| From: BLACKY | 08/03/2001
18:25:33 |
| Subject: White dwarfs and neutron stars | post id:
248046 |
| 1.How big are white dwarfs and
neutron stars. 2.What determines there size 3.If you were asked by a alien from another universe what are the properties of your universe what would you say. | |
| From: B.C. ® | 08/03/2001
18:32:08 |
| Subject: re: White dwarfs and neutron stars | post id:
248054 |
| White dwarfs are around Earth
size and smaller. Neutron stars are around a few kilometers in diameter. The original mass of the star determines the size of the white dwarf or neutron star. A point to remember, the bigger the parent star the smaller the white dwarf or neutron star. Properties of our universe....... Expansion. matter and energy[four forces] CMBR Life Universe being finite | |
| From: Chris (Avatar) | 09/03/2001
10:11:11 |
| Subject: re: White dwarfs and neutron stars | post id:
248483 |
1.How big are white dwarfs and neutrin stars. The Harrison-Wheeler equation of state for dead matter (see supernova tutorial for more detail) tells us that white dwarf stars have masses between about 1/4 and 1.4 (Chandrasekhar limit) solar masses. Neutron stars have a maximum mass between 2 and 3 solar masses and a minimum of about 1/2 a solar mass. 2.What determines there size Neutron stars and white dwarf stars are a balancing act between the inward push of gravity and the outward push of electron degeneracy pressure (for white dwarfs) and neutron degeneracy pressure plus strong nuclear force (for neutron stars). Degeneracy pressure occurs when either electrons or neutrons are forced from atoms/nuclei and pushed into close proximity. The pressure is independent of temperature and is finite. In this way this pressure is ultimately responsible for both mass and size restrictions on white dwarf and neutron stars: the range into which either electrons or neutrons can be compressed defines the size, and the limiting pressure defines the maximum mass of the star. From BC: Universe being finite Is it? Hope this helps! Chris | |
| From: Dropbear ® | 09/03/2001
10:14:07 |
| Subject: re: White dwarfs and neutron stars | post id:
248484 |
| Chris, how do they work out how much pressure needs to be applied to get electrons to ignore the Pauli Exclusion Principle?? | |
| From: Chris (Avatar) | 09/03/2001
10:38:39 |
| Subject: re: White dwarfs and neutron stars | post id:
248497 |
The electrons don't actually ignore the principle (you can't just ignore it). This is one of the problems which stems from tgreating the exclusion principle as the basis for the degeneracy pressure. Lets review the formation of a white dwarf through to type 1 supernova from an electron's perspective: First as a small to medium star undergoes core collapse (with, say, a mostly carbon up to an iron core) the pressure builds and is "token" resisted by heat pressure and by e/m pressure associated with the electrons' negative charge. The problem is that these pressures are finite - they're not being renewed by fusion because the temperature isn't high enough to ignite the next phase, and so cooling will eventually naturally reduce the pressure. The core's gravity will overcome the e/m pressure and force the electrons in closer. The electrons begin to ignore the nuclei with which they were associated (carbon, iron, etc) and start acting like a gas. Further pressure forces them into the range of the exclusion principle and the pressure becomes degenerate. At this stage each electron is confined to a very small region, and it starts acting more like a wave than a particle - confining the electron reduces its wavelength which increases its frequency and hence its energy. This energy is the degeneracy pressure which supports the star's gravity. Note that at this point the pressure is independent of temperature: you can't reduce the pressure by cooling because it results from the energy associated with close confinement. This state of affairs describes a stable lower mass white dwarf. Increasing the mass increases the confinement and the degenerate electrons' motions become relativistic. Chandrasekhar first realised that as the confinement of the electron becomes tighter its effective motion becomes a significant fraction of c, and from this point increased energy from confinement serves to increase the electron's inertia rather than its velocity (to understand this, consider the increase in relativistic mass of a particle as it approaches c). There is a smooth decrease in resistance to compression (adiabatic index) from 5/3 to 4/3 as the degeneracy pressure becomes relativistic. Now lets consider the white dwarf at the chandrasekhar mass. At this point the electron confinement is extreme (ie very very close to the Pauli limit), the degeneracy pressure relativistic. Increasing the gravity of the star now (by adding more mass) forces the electrons to begin dripping from the degenerate gas onto the forgotten nuclei where the extreme pressure fuels reverse beta decay - the electrons start fusing with protons to form neutrons. At this stage we're on the path to type 1 supernova and you know what happens from there. So you see the electrons never ignore the Pauli principle. Hope this helps! Chris | |