Mini Neutron Stars: What is the Smallest Possible?

[Albertgauss]

I know there is theoretical possibility of making mini black holes in particle acclerators, but what about mini neutron stars, or even mini quark stars?

I realize the neutron decays in 15 mins if left all alone. What is the minimum number of neutrons needed inside a nuclei for it to be stable? I.e., what is the smallest neutron star can you have?

 

[mfb]

Neutron stars are stabilized by gravity. You cannot make them small, they need a mass similar to the sun (the precise lower and upper limits are still discussed).

Their core might contain a quark-gluon plasma. We can make this in accelerators - but it is extremely short-living as nothing holds it together. Microscopic black holes, if we can produce them at all, would be extremely short-living as well.

 

[ChrisVer]

I realize the neutron decays in 15 mins if left all alone. What is the minimum number of neutrons needed inside a nuclei for it to be stable? I.e., what is the smallest neutron star can you have?

Number of neutrons for stable nucleus : it depends on the nucleus... As a general "rule", for atomic numbers (Z<20) the number of neutrons have to be approximately equal to the number of protons, while for larger nuclei the number of neutrons have to be larger.

 

[hsdrop]

Microscopic black holes, if we can produce them at all, would be extremely short-living as well.

sorry that this may sound dumb to ask but why would they be short-lived

 

[stoomart]

sorry that this may sound dumb to ask but why would they be short-lived

The smaller the black hole, the faster it evaporates; see my recent thread Black hole explosions.

 

[ChrisVer]

sorry that this may sound dumb to ask but why would they be short-lived

the black holes are supposedly radiating energy through what's called Hawking Radiation...
The evaporation time is calculated to be proportional to the mass cubed of the black hole; as a result a black hole with very small mass (as a microscopic black hole) would evaporate pretty fast... if microscopic black holes have a mass equal to the Planck mass for example, they will evaporate in approximately $10^{-39}~s$. Masses below the Planck mass would evaporate faster.

 

[Albertgauss]

Quick question. What prevents a ball of neutrons from sticking together, such that they need gravity like the sun to keep them together? Neutrons have no electric charge, so what causes them to repel? They can stick together, via the strong force, but what would make a pile of neutrons come apart?

 

[mfb]

The Pauli exclusion principle. All neutrons have to be in a different state, which means most neutrons have to occupy higher energy levels, that makes the system unstable.

 

[Chronos]

This relates to the Chandrasekhar limit where stars below this mass limit are stable due to electron degeneracy pressure. Stars above the Chandrasekhar limit will overcome electron degeneracy pressure. The next natural plateau is the neutron degeneracy pressure limit which is not very precisely known. Neutron stars slightly over 2 solar masses are known to exist, but, are uncommon. It is unknown whether any natural pressure limits exist beyond neutron degeneracy pressure. It is generally assumed that stars that exceed neutron degeneracy pressure face nothing to prevent them from collapsing to a black hole. This also explains why mini neutron stars cannot exist. It takes significant [super solar] mass to exceed the electron degeneracy pressure limit. This magnitude of force cannot be achieved by any known means other than gravity.

 

[nikkkom]

This relates to the Chandrasekhar limit where stars below this mass limit are stable due to electron degeneracy pressure. Stars above the Chandrasekhar limit will overcome electron degeneracy pressure. The next natural plateau is the neutron degeneracy pressure limit which is not very precisely known. Neutron stars slightly over 2 solar masses are known to exist, but, are uncommon. It is unknown whether any natural pressure limits exist beyond neutron degeneracy pressure.

I find descriptions such as above to be a bit misleading. There is no "overcoming of degeneracy pressure". When you add matter to a white dwarf, it shrinks, it does not "resist".

Added electrons have to go into higher-energy states. Degeneracy pressure grows (not surprising: you need higher pressure to support a now-smaller WD).

Chandrasekhar limit is not a moment when degeneracy pressure "breaks" (it never breaks), it is a moment when most energetic electrons have enough energy for p + e -> n reaction. The "eaten" electron no longer provides pressure, and WD loses stability.

