Why Does Dark Matter Appear Scale Variant in Galactic Rotation?

[StationZero]

One of the principal arguments for the existence of dark mater is, of course, that galaxies rotate as if they were on a plate as opposed to the differential rotations of planets in our solar system.

My question is, if the entire galaxy is infused with this dark matter, why does it seem to be scale variant. That is, why doesn't the dark matter in our solar system cause it to rotate as if on a plate just as the larger galaxy does as a whole?

 

[Chalnoth]

One of the principal arguments for the existence of dark mater is, of course, that galaxies rotate as if they were on a plate as opposed to the differential rotations of planets in our solar system.

My question is, if the entire galaxy is infused with this dark matter, why does it seem to be scale variant. That is, why doesn't the dark matter in our solar system cause it to rotate as if on a plate just as the larger galaxy does as a whole?

The solar system is far, far more dense than most of the galaxy, and the dark matter is spread thinly throughout. So there just isn't enough dark matter in the solar system for its gravitational effect to be measurable.

 

[StationZero]

Hmm, I'm surprised nobody else has commented on this thread. Thank you Chalnoth for that explanation but hopefully someone can offer an extended analysis. First of all, not only does this thinly spaced dark matter motivate a star at the edge of our galaxy to rotate at an absurdly high velocity, it also holds together our local group and also our local supercluster. This doesn't seem to be a trival effect. So, to eschew the effect of dark matter in our solar system for its lack of huzpah is well noted but it doesn't explain the apparent scale invariance of its effects at several other cosmological scales. Perhaps a reference would help me.

In any case, one would think that, however weak it may comparably be relative to larger scales, we might be able to detect some contribution of dark matter in the orbit of planets in our solar system?

 

[Chalnoth]

Hmm, I'm surprised nobody else has commented on this thread. Thank you Chalnoth for that explanation but hopefully someone can offer an extended analysis. First of all, not only does this thinly spaced dark matter motivate a star at the edge of our galaxy to rotate at an absurdly high velocity, it also holds together our local group and also our local supercluster. This doesn't seem to be a trival effect.

It's just a matter of scale. The galaxy is big, and clusters and superclusters are far, far larger.

The milky way, for instance, is tens of thousands of light years across, and you have to go a few hundred to a few thousand light years before the dark matter density becomes really apparent.

By contrast, our own solar system is less than 0.001 light years across (this is about the limit of the Kuiper belt, the large collection of icy objects out beyond the planets that supplies the inner solar system with the occasional comet). This is a massive difference in scale, and that makes a huge difference in the effect of dark matter.

This recent paper measures the local density of dark matter:
http://arxiv.org/abs/1205.4033

To put the density in more understandable terms, this means that we currently estimate the total density of dark matter within the solar system (out to 50AU, the extent of the Kuiper belt) to be about 10^{17}kg. That may sound like a lot, but Pluto's mass is 10^{22}kg. So the total dark matter in the Solar System is estimated to be about one ten thousandth the mass of Pluto, spread over the whole 50AU out to the edge of the Kuiper belt.

 

[StationZero]

Thanks again, Chalnoth, I'll check that out.