astrophysics - Did dark matter cause the formation of the Solar System?

This question is related to my previous question on Solar System Formation and is a pure thought experiment, with as few as possible assumptions made.

From my previous question, I learned that stars form from the condensation of a very large cloud of gas, producing perhaps 1,000 (or more) stellar mass objects.

I also learned that it usually takes a trigger, a shockwave from a supernovae or another giant gas cloud "bumping" into it, to start the condensation process. Without a trigger, collapse of a extremely low density giant gas cloud on it's own will take a very long time.

Currently, we do not have any evidence as to how the gas cloud, that our solar system is part of, collapsed 4,500 million years ago.

Now consider what we know about dark matter:

1. 
   

   It is not considered to be present in significant amounts in the galactic plane, but rather forms spherical halos surrounding the galaxy, stretching far beyond the visible matter in the galaxy.

   
   


2. 
   

   The Wilkinson Microwave Anisotropy Probe (WMAP) showed that the existence of dark matter is favored, implying that dark matter has been present in our universe for as long as ordinary matter has.

   
   
   


3. 
   

   Another point to bear in mind is that, without a dark matter halo, the arms of a spiral galaxy will be unable to maintain their shape over the lifetime of the galaxy.

   
   

Now assuming that the collapse of our giant gas cloud was not caused by a trigger, we have no evidence as to how the collapse occurred.

Assume that the dark matter is in a spherical halo around the gas cloud - obviously it will not be perfectly spherically distributed, it would almost certainly have higher concentrations of dark matter in some areas than others.

These dark matter mass concentrations would have drawn clumps of the enclosed gas cloud together, increasing the density in the clumps and allowing gravity to pull together protostellar cores, which eventually brought about the galactic structure of the present Milky Way.

My question is, given that we don't know by which method our star cluster was formed, is this scenario as plausible as any other or have I made wrong assumptions along the line?

Answer

In the "microscopic" sense, the formation of the Sun and solar system do not depend strongly on dark matter. Looking at things on the scale of GMCs, you can get a Jeans-unstable situation that will lead to star formation without invoking dark matter.

There's a step much earlier in the history of the Universe that needs dark matter, though. In the early Universe after inflation, you have a near-homogeneous distribution of dark matter and (in the same space of course) a near-homogeneous distribution of baryons. Consider a region that is randomly slightly denser than the average: matter in this region will begin to collapse, relative to its surroundings, the density contrast will increase. The baryons are strongly coupled to the photons; the radiation pressure + hydrostatic pressure will increase as the region compresses, causing the collapsing region to "bounce back". Similarly, an underdense region wants to expand, but the pressure drops and it re-contracts. So the baryon density at a given point oscillates (relative to the mean, which is always dropping with increasing time) in a characteristic way. The technical term is Baryon Acoustic Oscillations (BAOs).

The dark matter, on the other hand, does not feel pressure support and can simply collapse, forming dense structures called "haloes" (which are roughly spherical). By the time the Universe is cool enough for electrons to combine with protons to make neutral Hydrogen and become transparent to the photons, the dark matter has clumped substantially. With this recombination, the gas suddenly stops feeling the radiation pressure, and begins to collapse into the dark matter haloes, eventually forming galaxies.

Without the dark matter "backbone" formed during the BAOs, it's difficult to say what would happen, because you stop talking about the real Universe. Depending on the cosmology of the now-hypothetical Universe you choose, the gas might never collapse into dense structures, just stay diffuse and slowly cool along with the rest of the Universe, or it could collapse under its own self-gravity, but would form galaxies along a structure defined by its own gravity rather than the dark matter structure already in place.

So in this sense, dark matter is necessary to the formation of the Milky Way in the Universe as we know it, which of course later gives rise to the formation of the Solar System.

Incidentally, we have strong evidence that BAOs actually happened and aren't just in the feverish dreams of theorists.

Footnote about your point 3: a galaxy is plausibly a stable structure without a dark matter halo, but the halo is required to explain the rotation velocity in the outskirts of galaxies.

Footnote about dark matter clumping - dark matter can only collapse until it virializes, which puts a limit on how dense a structure of a given mass can get. You can have a Moon-mass clump of dark matter, but it will be much more extended than the Moon. You can have a Moon-sized clump of dark matter, but it will be much less massive than the Moon. You can't have a Moon-sized-Moon-mass clump of dark matter.