As I understand it, those simulations did not include three-body interactions that could leave particle pairs bound. If this happens, those binaries can now inject energy into the cluster as a whole, keeping it inflated and preventing collapse. Of course, the binaries' orbits shrink over time, so this doesn't go on forever.
The Gravo-Thermal Catastrophe
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Re: The Gravo-Thermal Catastrophe
#12Application of the 1/R2 gravity formula to the pointwise mass with R->0 can easily power your Romulan ships. In similar vein applying that classical gravity formula - which is valid only to spherical masses or masses at such large distances that they can be treated as such - to the stars inside disk galaxies gets you the "dark matter", and thus not surprisingly the flatter the disk galaxy the more "dark matter" :)
Re: The Gravo-Thermal Catastrophe
#13A) …why? What makes this interesting to physicists? I understand this as “if stars weren’t stars but instead rigid spheres, and if they were in an impossibly-impervious giant sphere, then weird stuff happens”. And…?
B) “since stars rather rarely collide” still blows my mind. I did some napkin math on Reddit a while back on why there will be very few stellar collisions (really, one star falling into another’s orbit?) when andromeda collides with the Milky Way, and the answer is that space is just mind-bogglingly huge. Even the most dense clusters in our galaxy are akin to ~70 1cm diameter spheres per olympic swimming pool.
If god is real, he is surely a giant.
Re: The Gravo-Thermal Catastrophe
#14Is this right?: * Although you can make the enveloping sphere as large as you want, the (anti-)equilibration process requires a sphere of some finite radius because if you wait long enough a few stars eventually get launched at escape velocity, and if these actually escaped they would effectively cool the remaining stars. * Therefore, the characteristic time scale for this process (i.e., the timescale on which the av…
> In real life, these turn into black holes I think this is right, and I think he explicitly calls out that these calculations were done with Newtonian physics modeling point particles - and we know that those two factors severely limit the application of this to the real-world.
Right, it wasn't criticism, but the point I added (that I think was not explicit in the article) is this: black holes provide a lower bound on the potential energy, not just an indication that the model is breaking down.
Re: The Gravo-Thermal Catastrophe
#15Application of the 1/R2 gravity formula to the pointwise mass with R->0 can easily power your Romulan ships. In similar vein applying that classical gravity formula - which is valid only to spherical masses or masses at such large distances that they can be treated as such - to the stars inside disk galaxies gets you the "dark matter", and thus not surprisingly the flatter the disk galaxy the more "dark matter" :)
>In similar vein applying that classical gravity formula - which is valid only to spherical masses
What? Newtonian gravity is defined for point masses. Anything else you derive from that by integrating a mass density over a region.
Re: The Gravo-Thermal Catastrophe
#16Application of the 1/R2 gravity formula to the pointwise mass with R->0 can easily power your Romulan ships. In similar vein applying that classical gravity formula - which is valid only to spherical masses or masses at such large distances that they can be treated as such - to the stars inside disk galaxies gets you the "dark matter", and thus not surprisingly the flatter the disk galaxy the more "dark matter" :)
>In similar vein applying that classical gravity formula - which is valid only to spherical masses What? Newtonian gravity is defined for point masses. Anything else you derive from that by integrating a mass density over a region.
it is equivalent formulations - the point masses case is obtained from the spherical in the limit. The spherical case is just more illustrative to show where the fantom of the "dark matter" in the disk galaxies comes from.
>by integrating a mass density over a region.
exactly. When you do that for a disk galaxy you get much flatter curves that the 1/R the proponents of the dark matter insist on (that 1/R is exactly what one would get if the galaxy was spherical or the star was far outside of the disk)
Re: The Gravo-Thermal Catastrophe
#17A) …why? What makes this interesting to physicists? I understand this as “if stars weren’t stars but instead rigid spheres, and if they were in an impossibly-impervious giant sphere, then weird stuff happens”. And…? B) “since stars rather rarely collide” still blows my mind. I did some napkin math on Reddit a while back on why there will be very few stellar collisions (really, one star falling into another’s orbit?)…
For A), if you have a bunch of tiny atoms bouncing around within a regular-sized sphere, then thermodynamics predicts that the sphere will experience some constant amount of pressure, with tiny fluctuations up and down. This result is interesting, since it just takes the ordinary system and asks, "What if we scale it up so that the atoms (stars) interact gravitationally?" Then, there is no equilibrium pressure experienced by the sphere, since the gravitational potential of the stars keeps increasing.
Re: The Gravo-Thermal Catastrophe
#18As I understand it, those simulations did not include three-body interactions that could leave particle pairs bound. If this happens, those binaries can now inject energy into the cluster as a whole, keeping it inflated and preventing collapse. Of course, the binaries' orbits shrink over time, so this doesn't go on forever.
What is a three-body interaction in classical gravity? If you calculate the force on each particle from every other particle, what’s left out?
Re: The Gravo-Thermal Catastrophe
#19A) …why? What makes this interesting to physicists? I understand this as “if stars weren’t stars but instead rigid spheres, and if they were in an impossibly-impervious giant sphere, then weird stuff happens”. And…? B) “since stars rather rarely collide” still blows my mind. I did some napkin math on Reddit a while back on why there will be very few stellar collisions (really, one star falling into another’s orbit?)…
For A), if you have a bunch of tiny atoms bouncing around within a regular-sized sphere, then thermodynamics predicts that the sphere will experience some constant amount of pressure, with tiny fluctuations up and down. This result is interesting, since it just takes the ordinary system and asks, "What if we scale it up so that the atoms (stars) interact gravitationally?" Then, there is no equilibrium pressure experi…
> Then, there is no equilibrium pressure experienced by the sphere, since the gravitational potential of the stars keeps increasing.
And GR fixes that by kind of moving the sphere walls farther away, ie. the space geometry changing by the changing gravitational potential.
Re: The Gravo-Thermal Catastrophe
#20My favourite along these lines is that the mass vs diameter relation for black holes scales in such a way that we are absolutely in a black hole right now according to current theory. As in the current mass of the universe is enough for a black hole with an event horizon diameter that extends beyond the universe.
This mass to event horizon radius relationship is a property of a Schwarzschild spacetime geometry, globally the universe has a FLRW spacetime geometry
The light has no chances of getting out of the 13.7B ly bubble due to Hubble expansion. Sounds a lot like black hole.