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Spectroscopic parallax is the technique whereby you estimate the absolute magnitude (i.e. the brightness it would have if it were placed at 10 pc) by estimating what "type" of star it is using information fro a spectrum. It can be applied to any kind of star where (a) you have a reasonable chance of determining the type of star from its spectrum and (b) ...

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A partially reflective Dyson sphere is equivalent to asking what happens if we artificially increase the opacity of the photosphere - akin to covering the star with large starspots - because by reflecting energy back, you are limiting how much (net) flux can actually escape from the photosphere The global effects, depend on the structure of a star and ...

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An analysis would have to look at the effects over time. With my limited understanding of physics and intuition, I see the outer layers of the star reabsorbing the rays. Where the outer portions of the star until now have experienced large amounts of energy flowing in one direction, now has a net outward energy flow of maybe 1/2 to 1/10 of what it used to. ...

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Sort of. This is demonstrated clearest in barred spiral galaxies, which make up about 1/2 to 2/3 of all spiral galaxies. A dramatic example is NGC 1365: Image courtesy of Wikipedia. Others, such as M95, have spiral arms that wrap even further around while still retaining the central bar: Original image courtesy of Wikipedia; color added by me in ...

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Yes, the exact solution is known. The general spherically symmetric metric is $$g=-B(r)\mathrm{d}t^2+A(r)\mathrm{d}r^2+r^2\mathrm{d}\Omega^2.$$ The solution for $A(r)$ is $$A(r)=\left[1-\frac{2G\mathcal{M}(r)}{r}\right]^{-1},\quad\mathcal{M}(r)=\int^r \rho \,\mathrm{d}V=\int_0^r 4\pi r'^2\rho(r')\,\mathrm{d}r.$$ The solution for $B(r)$ is ...

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The Pauli exclusion principle is being applied here to FREE neutrons. There are always free energy/momentum states for the neutrons to fill, even if they are compressed to ultra-high densities; these free states just have higher and higher energies (and momenta). One way of thiking about this is in terms of the uncertainty principle. Each quantum state ...

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Short answer: it is a combination of (1) the ignition occurring in an electron-degenerate, isothermal core in which the equation of state is independent of temperature; and (2) the extreme temperature dependence of the triple alpha He fusion reaction. Details: The helium flash occurs at the tip of the first ascent red giant branch in stars with masses ...

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This might not be a good explanation, but the gist of it is, as stars get hotter, even though they get less dense over time, the extra heat speeds up the fusion process. The helium fusion can only happen at about 100 million degrees. The temperature at the core of our sun is 15 million degrees - new energy is created all the time by hydrogen and ...

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Helium is chemically inert, but in the conditions present in the core of a star or on the surface of an accreting white dwarf helium is prone to fusion. The helium is degenerate, which means that the structure of the Helium core/white dwarf is not being supported by temperature, which means the energy produced during fusion does not cause the core to expand ...

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You have ignored outside influences. Something as simple as asteroids striking the outside of the sphere would push it out of concentric balance and cause a drift toward eccentricity, eventually leading to a contact between the star and the shere (or more likely a vaporization of part of the sphere well before a contact). There would need to be active ...

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It is a nice question, however the answer is complicated : I recommend to look at Eddington standard model in http://www.astro.umass.edu/~wqd/astro640/model.pdf, there are also nuerical methods mentioned there.

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The overly simplified (and empirically incorrect) way is to just balance the pressure at the surface $$P_{\text{gravity}} = \frac{Gm^2}{4\pi R^4}$$ And $$P_{\text{radiation}} = \frac{\epsilon \sigma T_{\text{surface}}^4}{c}$$

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You are correct that the status of a black hole is determined by its mass, but also by its radius. The gravitational field becomes stronger the bigger the mass and the closer you can get to that mass. A black hole forms once a mass $M$ is compressed inside the Schwarzschild radius $r_s = 2GM/c^2$. i.e. once its density achieves  \rho > \frac{3M}{4\pi ...

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How then, can they collapse, without violating the Pauli Exclusion Principle. At a certain point does it no longer apply? No. The Pauli Exclusion provides a "degeneracy pressure" as mentioned in the article. That degeneracy pressure is not great enough to stop the collapse in the case of a black hole. This isn't violating the Pauli Exclusion ...

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I don't know much about gravity, but, as far as I understand, collapse does not mean violation of the Pauli principle: I guess the radius of the black hole is still finite. Collapse just means that it becomes a black hole, that is, light cannot escape it.

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