[clueless (OP)]

Hello.

Sorry if I'm being a bore, but I need reassurance because I'm writing a SF story. 1) So, are there approximately 200 000 000 000 stars in the Milky Way (200 billion stars) and I take it that the number of the stars in the cosmos is infinite? 2) Is neutronium so heavy and dense that there is virtually no space between subparticles (in its atoms or molecules?)? Thanks.

[Halc]

I take it that the number of the stars in the cosmos is infinite?

Given an infinite space model, yes. The number of stars in the visible universe is some finite number like 10²³ or so.

2) Is neutronium so heavy and dense that there is virtually no space between subparticles (in its atoms or molecules?)?

There are neither atoms nor molecules in neutronium. The substance is more dense (but not a lot more dense) than the nucleus of any ordinary atom. It weighs a lot more only because it is only found in extreme gravitational fields under which it is stable. There is space between the particles, held at distance by the nuclear strong force which is strong enough to resist the pressure due to the gravity. The EM force is not strong enough. The center of neutron stars actually have a lot of protons, so perhaps that substance (something other than neutronium) is even more dense that it finds its way to the center. The neutronium is more at medium depths, and there's some actual atoms at the surface of such stars.

Saying there is no space between the particles requires a definition of space 'taken' by the particle. But no fundamental particle has a meaningful volume, so there is in theory no limit to how far it can be compressed given enough pressure.

[paul cotter]

Hi Halc, I take it from what you are saying that the strong force is repulsive at very short ranges? I had assumed( naively ) that a neutron star was one big "macro" neutron. Also, if there is a lot of proton matter at the centre there must be a collection of electron somewhere.

[clueless (OP)]

This is great stuff. Great. Much appreciated and keep ‘em coming as per an addendum considered. I guess I won’t make a fool of myself in writing SF story as long as I have You guys and gals.

[Halc]

I take it from what you are saying that the strong force is repulsive at very short ranges?

It is, and it is quite attractive at the normal separation between protons (only way to keep them together), so the packing in neutronium is going to be tighter to a point. I don't know the percentage density difference of each of the layers.

I had assumed( naively ) that a neutron star was one big "macro" neutron. Also, if there is a lot of proton matter at the centre there must be a collection of electron somewhere.

There's been a bunch of newer models that show different stuff at different layers, starting with hydrogen/helium/carbon atoms in the 'atmosphere'. Yes, the low-mass free electrons remain with some still-atomic nuclei ions in the outer crust of the otherwise heavily positively charged star. This is followed by inner crust of neutron superfluid where most of the neutrons are (and some electrons), and which insulates the negative particles above from the positive ones below. The outer core is superconducting protons and a sort of neutron-rich quantum liquid, and the inner core is still kind of a mystery exotic substance, perhaps a degenerate quark soup of some kind. The amazing part is how they've measured it all enough to know this stuff.
If the electrons could get to the protons, they'd likely be turned into neutrons as had occurred to most of the proton/electron matter, but the picture below has electrons quite deep where the protons are, so go figure.



Google says density varies from a billion kg/m³ (1e9) at the surface to perhaps 700 million times that at the core (7e17)
Mind you, the former figure (at the crust) is waaay below the density of an atomic nucleus, which is about 2.3e17. So most of the neutron star is less dense than any ordinary atomic nucleus, but near the middle it gets about thrice the density.
The picture above shows inner density at only 4e14 g/cm³ which is 4e17 kg/m³, which is a bit lower than the one google gives me..

[Eternal Student]

Hi.

Just thought I'd mention a couple of minor points, relating to the original questions in the first post.

1.   You can Google to get estimates of the number of stars in the Milky Way.  Estimates are between 1~4  x10¹¹ stars     (checked several references for consistency:   https://en.wikipedia.org/wiki/Milky_Way   ;
    https://earthhow.com/milky-way-galaxy/          and     https://asd.gsfc.nasa.gov/blueshift/index.php/2015/07/22/how-many-stars-in-the-milky-way/  ).
   The NASA reference describes in more detail precisely where some of the problems are and why this is JUST AN ESTIMATE and provides another 3 references with more discussion of the problem.
    Note that we do sometimes "un-discover" a star.  For example, a black hole can distort space and create a lensing effect.  What can happen is that you see two points of light on each side of the black hole which you may have thought were two stars in different places but they were actually light from just the one star that has been bent around both sides of the black hole.    Meanwhile, we also frequently discover two stars where we thought there was only one.  Two close stars forming a binary system can look like just one point of light until you get a better resolution image of the region of space.
   The key point then is that this is a very rough estimate, don't be surprised if it's an order of ten bigger or smaller.   If we do revise our estimate then your book can start to look quite dated.

