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BigDon
2015-Jul-14, 06:52 PM
Not worth putting in the other forum.

What is the diameter of a solar mass neutron star? And the event horizon diameter of an equally massed black hole? (Is that even possible?)

Thank you.

WaxRubiks
2015-Jul-14, 07:06 PM
neutron stars are about 25km(14miles) in diameter and have a mass 1-3 times that of the Sun,



a black hole the mass of the Sun would have a diameter of 5.9km


well summut like that.......:doh:

Swift
2015-Jul-14, 07:30 PM
Not worth putting in the other forum.

A lack of order bothers me more than a lack of worthiness (not that I think this an unworthy question). Moved from OTB to Q&A.

Ken G
2015-Jul-14, 08:53 PM
What is the diameter of a solar mass neutron star?There's really no such thing as a solar mass neutron star, because you can't make a neutron star unless the mass is above about 1.4 solar. So typically neutron stars are about 2 solar, and that would make their radius about 12 km (so says Wiki-- the exact models are not well known).

And the event horizon diameter of an equally massed black hole? (Is that even possible?)
It's probably not very possible, because generally you need even more mass than a neutron star to make a black hole. But there is a simple formula for the Schwarzschild radius given the mass, which comes out 3 km for a solar mass. If we take the same 2 solar masses as the neutron star, that doubles to 6 km, so basically a neutron star is about twice the size of a similar-mass black hole. Thus we can say that the neutron star is "barely hanging on" against gravity.

antoniseb
2015-Jul-14, 09:06 PM
There's really no such thing as a solar mass neutron star, because you can't make a neutron star unless the mass is above about 1.4 solar. So typically neutron stars are about 2 solar, and that would make their radius about 12 km (so says Wiki-- the exact models are not well known).
It's probably not very possible, because generally you need even more mass than a neutron star to make a black hole. But there is a simple formula for the Schwarzschild radius given the mass, which comes out 3 km for a solar mass. If we take the same 2 solar masses as the neutron star, that doubles to 6 km, so basically a neutron star is about twice the size of a similar-mass black hole. Thus we can say that the neutron star is "barely hanging on" against gravity.
Actually, the range in masses of neutron stars in binary systems is from 0.96 to 2.04 solar masses (IIRC). That 1.4 solar masses you are thinking about is the mass of a white dwarf before it becomes a Type Ia supernova, which does not leave a neutron star. Neutron star formation can be messy, and have less than a solar mass in the end product.

As to a one solar mass black hole, we don't know of a natural process in that could result in one forming, but that doesn't prevent one from being formed, or us from knowing the Schwarzschild radius of it.

WaxRubiks
2015-Jul-15, 12:00 AM
Actually, the range in masses of neutron stars in binary systems is from 0.96 to 2.04 solar masses (IIRC). That 1.4 solar masses you are thinking about is the mass of a white dwarf before it becomes a Type Ia supernova, which does not leave a neutron star. Neutron star formation can be messy, and have less than a solar mass in the end product.

As to a one solar mass black hole, we don't know of a natural process in that could result in one forming, but that doesn't prevent one from being formed, or us from knowing the Schwarzschild radius of it.

well there is one natural process, and that is simply evaporation down to one solar mass, from a larger black hole.

And there is the primordial black hole idea.

ShinAce
2015-Jul-15, 02:16 AM
I'll echo what Ken said.

A solar mass neutron star would be an oddity. Those should be white dwarves. They are expected above 1.39 solar masses (which is also the Chandrasekhar limit).

At 2 solar masses, you're looking at just under 15 miles across (or 7 miles radius) with a Schwarzchild radius just under 4 miles. So yes, a neutron star is ridiculously close to an equivalent black hole.

