...send an email to someone who knows what's going on.
[More of my misguided attempts to simulate a stable rotating galactic gas disc without dark matter]
Yesterday I realised that I was setting the xy velocity components incorrectly. I fixed that, but alas that wasn't enough to get me a nice stable gas disc. No matter what I alter I always end up with a ring.
On the left : my standard setup now setting the velocities correctly. Some of the material in the outer disc escapes, but worse, pretty much all of the inner material moves outwards. Since most of the outer disc is still there, the result is a dense ring that fragments into a couple of massive blobs. With most of the mass now in two blobs rather than a disc or a ring, the system becomes unbound and the two blobs fly off to have wacky adventures.
In the middle : the same disc but with no temperature. I thought that maybe it was the thermal motions of the gas that were throwing everything off, but apparently not because the same thing happens. The difference is that there's much more fragmentation because there's no pressure preventing local collapse. Possibly because of this the resulting ring of fragments is fairly stable, since everything remains sort of symmetric.
The third one shows a desperate attempt using a more massive disc without any hydrodynamic effects. Apparently fluid effects aren't responsible either because the ring still forms. This time there are five large blobs formed which slowly merge into two.
At this point I admit defeat and emailed an expert. Maybe there's a well-known result that uniform discs aren't stable, though I can't see why they should turn into rings. Oh well, at least the failures look nice.
I'm intrigued - what sort of sticking function is implemented? Soft and fluffy at all speeds, or billiard-ball like and elastic?
ReplyDeleteNeither exactly, it's smooth particle hydrodynamics. The particles don't stick together or bounce off, but their properties depend on those of nearby particles. If they appear to stick together that's because they've become gravitationally bound.
ReplyDeletethe third one looks very interesting- it looks like this one:
ReplyDeletehttps://en.wikipedia.org/wiki/Supernova#/media/File:Keplers_supernova.jpg
The second one is similar to this:
https://en.wikipedia.org/wiki/Crab_Nebula#/media/File:Crab_Nebula.jpg
are you modelling supernovae explosion?
Tim Stoev No, I'm modelling galaxy discs. And they've gone horribly wrong...
ReplyDeleteWhat you see here are the particles current positions (in blue) and their trajectories (grey). What they should be doing is spinning around happily minding their own business. Instead they've decided to join the, "look at me, I'm a spirograph !" club.
It occurs to me that I've still got my FLASH grid code setup to make a disc. The one that eventually gave a nice, well-behaved galaxy that did what it was told.
ReplyDeletehttps://plus.google.com/+RhysTaylorRhysy/posts/KB28nT6DU9V
That one used dark matter and an exponential gas disc but it should be easy to modify. If it gives a different result that would be very interesting...
I'm not so sure this is a failure. In a collapsing prestellar mass with excess angular momentum, most of the mass will reside in an envelope supported by angular momentum around a diminutive core. Then only a gradual or catastrophic outward exchange of angular momentum will wind up with most of the mass in the core.
ReplyDeleteThe initial gravitational collapse is catastrophic, while the outward transfer of angular momentum is assumed to be gradual, finally resulting in a diminutive protoplanetary disk which is much less massive than the central protostar or T-Tauri star.
In a universe governed by catastrophism, I suggest that gradualism points to deficiency in our current knowledge. (There's no doubt about the catastrophic gravitational instability leading to star formation; however, there's no confirmation of the suggested gradualism of pebble accretion.)
Catastrophic outward angular momentum transfer:
I suggest that an overlying envelope which is much more massive than a diminutive core is intrinsically unstable and subject to positive-feedback disk instability, such that minor envelope inhomogeneities become amplified into a full-fledged disk instability which inertially displaces the diminutive (gravitationally-bound) core to satellite status within its own gas-giant-planet Roche sphere.
