Earth at a shallow angle, the motion of the jet, combined with the finite speed of light, creates the illusion of faster-than-light motion.
For a jet moving with velocity v at an angle θ to the line of sight, the apparent velocity vapp can be greater than c due to relativistic beaming effects. The formula for the apparent velocity is given by:
vapp = (v sin(θ)) / (1 - (v/c) cos(θ))
When the velocity of the jet approaches c and the angle θ is small, the denominator in the equation becomes very small, leading to a high apparent velocity, often greater than the speed of light. However, this is an illusion; no physical object is actually traveling faster than light.
Superluminal motion has been observed in many quasars and AGN, particularly in radio-loud quasars and blazars. These observations are often made using Very Long Baseline Interferometry (VLBI), which provides high-resolution imaging of jet components moving over time. Superluminal speeds are commonly observed to be 2 to 10 times the speed of light, though even higher values have been reported in extreme cases.
While superluminal motion is an optical illusion, it offers valuable insight into the properties of quasars. It provides evidence for highly relativistic jets, and combined with the observed jet morphologies and emission, allows for the estimation of the Lorentz factor γ of the jet, which describes the relativistic boost. Typical values for the Lorentz factor range from γ ≈ 10 to 30 for quasar jets.
Superluminal motion also helps astronomers infer the orientation of the jets relative to the observer's line of sight. Quasars with more prominent superluminal motion tend to have jets aligned more closely to our line of sight, explaining why this effect is particularly strong in blazars (a subclass of AGN with jets pointed almost directly toward Earth).
Superluminal motion in quasars is a relativistic effect that results from the geometry and high velocity of quasar jets. Although it appears that the jets move faster than the speed of light, this is an illusion caused by the near-light-speed motion of the jets and the angle of observation. These observations are critical for understanding the dynamics of relativistic jets in quasars and AGN, shedding light on their orientation, speed, and emission processes.