Superluminal motion

Superluminal motion

In astronomy, superluminal motion is the apparently faster-than-light motion seen in some radio galaxies, quasars and recently also in some galactic sources called microquasars. All of these sources are thought to contain a black hole, responsible for the ejection of mass at high velocities.

When first observed in the early 1980s, superluminal motion was taken to be a piece of evidence against quasars having cosmological distances. Although a few astrophysicists still argue in favor of this view, most believe that apparent velocities greater than the velocity of light are optical illusions and involve no physics incompatible with the theory of special relativity.

Explanation

This phenomenon is caused because the jets are travelling very near the speed of light and at a very small angle towards the observer. Because at every point of their path the high-velocity jets are emiting light, the light they emit does not approach the observer much more quickly than the jet itself. To be more clear, the jet is essentially "chasing" the light it emits. This causes the light emitted over hundreds of years of travel to not have hundreds of lightyears of distance between it, the light thus arrives at the observer over a much smaller time period (ten or twenty years) giving the illusion of faster than light travel.

This explanation depends on the jet making a sufficiently narrow angle with the observer's line-of-sight to explain the degree of superluminal motion seen in a particular case.

Superluminal motion is often seen in two opposing jets, one moving away and one toward Earth. If Doppler shifts are observed in both sources, the velocity and the distance can be determined independently of other observations.

Some contrary evidence

As early as 1983, at the "superluminal workshop" held at Jodrell Bank, referring to the seven then-known superluminal jets,

Schilizzi ... presented maps of arc-second resolution [showing the large-scale outer jets] ... which ... have revealed outer double structure in all but one (3C 273) of the known superluminal sources. An embarrassment is that the average projected size [on the sky] of the outer structure is no smaller than that of the normal radio-source population.

In other words the jets are evidently not, on average, close to our line-of-sight. (Their apparent length would appear much shorter if they were.)

In 1993, Thomson et al. suggested that the (outer) jet of the quasar 3C 273 is nearly collinear to our line-of-sight. Superluminal motion of up to ~9.6c has been observed along the (inner) jet of this quasar.

Superluminal motion of up to 6c has been observed in the inner parts of the jet of M87. To explain this in terms of the "narrow-angle" model, the jet must be no more than 19° from our line-of-sight. But evidence suggests that the jet is in fact at about 43° to our line-of-sight. The same group of scientists later revised that finding and argue in favour of a superluminal bulk movement in which the jet is embedded.

Suggestions of turbulence and/or "wide cones" in the inner parts of the jets have been put forward to try to counter such problems, and there seems to be some evidence for this.

Signal Velocity

The model identifies a difference between the information carried by the wave at its signal velocity 'c', and the information about the wave fronts apparent rate of change of position. If you envisage a light pulse in a wave guide (glass tube) moving across an observers field of view, the pulse can only move at 'c' through the guide. If that pulse is also directed towards the observer he will receive that wave information, at 'c'. If the wave guide is moved in the same direction as the pulse the information on its position, passed to the observer as lateral emissions from the pulse, changes. He may see the rate of change of position as apparently representing motion faster than 'c' when calculated, like the edge of a shadow across a curved surface. This is a different signal, containing different information, to the pulse and does not break the 2nd postulate of SR. 'c' is strictly maintained in all local fields.

Derivation of the relativistic explanation

A relativistic jet coming out of the center of an AGN is moving along AB with a velocity v. We are observing the jet from the point O. At time t₁ a light ray leaves the jet from point A and another ray leaves at time t₂ from point B. Observer at O receives the rays at time $t_1^\prime$ and $t_2^\prime$ respectively.

