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The Neutron Star

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Wade Hampton III

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The Neutron Star

PostSun Aug 19, 2018 2:30 am

Alex Fleming, Graduate Research Assistant at Texas A&M University
(2016-present) asks...

How can a beam of light travel around the Earth roughly 7 times
in a second and a neutron star can supposedly rotate 1,000 times
in a second? Wouldn’t the rotational speed of the neutron star
exceed the speed of light?

Answered Fri · Upvoted by David Vanderschel, PhD Mathematics &
Physics, Rice (1970) and Paddy Alton, PhD in Astrophysics.

The reason we know that a neutron star CAN spin up to 716 times
in a second is because we have measured this in the fastest
spinning pulsar on record. A pulsar is a neutron star that has
a jet of high energy photons going off in two directions at
opposite poles. These photons are created along the direction
of the terrifyingly strong magnetic field generated by the neutron
star. The magnetic poles, just like on Earth, can occur on an axis
other than the axis of rotation. And as such, the pulsar acts kind
of similar to a lighthouse, sweeping a beam of light in a circle.
We can see a pulsar when we just happen to be in the direct path
of this beam of light. When we see this light, we can simply count
the number of pulses that we see in a second and we know how rapidly
the neutron star is rotating.
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Now to answer your question. I've read a lot of the given answers
that simply say how large a neutron star is. The reason we know how
large the neutron star is actually is BECAUSE people first asked
the very question you asked. The speed of light is actually an upper
limit that theoretical nuclear astrophysicists used to take a first
guess at approximating the radius of a neutron star. We know THAT
a neutron star can rotate at 700 times a second. Since the speed of
light is the fastest anything can go, that means that a perfectly
spherical object with an equatorial tangential velocity of the
speed of light and spinning 700 times a second would have a radius
of about 40 miles. This is a crude estimate, but it does tell us
that we cannot have a radius larger than this.

We can also use the mass of the neutron star to set a lower limit
on this radius. Within some minimum radius, a neutron star of a
given mass will collapse into a black hole. Knowing the mass, and
how fast its spinning can give us a definite range. With the help
of LIGO and other gravitational wave detectors, we can hopefully
in the future get better ideas of the upper and lower limits of
the mass of neutron stars.
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These two numbers, speed of rotation and mass, can help give us a
definite range of the size of a neutron star. To figure out the
EXACT radius of a given neutron star of a given mass is actually
a tremendous challenge, and still an ongoing problem in theoretical
nuclear astrophysics. We have to create models that use nuclear
physics and special and general relativity to take as inputs a set
of conditions we think exist inside neutron stars and then have
our model spit out a guess for the mass or radius. If the mass is
too large for too small a radius, it would collapse into a black
hole, the model is rejected. If the radius is so large that it
would break the cosmic speed limit, this too must be thrown out.
We have other conditions that limit the range further, but the
mass and rotational velocity are enough to make a good first guess.

So finally to answer your question, would the rotational speed of
a neutron star exceed the speed of light? No, because astrophysicists
based our best guess of the radius of a neutron star with the
speed of light in mind.
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