Neutron Star Properties: Density, Pressure, and Acoustical Velocity

[Orion1]

Neutron Stars:

For neutron stars, pressure is an elastic property, density is an inertial property.

$$\rho_n = 2.294*10^{17} kg*m^{-3}$$ - Neutronium Density

Radial solution for spherically symmetric 1 solar mass pure Neutronium Neutron Star:
$$r_n = \sqrt[3]{\frac{3M_\odot}{4 \pi \rho_n}}$$

Neutron Star Gravitational Pressure:
$$P_g = \frac{3GM_\odot^2}{16 \pi r_n^4}$$

$$v_s = \sqrt{ \frac{P_g}{\rho_n}}$$ - acoustical velocity

Acoustical velocity solution for spherically symmetric 1 solar mass pure Neutronium Neutron Star:
$$v_s = \sqrt{ \frac{3GM_\odot^2}{16 \pi \rho_n r_n^4}} = \frac{M_\odot}{4 r_n^2} \sqrt{\frac{3G}{\pi \rho_n}}$$

$$v_s = \sqrt{G} \sqrt[3]{ \frac{M_\odot}{4}} \sqrt[6]{ \frac{ \pi \rho_n}{3}}$$

Based upon the Orion1 equation, what is the velocity of sound through a pure Neutronium Neutron Star?

 

[meteor]

can you define what's a pure neutronium neutron star? Neutron stars do have an iron crust surrounding the neutronium

 

[Orion1]

Neutronium Nexus...



The definition of 'pure Neutronium' as defined by the equations above describes a hypothetical 1 solar mass sphere composed of incompressible 'solid' neutrons. No description of iron crust or superconducting protons or hyperon cores.

However, conventional neutron stars are not described as a Neutronium 'solid', but as a Neutronium 'fluid'. And this medium is also compressible with an increasing pressure and density as the measured radial location approaches the core.

The soluton above is an average acoustical velocity through such a hypothetical object. Therefore the above equations are describing an artificial ideal, and not necessarily an actual possible natural expression.

$$v_s = \sqrt{G} \sqrt[3]{ \frac{M_t}{4}} \sqrt[6]{ \frac{ \pi \rho_t}{3}}$$
$$M_t$$ - Terra's mass
$$\rho_t$$- Terra's density

Based upon the Orion1 equation, what is the seismic velocity of sound through Terra?, and how does this compare with actual Terra seismic velocity values?

Based upon the Orion1 equation, what is the seismic velocity of sound through Terra's Lunar?, and how does this compare with actual Lunar seismic velocity values?

$$v_s = \sqrt{G} \sqrt[3]{ \frac{M_m}{4}} \sqrt[6]{ \frac{ \pi \rho_m}{3}}$$
$$M_m$$ - Lunar mass
$$\rho_m$$ - Lunar density

 

[Labguy]

can you define what's a pure neutronium neutron star? Neutron stars do have an iron crust surrounding the neutronium

The original post must be purely hypothetical. From a dictonary definition of Neutronium:

"Neutronium is a colloquial and often misused term for an extremely dense phase of matter that occurs in the intense pressure found in the core of neutron stars and is currently not well understood. It is not an accepted term in astrophysics literature for reasons which will be explained below, but is used with some regularity in science fiction."

________________________
Labguy

 

[meteor]

ALthough neutronium is not a word very much heard, I think that some investigators refers to it like the substance forming the interior of a neutron star. Look page 5 of this review of general relativity by no other that John Baez
http://xxx.lanl.gov/abs/gr-qc/0103044

 

[Orion1]

Neutronium Nexus...

Labguy definition continued...[/color]

When the core collapses, the densities and pressures in the core overcome even the electron degeneracy pressure and the iron atoms' electrons are compressed into their nuclei where they combine with protons to form neutrons.

electron + proton ? neutron + neutrino

The neutrino is emitted from the core, leaving the neutron behind. The material that remains has a density of approximately 10^14-10^15 grams per cubic centimeter. A teaspoon full of this matter would have a mass of 100 million metric tons. This material has often been termed neutronium. However, because the physics of material at these high densities is unknown, it is far from clear if the interior of a neutron star is best described as a sea of neutrons. It is possible that rather than a sea of neutrons, the interior of a neutron star would best be modeled as a sea of free quarks or of heavy hyperons. It is also possible that neutron star material undergoes a number of phase transitions in which the material has radically different properties depending on the density and temperature of the material. It is also unknown how neutron star material would behave if the pressures on the star were suddenly reduced. Because of these uncertainties, the term neutronium is rarely found in the scientific literature.

It is theorized that when the neutronium which makes up a neutron star is put under sufficient pressure due to the star's gravity, the individual neutrons break down and their constituent quarks form strange matter. The star then becomes known as a "strange star" or "quark star". Strange matter is composed of strange quarks bound to each other directly, in a similar manner to how neutronium is composed of neutrons; a strange star is essentially a single gigantic nucleon. A strange star lies between neutron stars and black holes in terms of both mass and density, and if sufficient additional matter is added to a strange star it will collapse into a black hole as well.