Ken G
2015-Jul-15, 05:42 AM
It's an interesting issue, for example figure 2 in http://arxiv.org/pdf/1011.4291v1.pdf shows that a solar-mass neutron star would be an oddity. However, some of the stars in this distribution could have experienced mass gain after formation, and none of them are likely to have lost much mass, so the lower limits on the distributions could be more characteristic of their original formation. So antoniseb has a point. The 1.4 solar mass limit I cited is still somewhat relevant to any supernova, not just type Ia, but that number assumes the composition is mostly carbon, which is indeed strictly true of type Ia situations. The Chandrasekhar mass depends on the composition, so if you have a lot of iron, as you'd expect for a core collapse, the Chandrasekhar mass could be way less, maybe even as low as 0.5 solar masses. That we don't see such low masses suggests that the neutron star may take on more mass than its absolute limit, but certainly the number 1.4 solar masses that applies to carbon cores is at best characteristic of neutron stars, it's not a lower limit. So I appreciate the support, but I do stand corrected-- we can indeed entertain the notion of a 1 solar mass neutron star, and probably its radius is something like 10 km.

Shaula
2015-Jul-15, 06:15 AM
http://www.stellarcollapse.org/sites/default/files/masses.pdf gives a reasonable number of neutron star masses. There are usually large uncertainties, and most do form at around 1.4 solar masses but there are a fair few that have error bars constraining them to be far smaller than that. Notably SMC X-1 is fairly tightly constrained to be low mass.

There are some published articles claiming that the minimum theoretical stable mass for a neutron star is about 0.1 Ms (see: http://www.cenbg.in2p3.fr/heberge/EcoleJoliotCurie/coursannee/transparents/Lattimer-prakash%20NS.pdf - I have not had time to chase down whether this has been challenged). More practically they say that for realistic formation mechanisms proto-neutron stars smaller than 1 Ms are unstable, leading to a lower bound similar to the one Antoniseb gives.

On page 4 of the Latimer-Prakash paper it also shows the radii predicted for each equations of state and points to another paper that gives the range as 8-16km for a one solar mass object. More details on the approaches taken to calculating these values are given in http://iopscience.iop.org/0004-637X/550/1/426/pdf/0004-637X_550_1_426.pdf but it seems like the 8km limit is for a quark star while 16km is a based on a neutron/pion soup.

Figure 3 of the Science article (first reference) just about sums the problem up - a neutron star is made up of (from outside in) an atmosphere (probably iron and other 'normal' atoms), envelope (similar composition), a crust (probably neutron superfluid plus some atoms), outer core (probably neutron superfluid) and then inner core (our state of knowledge is summed up by a ?)

BigDon
2015-Jul-15, 06:51 PM
Thank you everybody for your replies.

Sorry for the late get back.

Shaula, thank you for your replies, but now I have other questions.

In the context of neutron stars:

What is the definition of "unstable"? Rapid radiation of mass into the surround medium or a catastrophic unbinding?

What would be the characteristics of an iron atmosphere of a neutron star? I can't resolve that in my mind's eye. I keep thinking of a solid layer of iron, that would be considered gaseous relative to what it was resting on.

Shaula
2015-Jul-15, 09:17 PM
Unstable neutron stars: In this case it means an explosion. The neutron star binding energy is strongly dependent on its mass. If it reaches the point where it is more energetically favourable for the neutron star to turn into a cloud of unbound iron nuclei then the models imply it will. I have only skimmed the relevant paper but it seems to imply that once you get to very small masses the radius of the neutron star actually increases. At some point the binding energy of the system is smaller than the amount of energy you'd get from converting the neutron star into a cloud of iron and boom!

Unstable proto-neutron stars: Sorry, have not had time to read the papers referenced. I think it has to do with the fact that proto-neutron stars are lepton rich and if there is more energy trapped in these particles than the proto-neutron star's binding energy the proto-neutron star can be blown apart by the rapid early lepton release cooling. Normal neutron stars are tightly enough bound to survive this phase.

The neutron star's 'atmosphere' is a mix, from what I understand. A thin layer of solid, mostly iron. Then a layer consisting of a mixture of iron and carbon which may be fluid in young pulsars and finally some hydrogen/helium mix (mostly from material falling onto the neutron star's surface). The gaseous/plasma part of the atmosphere is only a few micrometres thick. Bear in mind I am going on memory for this one - and it has been a while. Happy to be corrected if anyone has any better information.

