Re: what instruments are used to measure the speed of relativistic jets?

Relativistic jets have been found emanating from the cores of active galaxies as well as from binary systems containing a compact object (either neutron star or black hole) in the Milky Way Galaxy. All well-studied jets seem to be associated with a neutron star or black hole, so it is thought that relativistic jets require a compact object in order to form. The process by which they form is probably related to a disk of material orbiting the compact object and the magnetic fields within it. (It is also the subject of two separate answers on already on MadSci, "How would you explain the gas found 'blowing away' from a black hole [...]" "How can pieces of stars that collide while entering a black hole 'jet' out"!)

With rare exceptions (e.g., the nearby galaxy M87) these jets are seen only in the radio. The properties of the jets (their brightnesses and their polarizations) are consistent with the jets being produced by synchrotron radiation. This kind of radiation is produced by highly relativistic particles travelling in a magnetic field.

Thus, radio telescopes must be used to study them. The technique used is essentially "time lapse photography." That is, images separated by some amount of time are made. Depending upon the system being studied, one might have to make an image as rapidly as every week or only once every couple of months. (With enough images, one can even make movies, like this one of the quasar 3C 454.)

If you've viewed some of the images of these jets in the links I've provided, you've noticed that the jets are not uniformly bright, rather there are spots in the jet that are brighter than their surroundings. (The technical term for these bright spots is blob.) By comparing different images, one often notices that the locations of the blobs have changed. Typically there is a central blob that seems to be stationary and is associated with the location of the "central engine" or central black hole. This is also termed the core. The other blobs move away from the core, typically becoming dimmer as they do so. This behavior is interpreted as meaning that the material in the jet is not injected continuously. Instead, something happens occasionally at the base of the jet---probably resulting from an interaction of the black hole, its accretion disk, and the magnetic field---to cause slightly more material to be injected into the jet. Thus, the blobs are thought to be regions where the amount of material in the jet is slighly higher than the normal amount of material in the jet.

The term "relativistic" or superluminal jet arises from the apparent motion of the blobs (not from the relativistic motion of the particles within a blob!). From the time-lapse photography, one obtains multiple images of the jet with the blobs separated from the core If one knows (roughly) the distance to the object, one can translate the blob separations on the sky to a linear distance (i.e., convert from a separation of x degrees to y kilometers). Soon after radio astronomers started time-lapse photography for many sources, it was discovered that the apparent velocities of the blobs was comparable to, or in some cases larger than, the speed of light!

As you can imagine, when this was first discovered, it caused quite a stir. After all, special relativity predicts that nothing should be able to travel faster than the speed of light. This led to a number of suggestions, including the possibility that special relativity was wrong or that the distances to these quasars was overestimated dramatically. (If the estimated distance is too large then one's estimate of the linear separation, y km, will be too large as well.)

The accepted answer today is that superluminal motion is a projection effect. Consider a jet that is pointed almost directly, but not exactly, toward us. Suppose we obtain an image of the jet at the birth of a blob and one year later. The light from the time of the blob's birth travels toward us at the speed of light c. Let's suppose the blob itself travels at 0.9c, close to but still less than the speed of light. It is travelling both toward us and across our line of sight, but we can only detect its motion across our line of sight, i.e., across the sky. (The only way that one can tell that an object is moving closer is to see its size increase and the amount by which they come closer is such a small fraction of that distance that their size remains unchanged.) When we take the second image, one year later, we see the blob as having separated from the core. Because the blob is moving so fast, it is almost keeping up with the light that it emits. The apparent separation between the light waves (emitted at the time of blob birth and one year later) is not 1 light year but something smaller, say, 0.1 light year. Moreover, because we can see the blob moving only across our line of sight, we would consider all of this motion to have occurred in only 0.1 year. The result is that we think the blob is moving across our line of sight at a speed much faster than the speed of light.

Unfortunately, this is difficult to describe in words without also showing a picture. You might check out this radioastronomy tutorial, which shows a picture of how superluminal motion occurs.