# Talk:Neutron star

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## velocity units

The article makes several references to acceleration, escape velocity and speed of light using km/s. The speed of light is just under 300,000,000 m/s. It looks like some of the units are incorrectly marked km/s. From the text: ..."and would do so at around 2000 kilometers per second." Sherumgroup (talk) 16:42, 20 August 2014 (UTC)

No it isn't. 2000 km/s is just 0.007c. Also, if you do a rough recalculation you'll see the reference is correct. 1 solar mass (2e30 kg) in a 14 km sphere gives you a local g of 1.334e20 N/kg from Newton's law of universal gravitation. Given that the kinetic energy density (Ek/m) of an object dropped from a height is the g times distance (work = force × distance, divide by mass), you can calculate the velocity by solving the formula for kinetic energy, Ek/m = ½v2, for v. This gives v = √2gh, and inserting g = 1.334e20 N/kg and h = 1 m gives you 2.333e6 m/s, or about 2000 km/s, just as in the source. Objects move up to ca. 70 km/s even in the Solar System, so this is just two orders of magnitude higher. --vuo (talk) 19:08, 20 August 2014 (UTC)

## Mass range in lede

The range of masses in the lede is confusing and probably wrong. It states compact stars of less than 1.44 solar masses are white dwarfs, yet there are neutron stars in the literature with well constrained masses less than that, e.g. the companion to PSR J1756-2251 (1.230+/-0.007 MS), PSR J0737−3039 B (1.25 MS), and PSR J1906+0746 (also 1.25 MS). Then it states that compact stars between this limit and 3 MS "should" be neutron stars, but later that the maximum mass of a neutron star is about 2 MS. That is contradictory as to the state of objects with masses between 2 MS and 3 MS. Qemist (talk) 02:14, 10 August 2014 (UTC)

I didn't write the article but added some corrections, probably not all the corrections that would be desirable. 2 SM is the maximum observed mass of neutron stars based on a significant data base. The way I read it is 3 SM neutron stars might be possible based on the TOV equation. I think if the article says "neutron stars are" than what should be presented is observational data and not theoretical data, no disrespect to the theorists. I'm not sure the TOV equations allow up to 3 SM neutron stars (maybe the article is wrong on this) but if TOV equations predict this its OK to state it.
Please indent your responses appropriately. I agree observational data should take precedence over theoretical predictions and that the article should clearly distinguish between them. At the moment the article presents too much theory as fact. At the moment any object that is too small and dense to be a white dwarf and isn't a black hole is called a "neutron star". Their composition is unobserved and the idea that they are composed of neutrons is based on theory. There are competing theories that suggest they are composed at least partly of some sort of non-baryonic "exotic matter". The fact that no neutron stars with masses constrained to be strictly greater than 2MS have been observed does not mean that they don't exist; it may be they just haven't been sufficiently well observed. There are suggestions that some "black-widow" pulsars have higher masses, e.g. PSR J1311–3430 and PSR B1957+20. Qemist (talk) 11:42, 10 August 2014 (UTC)
Don't be too harsh on this good article, its a field still in flux. You make a profound point about the composition of "neutron" stars. (My personal thoughts are neutrons are probably about right.) Thanks for the info on these 2 stars .... the large mass is disturbing. I will take the safe cowardly route and for now modify the max observed mass of neutron stars to "about 2 SM". There is good reason to be skeptical a 2.4 SM compact star exists but if a 2.4 SM compact star existed it should be able to have some relativistic matter containment. Then it might be something between a neutron star and a black hole, neither a neutron star nor quite a conventional black hole, and it probably shouldn't be called a neutron star. Maybe the correct max mass for neutron stars is close to 2.0 SM. Food for thought. 72.69.11.171 (talk) 13:07, 10 August 2014 (UTC)

The figure of 2.4 SM is incorrect. Do you have a source for this other than the Black Widow Pulsar Wiki article? From this source the lower mass limit for this neutron star is about 1.6 SM: http://arxiv.org/abs/1009.5427 See the Wiki articles on PSR_J1614-2230 AND PSR J0348+0432. 72.69.11.171 (talk) 22:28, 13 August 2014 (UTC)

Lets consider for now 2$M_\odot$ is the max for a neutron star and 5$M_\odot$ the min for a black hole. A 5$M_\odot$ 22.5-km radius ultra-relativistic star has about the same gravitational acceleration and core pressure of a 2$M_\odot$ 13-km neutron star, yet a 5$M_\odot$ 22.5-km ultra-relativistic star theoretically contains light and a 2$M_\odot$ 13-km neutron star does not. (Note 25-km is 1.5 times the Schwarzchild radius) For an ultra-relativistic star gravitational acceleration and core pressure decrease as size increases. It does not collapse. 72.69.11.171 (talk) 14:32, 14 August 2014 (UTC)