2.  "Neutronium" seems to be a term used mainly in Science Fiction and some Pop Sci articles.  It's not really used in more formal scientific literature.  It can mean the material a Neutron star is made of,  it could mean something else.  Historically it was a hypothetical element on the periodic table with 0 protons in the nucleus.

...I take it from what you (Halc) are saying that the strong force is repulsive at very short ranges?

   It can be desirable to try and keep two terms slightly separate.  The strong interaction or "strong force" is a fundamentally quantum mechanical interaction between quarks.   The nuclear force or "strong nuclear force" is a residual effect from that,  where a classical Newtonian force is identified as something that exists between any two nucleons  (which, as I'm sure you know, is a collection of quarks).   All too frequently the terms are used differently and often interchangeably, which is just a shame.  Just go about reading an article with the idea that they are different, one acts only on quarks, the other acts on whole nucleons.   If you were trying to consider all things in a very Newtonian way (which isn't always a great idea) then the Strong force always acts so as to keep some quarks bound together.   However, the residual strong nuclear force is different.   There can be an attractive force between nucleons at large distance and a repulsive force at small distances.
   
   See this description and diagram in Wikipedia for a discussion of the nuclear force between nucleons.   (Especially the sub-section titled "The nuclear force as a residual of the strong force")

   image taken from  https://en.wikipedia.org/wiki/Nuclear_force

  That "force" is, of course, just treating the nucleons as particles and the interaction between them in a very mechanical or classical Newtonian way.  A fully quantum theory just has some other mathematics describing the more fundamental strong interaction and there is no need to assign a mechanical force or assume the nucleons were ordinary solid particles on which a classical Newtonian force can act.

   I hope that helps a bit.

Best Wishes.

(Another post has just been added by @Halc before I completed this.   I'll read that next and hope this isn't repeating anything).

[evan_au]

How dense is neutronium?

Neutron star material is remarkably dense: a normal-sized matchbox containing neutron-star material would have a weight of approximately 3 billion tonnes, the same weight as a 0.5 cubic kilometre chunk of the Earth (a cube with edges of about 800 metres) from Earth's surface

https://en.wikipedia.org/wiki/Neutron_star

how many stars are in the Milky Way?

It is estimated to contain 100–400 billion stars and at least that number of planets

https://en.wikipedia.org/wiki/Milky_Way

But no fundamental particle has a meaningful volume

Just expanding on Halc's comment a little...
- All subatomic particles (and even atom and molecule-sized objects) are not hard little balls with a definite radius
- In quantum theory, all subatomic particles (like neutrons and protons) are a little "fuzzy" or "blurry", meaning that there is no definite boundary. There are just regions where they are very likely to be found, fading off into regions where they are less likely to be found.
- You can still talk about the "average distance between protons & neutrons in a Uranium nucleus", as the uncertainty in the size of a Uranium nucleus is smaller than the uncertainty in the size of an individual neutron (relatively speaking)
- The strong atomic force between neutrons becomes repulsive at shorter distances, as if they were bumping into each other; but applying more force (eg the gravitational field of a collapsed star) will push them a bit closer together
See the graph here: https://en.wikipedia.org/wiki/Nuclear_force#Description
- Neutron stars start off extremely hot (like 10¹¹ °C), but cool down in a few years to something more like 10⁶ °C.
- Like the temperatures we are more familiar with, things at a higher temperature "jiggle" more, and the average distance between particles is greater than between cooler things, which vibrate less. This leads to the general rule that things shrink as they cool (freezing water being one notable exception). I expect that this would also apply to neutron stars, too.
https://en.wikipedia.org/wiki/Neutron_star#Mass_and_temperature

so there is in theory no limit to how far it can be compressed given enough pressure

There is another limit: If the total mass of the neutron star exceeds about 2.5 times the mass of the Sun (in a ball only 10km across!), it is thought that even the Strong Nuclear Force will not be able to withstand the pressure, and it will collapse into a black hole.

There are various theories about other subatomic particles (like the "Strange" particles and "Quarks") that are denser than neutrons, and may be able to withstand slightly higher pressures than neutrons.
- Evidence for this is being collected by the NICER X-Ray telescope mounted on the ISS, which is trying to measure the mass, size and density of neutron stars. This will give some clues about the density of neutron stars, and whether "Strange stars" or "Quark Stars" exist.
https://en.wikipedia.org/wiki/Neutron_Star_Interior_Composition_Explorer

Oops! Overlap with Halc's latest post. One comment:

otherwise heavily positively charged star.

