# Why does relativity affect relativistic jets?

Relativistic jets are regions outside black holes where matter is spewed out.

Wikipedia states that these jets will demonstrate relativistic effect such as relativistic beaming. I don't understand why relativistic beaming occurs.

They state:

Consider a cloud of gas moving relative to the observer and emitting electromagnetic radiation. If the gas is moving towards the observer, it will be brighter than if it were at rest, but if the gas is moving away, it will appear fainter.

But they give no explaination. There is also a similar statement from this paper:

Why does the cloud moving towards us make it brighter? I would agree it might take longer for us to see the light from the gas cloud moving away from us due to them being further away, but in the end of the day, shouldn't the same light still reach us?

I also don't understand why it would appear why it appears to move faster. Shouldn't both look like they're both moving at the same speed but one is towards me and the other at the same speed away from me?

Consider the light as electromagnetic waves. Neither the electric or mgnetic fields of the wave are Lorentz invariants - they are both transformed when observed in a frame of reference with a relative velocity.

In the case of light being emitted by something travelling at relativistic speeds towards an observer, the main effect is Doppler boosting of the fields - both the E-field and the B-field are boosted by a factor of $$\gamma (1+v/c)$$ in the observer's frame of reference, where $$v$$ is the relative velocity of the emitting object and $$\gamma$$ is the usual Lorentz factor. When $$v \rightarrow c$$ this increases the Poynting vector by a factor of $$4\gamma^2$$. In terms of the brightness of the source there is then a further factor of $$\gamma$$ caused by the Doppler effect increasing the observed rate at which the light is emitted.

In the case of light emitted at right angles to the line between the moving source and the observer (according to the moving source), the fields are transformed such that wave is both boosted and its direction of motion is bent towards the observer in the observer's frame of reference. When the source is moving relativistically, the angle which the light path makes with the observer-source reference line in the observer's frame of reference is approximately $$1/\gamma$$ (in radians). This angle is smaller for any light emitted in the source frame of reference at an angle less than 90 degrees to the observer.

Thus the radiation becomes collimated and boosted into a tight cone around the velocity vector of the moving source, with an angular width $$\sim 2/\gamma$$ radians.

If the source is moving away from the observer then all the boosting and beaming goes on in the opposite direction. Indeed, the electric and magnetic fields of light coming towards towards the observer are diminished by a factor $$\gamma (1-v/c)$$ and the Poynting vector consequently reduced to $$\sim 0$$.

The answer to the second part of the question is just due to the Doppler effect. The light coming from something moving towards us is moved to higher frequencies, as then are all observable phenomena associated with that object. It will thus appear to change its position (in the observer's frame of reference) at a faster rate than a symmetrically placed object moving in the opposite direction, for which everything appears shifted to lower frequencies. Hence clumps of emission in the jet coming towards us will appear to be moving faster than in the counter-jet.

I think we need to consider what the emission mechanism is.

Inverse Compton Scattering is a mechanism by which energy from moving electrons is transferred to the surrounding gas of photons and basically it results in an increase in the energy of photons moving in the same direction as the electron. So if you had a cloud of charged particles moving towards you, Inverse Compton Scattering results in a transfer of energy to photons also moving towards you, and the cloud looks brighter (since intensity is really just power per unit area). It occurs in reverse as well. Charged particles moving away from you will extract energy from the photon gas and so appear dimmer. I think this may address your first quote, but it is different to relativistic beaming in the sense that I've heard it used.

To me, relativistic beaming involves the Lorentz contraction of the electric parallel to the electron's motion (and its transverse dilation). When the charge is accelerated (say in a magnetic field), radiation can be preferentially emitted perpendicular to the direction of acceleration. This results in the "beaming" of gyro/synchrotron radiation at relativistic velocities, but I don't think that's what's being referred to here.

1. The exact reasons why you get relativistic beaming is due to the details of the geodesics of the kerr metric, which is considerably more mathematically complex than the newtonian gravity problem is. To understand why you might get an effect like this, though, it's worth noting the Penrose Process, which provides a mechanism where infalling matter can leave the black hole with more energy than it entered with, by basically stealing some of the black hole's angular kinetic energy. See here for more details.

2. This is easier. In the black hole's rest frame, the jet is ejected with speed $$v$$, which should only depend on the mass and angular momentum of the black hole, and the characteristics of the infalling matter. If the black hole is also moving toward the Earth with speed $$w$$, we will observe the jet coming toward blueshifted, and with speed $$\frac{v + w}{1 + vw/c^{2}}$$, and thus, more kinetic energy. If the black hole is moving away from us, then we have to subtract the velocities and will observe the jet coming toward us with speed $$\frac{v - w}{1 + vw/c^{2}}$$, and therefore, it will have less kinetic energy. this just follows from normal relativistic velocity addition.

• Is this different from the SR "relativistic beaming" described on p.33 here ? Commented Jun 7, 2021 at 2:32
• Commented Jun 7, 2021 at 2:35
• Yes I think you explained why the beams form, not the observer-dependent effects. Commented Jun 7, 2021 at 2:52