Imagine a Slinky made into a doughnut 'envelope' by bringing the two ends together around a golf ball 'core' in the center. Releasing the ends of the Slinky breaks the radial symmetry of the envelope, causing it to gravitationally (catastrophically) collect on one side of the former doughnut, and its greater inertia injects the smaller golf ball goes into a satellite orbit around itself as the newly centralized Slinky begins to form a new younger core. By this alternative mechanism, angular momentum is rapidly and catastrophically shifted outward in the unrecognized process of 'flip flop fragmentation'.
....................
So who's to say that your catastrophic runaway system is wrong and a finely-tuned gradualism is correct?
It must be that a large center mass is required.
ReplyDeleteHave you tried adding shepherd moons different orbits? I think I've seen them mentioned in the rings around some of the planets..
ReplyDeleteJungle Jargon this is what David Carlson is writing about. The way the current model is developed assumes a catastrophic event that gradually dissolves in the space. It lacks counter-catastrophy that will keep the system in place. This is why I correlated the model outputs to supernovae explosions- the model outputs show the consequences of a single event in a gas-particle system, it can not go recursive on itself rendering the initial event both outwards(what we see in the animation) and inwards(the counter catastrophy). I think the latter will fuck the simulation because it must try to create a computational super task- an exponential increase of operations in an exponential decreasing space where both operations and space are linked in an unknown way(a cool fractal :D). The only place where I have seen mathematical representation that may fit the relation between those is in the clustering algorithms.
ReplyDeleteThe successful attempt is interesting though. There is an interesting phenomenon related to the way the constrains are defined. Sadly I am neither familiar with modelling nor with the particular software. Maybe the phenomenon is related closer to the tool implementation than the actual astrophysics
OK, so after some emails and Google searching, I think I've worked out what's going on here.
ReplyDeleteWe're taught in undergraduate classes that if you're inside a sphere, you can neglect the mass above you (that is, further from the centre than you are) whereas the mass beneath you can be treated as a point mass at the centre of a sphere. It turns out that although this is true for a 3D sphere, it is not true for a 1D line or 2D ring. I've been assuming that one could say that a 2D disc is the same as a slice of a sphere. It isn't.
Imagine someone floating around at some random point inside a giant hollow sphere. Let's give them a telescope which has a very wide field of view, say, 45 degrees. Looking towards the centre of the sphere, they will see a very wide area that's a long way off. Looking in the exact opposite direction they'll see a much smaller area that's much closer. Both views span 45 degrees, but of course the more distant area is physically larger and more massive than the closer one.
It turns out that the area of each segment of the sphere they're looking at scales as the distance squared - the further away, the larger the area. Gravity scales in exactly the opposite way - the greater the distance, the weaker the force. Although the area you're looking at is larger, it's also more distant. The two effects exactly cancel, so you don't feel any force at all - even if you're really close to the sphere.
http://www.sparknotes.com/physics/gravitation/potential/section3.rhtml
But this does not work in a 1D or 2D case. The simplest example is to imagine two equal masses floating in space. It doesn't matter how they're arranged, I'm always going to be more strongly attracted to the nearby one - there's no way (unless I'm exactly midway between them) that one can cancel out the force of the other.
Now re-imagine that hollow sphere and cut a razor-thin hoop out of it. When you're looking through the telescope, the mass of the part of the hoop you're viewing will now scale as the distance - it's just a line, after all. But gravity still scales as distance squared. So the two effects do not cancel, and you'll be pulled more strongly towards the nearby part of the hoop.
In the case of a filled thin disc, I don't even want to think about how you treat the mass interior to any point. But any slight disturbance is going to turn the disc into something ring like, at which point there's a runaway effect as everything in the interior rushes outwards. Hence my using v = sqrt(GM/r) is simply wrong, unless this is corrected (which is horrendously complicated : http://arxiv.org/pdf/0903.1962.pdf) you'll always get rings. Nothing to do with hydrodynamics or angular momentum, just geometry.
Rhys Taylor Yes, that would make a big difference. : )
ReplyDelete