For those who haven't seen the previous efforts, I am trying to simulate a uniform, galaxy-sized disc of gas. Don't ask why. So far I've been plagued by my nice neat discs insisting on turning into rings, even when I tell them not to.
I realised that I was setting the velocity of the particles in a fundamentally wrong way. The classic equation v = sqrt(GM/r) assumes the system is a sphere, but it categorically does not work for a disc. The circular velocity (that is, the speed needed to stay in a stable circular obrit) depends strongly on the geometry. This is actually fiendishly difficult to calculate for a uniform disc - this paper (http://arxiv.org/ftp/arxiv/papers/0903/0903.1962.pdf) does it, but I don't care for all that mathematics.
What I've done instead is side-step the issue by letting the simulation code measure all the accelerations for the first frame, then I set the velocities to compensate for the radial acceleration. This gives me a result very similar to the analytic result, which is nice, albeit with a lot of scatter for reasons I'm still trying to determine.
Anyway, you can see above that this gives a different result to the earlier attempts. It still fails, but in a new way ! :) This time there is (at first) very little outward movement from the particles close to the centre of the disc. However, it still fragments due to the random motions and positions of the particles. These asymmetries build up and soon the thing is no longer even a disc or a ring at all, and consequently it breaks up. If I want the disc to be truly stable, I'll have to find a combination of parameters whereby the disc won't fragment but the particles aren't moving at escape velocity either.
I suspect that uniform pure gas discs, unlike spheres, need a lot of fine-tuning to remain stable. Inside a hollow shell a particle will stay at rest. This isn't the case for thin rings - particles inside the ring will move toward it. So rings are unstable, whereas shells are not. This means that whenever a ring develops (which can easily happen due to the random motions of the particles) it tends to get worse over time.
Of course in reality galaxies also have stars and probably a lot of dark matter as well which helps keep the gas stable. Intriguingly, the paper that calculates the velocity profile for a uniform gas disc also claims that far less dark matter is needed to keep discs stable than is normally supposed. That's something I can probably check. For now, it's fun to watch, at least.
God does not play dice with the universe. He adjusts parameters.
ReplyDeleteyour experiments in modelling starts shifting towards theology :P o divine creator of mathematical hacks based on trajectory frame lapses
ReplyDeleteFor someone who asked us to put space WMD to rest, you do spend a lot of time destroying galaxies and other gas clouds! :)
ReplyDeleteBy the way (and off-topic), what happens if you drop a black hole/wormhole into a star? How does it vary depending on the star (mass, stage of life/remnant), and the hole size (stellar, primordial, varied intermediary sizes) and type (black hole, womhole with empty space on the other size)?
There is one relatively famous SF example where they drop a (6.7m diameter, disc-shaped) wormhole in a (possibly Sun-like) star (with a planet in decaying orbit around a black hole on the other side) to blow it up it up in a matter of hours (and those are the good guys). I always wondered what would actually happen, accepting the fact that the wormhole-enabling structure would actually survive star core conditions.
Elie Thorne Well those galaxies had it coming. Damn things won't even spin right, I'll show them....
ReplyDeleteI am familiar with the example of which you speak. It always struck me as an odd way to creating a supernova given that stars which are less massive don't explode. Maybe it's about disturbing the balance between pressure and gravity by rapidly removing a lot of mass.
It's easy to estimate how much mass can be removed, but it depends strongly on where in the star the Stargate is since temperature varies massively from the interior (~15 million K) to the "surface" (~5000 K). That means the particle speeds will vary from something like 6.5 km/s to 350 km/s.
The average density of the Sun is only slightly higher than that of water, so the following approximation will give us a handle on how fast the Stargate will drop :
http://www.thenakedscientists.com/forum/index.php?topic=49977.0
A terminal velocity of a few m/s means we're looking at several years for the Stargate to reach the core. Or maybe it never will, since the density of the Sun at the core is many times that of iron or even (probably) naquada, which isn't that heavy.
Anyway, near the surface let's assume the average density for the Sun - 1410 kg/m^3. The area of the wormhole is pi*(6.7/2)^2 = 35 sq m. Velocity of the plasma into the wormhole is 6.5 km/s. So in 1 second we get a volume of material equivalent to 35*6500 = 2.3E5 cubic metres = 3.2E8 kg. In 12 hours that's 1.4E13 kg. Alas, the mass of the Sun is 2E30 kg, so we've only decreased the mass by around 7E-16 %. This will achieve precisely diddly-squat.
If we allow the Stargate to have some technomagical propulsion so that it reaches the centre of the Sun, the total mass lost in 12 hours will be about 3E-16 %. Still useless.
You may be wondering about the black hole's gravity sucking in matter faster, as clearly shown in the original "oops, we've connected to a black hole" episode. Well, even at its most extreme that clearly never reached more than a few gs, which means the infall rate won't be significantly higher.
So the method in the show just doesn't work at all. As to whether removing a really large amount of mass would cause a supernova, I'm not sure. Maybe if you removed all of the outer material around the core, it would expand to reach a new equilibrium. I don't think it would explode though. To do that you'd need to increase the pressure drastically, and I can't see any way to do that by removing mass.
Stars being eaten by black holes have been observed. They don't explode, but they do do interesting stuff :
http://www.huffingtonpost.com/entry/black-hole-ate-star-burped_us_565cbaace4b079b2818b5b90
Oops, I forgot to account for the higher density of material in the core. It's about ~100x that of the surface, so still nowhere near enough mass will be lost to be significant.
ReplyDeleteI feared that much, alas, with such a small cross-section compared to the vastness of a star. But I forgive them for of the sheer ludicrousness of jury-rigging a star.
ReplyDeleteWhat would be the longer effects and/or a bigger cross-section, or if it had been a black hole instead? Would it have slowly eaten the entire star away?
Also, what would happen to a stellar remnant? Would it make a dwarf star evaporate? Would it crack a neutron star open?
https://plus.google.com/u/0/103860147871348309151/posts/ddhdaj8MTyB
ReplyDeleteElie Thorne To follow up on that, if you threw a neutron star or white dwarf into a giant star, you could potentially trigger a supernova or at least a nova. Novae happen when material accumulates on the surface of a white dwarf to the point where there's a massive fusion explosion. I don't think this is possible in the case of a wormhole, where material is being drained.
ReplyDeleteStill, if you did remove enough of the star you could destroy a planetary system, albeit in a more stately manner. If you remove the entire fusing core of the Sun (which extends to about 0.25 solar radii) you'll have removed enough mass to send all the planets into highly elliptical orbits. Not quite enough to send them hurtling into intragalactic space, but close. Which is not terribly threatening to Apophis though.
But then it hit me that the best way to destroy a star with a wormhole is obvious : don't link a star and a black hole, ,link two stars. Massive stars for preference. But if you really really want to make sure, link to a neutron star.
If you had a massive Stargate that could swallow the neutron star whole and spit it into the target star, you'll get a TZW object. That might be short-lived on astronomical timescales, but probably won't instantly explode. Probably the increased density of material around the neutron star causes an increased temperature, preventing material from quickly infalling.
However, if you have a regular sized gate (assuming it can survive), then things get much more spectacular. Pulled by the neutron star's tremendous gravity, the gate will slice through it at nearly the speed of light. As it does so it will spew neutron-degenerate matter into the target star. Without the gravity of the neutron star to hold it together, this will be bad. Like, seriously mega-hyper-total bad.
https://www.youtube.com/watch?v=o_EBqZPCZdw
http://io9.gizmodo.com/5805244/what-would-a-teaspoonful-of-neutron-star-do-to-you