Pulsars and relativity

[Adrian]

The little bit about pulsars on stargazing live last night got the mrs & I thinking and, with only half a physics degree 15 years ago, I rapidly got out of my depth:

The fastest known pulsar spins at over 700 times a second and has a maximum radius of 16km (according to wiki ) - if it is close to this maximum size then the speed of rotation of the surface at the equator is approaching 25% of the speed of light so relatavistic effects should become significant. How would these manifest? Please help with the following if you can:

- As an observer next to the pulsar (ignoring radiation and tides ) would the pulsar appear as a fattened/flattened sphere/ellipsoid due to length contraction most pronounced at the equator? (and would an observer on the surface measure the shape as a 'spindle' shape)

- is it really spinning 700 times a second or is this altered by time dilation effects?

- does this mean that the mass of the equator of the pulsar is greater than the centre/poles and could the increased gravitation of this pull the matter of the pulsar into a ring shape?

- if a pulsar this size was spinning at say 3000 Hz then it's equatorial surface would be moving faster than light; Would this be a black hole?

I'm kind of coming at this from special relativity, but obviously gravity cannot be ignored here so general relativity is needed (but beyond me for now )

[alan_g]

Hi Adrian

I'm not an expert by any stretch of the imagination but I'll have a bash at answering your questions (I'll refer to a single neutron star rather than a pulsar):

1. It would look like a flattened sphere (much like Jupiter, Saturn etc.) due to its rotation rather than length contraction. The effect would be much more pronounced though as it's mass & therefore gravity is much greater.

2. It is rotating 700 times per second as viewed in our reference frame on Earth. If you were to stand close to the neutron star you'd observe it to be rotating slower but a 'second' would also be longer due to gravitational time dilation

3. See Equatorial bulge - Wikipedia, the free encyclopedia

4. It won't travel faster than c, the Universe will prevent it somehow! Bear in mind that a neutron star can't rotate arbitrarily fast, it would tear itself apart long before approaching c.

[acey]

The question of radial velocity of a rotating body was considered by Einstein, who considered a rotating disc ("Ehrenfest's paradox"). He argued that an observer beside the edge should see length contraction of the circumference, but not of the radius, hence this observer would consider the disc to be non-Euclidean (circumference divided by diameter would not equal pi: effectively the geometry of a cone). This appears to be what first got Einstein on the track of non-Euclidean geometry.

What would observers on or off the disc "see"? This is a separate question from what geometry they would measure: observers travelling close to light-speed (relative to their surroundings) observe incoming radiation as a "spindle" (fore and aft) but that is an observation effect, not intrinsic geometry. An observer beside a spinning disc would, I presume "see" a flat disc (at any rate they wouldn't see a bent or conical one), though they would measure its geometry as non-Euclidean.

Likewise, in the case of pulsars, an observer would, I think, find its geometry to be non-Euclidean, though this needn't mean they would see it as something other than a sphere.

Neutron stars are in any case held up as examples of the most perfect spheres in nature, their high density meaning that any surface irregularity above a few millimetres counts as a "mountain" (the surface being solid iron at very high temperature).

High-density stars (specifically white dwarfs) provided one of the earliest observational tests of relativity because of their gravitational dilation effects (red-shifting of spectral lines). This was mentioned by Einstein himself in his book "The Meaning Of Relativity".

[Adrian]

Cheers guys

Neutron stars are in any case held up as examples of the most perfect spheres in nature, their high density meaning that any surface irregularity above a few millimetres counts as a "mountain" (the surface being solid iron at very high temperature).

The problem I have with this is that it is one of those neat little theory statements - as far as I know no-one has actually seen a neutron star in such a way as to be able to measure this (hell, we can't measure our planet/star to that accuracy).

I agree that in theory they should be perfect spheres however that idea tends to ignore that they are spinning at high/relativistic velocities. I could easily be wrong, though.

[acey]

Wobbling pulsar discovered - physicsworld.com

"Pulsars are ... typically 20 km across... Ingrid Stairs and her colleagues believe that the variation in the pulses suggests the neutron star is not spherical, but very slightly squashed... The bulge is extremely small: the new pulsar departs from being a sphere by just 0.1 mm in 20 km."

NASA - Einstein's Gravitational Waves May Set Speed Limit For Pulsar Spin

Nuclear-powered millisecond pulsars and the maximum spin frequency of neutron stars : Abstract : Nature

Period of a Pulsar

A Pulsar Discovery - Moments of Discovery