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1

When we assume hydrostatic equilibrium, the pressure gradient is taken. Maybe the pressure should be 0 when $\xi>\xi_0$, so that constraint should be explicitly applied. This is generally understood as an implicit restriction/constraint of the hydrostatic equilibrium (HSE) condition for starting the Lane-Emden equation: HSE is for the star and not ...


0

The assumption $$ P=K\rho^{1+1/n} $$ is a very simplistic mathematical model and should be applied with care. When the model predicts matter has negative density at some point, it is a sign that it is too simple to get it right there. The model neglects lots of things - radiation, magnetic field, solar wind, etc.


1

I would go with the hydrostatic equilibrium condition being the source of the issue here. When there is no polytropic gas when $\xi \gt \xi_0$, there is no need for any hydrostatic equilibrium to be in place - the gravitational potential is free to take on any value, determined (together with boundary conditions) by Laplace's equation: $$\nabla^2\Phi = 0$$ ...


0

The "core" of a neutron star is of debatable composition and is dependent on the highly uncertain equation of state of matter compressed to $10^{18}$ kg/m$^3$. It is possible that the core consists almost entirely of a solid neutron lattice with some protons that possibly form a superfluid. Other possibilities include new mesonic (pions or kaons) or ...


-1

In my Physics Class we had to look into possible areas where Dark Matter could be "hiding". Where is all the dark matter? Actually, I think it's hiding in plain sight. If you've read up on relativity I think you can work it out. See Einstein's Leyden Address where he described a gravitational field as space which was "neither homogeneous nor isotropic", and ...


-9

There are two main misconceptions about dark matter. One is that dark matter is a clump of stuff traveling with the matter. The other is that matter does not interact with dark matter. Dark matter fills 'empty' space. 'Empty' space has mass. Spacetime has mass. Dark matter is displaced by matter. The Milky Way moves through and curves spacetime. The ...


2

The discrepancy between the predicted big bang nucleosynthetic abundance of Lithium 7 and the measured value can be summarised as follows. If we take what we know about the the baryonic mass density of the universe and the Hubble constant, we get a self-consistent picture between the cosmic microwave background, observations of galaxy recession etc. and the ...


10

There are several reasons to believe that dark matter is a particle. The most widely accepted alternative explanations for the different phenomena that led us to conjecture dark matter in the first place, can collectively be labeled "we don't understand gravity well enough". But no matter what, the effects of dark matter are sort of "localized". The ...


3

The latter idea you talk about is the Giant Impact Hypothesis. It turns out that you can make a moon in a few easy steps (given the correct conditions): Have a bunch of protoplanets whiz about on semi-chaotic trajectories. Smack two of them together at a 45° angle. Let the bits of the protoplanets that don't merge together be ejected from the resulting ...


0

Full ionization means that the electrons are no longer bound to the nuclei: the electrons and the nuclei behave as independent particles. I think this means you can treat them as a gas - the same way that you would treat a mixture of gases.


0

More on the perytons being caused by microwave ovens being opened while still operating. The microwave oven's magnetron is still generating the microwaves when the door is open before the timer has stopped the microwave. Article: http://phenomena.nationalgeographic.com/2015/04/10/rogue-microwave-ovens-are-the-culprits-behind-mysterious-radio-signals Study: ...


5

A paper came out this week pointing to them having a banal (if amusing) origin: they are from two 27 year old microwave ovens. When people get impatient and open the door before the timer runs down, a short burst from the ovens' magnetron is released, which appears as a peryton if the telescope is pointed in the right direction. Figure 7. shows the perytons ...


3

The gas outside the white dwarf (and actually, in the interior of the white dwarf but close to the surface) is non-degenerate. So I don't see what the presence of the white dwarf has to do with the question unless it is significantly photo-ionising the cloud? Anyway for spherically symmetric accretion onto an object, one approach is to make an assumption ...


7

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 ...


2

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 ...


3

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 ...


1

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 ...


5

The combined rest mass of a proton and an electron is less than that of a neutron. Fundamentally then, what you need to start turning a star into a neutron star is that the protons and electrons need kinetic energy as well as rest mass energy. How much energy: Well at a minimum (assuming the neutrino doesn't get much), then an electron interacting with a ...


