Pulsars

1967: Jocelyn Bell detects a radio "pulse" coming from the stars, repeating at intervals of 1.337 seconds.

Aliens?

Then another was found, and another. Not likely to be aliens, these things were coined "pulsars".

Typical periods: 0.25 - 2 seconds (Longest: 4.308 seconds, shortest: 0.0016 seconds)
Very regular: PSR 1937+214 has a period of 0.001155780644887275 seconds.
Periods are slowing: dP/dt ~ 10^-15, so that the lifetime P/(dP/dt) ~ 10⁷ years.

What are they?

Orbiting neutron stars? No -- a binary neutron star would suffer orbital decay (GR), so that they would spiral inwards and their period would shorten.
Pulsating stars? No -- Pulsation periods are too short for white dwarfs, too long for neutron stars (remember that, for oscillation, like grav collapse, P ~ 1/sqrt(rho) ).
Rotating stars? Ding! Rotation periods for collapsed neutron stars are just about the right period to explain pulsars.

If pulsars come from neutron stars, and neutron stars come from supernovae, then we should find always pulsars in supernovae remnants, right?

Not really:

Pulsar lifetime (10⁷ years) is much longer than the SN remnant lifetime (10⁵) years. Many "naked" pulsars exist.
Also, the supernova explosion can kick the pulsar away from the supernova remnant itself.

Do we see any supernova remnants with pulsars?

Back to the Crab Nebula

In the heart of the Crab Nebula lives a pulsar, with a period of 0.0333 seconds. We can even see the pulses in visible light:

How would this make the nebula shine?

Synchroton radiation

Charged particles emit radiation when they are accelerated. Relativistic, accelerated charged particles will emit synchrotron emission, which has a spectral signature that depends on the particles energy and looks very different from a blackbody.
So how could a pulsar be accelerating charged particles? Hint: Think about their strong magnetic fields...
The "shine" from the Crab comes from synchrotron radiation (L=5x10³⁸ erg/s), but this energy has to come from somewhere (no free lunch!). Where does it come from?
The kinetic energy of a rotating object is given by
So the rate at which kinetic energy is changing is If we assume the Crab pulsar is a uniform sphere, then the moment of inertia is given by
And putting in numbers for mass, size, period, and dP/dt, we get

In other words, the rate at which the Crab Pulsar is losing kinetic energy is almost exactly equal to the energy with which the nebula is shining.
Note that this is not the energy of the pulses -- they are much smaller in energy... Well, then, what about those darned pulses -- what are they?

The Pulsar Mechanism

Pulsars are rapidly rotating neutron stars with strong dipole magnetic fields. But the magnetic field axis is not necessarily aligned with the rotation axis (for example, on the Earth). As a result, the magentic poles will "sweep through space" as the neutron star spins. If radiation from the pulsar is entrained along the magnetic axis, a "lightouse effect" occurs.

Question: How common are pulsars? We see ~ 600 or so. Are there more?

What causes this emission? It's not well understood, but along these lines:

Near the surface of the neutron star, the magnetic field is changing rapidly as the neutron star spins. A changing magnetic field induces a strong electric field. This electric field can be stronger than the force of gravity holding the charged particles onto the neutron star's crust. So charged particles are pulled off the surface and flung off into space, continually powering the synchroton radiation.
The charged particles can emit radiation beamed along their direction of motion, making the coherent beam from the pulsar.