Some theories suggest that strange matter, unlike neutronium, may be stable outside of the intense pressure that produced it; if this is so, then small substellar pieces of strange stars (sometimes called "strangelets") may exist in space in a wide range of sizes all the way down to atomic scales.

The term 'Neutronium' should not be considered any more colloquial in astrophysics than terms such as 'strange star', 'quark star', 'black holes' or even 'strangelets'.[/color]

Reference:
http://www.wordiq.com/definition/Neutronium
http://www.wordiq.com/definition/Strange_matter

 

[Labguy]

Orion1;

Ok, I would have to agree that if it (Neutronium) is being used as in your second link, then it has become an "accepted" word used for pure neutrons. That means that the definition I posted, and the same in your first link, should be dropped and Neutronium becomes an official term.

However, I think that your description of a quark-gluon "plasma" is more likely than any structured ball of "Neutronium".

A source quote:
"Deeper yet, at a density around 4x10^11 g/cm^3, you reach the "neutron drip" layer. At this layer, it becomes energetically favorable for neutrons to float out of the nuclei and move freely around, so the neutrons "drip" out. Even further down, you mainly have free neutrons, with a 5%-10% sprinkling of protons and electrons. As the density increases, you find what has been dubbed the "pasta-antipasta" sequence. At relatively low (about 10^12 g/cm^3) densities, the nucleons are spread out like meatballs that are relatively far from each other. At higher densities, the nucleons merge to form spaghetti-like strands, and at even higher densities the nucleons look like sheets (such as lasagna). Increasing the density further brings a reversal of the above sequence, where you mainly have nucleons but the holes form (in order of increasing density) anti-lasagna, anti-spaghetti, and anti-meatballs (also called Swiss cheese).

When the density exceeds the nuclear density 2.8x10^14 g/cm^3 by a factor of 2 or 3, really exotic stuff might be able to form, like pion condensates, lambda hyperons, delta isobars, and quark-gluon plasmas."

That's a good possible model that agrees with the remainder of your post, especially the last part, but I'm not ready to start accepting the "pasta-antipasta sequence" as an official term yet...

_______________
Labguy

 

[Orion1]

"pasta-antipasta, meatballs, spaghetti, lasagna, Swiss cheese", is this the description of a neutron star, or the menu of an italian restaurant?

Someone definitely needs to have talk with these scientists...
[/color]

 

[selfAdjoint]

"pasta-antipasta, meatballs, spaghetti, lasagna, Swiss cheese", is this the description of a neutron star, or the menu of an italian restaurant?

Someone definitely needs to have talk with these scientists...
[/color]

Grad students are always hungry. It marks them for life.

 

[Entropy]

Can someone explain to me how strange quarks come into this? I thought that nucleons where only made of up and down quarks, how do strange quarks form?

 

[Orion1]

Strange Stellars...


Can someone explain to me how strange quarks come into this? I thought that nucleons where only made of up and down quarks, how do strange quarks form?

Strange quarks are generated in the cores of 'quark stars' through Conservation of Fermi Momentum within a Fermi gas from transformation of down quark populations to strange quark populations. However according to models, strange quark matter is density dependent and can only exist in a stable state between densities of $$\rho_s = 4.293 \rho_n$$ and $$\rho_{smax} = 13.557 \rho_n$$, and a maximum mass of $$M_s = 1.61 M_\odot$$, where $$\rho_n$$ is the neutronium density.

The existence of 'quark matter' in such a state was posited in 1984 by Professor Edward Witten of the Institute for Advanced Study in Princeton.

The mass equation of state for 'quark matter' in 'quark stars' is:
$$M_s = dr \int_0^R 4 \pi r^2 \left( 1 - \frac{2Gm(r)}{c^2r} \right)^{-1/2} \rho(r)$$

Based on these same models, there is also a maximum upper mass and density limit in which 'strange stars' can exist, $$\rho_s = 3.11*10^{18} kg*m^{-3}$$ or $$\rho_{smax} = 13.557 \rho_n$$, and a maximum mass of $$M_{smax} = 1.61 M_\odot$$ with a maximum radial upper limit of $$r_s = 8.740 km$$.

$$v_s = \sqrt{G} \sqrt[3]{ \frac{M_s}{4}} \sqrt[6]{ \frac{ \pi \rho_s}{3}}$$

Based upon the Orion1 equation, what is the seismic acoustical velocity through 'Quarkonium' within a 'quark star'?
[/color]
Reference:
http://chandra.harvard.edu/photo/2002/0211/0211_illustration.jpg
http://chandra.harvard.edu/press/02_releases/press_041002.html
http://chandra.harvard.edu/photo/2002/0211/index.html
http://antwrp.gsfc.nasa.gov/apod/ap020414.html
http://www.iop.org/EJ/article/1367-2630/4/1/314/nj2114.html

 

[Entropy]

Neat. But I don't think we'll ever see a chunck of neutronium floating around in space. The force to get even a mircoscopic piece of matter off a neutron star is pretty extreme.

 

[Chronos]

Agreed. Remove the intense gravity and neutronium should 'uncloak' into ordinary baryonic matter. Massive explosion would be my best guess. I hesitate to say gamma burst, but, it appears a possibility. It is easier to work out than 5th order derivatives.. which hurt my brain.