As required with any neutron star story on HN, recommendation for “Dragon’s Egg” by Robert Forward. Science fiction novel which takes the surface of a neutron star as its setting.
The article mentions why this is important but doesn't really explain the details.
We don't have an equation of state [1] for neutron stars. Part of the reason why is that neutron stars are incredibly complex. You have fluid dynamics. Because matter is so dense you likely have neotronium and probably weird states and interactions with quarks.
Contrast this with black holes. Black holes can be perfectly described with 3 properties, only 2 of which are really relevant. The two relevant ones are spin and mass. The less relevant one is electric charge. Why is it less relevant? Because if the charge is too high then it can't be a black hole.
Because of this we can calculate how large black holes can be, figure out the fastest that they can grow (ie by sucking matter from the accretion disk; there's an uppper bound to that), etc.
So we have a rough guess on the range of masses neutron stars can be but we observation is really our only tool here. This is why examples outside of our estimated range are important.
As far as I am aware there is no theoretical limit that they cannot surpass, but of course they are limited in practice by the available mass, and how fast they can consume that mass; a lot of mass ends up orbiting, instead of falling into the black hole. So black holes such as the one mentioned in the article are expected to be rare.
Once they reach a certain size the stars in the closest stable orbit are no longer ripped apart by tidal forces, which means that they do not grow significantly beyond this.
Fun question: can spinning this fast allow for larger neutron stars?
The neutron star keeps growing, and eventually may have too much mass, causing it to collapse into a black hole. The forces pulling inward are just too much.
But if it's spinning fast enough, then centripetal forces would be pulling outward as well. This one is completing a full rotation in 1.41 ms- that's a lot of rotational speed.
Or is there some intrinsic property of black hole formation that does not care about this?
Rotation does indeed allow for heavier neutron stars, the outward force helps counteracting the inward pull of gravity that would otherwise overcome the forces that keep neutrons not turning into black holes.
edit:
There is a relativistic limit, as faster rotation eventually is not possible without adding ludicrous amounts of energy that would make the neutron star too heavy.
The non-rotating limit is about 2.1 solar masses (2.1 to 2.9), the rotating limit is about 20% higher (2.5 - 3.6 solar masses)
> There is a relativistic limit, as faster rotation eventually is not possible without adding ludicrous amounts of energy that would make the neutron star too heavy.
That is exactly the kind of thing I'm here for. Spinning so fast that the energy adds more mass than the spinning can counteract. Delightful.
There is an upper limit to how fast a black hole can spin. I'm not sure if that's the same limit you'd get if you tried spinning a material object as fast as possible while increasing its mass until it became a black hole.
Black holes don't have a limit on their rotation rate as far as current physics go, since black holes do not have a traditional surface. If the spin exceeds the speed of light, that simply makes the event horizon go away and leaves you with a naked singularity.
Can one theoretically increase the spin of a black hole by adding mass at the right angle? IE: give it more and more angular momentum until you achieve the naked singularity?
Perhaps that is the final experiment of Kardashev level whatever civilization.
You absolutely could keep adding momenting in just the right way. Though I will add, as spin goes up, so does frame dragging, which makes it actually difficult to hit a black hole as space begins spinning with it.
It makes for a very nice sci-fi story setting though. A very far flung future in which some very post-humans are attempting to break the universe in this way.
The event horizon going away is entirely valid, the naked singularity is not. So the limit is rather in that we can't explain what would come out of it, rather that the event horizon can't go away.
This begs the question: what _is_ angular momentum?
How does it gets transferred from the swirling gas to whatever degenerate state of matter is inside the neutron star? What kind of interaction is that?
Almost nothing falls straight into a star/neutron star/black hole. For it to fall straight in, it would have to be moving exactly towards the location of the s/ns/bh, which is very unlikely (and won't happen for lots of matter at the same time).
Generally, matter that's near a large mass is circling in a disc; if it isn't, then the particles will collide with each other until they've averaged out their motion. So, relative to that large mass, there will be a whole lot of angular momentum in that matter. The angular momentum doesn't go away as it approaches the mass; if it manages to hit the mass then the angular momentum will be added to the mass.
