When will a neutron star collapse to a black hole?

April 7, 2016, Goethe University Frankfurt
Simulation of gravitational waves from a collapsing Neutron star. Credit: Luciano Rezzolla

Neutron stars are the most extreme and fascinating objects known to exist in our universe: Such a star has a mass that is up to twice that of the sun but a radius of only a dozen kilometres: hence it has an enormous density, thousands of billions of times that of the densest element on Earth. An important property of neutron stars, distinguishing them from normal stars, is that their mass cannot grow without bound. Indeed, if a nonrotating star increases its mass, also its density will increase. Normally this will lead to a new equilibrium and the star can live stably in this state for thousands of years. This process, however, cannot repeat indefinitely and the accreting star will reach a mass above which no physical pressure will prevent it from collapsing to a black hole. The critical mass when this happens is called the "maximum mass" and represents an upper limit to the mass that a nonrotating neutron star can be.

However, once the maximum mass is reached, the star also has an alternative to the collapse: it can rotate. A rotating star, in fact, can support a mass larger than if it was nonrotating, simply because the additional centrifugal force can help balance the gravitational force. Also in this case, however, the star cannot be arbitrarily massive because an increase in mass must be accompanied by an increase in rotation and there is a limit to how fast a star can rotate before breaking apart. Hence, for any neutron star there is an absolute maximum mass and is given by the largest mass of the fastest-spinning model.

Determining this value from first principles is difficult because it depends on the equation of state of the matter composing the star and this is still essentially unknown. Because of this, the determination of the maximum rotating mass of a neutron star has been an unsolved problem for decades. This has changed with a recent work published on Monthly Notices of the Royal Astronomical Society, where it has been found that it is indeed possible to predict the maximum mass a rapidly rotating neutron star can attain by simply considering what is maximum mass of corresponding the nonrotating configuration.

"It is quite remarkable that a system as complex as a rotating neutron star can be described by such a simple relation", declares Prof. Luciano Rezzolla, one of the authors of the publication and Chair of Theoretical Astrophysics at the Goethe University in Frankfurt. "Surprisingly, we now know that even the fastest rotation can at most increase the maximum mass of 20% at most", remarks Rezzolla.

Although a very large number of stellar models have been computed to obtain this result, what was essential in this discovery was to look at this data in proper way. More specifically, it was necessary to realise that if represented with a proper normalisation, the data behaves in a universal manner, that is, in a way that is essentially independent of the equation of state.

"This result has always been in front of our eyes, but we needed to look at it from the right perspective to actually see it", says Cosima Breu, a Master student at the University of Frankfurt, who has performed the analysis of the data during her Bachelor thesis.

The universal behaviour found for the maximum mass is part of a larger class of universal relations found recently for . Within this context, Breu and Rezzolla have also proposed an improved way to express the moment of inertia of these rotating stars in terms of their compactness. Once observations of the moment of inertia will be possible through the measurement of binary pulsars, the new method will allow us to measure the stellar radius with a precision of 10% or less.

This simple but powerful result opens the prospects for more universal relations to be found in rotating stars. "We hope to find more equally exciting results when studying the largely unexplored grounds of differentially rotating neutron stars", concludes Rezzolla.

Explore further: How neutron stars can break up clusters

More information: Cosima Breu et al. Maximum mass, moment of inertia and compactness of relativistic stars, Monthly Notices of the Royal Astronomical Society (2016). DOI: 10.1093/mnras/stw575

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Jeffhans1
5 / 5 (1) Apr 07, 2016
In my mind, I always picture binary neutron stars spun up in opposite directions. I'm sure that almost never happens but the universe is a huge place.
Solon
2 / 5 (8) Apr 07, 2016
When will one theorised entity collapse to form another theorised entity? Hmm, how about "in your dreams, buddy"?
Da Schneib
4.3 / 5 (6) Apr 07, 2016
The independence from the equation of state is an important discovery for these important objects, which are the strong limit for how massive and dense an object can be, and must spin, without collapsing into a black hole.
tblakely1357
5 / 5 (1) Apr 08, 2016
"The critical mass when this happens is called the "maximum mass" and represents an upper limit to the mass that a nonrotating neutron star can be."

So, anyone know what the tensile properties of Neutronium are?
Da Schneib
4 / 5 (4) Apr 08, 2016
So, anyone know what the tensile properties of Neutronium are?
I wouldn't call it "tensile," because that's a term used of matter made from atoms, not constituents of nuclei, but probably far beyond anything even remotely like tensile strength in normal matter considering the color force interactions that must be taking place. This is the force that holds the nucleus together; it's far stronger than electromagnetism. They're electrically neutral being made almost entirely of neutral neutrons so I wouldn't expect to see any contribution from electromagnetic forces. ("Almost" because they're theorized to have a very, very thin (like inches- centimeters if you insist) crust of normal matter on their outsides.)

