[btilly]

We've never been up close, but the neutron star is probably smoother.

A neutron star has a diameter of about 20km and surface irregularities are currently estimated at under 1 mm. (See https://www.livescience.com/millimeter-tall-neutron-star-mou... for verfication.) Scale that up to the Earth's diameter and irregularities are on the scale of 64 cm.

[dmurray]

Are neutron stars spherical or do they tend to become oblate spheroids (even if perfectly smooth) because, like the Earth, they spin on an axis?

[colechristensen]

Yes magnetic fields and spin are expected to deform neutron stars slightly.

[cbanek]

Ah yes good point. I didn't take into account the rotation of a star in my answer around its axis. But yes you're right. And that's why the earth is also kind of a spheroid (squished sphere).

Einstein you crazy bastard, you were so ahead of your time. I wish we could have met. I think you're quite a Feynman, if you catch my meaning.

[cbanek]

I think they'd probably be spherical. They are super dense, so there's not much space between the atoms. That's what makes them dense and heavy. So imagine a bag of popcorn with all the little popcorn bits popping out at weird spots. Then take it and crush it in your hands to make a circle. It's still the same mass (weight), but now it's more dense since it's smaller. And as you squeeze the popcorn it sticks out less. That's mostly because you're squeezing the popcorn, and applying a force to drag things to the center. There's still gravity inside a star, so that's what gravity is doing. And the more dense it is, the more tightly packed, and so the gravity will keep it tightly together. So that's why I think it'd be spherical.