Fun fact: it's hard for us to send an object to collide with our Sun, because you have to cancel out all the angular momentum that everything on Earth carries.
One nice perspective on what angular momentum _is_:
It's a consequence of the laws of physics being the same for all directions.
Noether's theorem can be paraphrased as:
If a system has a continuous symmetry property, then there are corresponding quantities whose values are conserved in time.
If the laws of physics are the same even if your coordinate system is rotated that means there is a continous symmetry for that. When The conserved property is written out is is angular momentum.
I think it's an interesting question, it got me thinking a little bit (ianap). If you break down thinks at the microscopic level, angular momentum seems to not be a thing in itself, but rather a combination of momentum and some force that keeps things from going away from a center, like gravity in the case of interstellar gas, or chemical bonds in the case of a solid object. So what gets transferred in the end is momentum of all the gas particles that get assimilated in the neutron star. That begs the question, what is momentum? I don't really know, I guess it's a fundamental property of matter that can't get broken down further.
Im not completely confident, given my knowledge isn’t by an understanding of momentum in “particle physics” … but at least as far as I understand it, momentum and angular momentum are the same “thing”, angular momentum is just momentum constrained by some other physical force (such as gravity for things moving on their obits, or a gravitationally bound object such as stars or rubble pile asteroids spinning on their axis of rotation)
Perhaps I'm really being thick, but I take the answer as: if matter falls directly down onto a neutron star, that infalling mass doesn't add any spin.
If that mass comes down at an angle to the star (and it's swirling, right?), the kinetic energy gives a sideways push where it hits, like someone brushing the side of a football - it adds some rotational energy.
But that seems a trivial answer so I guess you're asking something deeper?
I may be entirely wrong, but I don't think the analogy holds, as friction is what makes the football spin.
Maybe a better one would be a spinning ice skater: going from wide arms to closed arms increases angular velocity.
Indeed consider the ingress mass and the neutron star as a single system, ingress mass gets closer (as the ice skater arms do) and angular velocity increases. Collapse is what makes it spin faster.
"Neutron stars are the city-size, extremely compact leftovers of supernova explosions. Beams of high-energy particles and radiation from their magnetic poles sweep through space as they rotate. "
I wished they would define what they mean by City as globally that varies even per country.
I was also wondering how much mass it is loosing as from my understanding the mass is converted to energy it emits and given the amount of energy - how much mass would that be. I did have a read of https://www.physicsforums.com/threads/do-neutron-stars-decay... though not clear and is it that they are just emitting massless particals in the form of neutrons so the mass does not change?
Regarding the city-size: you are right that "city" is a whole range of sizes but so is the size of a neutron star, they are not all of the same size. Don't read too much into it, they just want to give a very rough idea.
You can easily calculate how much mass it is losing via E=mc^2.
If something emits neutrons then it is losing energy and therefore mass. There are no energyless particles. Everything has a certain energy and by that mass. Some particles have no rest-mass but that is something different.
Fun fact: you could create a black hole from beams of light.
While you are correct that the neutron star has angular momentum and then you'd use the E^2 = (pc)^2 + m0^2c^4 for it, the question was if it is losing mass by emitting neutrons and how much. For that, the momentum energy of the Neutron star can be ignored. What does though play a role is the momentum of the particles that get shot into space and due to the escape velocity of these stars being so high it would still make sense to use this formula instead of E = mc^2.
BTW these stars emit a lot more than neutrons just in case the GP thought due to their name that that's what they emit mostly. Most of the emission of neutron stars is electromagnetic radiation (EMR) aka photons.
Actually neutron stars have two ways to lose energy: slowing down their rotational speed ("spin down") and losing mass. Which one of these contributes more to the EMR varies. For magnetars for example, only about 1% of the radiation is thought to be powered by rotation and for those we could actually use E = mc^2 to calculate how much rest mass the star is losing due to its radiation.
Not even neutrinos, which is probably what you meant, are quite massless. But my understanding is that the radio beams and such come out of the neutron star's magnetic field, and maybe its interaction with the surrounding gas. So its energy budget probably comes from the star's angular momentum, not converting its mass into energy.