BigDon
2015-Jul-15, 09:29 PM
Unstable neutron stars: In this case it means an explosion. The neutron star binding energy is strongly dependent on its mass. If it reaches the point where it is more energetically favourable for the neutron star to turn into a cloud of unbound iron nuclei then the models imply it will. I have only skimmed the relevant paper but it seems to imply that once you get to very small masses the radius of the neutron star actually increases. At some point the binding energy of the system is smaller than the amount of energy you'd get from converting the neutron star into a cloud of iron and boom!

Unstable proto-neutron stars: Sorry, have not had time to read the papers referenced. I think it has to do with the fact that proto-neutron stars are lepton rich and if there is more energy trapped in these particles than the proto-neutron star's binding energy the proto-neutron star can be blown apart by the rapid early lepton release cooling. Normal neutron stars are tightly enough bound to survive this phase.

The neutron star's 'atmosphere' is a mix, from what I understand. A thin layer of solid, mostly iron. Then a layer consisting of a mixture of iron and carbon which may be fluid in young pulsars and finally some hydrogen/helium mix (mostly from material falling onto the neutron star's surface). The gaseous/plasma part of the atmosphere is only a few micrometres thick. Bear in mind I am going on memory for this one - and it has been a while. Happy to be corrected if anyone has any better information.

Working from memory myself, is that similar to a core collapse supernova when things get dense enough to actually trap neutrinos and it's their energy added to the mix that releases all that near god-like energy?

Or is that a mishmash of old theories and word salad?

Ken G
2015-Jul-16, 03:35 AM
Working from memory myself, is that similar to a core collapse supernova when things get dense enough to actually trap neutrinos and it's their energy added to the mix that releases all that near god-like energy?It actually sounds more like an analogy with type Ia supernovae, because there the explosion energy is nuclear, and nothing is left behind. A core collapse gets its energy from gravity instead, so must leave behind the object that contributed all the gravitational energy.

Shaula
2015-Jul-16, 04:15 AM
Working from memory myself, is that similar to a core collapse supernova when things get dense enough to actually trap neutrinos and it's their energy added to the mix that releases all that near god-like energy?
I'd say there is definitely a similarity there - the leptons are created or freed during the state change from atoms to degenerate neutron matter and essentially it is a form of trapping that stops them escaping for little energy cost. I guess the real difference is that rather than just drive off the material these leptons disrupt it more fundamentally, interrupting a state change. I have no idea what happens to the stellar remnant, in detail. I am relying on what the references I gave said. Definitely a topic I'd like to add to my reading list though, thanks for making me aware of it with your question!

trinitree88
2015-Jul-19, 03:13 PM
I'd say there is definitely a similarity there - the leptons are created or freed during the state change from atoms to degenerate neutron matter and essentially it is a form of trapping that stops them escaping for little energy cost. I guess the real difference is that rather than just drive off the material these leptons disrupt it more fundamentally, interrupting a state change. I have no idea what happens to the stellar remnant, in detail. I am relying on what the references I gave said. Definitely a topic I'd like to add to my reading list though, thanks for making me aware of it with your question!

The stellar remnant erupts into a prolate spheroid ...a little bit football shaped. Arguments from dynamical considerations, in that the collapsing core should conserve angular momentum, and spin up, producing high equatorial velocity, and hence a lower required escape velocity, led theorists to believe that the ejecta would be spherical with a touch of oblateness. Nothing of the kind. Radio imagery of supernova remnants conducted in the late 80's @ the Molonglo Observatory Synthesis Telescope, Epping, N.S.W. by R. N. Manchester , M.J.Kestevan, showed that the remnants were barrel-shaped, with radial symmetry. That means the magnitude will vary some with viewing angle.
In addition, the floods of neutrinos occur in the neutrinosphere along with magnetic fields of 10 11 Gauss - 1013 Gauss @ the nascent pulsar's poles. Since they only interact via the weak interaction, a parity effect is also present in the forward scattering. The pulsar is ejected and the remnant recoils. Wrote a short paper on it in 1986, and gave a talk @ Vassar at the AAPT 1992 Meeting " Parity, Pulsars and Supernova Remnants". The pulsar should always be ejected from the same pole, somewhat akin to Wu, Ambler cobalt 60 beta decays...though there it was asymmetrical. pete