Statistical physics

[masta_shady]

Let's say I was going to use statistical physics to study a white dawrf, considering it as Fermi Gaz.<br />The particles in this gaz are not quiet free , they are not free particles , they are actually under the gravitational force.<br />now here is my question when calculating for example the total enegry of the star or how much radiation we are getting out of it, how much would i should take in consideration the relativistic effects from the gravitational force ,in calculation of an Idealised model of a white dwarf.<br />(Helium as content, Density around 10^7 of sun's , Mass = mass of the sun , and central T around 10^7 K)<br /><br />would the numbers change a lot ?<br /><br />And how would i be able to include the relativisitc corrections?

 

[doubletruncation]

General relativistic corrections would be fairly small for a white dwarf. The gravitational potential energy per unit mass at the surface of the white dwarf would be ~GM/R ~ 6.7E-8 * 2E33 / 6E8 ~ 2E17 erg/gm which is less than 0.1% the rest mass energy of the test particle. To include general relativistic corrections you would need to replace the newtonian equation of hydrodynamic equilibrium with a general relativistic one (this plus your fermi gas equation of state and your equation of mass conservation should be sufficient to solve for the star). I think the equation to use for hydrodynamic equilibrium would be the oppenheimer-volkov equation. In geometrized units it is:<br /><br />dp/dr = -(rho + p)*(m + 4*pi*r^3*p)/(r*(r-2m)) <br /><br />where rho is mass density, p is pressure, r is distance from the center of the star and m is the mass within radius r - again these are all in geometrized units where c = G = 1. Note that you would have to solve the system of equations numerically, exact analytic solutions only exist for unrealistic equations of state. <div class="Discussion_UserSignature"> </div>

 

[masta_shady]

So it shouldn't be a problem using classical approximation , I already tried the calculation this way and got some answers.<br />anyway thx a lot.

 

[mikeemmert]

I read somewhere that degenerate matter at the cores of white dwarf or nonfusing matter is a crystalline solid, with the electrons, trapped by gravity, condensing into ordered arrays that are not associated with nuclei. This strange form of matter has the notable characteristic of conducting heat at the speed of sound, which is very high in this "crystal of a single molecule".<br /><br />I wonder if this is the basis for an observation that has been around for a long time (I read about it in an Asimov book). As one increases the power of the telescope used for observing, one sees more and more stars. However, at some point, detection of stars tapers off, and one begins to see more and more galaxies.<br /><br />A mass of hydrogen 0.08% of a solar mass, 1/12 of the Sun, would fuse hydrogen in the normal fashion and be a star. However, these objects are not observed. Instead, the minimum mass star seems to be 0.10% of the Sun, 1/10 of a solar mass.<br /><br />However, theory and the most recent observations (after the passing of Isaac Asimov) indicate that objects can form via the same mechanism as stellar collapse that are as small as 0.008% of a solar mass, or one tenth the minimum mass of a star.<br /><br />Unfortunately, any object not fusing hydrogen is extremely hard to see. There have not been enough detected to make meaningful statistical studies. The only ones seen (except for a tiny handful) are very, very new and fusing deuterium. Deuterium is only 1% -2% of the interstellar medium and burns much faster than hydrogen, thus these objects are only detectable for a few tens of millions of years and are mostly seen in or near star-forming regions.<br /><br />All objects larger than 0.013 solar masses start by fusing deuterium with hydrogen to form helium-3, which is a reactive fusion fuel. When the deuterium is depleted, the star collapses until the helium-3 starts fusing.<br /><br />Could it be that objects between one tenth and one twelfth solar masses form a cor

 

[masta_shady]

lol mike , i wasn't so intrested in all of that i was studying for my exam in statistical physics , and there is an excercise about white dwarfs , but with no solution , so i asked the following.<br /><br />Maybe i should apply statistical physics to these kind of stars you are talking about , maybe i can find an answer.. <br />A question for the expert here if i wanted to do that , should i go with the sun model ? i mean consider them as a gaz of photons ?or what?