$AB \ = \ v\delta t$

$AC \ = \ v\delta t \cos\theta$

$BC \ = \ v\delta t \sin \theta$

$t_2-t_1 \ = \ \delta t$

$t_1^\prime = t_1 + \frac{D_L+v\delta t \cos\theta}{c}$, $t_2^\prime =t_2+ \frac{D_L}{c}$

$\delta t^\prime = t_2^\prime - t_1^\prime = t_2 - t_1 - \frac{v\delta t \cos\theta}{c} = \delta t - \frac{v\delta t \cos\theta}{c} = \delta t (1-\beta \cos\theta)$, where $\beta=\frac{v}{c}$

$\delta t = \frac{\delta t^\prime}{1-\beta\cos\theta}$

$BC \ = \ D_L\sin\phi = \phi D_L = v\delta t \sin \theta \Rightarrow \phi D_L = v\sin\theta\frac{\delta t^\prime}{1-\beta\cos\theta}$

Apparent transverse velocity along CB, $v_T = \frac{\phi D_L}{\delta t^\prime}=\frac{v\sin\theta}{1-\beta\cos\theta}$

$\beta_T = \frac{v_T}{c} = \frac{\beta\sin\theta}{1-\beta\cos\theta}$

$\frac{\partial\beta_T}{\partial\theta} = \frac{\partial}{\partial\theta} \left[\frac{\beta\sin\theta}{1-\beta\cos\theta}\right] = \frac{\beta\cos\theta}{1-\beta\cos\theta} - \frac{(\beta\sin\theta)^2}{(1-\beta\cos\theta)^2} = 0$

$\Rightarrow \beta\cos\theta (1-\beta\cos\theta)^2 = (1 - \beta\cos\theta) (\beta\sin\theta)^2$

$\Rightarrow \beta\cos\theta (1-\beta\cos\theta) = (\beta\sin\theta)^2 \Rightarrow \beta\cos\theta - \beta^2\cos^2\theta = \beta^2sin^2\theta \Rightarrow \cos\theta_{max} = \beta$

$\Rightarrow \sin\theta_{max} = \sqrt{1-\cos^2\theta_{max}} = \sqrt{1-\beta^2} = \frac{1}{\gamma}$, where $\gamma=\frac{1}{\sqrt{1-\beta^2}}$

$\therefore \beta_T^{max} = \frac{\beta\sin\theta_{max}}{1-\beta\cos\theta_{max}} = \frac{\beta/ \gamma}{1-\beta^2} = \beta\gamma$

If $\gamma \gg 1$ (i.e. when velocity of jet is close to the velocity of light) then $\beta_T^{max} > 1$ despite the fact that β < 1. And of course β_T > 1 means apparent transverse velocity along CB, the only velocity on sky that we can measure, is larger than the velocity of light in vacuum, i.e. the motion is apparently superluminal.

History

In 1966 Martin Rees predicted (Nature 211, 468) that "an object moving relativistically in suitable directions may appear to a distant observer to have a transverse velocity much greater than the velocity of light".

A few years later (in 1970) such sources were indeed discovered as very distant astronomical radio sources, such as radio galaxies and quasars. They were called superluminal (lit. "above light") sources. The discovery was a spectacular result of a new technique called Very Long Baseline Interferometry, which allowed astronomers to determine positions better than milli-arcseconds and in particular to determine the change in positions on the sky, called proper motions in a timespan of typically years. The apparent velocity is obtained by multiplying the observed proper motion by the distance and could be up to 6 times the speed of light.

In 1994 a Galactic speed record was obtained with the discovery of a superluminal source in our own Galaxy, the cosmic x-ray source GRS 1915+105. The expansion occurred on a much shorter timescale. Several separate blobs were seen (I.F. Mirabel and L.F. Rodriguez, Nature 371, 48, "A superluminal source in the Galaxy") to expand in pairs within weeks by typically 0.5 arcsec. Because of the analogy with quasars, this source was called a microquasar.

See also

• Ultra-high-energy cosmic ray
• Faster-than-light
• Superluminal communication

External links

• A more detailed explanation.
• A mathematical deduction of superluminal motion.
• Superluminal motion Flash Applet.