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As I know, some stars produces carbon, nitrogen and oxygen when they are old and become white dwarfs or neutron stars. And even their surface gravity is strong, it may rotate very fast so that the surface gravity is diminished, hence materials such as rocks and water can present at the surface normally.

My question is, is it possible for life (eg:bacteria) to survive on the equator of white dwarf or neutron star if it is cooled and rotate very fast? Or is it even possible for the equator of white dwarfs or neutron stars become the origin of life?

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    $\begingroup$ How are you simultaneously going to cool it and have it rapidly rotating? The situation you describe seems impossible because neutron stars and white dwarfs spin down as they cool. $\endgroup$
    – ProfRob
    Mar 10, 2016 at 7:44
  • $\begingroup$ The surface gravity of a white dwarf is something like A LOT stronger than on Earth. Together with the degenerate matter and intense magnetic field probably nothing could survive there. Chemistry is different there than in our kitchen. $\endgroup$
    – LocalFluff
    Mar 10, 2016 at 16:08
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    $\begingroup$ @RobJeffries - I think the OP is asking about a hypothetical object cool enough and spinning fast enough. Gedankenexperiment if you will. $\endgroup$
    – Florin Andrei
    Mar 10, 2016 at 20:58
  • $\begingroup$ @FlorinAndrei Clearly I know it is hypothetical, since I pointed out it is not possible. You also have to hypothesise a neutron star with no magnetic field, since otherwise it will almost instantly spin down sufficiently to make gravity enormous again. $\endgroup$
    – ProfRob
    Mar 10, 2016 at 21:34
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    $\begingroup$ Interesting and related: en.wikipedia.org/wiki/Dragon%27s_Egg $\endgroup$
    – CDspace
    May 10, 2016 at 22:09

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I am going to attempt a weak answer, mods feel free to delete it, but I'm fairly certain I'm right.

Shortly - no. It's not possible. Even if you balance gravity and centrifugal force perfectly at ground level at the equator, they will very, very quickly become imbalanced as soon as you move north, south, or up from there. So quickly in fact that the gradients may be too big even for a human being not moving at all. Maybe if you're laying down, with your body oriented along the equator, but even then I think the gradients would be too big.

Maybe bacteria would survive, briefly.

I'm sure the math could be done quite easily to estimate the gradients. This is based entirely on intuition.

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Let us consider a 1.4 solar mass neutron star, which, if not spinning would have a radius of about 10km. Ignoring relativistic corrections (which will be significant) the angular velocity $\omega$ of a circular orbit just above that surface is given by $$r\omega^2 = GM/r^2$$ so $$\omega = \sqrt{\frac{GM}{r^3}}$$ and putting in values, we find $\omega = 13.6 kHz$, so that the period $2\pi/\omega$ is about 460 microseconds. So for our "life" to experience moderate gravity, the neutron star will need to be spinning at something like 2000 rotations/second, or about 30% of lightspeed at the surface.

Of course that makes the rather large assumption that a spinning neutron star would still be spherical, which is most certainly would not. Working out exactly what shape and density distribution it would adopt is probably rather hard. I suspect you'd need to know a lot about the equation of state (density-pressure relationship) of nuclear matter. I speculate that you'd end up with a somewhat oblate neutron star with an much thicker crust of "normal" nuclear matter at the equator, the very top of which would be almot in orbit. A little like Mesklin on steroids. I also suspect the whole thing might be quite unstable, since if a chunk of the equatorial belt rose up some reason, it would experience less gravity and so less pressure and so expand, causing at least parts of it to stick up further and be spun off into orbit. Conversely, if it dropped a little, it would become denser and drop further.

Assuming some freak of nature or alien technology kept it stable, and plucking a figure from the air, suppose the equatorial diameter of the discus shaped star was 50km, so that the surface at the equator was essentially in a 25km radius circular orbit the period would need to be about 2ms. We can calculate the tidal forces experienced by an object on the equator using a formula from Wikipedia

The tidal acceleration in $g$'s per meter is $$2GM/gr^3 = 2.4 \times 10^6 g/m$$ That is two objects 1m apart would "fall away" from one another with an acceleration of 2.4 million gravities, so any life there would need to be very small and very tough.

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It is quite difficult to say about the presence of life, however it cannot be neglected as we know by researches that even on earth there are also many place where life was supposed to be impossible to exist but life exist . Now see average temperature on the surface of the dwarf star is about 2 times of our Sun's temperature and have more gravity and also the gases and liquids will not present at this much temperature hence it is very very difficult for life to exist there.

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