MOND: Explaining the “Missing Mass” Problem in Galaxies

[exmarine]

I’ve been reading various things on the internet about how Modified Newtonian Dynamics attempts to solve (or just model?) the “missing mass” problem in galaxies. It sounds more reasonable to me than hypothesizing conveniently undetectable dark matter. But I am wondering why they are using what seems like more complicated expressions than necessary. Isn’t it a simple curve fit for the universal gravitation “constant”? I am assuming there must be good reasons why it is not that “simple”. Any help in understanding this is appreciated.

 

[Vanadium 50]

MOND adds one parameter to the equations - can't get much simpler than that. It uses the simplest equation that matches the data.

Note that while MOND does well on galactic scales, it does not do well at larger scales.

 

[exmarine]

I see. So that makes it difficult or impossible to correct by adjusting a universal “constant” and making it a function of distance.

Are we – our solar system – on the flat part of our own galaxy’s rotation curve? Are we rotating “too fast” about the galaxy center?

Is our solar system then permeated with Dark Matter? If so, wouldn’t that require reformulation of Newton dynamics / Kepler’s laws?

What distribution of DM is suspected in our galaxy, and within our solar system?

 

[Bandersnatch]

Are we – our solar system – on the flat part of our own galaxy’s rotation curve? Are we rotating “too fast” about the galaxy center?

Here are example graphs with plotted approximated mass distribution and its contribution to rotation curves in the MW (precision is exaggerated):

The sun is at approx. 8 kpc from the centre. As you can see, it's a roughly flat curve at that distance.

Is our solar system then permeated with Dark Matter? If so, wouldn’t that require reformulation of Newton dynamics / Kepler’s laws?

The graph on the right shows that there's approx. 25% more dark matter than baryonic (i.e. Disc+Bulge) matter enclosed within the radius of the orbit of the Sun. However, unlike baryonic matter DM does not clump, so its density in any given region of space is extremely low - so low that any effect it might have on the dynamics within the solar system is negligible.
The graph to the right allows you to make a rough calculation of the density of DM in the solar system using simple algebra - the result being about 10¹³ kg per AU³. That is, according to this estimate, at any given time there's about 100 000 supertankers' worth of DM spread around in a sphere inside Earth's orbit, or ~10^-22g/cm³, which is not far from estimates done using other, more precise methods (such as here or here).

These values are too low to have a noticeable effect, unless you look extremely carefully - the first of the two papers quoted above actually attempts just that. As such, they could not affect formulation of Kepler's, Newton's and other laws or experiments with insufficient precision.

What distribution of DM is suspected in our galaxy, and within our solar system?

The distribution in its simplest form is shown on the graph above (right). Linear growth of enclosed mass translates to a spherically symmetric cloud whose density is falling with the square of the distance.
Unless it turns out DM can sufficiently interact with matter (e.g. weak force), it will be freely streaming through the solar system with density corresponding to the density in the galactic DM profile at this distance from its centre.

 

[exmarine]

Thanks for the info and the papers! Fascinating subject.