Neutron Stars

Q. If a sphere collapses from a radius of 7 x 105km to 10km, by what factor does its spin rate increase?

Conservation of angular momentum means:

Linitial = LFinal

Iinitial x ωinitial = Ifinal x ωfinal

(2/5) x M x Ri2 x ωi = (2/5) x M x Rf2 x ωf

( Ri

)2 =   ωf

Rf ωi
ωf = ( 7 x 105

)2 x ωi = 4.9 x 109 x ωi

The Sun rotates at 1 rev per 30 days. Compress it to 10 km and conserve angular momentum, it would spin up to 1890 revolutions/second (and fly apart).

So, at the center of a SNII remnant we expect to find a Rapidly Spinning, Extremely Dense ball of Neutrons with a Huge Magnetic Field

This was worked out back in the 1930's but it was assumed it was impossible to ever test it and it also seemed like science fiction even to the researchers who worked in the area.

But, Jocelyn Bell and Tony Hewish out together a rickety barbed-wire fence in a field in the countryside near Cambridge (England) in 1967 to do some routine radio observations.

They discovered a source in the constellation Vela that let out a little pulse every 1.3 seconds, then they realized it was every 1.337 seconds, then 1.3372866576 seconds. Eventually they realized that the best clocks of the time were not accurate enough to time this object which they christened a "LGM".

Timing curve for a neutron star

The announcement of this discovery was withheld for awhile while they tried to decide if they had discovered extra-terrestrial life. But soon others were discovered. This discovery set off more than a year of wild speculation as to the nature of the rapidly varying sources. But the possibility that it was a neutron star pretty quickly rose to the top.

Looked at the Crab nebula (ejected shell of the 1054 AD SN explosion) and detected another pulsing source with a period of 0.033 seconds (or, 30 pulses per second). This cinched it.

New name: Pulsars


There are now more than 500 pulsars known in the Galaxy

These are almost certainly rapidly rotating neutron stars with large magnetic fields.

If we spin the Sun or Earth or a WD to 30 times/sec, they would break up. So we need something with small radius and very large material strength.

The Crab pulsar and most of the rest of the pulsars are slowly, slowly slowing down. This was the solution to the mystery of the power source for the Crab.

So, what is the pulsing all about?

The Lighthouse Model for Pulsars

The key is to have the Magnetic field axis misaligned with the rotational spin axis.

What is a rotating powerful magnetic field called? A GENERATOR!

The intense, rapidly moving field generates huge electric fields at the surface of the pulsar which rips off e- and p+ (hey, I thought this was a neutron star!) which then fly out along the magnetic field lines emitting a beam of radiation along the magnetic field axis.

Pulsars are like lighthouses

The Pulsar Dynamo is typically around 1029X more powerful that all the powerplants on Earth combined.

Having the magnetic field and spin axes misaligned results in a lighthouse-like effect and the beam sweeps past the Earth once per rotation period.

The slowdown: The period of the Crab pulsar is decreasing by 3 x 10-8 seconds each day. This means the rotational energy of the Crab is decreased every day and the amount the rotational energy decrease is exactly equal to the luminosity of the nebula. So SOMEHOW, the slowing of the pulsar is what is powering the nebula.

This also implies that pulsars spin more slowly with age. The Crab pulsar at 900 years old is spinning much faster than the Vela pulsar (in the Gum Nebula) which is thought to have formed in a SNII explosion from around 9000 B.C.

The is a mysterious cutoff in the periods of pulsars at around 4 seconds. The Crab will slow to this period in about 10 million years. The neutron star will not go away, but it will essentially become invisible.

Misc. Fun Facts about Pulsars

  1. There are sometime glitches in the spin-down with a sudden increase in rotation rate. This is thought to be the equivalent of an earthquake where the crust of the neutron star settles a little bit, decreasing the radius and moment of inertia.

  2. Most pulsars are traveling a high speeds through the Galaxy, and many are exceeding escape velocity. This is though to be due to tiny asymetries in the SN explosion and recoil.

  3. There is a special class of pulsar discovered in 1982 with VERY short periods - the milli-second pulsars.

    In MOST cases these stars are members of close binary systems and it is thought that these pulsars are "spun-up" due to accretion of mass from their companion. The companions may have survived the SNII explosion or may be captured in the case of globular cluster milli-second pulsars.

    These systems are also commonly bright X-ray sources.

    Some VERY strange cases of apparently single milli-second pulsars are convincingly explained by having the pulsar's intense radiation field ablate the companion away.

Q. Do all SN remnants have pulsars in them? NO.

  1. Some SN are from SNI

  2. Some pulsars are not oriented correctly for us to be in the beam

  3. All single neutron stars older than around 10 millions years have slowed beyond the 4 second period cutoff.

Milli-second Pulsars

These are in mass-transfer systems and give rise to an interesting class of x-ray bright sources.

In the 1960's the first x-ray detectors where launched via rockets and balloons to catch a little glimpse of the x-ray sky. (Recall that x-rays don't make it through the Earth's atmosphere).

To everyone's surprise, there were lots of bright x-ray sources in the sky, most of them in the plane of the Galaxy.

Eventually an x-ray detecting satellite was launched (UHURU) a and catalogued more than 300 x-ray sources in the sky. This set off a big industry of follow-up observations to try and determine what these x-ray sources were.

The sources generally turned out to be uninteresting cool dwarfs with strong chromspheres and coronae, but some were associated with much more exotic things like close binary systems comtaining neutron stars.

The x-ray emission comes about when mass transfered from the ordinary star flies down along the magnetic field lines and crashes into the poles of the neutron star. The X-ray emission then is pulsed at the rotational rate of the neutron star (the hot spot comes in and out of view) and sometimes these are also seen as eclipsing systems as the neutron stars becomes hidden by the ordinary star.

For these eclipsing binary systems it is possible to measure the mass of the neutron star! For the 11 masses so far measured, the mass is 1.4MSun in 10 cases and 1.8MSun in the 11th.

This is good! Neutron stars are supposed to be greater than 1.4MSun and there is even reason to think that they should all be pretty close to the Chandrasekar Limit since that is what initiates the core collapse in a SNII.

Relative sizes of the Sun, a neutron star, and a white dwarf