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19

The accretion of matter onto a compact object cannot take place at an unlimited rate. There is a negative feedback caused by radiation pressure. If a source has a luminosity $L$, then there is a maximum luminosity - the Eddington luminosity - which is where the radiation pressure balances the inward gravitational forces. The size of the Eddington ...


15

The reason is electron degeneracy pressure. The cores of giant planets are dense enough that the electrons in the gas occupy about $h^3$ of phase space each. The Pauli exclusion principle means that they cannot all occupy low energy/momentum states. This means that even at relatively cool temperatures the gas can still exert considerable pressure due to the ...


12

Just imagine an expanding shell. Then all the parts are moving at the same speed. If the mass is $M$ and the radius is $R$, then the kinetic energy is $\frac{1}{2} M \dot{R}^2$. A sphere is just a series of shells. A shell at radius $r$ has mass $\mathrm{d}m = \frac{M}{4/3 \pi R^3} 4\pi r^2 \mathrm{d}r$ and is expanding at a rate proportional to the ...


9

A 12 billion Solar mass black hole sounds massive, but actually it's not all that big. The radius of the event horizon is given by: $$ r_s = \frac{GM}{c^2} $$ and for a 12 billion Solar mass black hole this works out to be about $1.8 \times 10^{13}$m. This seems big, but it's only about 0.002 light years. For comparison, the radius of the Milky way is ...


8

Maybe the simplest way to think about this is that the Sun is in approximate thermal equilibrium and would absorb any photon, of any frequency, that is incident upon it. This is essentially the definition of a BB. There are many radiative processes that can absorb (and hence emit) radiation at all frequencies, not just those corresponding to atomic ...


5

Short answer: gravitational potential energy is converted into heat. Let's look at the Sun as an example. Its mass is $M_\odot = 2.0\times10^{30}\ \mathrm{kg}$ and its radius is $R_\odot = 7.0\times10^8\ \mathrm{m}$. If its density were uniform, its gravitational binding energy would be $$ U_{\odot,\,\text{uniform}} = -\frac{3GM_\odot^2}{5R_\odot} = ...


4

I'm not going to attempt to usurp Chris White's perfectly good answer - but just fill in some detail and answer the edit. For a star like the Sun, the collapse proceeds in 4 basic stages, each takes about 10 times as long as the previous one. Pseudo-spherical collapse of the cloud - not far from a free fall timescale, often quoted as a few $10^4$ years. ...


4

Theoretical physics, in general, does not have to be confirmed by observations. Theories are proposed as an effort to explain observations, so some consistency with observations is expected. However, it's not necessary to wait for observations. A theoretical astrophysicist can propose work that is consistent with current observations and build off of it, ...


4

Black body radiation is given by Planck's formula (see link for variables) Here is the measured irradiance of the sun and the attempt to fit it with the black body formula: The effective temperature, or black body temperature, of the Sun (5,777 K) is the temperature a black body of the same size must have to yield the same total emissive power. ...


4

I think you already know the answer... Pop III stars, by definition, are born from primordial gas that is basically Hydrogen, Helium with trace amounts of deuterium, tritium, lithium and beryllium; they initially contain almost no C, N, or O. Therefore the primary fusion in massive Pop III stars has to be (well, initially the deuterium is burned but this is ...


3

$^{56}Ni$ is produced in silicon-fusion stars. The fusion process doesn't "stop" at $Fe$. Several A=56 nuclides show up. See the Wiki-pedia article on :Silicon burning. Also, Introductory Nuclear Physics by Krane, Chapter 19, Section 4.


3

Well there are problems in your question and analysis. First off, there have been a few SE questions recently about this "Keplerian" treatment of dark matter. The shell theorem, that the gravitational field is the equivalent of that due to the mass inside radius $r$, and that exterior masses can be ignored is only true for spherically symmetric mass ...


2

You would be very interested in one of the recent Kepler discoveries - Kepler 444. The star is estimated to be 11.2 billion years old (using asteroseismology) and is surrounded by a number of rocky exoplanets. These planets are all too close to their parent K-dwarf star to be in the habitable zone, but there is no reason there couldn't be planets further ...


2

Sometimes the word universe is just used colloquially and can just refer to everything on some side of a horizon (an event horizon, a causality horizon, etc.) But when used precisely, I'm sure different definitions are used in different fields. For instance, in mathematical general relativity, you assume that your universe is a connected four dimensional ...


2

If the question is asking whether there is a definition that encapsulates our universe, then I believe the answer is No. This is because encapsulating a "space" into a formal system requires defining bounds. However, we don't know the bounds of our own universe--let alone what bounds might be possible for any universe. We can only describe what we can ...


1

A star is neither "flaming" nor "fire" in the sense that we use those words about things on Earth. It's just a big, hot ball of ionized gas. The only thing that happens "to" it is that it gets hotter and denser. At some point the temperature rises high enough to ionize the gas. Later still fusion becomes possible at non-vanishing rates. The energy for the ...


1

After (re)combination (I never understand why the "re" is used) and the formation of the CMB, the universe was transparent and the only light in it was from the rapidly cooling CMB. The baryonic universe was composed almost entirely of neutral hydrogen and helium. After perhaps 100 million years, the first galaxies and stars (assisted by dark matter) were ...


1

I don't see an "equivalence between the partial and total derivative" of H in anything you've written; it's always written $dH/dt$ as a total derivative. The reason that the partials emerge within the volume integral is because A and B are also functions of space, and so the time derivative must be taken while holding position constant; it's basically that: ...



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