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I've been reading up on some pulsar emission theory (admittedly written in the 70's and 80's, but I figured that's a good place to start), namely this review by Curtis Michel as well as the book Black Holes, White Dwarves and Neutron Stars - Shapiro and Teukolsky.

They both mention that a pulsar predominantly emits radiation from it's magnetic poles, even though it has a dipolar magnetic field. In the case of a charged plasma-filled magnetosphere, I understand that the charged particles (electrons/positrons) are pulled out from the surface due to the large electric field, and this causes them to radiate in the direction of the magnetic pole, but why don't they radiate while circulating around the magnetic field lines?

Surely since the field lines are curving themselves, they will provide acceleration to the charged particles causing them to radiate? Or am I missing something?

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3 Answers

First, Shapiro and Teukolsky is gospel---it will never be outdated.

Regarding your question: are you asking why emission doesn't come from the entire magnetic field region? I.e. why doesn't emission come from everywhere along the field-lines connecting the poles?

enter image description here

The most important answer is that there is radiation from the particules trapped along the closed field-lines --- it's just not where the strongest emission comes from. The strength of the emission is roughly proportional to the square of the magnetic field strength, $\propto B^2$, and remembder that magnetic field strength corresponds to the density of field-lines in a depiction like the one above. Clearly the field-lines are most dense at the poles, and thus the strongest fields, and the strongest radiation come from there.

When you're looking at x-ray emission, it also becomes important that the electrons can actually escape the system from the open field lines, allowing them to compton scatter photons.

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But since I asked the question, this also struck me - That the electrons will be emitting synchrotron radiation, and therefore beamed in the direction of their motion. So we wouldn't see it at all under some circumstances. –  Kitchi Mar 20 '13 at 9:35
    
That is definitely true. –  zhermes Mar 20 '13 at 16:02
    
But I've also read that radio astronomers didn't really expect off pulse emission from pulsars... from this model it seems obvious that there should be off pulse continuous emission. I'm quite confused. –  Kitchi Mar 20 '13 at 16:44
    
If you were a parsec away, you would see continuous emission. The beam emission is just tremendously more powerful, and thus you expect it to statistically dominate. –  zhermes Mar 20 '13 at 17:24
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The exact radiation mechanisms involved in the radiative emission from neutron stars and pulsars is still a very active area of research. The questions you ask are good ones and worthy of discussion.

Firstly, the claim that "a pulsar predominantly emits radiation from it's magnetic poles" is subjective. It is always true (as far as we have observed so far) that pulsars emit radiation from their pole with the greatest intensity, but it is not true to say that all pulsars (if you include their winds) predominantly emit radiation from their magnetic poles when considering then entire electromagnetic spectrum.

The Crab Nebula was mentioned in another answer, and it is worth noting that this nebula is the archetypal (original model or type after which other similar things are patterned) pulsar wind nebulae.

There are two distinct regions that both lead to the emission of radiation from rapidly rotating neutron stars:

  1. The region from the surface of the star to the edge of the light cylinder.

  2. The edge of the light cylinder through the wind-zone into the nebula bubble.

In region 1 the basic outline of what is going on is as follows. At the stellar surface, the pulsar’s huge magnetic fields and rapid rotation induce enormous electric fields within the magnetosphere, these consequently tear particles from the stellar surface and accelerate them to high energies. Plasma then fills the magnetosphere and the extreme magnetic field present is sufficient to cause the plasma to rigidly co-rotate. However, this co-rotation must cease somewhere near the light cylinder, and the particles flow along the opened magnetic field lines, carrying away energy in the form of an ultrarelativistic magnetized wind. Inside this region, the magnetic field aligned with the axis of rotation provide open magnetic field lines on which charged particles can escape. However, due to the vast magnetic fields involved that vast majority of the plasma is confined to the equatorial disk, and flows outwards through the light cylinder as and ultra-relativistic wind. So, plasma is emitted from the polar region, and this plasma (predominantly made up of positrons/electrons) moves along the field lines, emitting a small fraction of the total (Inverse Compton/Synchrotron et al. with some vast Doppler beaming effects) radiation seen emanating from the nebula.

The second region is the one we know more about. This is because the flow produced by the stars relativistic wind and the subsequent radiation from this charged plasma allows us to gain insight in to the magnetohydrodynamics at work. I must note however, that the mechanism behind how the wind is accelerated (known as the sigma-problem) is still not very well understood. This relativistic wind cannot accelerate forever, and must at some point match the boundary conditions of the confining supernova remnant. This occurs at a strong reverse shock known as the termination shock, where the cold collimated plasma of the wind is heated, the magnetic field is amplified, and particles are boosted to ultra-high energy. These particles then inflate a bubble of shocked heated plasma which produce nebulae of radiating particles which are continuously decelerated by the nebula magnetic field (the dynamics of the termination shock is the likely cause of the 'wisp'-like structures [highly radiative structures produced by synchrotron emission] moving away from the pulsar in the equatorial disk). As a result a non-negligible fraction of the pulsar’s spin-down energy lost through its wind becomes detectable as non-thermal radiation (enabling us to create the pretty picture of the Crab).

The termination shock

The above image shows the [toroidal] termination shock in detail. The quantity being shown is Lorentz factor. The labels refer to: A. ultrarelativistic wind zone; B. The Mach belt; C. Arch Shock; D. shear layer; E. gamma-stream; F. rim shock. G. Polar Jet. H. The bright knot (thought to be responsible for large intensity gamma-ray emission). Aside. To provide some scale here, the magnetosphere is off the grid, that is it could be comfortable contained within the white dot in the centre of the image! Our entire solar system would comfortably fit inside the termination shock (although that is one scary thought!).

Now, there are some complex dynamics in the vicinity of termination shock, and it is this down-stream flow that is the suspected primary cause of the formation of relativistic jets. For pulsars and magnitars is it the magnetic hoop stresses which cause the bulk flow away from these objects down stream of the termination shock, to be collimated and redirected from the equatorial disc back towards the polar axis, this causes large increases in the total pressure in the polar region (outside of the termination shock) and causes vast acceleration along the rotation axis and away from the star (note, there is much more going on but this is the general gist!). The formed jets remain collimated (cylindrical - with perhaps some sausage instabilities as it travels away from the star) due to the 'local' Z-pinch in the 'vicinity' of the star. See models for astrophysical relativistic jets from compact objects for some further information and some links to animations of this phenomenon.

Here is a paper I wrote on this subject a while back Observations of Wisps and a great follow up paper of the physics behind the recent gamma-ray variability seen from the Crab Nebula and the suspected causes.

Of course there is a lot more to be said on this topic, but I am afraid you will have to follow the paper trail for your self from here on! Feel free to come back and ask more questions when you are ready...

I hope this helps.

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Mmmmmm..... sausage instabilities –  Jim Apr 9 at 17:27
    
Very thorough and well written +1! My only beef with this answer is the ninth word in the third paragraph; "above". This answer may well outscore the original, consider updating that –  Jim Apr 9 at 17:30
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In some pulsars off-pulse emission is detected. In fact it is coherent emission resulting from cyclotron resonance between highly energetic primary particles and the low gamma secondary particles in the pulsar magnetosphere

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