# Neutron stars

What are the forces that give asteroids their shapes? And what shape do neutron stars that do not rotate around its axis have?

## Answers and Replies

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jingles2005 said:
What are the forces that give asteroids their shapes? And what shape do neutron stars that do not rotate around its axis have?
Let me try. Corrections welcome.

a. Fracture.
b. Sphere.

Chronos
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Neutron stars spin to conserve the energy released by the supernova explosion that preceeded them. They typically spin very fast. My argument [and I allow for the possibility I am wrong] is the explosion is assymetric and imparts a huge amount of angular momentum on the fragment.

Addendum: Listen to selfAdjoint before you even consider what I have to say. He is much more knowledgeable and I defer to his judgement. I just try to give my spin.

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SpaceTiger
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Chronos said:
Neutron stars spin to conserve the energy released by the supernova explosion that preceeded them. They typically spin very fast. My argument [and I allow for the possibility I am wrong] is the explosion is assymetric and imparts a huge amount of angular momentum on the fragment.
Neutron stars are indeed born spinning quickly, but I think the primary cause is conservation of angular momentum. That is, the radius shrinks by orders of magnitude, so small initial spin rates will be magnified:

$$I_1\omega_1=I_2\omega_2$$

$$\frac{2}{5}MR_1^2\omega_1=\frac{2}{5}MR_2^2\omega_2$$

$$\frac{\omega_2}{\omega_1}=\frac{R_1^2}{R_2^2}$$

This still isn't enough to get the fastest pulsars. These are actually created by accretion torques. This means that a nearby star is dumping matter onto the neutron star and spinning it up when the matter collides with the surface. That's how we get "millisecond pulsars".

You mentioned asymmetric supernova explosions; those are actually what we believe cause "neutron star kicks". We see neutron stars in the galaxy that are moving at unusually high velocities, implying that they were somehow "kicked" by something. Naturally, we think it has something to do with the supernova.

Finally, to the original question, a non-rotating neutron star should be very nearly a perfect sphere. In fact, it may be the best approximation to a perfect sphere that can be naturally created.

James R
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And about those asteroids...

The shapes of asteroids are fairly random. They are usually too small for gravity to play much of a role. Their shapes are determined by the random way their contents happen to come together, as well as what hits them in their travels.

Chronos
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OK, I'll bite, ST. Does not accretion from a binary partner tend to slow down the rotation of a neutron star. I'm thinking tidal forces. Humm, it just occured to me it can also have a spin up effect... astrophysics can be so confusing sometimes...

SpaceTiger
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Chronos said:
OK, I'll bite, ST. Does not accretion from a binary partner tend to slow down the rotation of a neutron star. I'm thinking tidal forces. Humm, it just occured to me it can also have a spin up effect... astrophysics can be so confusing sometimes...
You're right that it can do both. The torque from the flow of accretion depends on the direction of the orbit. In other words, the infalling matter will hit the neutron star in the same sense as the companion is orbiting around it. If this opposes the spin, then it will be spun down by the torque. One would usually expect them to be spinning and orbiting in the same direction (for the same reason the planets tend to orbit and spin in the same direction), but it's not required. Even if it were spun down, it would eventually be spun up in the other direction as the torque continued.

The other effect that you're referring to (tidal locking), would be much smaller in this case, mainly because a neutron star is an extremely sturdy beast. The spin-down of the earth arises because the moon distorts its shape a little bit and torques it as it spins. A neutron star's shape would be barely changed at all by its companion, both because of its small size and because of its resistance to compression. Instead, I'm talking about the direct impact of material with the surface of the neutron star.

Chronos
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Agreed, the accreting mass would be a trivial effect. I percieve a neutron star gaining a huge jolt of angular momentum from the massive ejection of material during a supernova event. While the EM disturbance would be spectacular in all directions, I would expect a polarized burst of neutrinos and gammas in the ejection plane.

SpaceTiger
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Chronos said:
Agreed, the accreting mass would be a trivial effect.
Actually, I'm saying it wouldn't be. Tidal dissipation would be a trivial effect.

Phobos
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James R said:
And about those asteroids...

The shapes of asteroids are fairly random. They are usually too small for gravity to play much of a role. Their shapes are determined by the random way their contents happen to come together, as well as what hits them in their travels.
As you might suspect, the more massive the asteroid, the more significant gravity becomes in determining its shape. The largest asteroids are roughly spherical. The type of asteroid is also important. Some asteroids are self-gravitating gravel piles whereas others are more solid rock (which would have more odd shapes due to past collisions, etc.).

Chronos