# B Neutron stars and black holes

1. Dec 22, 2017

### Chronos

The difference between neuton star & black hole mass is one of the great questions in astrophysics. According to google, the most massive known neutron star [J0348-0432] weighs in at an impressive 2.0 Msun, whereas the least massive black hole [XTE J1650-500] tips the scales at 3.8 Msun. While this is not necessarily spectacular, it certainly is enough to arouse suspicion. Are gap mass degenerates just inexplicably rare within our observational stewardship, or, are we even more naïve than we suspect? Granted, achieving accurate mass measurements at interstellar distances is not always a trivial matter, but, this is akin to randomly turning up a thousand spades of dirt in your backyard only to find all worms revealed run either less than 2 grams or more than 3.8 grams in mass. It certainly appears to suggest either improbable luck, or your yard is inhabited by separate earthworm species.

Last edited: Dec 22, 2017
2. Dec 22, 2017

### Ken G

What doesn't make sense about that is that it usually doesn't matter to the mass if you get a neutron star or a black hole, the mass is set first, and then you get what you get. If there really is a gap from 2 to 3.8, it implies that the mass you end up with is controlled by the object that is created, rather than the other way around. I would find it much easier to believe that either the masses between 2 and 3.8 are hard to pin down, or that they simply aren't classified as either a neutron star or a black hole because it isn't known which to classify them as. If it is true that the mass is pretty well known, and there really is a gap in mass, then I agree that would be of great significance to the formation process of whatever these objects are. Perhaps the neutron star is capable of "bouncing out" any mass that would raise it just a bit above 2 solar masses, but if you really pile on about 4, then it cannot be bounced out. But all that would involve extremely complex physics including rotation, magnetic fields, and equations of state-- not just a treatment of gravity.

3. Dec 23, 2017

### Chronos

The issue is beyond a mere curiousity. In fact,t.one of the leading authorities on stellar mass black holes has already asserted evidence for a preferred mass range of.stellar mass black holes, as discussed in this paper; https://arxiv.org/abs/1006.2834,The Black Hole Mass Distribution in the Galaxy. Ozel also comments on the mass gap between black holes and neutron stars. A variety of methods have been developed to enhance the reliability of black hole mass estimates as discussed here; https://arxiv.org/abs/0902.2852,Determination of Black Hole Masses in Galactic Black Hole Binaries using Scaling of Spectral and Variability Characteristics.and as touched upon in this article https://www.theregister.co.uk/2008/04/01/smallest_black_hole_known_discovered/. For a discussion more specific to the mass gap issue, this may prove interesting; https://arxiv.org/abs/1110.1635,Missing Black Holes Unveil The Supernova Explosion Mechanism. We remain in interesting times.

Last edited: Dec 23, 2017
4. Dec 23, 2017

### Ken G

That's quite interesting, thank you!

5. Dec 23, 2017

### Ken G

General relativity is normally thought to imply that anything that creates an event horizon around itself will also collapse into a singularity. I personally don't know what theorems are needed for that conclusion, but I still don't see in the above any evidence that the mass of the remnant is determined by the equation of state of the remnant in the range 2 - 5 solar masses, that feedback is missing from the argument. Intermediate mass black holes are much more massive than that.

6. Dec 24, 2017

### Ken G

The interesting gap is between 2 and 5 solar masses, not 15 and 50,000, as the latter is expected from stellar mass issues. Also, there is not a direct connection between a mass gap and a density gap, as the latter is expected and the former is not.

7. Dec 25, 2017

### Chronos

Last edited: Dec 25, 2017
8. Dec 26, 2017

### Chronos

There is always uncertainty in data - especially astrophysical data. But strong outliers [like 5000-7500] must be taken seriously when uncertainty of the data is more tightly constrained than those of any assumptions underlying predictive models. The lack of prolific exceptions is less noteworthy than the existence of any confirmed exception..

Last edited by a moderator: Dec 29, 2017
9. Dec 28, 2017

### PAllen

This gap seems to have been bridged by the LIGO neutron star merger, which is believed by most subject matter experts to have produced a 2.7 solar mass BH within about 10 to 100 milliseconds after initial merger.

10. Dec 29, 2017

### Staff: Mentor

A few misconceptions/open questions that have appeared in this thread need to be cleared up:

This is not possible; there is not a continous series of stable (i.e., non-collapsing) states between any neutron star and any black hole. The reason is something called Buchdahl's Theorem, which says that no stable configuration of matter can have a radius smaller than 2.25M, where 2M would be the Schwarzschild radius of a black hole with the same mass. So there's no way for a stable object like a neutron star to be "just short" of being a black hole, because that would correspond to a stable configuration of matter having a radius of, say, 2.0001M--i.e., just a bit larger than a black hole of the same mass--and that is ruled out by Buchdahl's Theorem.

This is not correct. No locally measured speed will be faster than light, even inside the horizon. A coordinate speed in particular coordinates might be greater than $c$, but this has no physical meaning. And none of this has anything to do with whether a singularity is present or how long it takes an infalling observer to reach it.

It is, relative to an observer "hovering" at a constant altitude just above the horizon. Only local relative speeds are physically meaningful in a curved spacetime.

Because no compact body can exist with a radius smaller than 2.25M. See above.

The Einstein-Bohr debate is irrelevant, as is the uncertainty principle; we are talking about classical GR here, not QM. If you want to talk about how quantum gravity might affect possible black hole states, please start a new thread (and it should be either in the QM forum or, more likely, the Beyond the Standard Model forum, since there is no established theory of quantum gravity at present).

The Hawking-Penrose singularity theorems are the ones that establish this conclusion: a good brief statement of the conclusion is that the presence of a trapped surface implies geodesic incompleteness. The assumptions required are an energy condition (which one depends on what kind of geodesic incompleteness is being addressed--timelike or null) and a condition on the global structure of the spacetime (typically that there is a Cauchy surface with certain properties). The Wikipedia page gives a decent brief overview:

https://en.wikipedia.org/wiki/Penrose–Hawking_singularity_theorems

11. Dec 29, 2017

### Staff: Mentor

A number of posts relating to an unacceptable reference given by a particular member have been deleted. This thread is closed as the OP question, which was based on a simple misconception, has now been answered. If further discussion of the gap between known neutron star and black hole masses is desired, please start a new thread.