Are neutron stars immortal?

Dremmer

If proton decay does not occur, are neutron stars immortal? I was hearing that that was the case.

RocketSci5KN

Well, I would think so. Clearly the neutrons are as stable as if they were in a nucleus, so the 'free neutron' half life (614 sec) doesn't apply. Some could decay into a proton and electron, but a large part of the star started out this way, and clearly neutrons are energetically preferred. I suppose it would just slowly cool off by radiating away photons until it matched the cosmic background temp...

Here's a question: Is the density of a neutron star higher at it's core than at the surface? Is there a theoretical limit to this density?

twofish-quant

I don't think that neutron stars are immortal, because if there is proton decay then this will change neutron stars, but their lifetimes are much larger than the age of the universe.

1) yes. You need higher density to support stuff

2) yes. If it gets too dense, then it collapses and turns into a black hole. What that theoretical limit is turns out to be very difficult to calculate since it involves dealing with a lot of nuclear physics that we don't really understand.

bcrowell

Over extremely long timescales, I would expect that neutron stars would either undergo collisions with other objects in their own galaxies, or else possibly be ejected from their galaxies.

vanesch

I don't know if there is something like "evaporation" of a neutron star, like there is evaporation of a black hole (assuming Hawking radiation to be true).

twofish-quant

Question: Does anything in Hawking's calculation require that the object producing radiation be a black hole? Does the earth put out Hawking radiation?

neilvanrijn

I'd like to add two questions to this thread.
1. what is the relationship between a Bose-Einstein condensate and a neutron star
If you were able to produce a BEC of sufficient mass would that become a neutron star and or would a BEC produce something like Hawking radiation.

Dremmer

I know that proton decay would make neutron stars mortal, but I was talking about if there isn't proton decay. If there isn't, are they immortal?

Kracatoan

Hawking radiation is nothing to do with whatever your mass is made out of, it is just the fact that when you haven a spontaneous creation of a particle-antiparticle pair, i.e electron and positron, one passes the black-hole's event horizon and the other one does not, this means the one which passes the event horizon is lost forever and the other one is emitted as radiation, of a sort. The Earth can't doo this because its gravity is too pitiful to prevent the pair joining back up and annihilating.

BECs and Neutron Stars arn't really that similar, in fact they are quite the opposite. A BEC is formed when the species within the compound no longer obey the Pauli Exclusion principle and effectively occupy the same space (but not really), whereas a neutron star only exists because the Pauli Exclusion principle is preventing the neutrons from collapsing in further.

Technically yes, if you had a BEC of sufficent mass it would form a neutron star, but this would only be because it would just be undergoing the same processes as a collapsing star:

Protons + Neutrons get crushed close together, pauli stops them getting too close, so they joina nd form neutrons => Neutron Star.

Which has nothing to do with the properties of BECs. The only similarity between a BEC and a neutron star is that they are interesting scientific objects.

bcrowell

You only get Hawking radiation if there's an event horizon. An event horizon is a defining characteristic of a black hole.

twofish-quant

I need to go through Hawking's papers, but off the top of my head, I don't quite see quite why this is true. The event horizon is a global boundary, and when you cross an event horizon, there is nothing to tell you that you've crossed the event horizon.

The gravitational field of the earth should be producing pairs of matter/anti-matter and if the anti-matter gets annihilated then you should see some radiation leakage through a Hawking like process.

For that matter a lot of the thermodynamic results that come from black hole seem to hold if you apply them to *any* boundary.

bcrowell

It's certainly true that, e.g., an accelerated observer in Minkowski space will see Hawking radiation from a horizon that exists only because he/she is accelerating. But the energy source for this radiation is whatever energy source is accelerating the observer. I have never heard anyone suggest that, e.g., the earth would evaporate on long time scales. I think that's just plain wrong; if you think it's correct, please provide some evidence. If you can get Hawking radiation observable from infinity in an asymptotically flat spacetime, from an object that has no event horizon according to an observer at asymptotic infinity, then I suppose proton decay would follow trivially from the existence of Hawking radiation!?!?

twofish-quant

Cool. That means I may have come up with something original. Time to pull up the research databases.

Any particular reason or general gut feeling? The reason I'm asking is that if you have a specific reason in mind why it won't work (i.e. conservation of energy) they it may save me the trouble of spending a few weeks trying to get it to work.

Right now, it's at the "gee this might be a cool idea" stage. To get it to a "I can publish in Ap J. Letters" is going to take another two or three months of work assuming that I don't spend a few weeks and then figure out that it won't work. Also, I'm not terribly possessive, if someone else wants to spend some time getting this into a journal article, feel free to steal the idea. I got lots of other stuff to do.

Or electron decay. Suppose we establish that any massive object will produce Hawking radiation. What does that mean for an electron?

bcrowell

The first thing I would worry about would be that there should be some time-scale for this decay of a particle of mass m. In units where c=G=1, there is only one time-scale that you can derive from m, and I think it comes out waaaaay wrong.

Chronos

Question - assuming earth suddenly collapsed to form a black hole [reasons irrelevant], what would be its event horizon radius?

bcrowell

2Gm/c^2

Lievo

Penrose would love it, wouldn't he? ;-)