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Zero Signal
2003-Jun-25, 06:05 PM
I haven't been able to find much of anything regarding these things, so I want to know if any of you have any answers.

Q1: I've noticed that many red and brown dwarfs with smaller diameters (<0.15 solar radii) have very high overall densities (specific gravities of 460 for Ross 128, 412 for Luyten's star, 211.5 for Wolf 359, and anywhere from 40-100 for many others). So what is the cause for the high density? Are red & brown dwarfs composed partially of degenerate matter? Or do they have somewhat large cores that have densities much, much higher than the Sun's (sp. gr. 150)?

Q2: What is the general structure for a white dwarf star? I've yet to see any diagrams or other illustrations or any detailed explanations as to what their internal structure looks like. I've seen illustrations of the structures of various main seqencers, giants, and neutron stars, but not white dwarfs.

Q3: Does general relativity require curved space? I know GR is a very well-confirmed theory, but I always thought it was weird that space could curve, since it has no immediately obvious underlying structure to it (to my knowledge, anyway). So does GR need curved space in order to work?

Thanks.

BigJim
2003-Jun-25, 06:18 PM
Hi, Zero Signal. Interesting questions.


Q1: I've noticed that many red and brown dwarfs with smaller diameters (<0.15 solar radii) have very high overall densities (specific gravities of 460 for Ross 128, 412 for Luyten's star, 211.5 for Wolf 359, and anywhere from 40-100 for many others). So what is the cause for the high density? Are red & brown dwarfs composed partially of degenerate matter? Or do they have somewhat large cores that have densities much, much higher than the Sun's (sp. gr. 150)?

Not really. Red dwarfs would be more dense than brown dwarfs, which are more dense than planets. But the Sun would be more dense at its core than a red dwarf. Red and brown dwarfs, or any main-sequence stars for that matter, lack degenerate matter. Have you checked the specific gravity of other stars? Remember that red dwarfs are much smaller and cooler than the sun, and as a result their cores will be less dense. Brown dwarfs do not even undergo normal fusion and are that much less dense.




Q2: What is the general structure for a white dwarf star? I've yet to see any diagrams or other illustrations or any detailed explanations as to what their internal structure looks like. I've seen illustrations of the structures of various main seqencers, giants, and neutron stars, but not white dwarfs.

As far as I know, solitary white dwarfs, as well as solitary neutron stars, should be fairly homogenous. Solitary white dwarfs should be made up of fairly consistent degenrate electron matter. White dwarfs in a binary system are different, though. If their companion is a main sequence star, the star will transfer mass to the white dwarf. The hydrogen and helium from the main sequence star will collect on the surface of the white dwarf. When a later several meters deep builds up, it will explosively fuse into carbon in what we call a nova. If mass is kept by the white dwarf until it exceeds 1.4 solar masses, it becomes unstable and is destroyed in a type Ia supernova.



Q3: Does general relativity require curved space? I know GR is a very well-confirmed theory, but I always thought it was weird that space could curve, since it has no immediately obvious underlying structure to it (to my knowledge, anyway). So does GR need curved space in order to work?

Absolutely. General relativity's defining feature is warped space-time. General relativity tells us that all object with mass warp the curvature of space-time, prodcuting the phenomena we call gravity. To simplify this, think of space as a large bed sheet, and the sun as a bowling ball. When the sun is placed on the sheet, it will warp. If we were to put, say, a ball bearing, representing a planet, on the sheet, it would be able to orbit the sun. This is a simplified representation of gravity. General relativity was virtually proven in 1919, with observations of a solar eclipse. The light from the stars near the sun was bent by the sun's gravity, or curvature of space-time.

Another feature of general relativity is "time dilation". Someone moving at high speeds relative to you will appear to age less quickly than you will. To visualize this, think of a clock called a "photon clock." The "photon clock" is two mirrors with a photon bouncing between them. Say this photon clock were to remain stationary. The photon would go between them, say, a billion times per second. But if you were to slide the clock across the table, the photon to the nonmoving observer would appear to be taking a slanted path, hence each second would appear longer to that observer. But the moving observer would experience the same time flow.

kurtisw
2003-Jun-25, 06:39 PM
Not really. Red dwarfs would be more dense than brown dwarfs, which are more dense than planets. But the Sun would be more dense at its core than a red dwarf. Red and brown dwarfs, or any main-sequence stars for that matter, lack degenerate matter. Have you checked the specific gravity of other stars? Remember that red dwarfs are much smaller and cooler than the sun, and as a result their cores will be less dense. Brown dwarfs do not even undergo normal fusion and are that much less dense.

Actually, less massive stars do have more dense cores. The least massive red dwarfs have central densities approaching 1000 g/cm^3, about 10 times the sun's central density. And this does border on degeneracy. The reason that lower mass stars are more dense is that energy from fusion counteracts gravity. The lower temperatures in the core low-mass stars do not permit fusion to take place until the star is extremely dense. Below about 0.08 solar masses, the core degeneracy prevents further collapse, but the core is still not dense enough for sustained fusion to take place,





As far as I know, solitary white dwarfs, as well as solitary neutron stars, should be fairly homogenous. Solitary white dwarfs should be made up of fairly consistent degenrate electron matter. White dwarfs in a binary system are different, though. If their companion is a main sequence star, the star will transfer mass to the white dwarf. The hydrogen and helium from the main sequence star will collect on the surface of the white dwarf. When a later several meters deep builds up, it will explosively fuse into carbon in what we call a nova. If mass is kept by the white dwarf until it exceeds 1.4 solar masses, it becomes unstable and is destroyed in a type Ia supernova.

Yup. The central regions of white dwarfs are isothermal, meaning all the same temperature, though for solitary white dwarfs there is probably a chemical gradient, with more oxygen toward the center and more carbon toward the edge. The outer regions of a white dwarf are a non-degenerate atmosphere on helium (up to 1% of the white dwarf's mass) and hydrogen (up to 0.1% of the white dwarf's mass).




Another feature of general relativity is "time dilation". Someone moving at high speeds relative to you will appear to age less quickly than you will. To visualize this, think of a clock called a "photon clock." The "photon clock" is two mirrors with a photon bouncing between them. Say this photon clock were to remain stationary. The photon would go between them, say, a billion times per second. But if you were to slide the clock across the table, the photon to the nonmoving observer would appear to be taking a slanted path, hence each second would appear longer to that observer. But the moving observer would experience the same time flow.

Actually, this is a feature of special relativity. General relativity also has time dilation due to a gravitational field.

tracer
2003-Jun-26, 11:49 PM
I've noticed that many red and brown dwarfs with smaller diameters (<0.15 solar radii) have very high overall densities (specific gravities of 460 for Ross 128, 412 for Luyten's star, 211.5 for Wolf 359, and anywhere from 40-100 for many others).
You sure the average densities of those 3 stars are really that high?

Wolf 359, at last count, had a mass of about 0.093 x Sol and a diameter of about 0.13 x Sol. This would make its overall density 42.3 x Sol, which is only a specific gravity of 60.

kilopi
2003-Jun-26, 11:53 PM
Actually, this is a feature of special relativity. General relativity also has time dilation due to a gravitational field.
General relativity subsumes special relativity, though. They're not mutually exclusive.

In the same sense, special relativity has time dilation in an accelerated frame--general relativity just makes the equivalence between accelerated frames and gravitational fields.