# Would a tablespoon of a neutron star remain intact?

I've heard people say that a tablespoon of neutron star would weigh over a billion tons. If we ever could take a tablespoon of one would it still remain intact with the same density?

If we take neutron star material and somehow transport it somewhere for examination (say the Earth!), the results would be catastrophic. At say a density of $\sim 10^{17}$ kg/m$^{3}$ the neutrons have a number density of $\sim 6\times 10^{43}$ m$^{-3}$ an internal kinetic energy density of $3 \times 10^{32}$ J/m$^{3}$ (calculated using the relevant equations for an ideal gas of degenerate neutrons at this density). So even in a tablespoonful (say 20ml, which would have a mass of 2 billion tonnes!), there is $6\times10^{27}$ J of kinetic energy (15 times more than the Sun emits in a second, or a few billion atom bombs) and this will be released instantaneously.

The energy is in the form of around $10^{39}$ neutrons travelling at around 0.1-0.2$c$. So roughly speaking it is like half the neutrons (about a billion tonnes) travelling at 0.1$c$ ploughing into the Earth. If I have done my Maths right, that is roughly equivalent to a 50km radius near-earth asteroid hitting the Earth at 30 km/s.

The neutrons in a dense neutron star gas are relatively stable (beta decay is blocked by electron degeneracy). The expansion described above would allow beta decay into protons and electrons, but as this happens on timescales of 10 minutes, it is hardly relevant to the initial destruction. However, you would end up after a few tens of minutes with an expanding cloud of ionised hydrogen a few light minutes across.

The minimum possible size to gravitationally bind neutron star material is thought to be around $0.15 M_{\odot}$ (see here). The equilibrium electron density (there are always some electrons and protons present in neutron star material) for lower masses is too low to block neutron beta-decay.

• What if we picked inert neutronium? (btw, "A free neutron will decay with a half-life of about 10.3 minutes"-> so it shouldn't blow up all instantly... although the "decay radiation" intensity of a spoon of this material would probably overshadow any atom bombs even without chain reaction. – SF. Sep 20 '15 at 13:33
• @SF You have completely misunderstood my answer. The material blows up (expands at a significant fraction of $c$) because of its massive degeneracy pressure and hence kinetic energy. Nothing to do with neutron decay at all. What is "inert neutronium"? – Rob Jeffries Sep 20 '15 at 13:46
• Okay, now I'm getting it - you confused me with "kinetic energy" which is usually associated with motion while in this case it's more of a sub-atomic counterpart of elasticity. – SF. Sep 20 '15 at 13:50
• @SF No it's motion. Pressure, kinetic theory etc. The neutrons have huge momenta. – Rob Jeffries Sep 20 '15 at 14:50
• Impressive. This should be in the next "What If" installment. – Peter - Reinstate Monica May 24 '16 at 15:50

No, it's not stable without the huge pressure from gravity. There is a minimum stable size, but it's definitely much greater than a spoon.

• Would the neutrons go back to being an electron and a proton? Or is that not possible because the neutrinos that were created at the same time are no longer around? – matryoshka Apr 28 '15 at 0:43
• @Grace, free neutrons spontaneously decay to protons and electrons and neutrinos. Look up beta decay for more information. – Spencer Apr 28 '15 at 1:25
• @Spencer free neutrons in a low density environment spontaneously decay into protons and electrons. They don't in neutron star material (or not readily). – Rob Jeffries Apr 28 '15 at 8:12
• @RobJeffries, thats true but the environment is not likely to stay in its high density state without the gravitational force of a full neutron star there to keep it that way. – Spencer Apr 28 '15 at 20:49