# How is a neutron star's maximum mass calculated? **URL:** \ **Category:** Factual Questions\ **Created:** [June 21, 2023, 6:31pm UTC](https://boards.straightdope.com/t/how-is-a-neutron-stars-maximum-mass-calculated/985895 "2023-06-21T18:31:36Z")\ **Posts on this page:** 10\ **Page:** 1
**Author:** ![EdwardFound](https://avatars.discourse-cdn.com/v4/letter/e/4af34b/32.png) [@EdwardFound](https://boards.straightdope.com/u/EdwardFound)\ **Post date:** [June 21, 2023, 6:31pm UTC](https://boards.straightdope.com/t/how-is-a-neutron-stars-maximum-mass-calculated/985895/1 "2023-06-21T18:31:36Z")
I have a sense of how physicists calculate the collapse of atoms into neutronium: A neutron has a mass greater than a proton + electron, but when the gravitational potential energy of an atom exceeds a certain point then neutronium becomes the lower-energy state. What, though, determines the stability of the neutronium and the gravitational force necessary to collapse it further? Is it calculated based on the strong force? Does neutronium go to quarkium - or just to point-massium? ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [June 21, 2023, 6:55pm UTC](https://boards.straightdope.com/t/how-is-a-neutron-stars-maximum-mass-calculated/985895/2 "2023-06-21T18:55:00Z")
There’s a lot more here that we don’t know than what we do. In a nutshell, what you want is called the “equation of state” of neutronium: That’s an equation that relates the density of the material to its pressure. Once you have that, it’s a straightforward (though somewhat tedious-- You definitely want a computer to do it) calculation to determine the maximum radius before it collapses anyway. In principle, it should be possible to determine the equation of state of neutronium from the details of the Strong Force. But unfortunately, we don’t know enough details of the Strong Force. So in practice, what we do is just look at what neutron stars we can find, and come up with various simple equations that are consistent with all of them. A little over a decade ago, a neutron star was discovered that was twice the mass of the Sun, and that one data point was enough to eliminate a lot of the models. > [@EdwardFound](#): > > Does neutronium go to quarkium - or just to point-massium? That’s one of the known-unknowns. There is speculation that you can have something called a “quark star”, and even that they might be relatively common-- The Crab Pulsar might, according to some models, be a quark star. But so far as I know, it’s never been proven one way or the other. ---
**Author:** ![EdwardFound](https://avatars.discourse-cdn.com/v4/letter/e/4af34b/32.png) [@EdwardFound](https://boards.straightdope.com/u/EdwardFound)\ **Post date:** [June 21, 2023, 8:22pm UTC](https://boards.straightdope.com/t/how-is-a-neutron-stars-maximum-mass-calculated/985895/3 "2023-06-21T20:22:59Z")
Thank you. So the stability limit is at least 2 SM. If the limit were significantly larger - say 3 or 10 - would observers have expected to find them? That is, is the lack of examples larger than 2 evidence that the limit must be close to 2? Does LIGO provide data on this? That is, can LIGO signatures distinguish events involving black holes vs. neutron stars? ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [June 22, 2023, 1:44pm UTC](https://boards.straightdope.com/t/how-is-a-neutron-stars-maximum-mass-calculated/985895/4 "2023-06-22T13:44:11Z")
LIGO probably could detect a neutron star collision, and might be able to distinguish it from a black hole collision… if it was close enough. So far as I know, though, LIGO has never actually detected a neutron star. LISA, the proposed space-based gravitational wave detector, would be able to detect them when they’re just orbiting, not colliding, which means it’d find oodles of them, for much better data. As it is, we generally can’t determine the mass of isolated neutron stars: They need to be orbiting with something else. That gives us a fairly small data pool, enough so that it’s difficult to rule out the possibility of outliers more massive than the most massive one we’ve found. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [June 22, 2023, 1:47pm UTC](https://boards.straightdope.com/t/how-is-a-neutron-stars-maximum-mass-calculated/985895/5 "2023-06-22T13:47:39Z")
> [@Chronos](#): > > So far as I know, though, LIGO has never actually detected a neutron star. …And I find I must amend that. It did detect a neutron star merger, in 2017. Still, mergers are relatively rare events, not enough for good statistics. ---
**Author:** ![dtilque](https://avatars.discourse-cdn.com/v4/letter/d/d6d6ee/32.png) [@dtilque](https://boards.straightdope.com/u/dtilque)\ **Post date:** [June 22, 2023, 3:16pm UTC](https://boards.straightdope.com/t/how-is-a-neutron-stars-maximum-mass-calculated/985895/6 "2023-06-22T15:16:33Z")
> [@Chronos](#): > > It did detect a neutron star merger, in 2017. Still, mergers are relatively rare events, not enough for good statistics. It’s observed dozens of BH-BH mergers, but only one NS-NS merger and no BH-NS mergers. Considering that the latter two are where several elements (including gold) are made, I’m surprised there aren’t more of them observed. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [June 22, 2023, 11:43pm UTC](https://boards.straightdope.com/t/how-is-a-neutron-stars-maximum-mass-calculated/985895/7 "2023-06-22T23:43:03Z")
> [@dtilque](#): > > but only one NS-NS merger Two: > **[LIGO-Virgo Network Catches Another Neutron Star Collision](https://www.ligo.caltech.edu/news/ligo20200106)** > > LIGO and VIrgo detect another binary neutron star collision, dubbed GW190425. ---
**Author:** ![EdwardFound](https://avatars.discourse-cdn.com/v4/letter/e/4af34b/32.png) [@EdwardFound](https://boards.straightdope.com/u/EdwardFound)\ **Post date:** [June 23, 2023, 1:00am UTC](https://boards.straightdope.com/t/how-is-a-neutron-stars-maximum-mass-calculated/985895/8 "2023-06-23T01:00:19Z")
The article states that LIGO’s signal contains only information on the objects’ masses, so the assignment of BH vs NS would be based on the theoretical maximum mass for a NS. So if neutron stars could be significantly heavier than current estimates, the only hope of identifying a big NS would be from a LIGO event accompanied by a light signal. ---
**Author:** ![Whack-a-Mole](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whack-a-mole/32/141_2.png) [@Whack-a-Mole](https://boards.straightdope.com/u/Whack-a-Mole)\ **Post date:** [June 23, 2023, 8:58am UTC](https://boards.straightdope.com/t/how-is-a-neutron-stars-maximum-mass-calculated/985895/9 "2023-06-23T08:58:30Z")
> [@Chronos](#): > > There is speculation that you can have something called a “quark star” Or, more fun, a “strange star” (made out of strange quarks which, some speculate, could change any normal matter it touches into stranglets). ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [June 23, 2023, 2:50pm UTC](https://boards.straightdope.com/t/how-is-a-neutron-stars-maximum-mass-calculated/985895/10 "2023-06-23T14:50:08Z")
> [@EdwardFound](#): > > The article states that LIGO’s signal contains only information on the objects’ masses, so the assignment of BH vs NS would be based on the theoretical maximum mass for a NS. That’s the easy information, at least. But while black holes are very simple objects, completely described by known physics, neutron stars can stretch, squish, vibrate, splash, and otherwise do messy things that might in principle show up in the details of the signal. Of course, gravitational wave detectors in general have very low signal to noise ratios, so we probably couldn’t get good enough data to tell, unless the event were very close. Also, at least one of the NS-NS mergers LIGO detected was also detected as a gamma-ray burst. That’s a definitive indicator that at least one non-black-hole object was involved. The lack of a gamma signal could have many possible causes, though, so we can’t conclude much from all of the cases where there wasn’t one found.