Radius? What is radius in the case of a potential singularity? Do you mean circumference divided by 2π? (I know it's called Schwarzchild radius that doesn't mean there is an actual radius involved.) In any case, "contain light" is an interesting term, also. If it's larger than 1.0 times the Schwarzchild radius, it's not necessarily "black"; photons from the surface can escape. If within 1.5 rs (and the field equations agree with the Schwarzchild solution outside the body, which is not a foregone conclusion), then there are closed photon orbits. — Arthur Rubin (talk) 00:56, 15 August 2014 (UTC)
I'm saying there is no point singularity but instead a star composed of ultra-relativistic material and photons of radius 1.5 rs. This star acts radically different (size and pressure wise) from other stars in that its radius is proportional to its mass, unlike a neutron or conventional star. The basic equation of state for quark matter or photons in this star is the pressure P = (pc^2)/3, where p is the energy density. The supporting energy (viral energy) of material in this star = ∫PdV = (mc^2)/3, meaning a whopping 1/3 of the mass energy of this quark/photon mix is used just to oppose the force of gravity, but its still only 1/3 of mc^^2 and not 1.0 or 0.67 or even 0.5 of mc^^2. Ultra-relativistic material or photons can't escape the surface of a 1.5 rs star. 72.69.11.171 (talk) 16:37, 15 August 2014 (UTC)
That's just wrong. Photons can escape the surface of a R;; = 1.5 rs star. I'm willing to believe that there are situations in which light (null geodesics) cannot escape but a particle (time-like curve) can escape, but it's not as simple as R = 1.5 rs. — Arthur Rubin (talk) 16:07, 16 August 2014 (UTC)
Well, somebody is wrong. Infalling material can have mc^^2 available but not contained material. Do you think the thermal energy (pressure creation ability, the ability to do work) of photons or ultra-relativistic material is (mc^2) or (mc^2)/3 ? I also used to think the pressure of light was pc^^2 when I guessed at it 3 years ago. A better way of explaining it is that ultra-relativistic material of mass m only has (mc^^2)/3 available to push itself out of a star. BTW the exact radius I came up with for this star is 1.66 rs and not 1.5 which some people may find confusing. I should probably use 1.66 instead of the 1.5 approximation. People might be confused by the 1.5 figure because that is coincidently the accepted radius for orbital light for a black hole. If you check into it a black hole can contain some types of light to within 3X the Schwarzchild radius.
A 1.66 rs star would explain the huge amounts ejected from black holes.
I was at a NYU university forum on black holes 2 months ago and although a 1.5 rs star was not accepted, anyone expressing an opinion (many physics doctorates were there) said a 1.5 star would contain light, but not as well as a 1.0 rs star or point singularity. Note they teach a point singularity is reality and a star smaller than 2.0 rs is impossible based on the TOV equation, but I think the TOV equation is wrong because it predicts collapse of a 0.7 SM neutron star and TOV does not even acknowledge a back pressure of (pc^^2)/3. Note a 1.66 rs star doesn't even contain orbital light; light it contains would just about have to hit it bulls eye. But it would bend nearby light similar to a point singularity. Light is easier to contain than some might think. A 2 SM neutron star comes dang close and a hypothetical 3 SM neutron star would contain light. Intelligent people would logically but incorrectly therefore conclude that as some mass is added to a 2 SM neutron star it would collapse directly into a black hole.
Schwarzchild proposed a point singularity that mathematically contained light. That doesn't mean a point singularity is reality. A small enough finite sized star of enough mass would also contain light. 72.69.11.171 (talk)BG — Preceding undated comment added 17:52, 16 August 2014 (UTC)
Please remember that the purpose of this page is to discuss improvements to the article, not to have a general discussion of the topic. Nothing you heard at a seminar (let alone your own opinions), could be a suitable verifiable basis for inclusion in the article. Qemist (talk) 04:17, 17 August 2014 (UTC)
OK you are right this has probably diverged too much. But neutron stars being limited to about 2.01 SM is relevant. Theories on why this is so should be added to the article if those theories are sourced. I'm sure you agree why black holes start at 5 SM and not directly from a >2 SM neutron star is relevant, and understanding this will require understanding both >2 SM neutron stars and 5 SM black holes 72.69.11.171 (talk) 20:30, 17 August 2014 (UTC)BG

BTW, there is an interesting formula about the radius and radiated energy from infalling matter into a neutron or compact star: Accretion energy conversion efficiency = (Schwarzchild radius)/(2R) ..... where R is the radius of the star. (see: http://www3.mpifr-bonn.mpg.de/staff/mmassi/lezione2WEdd.pdf ) If a black hole is a point singularity its image should be different than that of a neutron star. 72.69.11.171 (talk) 19:07, 1 October 2014 (UTC)BG

## Lede clutter

This article is suffering from a rather serious case of ledeclutter, at five paragraphs with comparisons to the sun, Manhattan, atomic nuclei, a 747, sand, a matchbook, and rock, as well as a lot of specific information (Neutron stars have overall densities of 3.7×1017 to 5.9×1017 kg/m3 (2.6×1014 to 4.1×1014 times the density of the Sun) etc. I propose consolidating the important information into a nice three or four paragraph summary and moving details to the body. Comments? A(Ch) 08:48, 13 January 2015 (UTC)