I expect that a neutron star would be electrically neutral, overall. Electrons will be attracted into regions with protons by the electric force. Due to the size and temperature of the neutron star, I expect that atomic orbitals will not exclude electrons from proton-rich regions.

PS: In our normal experience, the electric attraction between electrons and protons is far greater than the gravitational attraction of electrons and protons. But in the extreme environment of a neutron star, the gravitational force is more comparable to the electric force.

[Eternal Student]

Hi again.
    Looks like everyone was writing a post at the same time.
Somehow everyone forgot to mention the important point about degeneracy pressures.

From one of the very early posts:

There is space between the particles, held at distance by the nuclear strong force which is strong enough to resist the pressure due to the gravity.

   Which is not entirely true and also uses the term "pressure" in a very informal way (I think "compression due the gravity" might have been better.  You can see that calling it pressure instead of compression has started a bad trend because @evan_au has gone right down the same road).

(i)  To keep it simple, gravity produces a net inward force, pressure does not.  Pressure is a force in all directions and the gradient in pressure is what can give rise to an outward force that can help to fight against gravity and prevent further collapse.
(ii)   It isn't just the strong nuclear force that stops the collapse.   The degeneracy pressure is a significant contributor.   Just to be clear then for anyone else reading, the collapse of the star is not caused by pressure, quite the opposite, pressure is on our side fighting against the collapse.

   What is degeneracy pressure and why would it form a gradient (With P decreasing from the centre to the outer edge of the star)?
[LATE EDITING - surplus discussion removed]  ...Well no-one asked and it's not entirely relevant to the OP, so I won't bore everyone with that.

If the electrons could get to the protons, they'd likely be turned into neutrons as had occurred to most of the proton/electron matter, but the picture below has electrons quite deep where the protons are, so go figure.

     The Chandrasekhar limit describes the point where the density of electrons would exceed that permitted by the Pauli exclusion principle.  If the star has mass above the Chandrasekhar mass, then gravity is too strong and the pressure due to electron degeneracy is insufficient to stop it.  At that point, either the temperature has to increase, so that the degeneracy of the electron gas is lifted and higher energy states are available to the electrons  (which doesn't happen*)  OR ELSE  the usual thing happens.
   *I'm going to pause here and just mention that there really was a good way out of the problem - electrons could have just occupied ever-higher energy states (which is just saying they could have higher momenta).   However, there was already high enough temperatures and pressures so that electrons and protons can fuse and that is the escape route from the Pauli exclusion principle that will be taken.   Pop Sci articles often skip that and just imply that violating the Pauli exclusion principle was inevitable at this point.
   As the star continues to collapse (and since promoting electrons to even higher energy states isn't done) the Pauli exclusion principle is about to be violated and that just cannot happen,  that number density of electrons has to be brought down somehow.   What seems to happen is that protons in the region pick up some electrons and form neutrons.  This is where or why we get a Neutron star,  the electrons are being depleted and only Neutrons tend to persist.   However, there is no need to deplete ALL the electrons,  Pauli is quite happy with their being some density of electrons,  it just can't exceed a certain density.
   In a simple model we have:    At any place in the universe,
n_e(p) dp  ≤     
  where n_e(p) dp =  number density of electrons (number per unit volume) with momentum between p and p+dp.
   There's nothing really special about a Neutron star in this respect, it abides by the same limits imposed by the Pauli exclusion principle.   It's just that the density can be so high that the limit of n_e(p) dp  was reached.
   To say this another way,  an ordinary lump of iron on your desk at home can have a free electron density of about 10²⁸  electrons per cubic metre.   So a Neutron star can also have an electron density of 10²⁸ electrons per cubic metre anywhere in it, even right at the centre.   
    Actually the momentum distribution of the free electrons in the lump of iron on your desk followed a Maxwell-Boltzmann distribution (more or less) which meant that the temperature had to be quite high to support that density (room temperature say, otherwise at some value of momentum p, the quantity  n_e(p) dp  would have exceeded the limit).  Meanwhile the electron gas in a Neutron star is almost fully degenerate (which means all of the lower energy states are filled only) and so that has a very different probability distribution for momenta.  Being fully degenerate is the optimum way to accomodate all of the electrons while having the lowest total energy.  This means, a degenerate gas of electrons would support a total electron density of 10²⁸ at a much lower temperature  (an equivalent way of saying this is that an electron gas with that total number density of electrons would not be fully degenerate unless the temperature is close to 0 kelvin).  I'm mentioning this because a simple model would treat the electrons in a Neutron star as an electron gas which is assumed to be fully degenerate - and yet the temperature is many thosuands of kelvin.  So that the total number density of electrons is necessarily way above 10²⁸ electrons/m³ everywhere.

