experimental physics - Distribution and detection of dark matter

I feel in the dark (no pun intended :),

I'm sure most of you are familiar with this image I pulled from wikipedia:

The caption reads: "3D map of the large-scale distribution of dark matter, reconstructed from measurements of weak gravitational lensing with the Hubble Space Telescope."

I'm wondering what makes us think that we should be able to detect dark matter on Earth and if it's possible that we could be in a region where dark matter doesn't exist, or how do we know that we lie in a region where dark matter lies? Would it be easier to detect dark matter particles in other places?

Can someone shed some light in this for me?

Answer

I was led to your question after answering a related question.

We think that the dark matter in the vicinity of the solar system has a rather smooth distribution and that there actually isn't very much of it - in terms of a density. It is estimated that the local dark matter density is around $\sim 0.01$ $M_{\odot}$/pc$^3$ (Garbari et al. 2012, Bovy & Tremaine 2012) corresponding to only a few $10^{-22}$ kg/m$^3$. For comparison, the density of the interplanetary medium is abut 100 times greater.

The reasons that dark matter is unimportant on solar system scales, but dynamically important on galaxy scales and utterly dominant on galaxy cluster scales is that the total gravitating mass goes up with volume (i.e. the cube of the length scale).

The Galaxy probably has an approximately spherically symmetric distribution of dark matter. Dark matter does not readily "accumulate", either in the disk of our Galaxy or around individual stars or solar systems. It interacts very weakly with normal matter and is primarily influenced by gravity. The Earth's gravity for example is far too small to make a local concentration of dark matter. The local dark matter would be moving in the Galactic potential at speeds similar to that of the Sun around the Galaxy ($\sim 250$ km/s); much faster than the 11 km/s escape velocity of the Earth or the 42 km/s escape velocity of the solar system at the Earth's orbit.

The net outcome of this is that we do expect there to be some dark matter present everywhere on Earth, and that it should have roughly the density expected for its orbital radius in the Galaxy. However, yes, there are places where dark matter could be more concentrated - the centres of large spiral galaxies for example. There are even calculations that suggest that dark matter could be captured in the centres of stars (e.g. Vincent et al. (2015)).