0

The minimum mass for one to form is 1.44 solar masses. Energy barrier: Neutron mass - 1 Proton mass - 0.99862349 Electron mass - 0.00054386734 $p+e→n+v_e$ Assuming that the neutrino mass is negligible, we get the difference between the neutron mass and the electron-proton mass to be 780 keV, meaning this is the energy barrier.


3

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 ...


0

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.


0

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 $$ P_{\text{radiation}} = \frac{\epsilon \sigma T_{\text{surface}}^4}{c} $$


-1

Figure out a planet in orbit of 360 degree. You would have a 45 degree axis at start and -45 degree axis at mid course of this planet around the orbit. It would means that this planet would have taken a speed or inclined throughout that course implying that from Her own, it developed a way to tilt like around an ice cream cone. This could means that a ...


2

For a conventional planet (i.e. one that is self gravitationally round), conservation of the planet's angular momentum makes this impossible (except for the trivial case of the axis perpendicular to the orbital plane. A non-spherical planet with a tilted axis will precess under the influence of tidal forces. It takes the earth about 26,000 years to go ...


0

Could gravitational lensing be the refraction of hydrogen, helium, gases and cosmic dust? You can add up the total density required. You can then look for the spectroscopic effect that this density would imply. We don't see them. So, no, it couldn't.


2

No, because we've seen it happen between galaxies, where there's not enough intergalactic material to account for this. Here's an example: the galaxy cluster Abell 2744: Then there's Einstein's cross: You need something extremely massive to account for the lensing shown here. Gravitational lensing can accurately predict these images, and the ...


2

I had the same feeling as you when I watched the video again recently. It seemed like one of the ice giants would get ejected after coming too close to Jupiter. It turns out that there's a name for this: the jumping Jupiter scenario. Outside Wikipedia, it's described in Fassett & Minton (2013) (paywall!) and tangentially in Deienno & Nesvorny (2014). ...


4

I got a translation of the article from the German Wikipedia. Here's an excerpt: Perytons are in radio astronomy short radio signals having a length of a few milliseconds, which probably terrestrial are origin. The Perytons are named after mythical creatures . In radio astronomy, terrestrial are noise is always a problem. A well-known noise signal ...


1

This paper describes them. http://www.ursi.org/proceedings/procGA11/ursi/GP2-41.pdf They were apparently given a new name because their origin was uncertain.


0

This presentation might be helpful to you. Based on dust density and mass density in each pixel of an image, the luminosity is calculated as $$L=L_0 \cdot \exp \left( \int \kappa \rho ds\right)$$ where $\kappa$ is a constant and $\rho$ is the density of the interstellar medium (I believe). A more helpful relation for pixel-mass-to-luminosity is ...


-2

NO, at least by 3 reasons : recently,as 2003, it was found that 40% of the matter in the vicinity (accretion disk) of the BH will be radiated away. I'm convinced that all the matter, in excess above the limit, will be radiated away before a BH can be formed. quoting from WP-Black-Hole In the case of compact objects such as white dwarfs, ...


3

Mass of Sun = 1.989 x 10^30 Kg Mass of 1 lion = 190 Kg Mass of 1 lion in spacesuit = 250 Kg Mass of 1 trillion lions = 190 x 10^12 Kg Mass of 1 trillion lions in spacesuit = 250 x 10^12 Kg Mass of 1 trillion pregnant lioness in spacesuit = 300 X 10^12 Kg Temperature of Sun's surface = 5778 K Any objects would instantly disintegrated at close ...


3

The best paper on I've found on tidal tails is Reshetnikov & Sotnikova (2000). Their simple description of tidal tail formation is: To understand the development of tidal tails, one must recall how the water surface of the oceans get stretched radially by differential gravitational attraction exerted on it by our Moon. The differential forces ...


1

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 ...


0

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.


2

As Ben Goldacre says, "I'm afraid it's a bit more complicated than that." Phil Plait (Bad Astronomy) has occasionally written about this. Astronomers don't have a firm definition for the 'border' of a galaxy, tho' certainly objects classified as belonging should show some sort of contained orbit. But it gets worse, as they also have rough categories of ...



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