Then there's the gravity. And the gravity is strong enough that the neutron star is only the size of Manhattan, but it weighs as much as our Sun.
Da Schneib
4.2 / 5 (5) Apr 08, 2016
Nope, I was wrong- according to the Wikipedia article the strong force is negligible inside a neutron star. I'm not sure I understand quite why, and I'd like to hear an explanation if one of our resident astrophysicists would chime in. Seems to me a bunch of neutrons would swap quarks and gluons as much as a bunch of neutrons and protons would, and that's how the strong force works

Anyway, that means it's all gravity. How fast it can spin without coming apart is completely dependent upon the strength of its gravity field.
Starchaser
5 / 5 (1) Apr 08, 2016
The article states that the upper mass limit for a neutron star (the TOV limit) is less than two solar mass - although the equation of state, and therefore the limit, is still undetermined, the limit is usually held to be between two and three solar mass.
Protoplasmix
5 / 5 (3) Apr 08, 2016
according to the Wikipedia article the strong force is negligible inside a neutron star. I'm not sure I understand quite why, and I'd like to hear an explanation if one of our resident astrophysicists would chime in
What happens to the strength of the strong force when you try pulling two quarks apart? What happens to the strength when you push two quarks together? Am guessing gravitational confinement makes the strong force kind of a moot point (not an astrophysicist, just a resident chimer inner, so there's 2 out of 3 anyway).
cantdrive85
1 / 5 (3) Apr 10, 2016
When will a neutron star collapse to a black hole?

That's obviously a rhetorical question considering the fact that neither of these objects exist in reality. In a similar light, how many unicorns horns are not twisted. Which rainbow is the leprechaun's pot o' gold beneath? How much of it have they spent? When will astrophysicists stop relying on pseudoscientific mumbo jumbo? This will likely never happen being it would end the gravy train of "other people's money" that they so tirelessly rely upon. Silly me, the astrophysicists have found the leprechauns pot o' gold, it's in the form of grants and tax dollars that pay their salaries. Sadly, it is very real money they are paid. Luckily for them real results are not necessary for them to get paid. If it were, they'd certainly be little more than paupers begging for crumbs.
Speaking of the absurdity of the neutron star;
https://www.youtu...moFmBnN8
Protoplasmix
5 / 5 (7) Apr 10, 2016
Silly me
Very.

Your guy says stuff like, "That's 24,000 rpm! Just like a dentist's drill. Can you imagine what the torque would be? The lighthouse model is falsified." Why would you think the astrophysicists have to imagine something like torque? – they just do the calculations and show the maths. And what does torque have to do with it anyway? Where're the dude's calculations??

Your guy says a pulsar is actually two stars connected by a "plasma bridge" and one star is somehow "driven" to high voltage, and it somehow discharges through the plasma bridge where the other (undriven?) star somehow absorbs it, and the entire bridge flashes in an instant, and it's just like an old-fashioned strobe light, and who cares how many AU long the bridge is because we don't need to calculate anything when electricity explains everything so easily.

That's beyond silly.
cantdrive85
1 / 5 (4) Apr 11, 2016
Why would you think the astrophysicists have to imagine something like torque?

Yeah you're right, several solar masses spinning faster than a Dremmel experience any centrifugal forces whatsoever. Especially when you have gravity the weakest force in nature.
"plasma bridge"

I'm sure I've mentioned Birkeland currents before, these are ubiquitous in plasmas. And how would a bridge form between them? Right. A current.
https://en.m.wiki...periment
who cares how many AU long the bridge is

Birkeland currents can be many light years long.
http://www.plasma...currents

Silly is a 25k(or more) RPM star point right at the center of the Universe, the Earth.
Protoplasmix
5 / 5 (3) Apr 11, 2016
Yeah you're right, several solar masses spinning faster than a Dremmel experience any centrifugal forces whatsoever.
Right, why did your guy mention torque when he should've called it centrifugal force?
Especially when you have gravity the weakest force in nature.
Have you calculated the gravitational acceleration near the surface of a neutron star? If you were to drop a small pebble from a height of 1 meter above the surface, what would its velocity be when it hit the surface, and how long would it take?
Birkeland currents can be many light years long.
Even if that's true, how does the current propagate the length of the "plasma bridge" in a millisecond? Even if the bridge were only 1 AU in length, the "stroboscopic flash of light" would be 8 minutes in duration. Your guy's binary system plasma bridge strobe light model is not at all realistic.
Protoplasmix
5 / 5 (3) Apr 11, 2016
Birkeland currents can be many light years long.
Even if that's true, how does the current propagate the length of the "plasma bridge" in a millisecond? Even if the bridge were only 1 AU in length, the "stroboscopic flash of light" would be 8 minutes in duration.
Late edit, okay, if it's an electric circuit it could have a short-duration flash, but how exactly is one star "driven" to high voltage while the other isn't, and where's the return path for the current?
antialias_physorg
5 / 5 (3) Apr 11, 2016
Neutron star with 12km radius at 24k rpm gives a centrifugal force at the surface of 7.5 x 10^10 m/s*s

Typical surface gravity of a neutron star: about one to two orders of magnitude higher (1-7 x 10^12 m/s*s)

No tensile strength required whatsoever to keep these critters intact.
cantdrive85
1 / 5 (2) Apr 11, 2016
Neutron star with 12km radius at 24k rpm gives a centrifugal force at the surface of 7.5 x 10^10 m/s*s

Typical surface gravity of a neutron star: about one to two orders of magnitude higher (1-7 x 10^12 m/s*s)

No tensile strength required whatsoever to keep these critters intact.