There is another limit: If the total mass of the neutron star exceeds about 2.5 times the mass of the Sun (in a ball only 10km across!), it is thought that even the Strong Nuclear Force will not be able to withstand the pressure, and it will collapse into a black hole.

   That comment from evan_au was just another example where it reads as if "pressure" is what was causing the inward collapse and not the thing opposing it.  Additionally, degeneracy pressure has to be mentioned again.  It's not just the strong force that is keeping the Neutrons apart.  Neutrons are also fermions - they behave much like electrons and must comply with the Pauli exclusion principle.  The degeneracy pressure of the Neutron soup is the last bastion that gravity has to overwhelm.   This one is a much more genuine last great barrier where degeneracy pressure and the Pauli exclusion principle really is everything because there is no alternative this time.  The electrons could combine with protons and be removed.  The neutrons don't seem to fuse with anything and be removed.

Best Wishes.

LATE EDITING:  Changed notation   n(e) dp   to    n_e(p) dp     which is more sensible to describe the number density of electrons at a given momentum p.

[Peter11]

A teaspoon full would wiegh 10 million tons you could never obtain it but its a scientific stoŕy so you could come up with ways to get around it.It would be like having Mount Everest on a spoon.It would also be extremely hot I don't know if there is such a thing as cold nuetronium but its a scifi story so it can exist.

[Eternal Student]

Hi.

its a scifi story so it can exist.

   That's fair enough.

    If the story is based on existing science then Neutron star material probably needs the extreme gravity conditions of a Neutron star to retain the properties of Neutron star material.  (Obviously I haven't done the experiment but we can assume that if you removed it from a Neutron star then it expands, interacts with other particles etc.)

Best Wishes.

[Kryptid]

I don't know if there is such a thing as cold nuetronium

You can have cold neutronium. All neutron stars will eventually cool off since they are emitting radiation. It takes a very long time, though.

If the story is based on existing science then Neutron star material probably needs the extreme gravity conditions of a Neutron star to retain the properties of Neutron star material.

Yep, that's what keeps it stable. Take a little piece of neutronium out of a neutron star and it will rapidly disintegrate (since it's essentially like an extremely heavy, extremely neutron-dense atomic nucleus). If the OP is looking for something with extreme density that is stable under standard conditions, strange matter would fit the bill. Under some theoretical conditions, such a thing is plausible.

[Peter11]

There you go you can't have it in your story because you want to base it on fact - no human could get or handle it in anyway so that ruins the neutronion part of your story.
The star does not create the dencity the colapsing magnetic field did it when the star colapsed.The idea that if you took a sliver away it would become less dence and go back to its regular state is complately wrong.

[evan_au]

I haven't done the experiment but we can assume that if you removed it from a Neutron star then it expands, interacts with other particles etc.

Playing with neutron stars is also beyond my rating on the Kardashev scale: https://en.wikipedia.org/wiki/Kardashev_scale

However, we have observed the collision of two neutron stars.
- This cosmic collision blasted large amounts of neutronium into space, where it promptly decayed into more familiar elements.
- Detection of the colission was only possible through the unique gravitational wave signature https://en.wikipedia.org/wiki/Neutron_star_merger#Observed_mergers
- This lasted long enough, and was observed by 3 detectors, enabling a direction to be determined for follow-up observations by optical and X-Ray telescopes
- This obscure astronomical event (which would have passed almost unnoticed* just a few years before) made the Wall Street Journal, on the basis that it produced the mass of the Earth in gold.
https://www.wsj.com/articles/a-clash-of-neutron-stars-forges-gold-1508162400  (behind a paywall... I get 2 seconds!)

*PS: Apparently the gravitational wave event coincided with a Gamma-Ray Burst which was detected in the same general region of the sky by two gamma-ray satellites. It is now believed that many "short" Gamma Ray Bursts like this (lasting only 2 seconds) were caused by neutron star mergers.

[Kryptid]

There you go you can't have it in your story because you want to base it on fact - no human could get or handle it in anyway so that ruins the neutronion part of your story.
The star does not create the dencity the colapsing magnetic field did it when the star colapsed.The idea that if you took a sliver away it would become less dence and go back to its regular state is complately wrong.

Gravity is what compressed the star to those densities.