In neutron stars situation is similar. Adding more neutrons makes it shrink. And since NS in general have dimensions only a few times more than their Schwarzschild radius, there is a point when adding more neutrons will make it smaller than its Schwarzschild radius, after which it is a black hole. My understanding is that collapsing NS continues to push neutrons into ever higher energy levels even _after_ it is under event horizon: Pauli exclusion principle still works even there!

 

[Chronos]

I assume we can agree there is a point beyond which electron degeneracy pressure is insufficient to prevent further gravitational collapse of a white dwarf. That point is commonly referred to as the Chandrasekhar limit, as discussed here - http://astronomy.swin.edu.au/cosmos/E/electron+degeneracy+pressure. We don't know the point at which degenerate neutron matter can no longer resist further gravitational collapse [hence if has no officious sounding name].

 

[ChrisVer]

We don't know the point at which degenerate neutron matter can no longer resist further gravitational collapse

isn't that the Schwarzschild's radius?

 

[Chronos]

It is almost surely much bigger than the Schwarzschild radius. While the equation of state for neutron matter is not known, plausible size constraints can be approximated as shown here: http://www.rpi.edu/dept/phys/Courses/Astronomy/NeutStarsAJP.pdf

 

[nikkkom]

Chandrasekhar limit is not a moment when degeneracy pressure "breaks" (it never breaks), it is a moment when most energetic electrons have enough energy for p + e -> n reaction. The "eaten" electron no longer provides pressure, and WD loses stability.

To expand on this a bit: if we would "switch off" the possibility of p + e -> n reaction, this would not make WDs stable. Adding matter to them would still shrink them, and as you near the Chandrasekhar limit, WDs would quickly become very small: they would shrink from being ~Earth-sized to a few tens of kilometers, and after a bit more added matter they'd go under Schwarzschild radius and become black holes.

 

[snorkack]

When a neutron star accretes mass to the point it collapses into a black hole, is the disappearance of the neutron star observable?
Both neutron star and black hole have accretion discs, but the neutron star itself has to radiate away all energy of infalling matter, while the energy of matter falling in black hole vanishes past event horizon. Also a neutron star can have magnetic field and radiate as a pulsar, which hair a hole cannot have.

 

[ChrisVer]

When a neutron star accretes mass to the point it collapses into a black hole, is the disappearance of the neutron star observable?

It is similar to a Supernova I think.

 

[tzimie]

I think nobody knows what is the smallest size of strange star
How much gravity makes strange matter stable?

 

[stoomart]

I think nobody knows what is the smallest size of strange star
How much gravity makes strange matter stable?

I'm not sure what impact gravity has on strange matter, but stability is thought to exist in strangelets per the strange matter hypothesis (Bodmer, Witten, Farhi, and Jaffe); strangelets may be the true ground state of hadronic matter.

https://en.m.wikipedia.org/wiki/Strangelet
https://arxiv.org/abs/1405.2532

 

[Chronos]

While no confirmed definitive example of a quark star has been identified to date, several candidates have been found. The best known candidate is a putative neutron star known as 3C 58 in Casseopeia, a possible remnant from the supernova observed circa 1181, in China. Its xray emissions suggests a surface temperature of about 1 million ^oC - which sounds plenty toasty, but, is only about half the expected temperature of a neutron star at the tender of ~ 900 years. Another good candidate is RX J1856–3754 in Corona Australis, whose effective blackbody temperature is 700,000^oC and appears to be 5-10 km in diameter - both much lower than expected for any existing neutron star model. One problem with these possible quark stars is they should be far more common than observed, unless they are naturally unstable and 'rapidly' [cosmologically speaking] morph into something else like an normal neutron star or stellar mass black hole. Even so, if RX J1856-3754 is a quark star, it is still safely larger than its Schwarzschild radius. For additional discussion on these two odd stars, see http://www.solstation.com/x-objects/rxj1856.htm