Well I guess the hypothetical mathematics works. What would be swell is an experimental demonstration of this abomination of physics.
dtxx
5 / 5 (1) Apr 11, 2016
Neutron star with 12km radius at 24k rpm gives a centrifugal force at the surface of 7.5 x 10^10 m/s*s

Typical surface gravity of a neutron star: about one to two orders of magnitude higher (1-7 x 10^12 m/s*s)

No tensile strength required whatsoever to keep these critters intact.

Well I guess the hypothetical mathematics works. What would be swell is an experimental demonstration of this abomination of physics.


So your model is based on measurements taken at the systems you propose? Or is it based on your imagination, i.e., the drill example which you gave? Or your guess that "mathematics works?"
cantdrive85
1 / 5 (2) Apr 11, 2016
While the "(hypothetical)mathematics works" for some aspects of this nonsense. However, it in no way conceivable can explain the "glitches" observed on Vela as he discussed. Please do explain how something spinning at 24k RPM can suddenly drop to 21k, then back to 24k, and variably back and forth. Good luck.
So your model is based on measurements taken at the systems you propose?

No, but it is based upon experiments which were able to a accurately reproduce 17 characteristics of pulsars. If the mainstream could reproduce two they'd accept sigma 7 or whatever ridiculous chart they use to convince themselves they got it right.
cantdrive85
1 / 5 (2) Apr 11, 2016
how exactly is one star "driven" to high voltage while the other isn't

He explained that in the video. If it has a larger surface area it will have a larger capacitance. And these circuits are being driven by the interstellar Birkeland currents that power them and with which they are immersed.
where's the return path for the current?

First, Birkeland currents are coaxial.
http://www.ptep-o...1-13.PDF
Bee, the mainstream already acknowledges "mass exchange". Of course this is matter, ionized matter-plasma-,which is flowing, are Birkeland currents transporting energy and mass between the stars. Very close stars such as this are likely millisecond types. These are likely newly born stars that are so close to their binary, those bridges being analogous of an umbilical. The explosive birth of the binary creates the nebula.
antialias_physorg
5 / 5 (2) Apr 12, 2016
Well I guess the hypothetical mathematics works.

Which you could have figured out yourself in less time than it took you to write your inane comment. But I guess physics isn't your strong suit.

(And what exactly is 'hypothetical' mathematics? this is the physics of it - plain and simple.)
Captain Stumpy
3 / 5 (2) Apr 13, 2016
(And what exactly is 'hypothetical' mathematics? this is the physics of it - plain and simple.)
@AA_P
it is a buzzword used by cults to denote derision of a non-believer by indicating the noncompliance of those who don't accept the cult tenets

kinda like the repetitious mantra beats the lie into the head of the cult member (see any cd post about Astro's not knowing plasma physics, like here: http://phys.org/n...ars.html ) ...the buzzword is used as a defensive manipulation of oneself in order to cling to a belief without having to actually provide evidence

they use buzzwords, also in pseudoscience (See any jvk post), as a means to establish the special jargon which indicates "superior intellect" by the cult because of the inability to comprehend actual technical jargon - essentially they think that using buzzwords makes them sound smarter

until someone educated points out the flaw, that is
so repeat ad nauseum
RealityCheck
2.3 / 5 (3) Apr 13, 2016
Hi antialias_physorg. :)
Neutron star with 12km radius at 24k rpm gives a centrifugal force at the surface of 7.5 x 10^10 m/s*s

Typical surface gravity of a neutron star: about one to two orders of magnitude higher (1-7 x 10^12 m/s*s)
Hmmm, considering that even Earth's mild centripetal-centrifugal force 'balances' produce an oblate spheroidal type shape due to polar regions being pressed down more than equatorial regions, then how much more severely 'spheroidal' would a Neutron Star be as a result of its own 'balances' between centripetal-centrifugal forces?

Would it look like a disc of solid matter? Would it behave like a Homopolar Generator 'circuit' encompassing any accreting/inflowing/swirling discs/streams of matter/plasma/energy or whatever you like to call it?

Has anyone mathematically described actual variations of Neutron Star centripetal-centrifugal forces "balances" at various "spin rates" and consequential Neutron Star shapes for range of rate/balance?

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