How much Dark Matter do you hold in your hands?

Jul 09 2009 Published by under Physics & Astronomy, Science

Via a Cosmic Variance blog post, I found this astro-ph paper by Catena and Ulio that claims the local density of Dark Matter is 0.39 GeV/cm3.

What does this mean?

Well, first, you may object that GeV is a unit of energy, so really what we've got here is an energy density of Dark Matter, not what most of us mean when we say "density" all by itself (which is mass density). Physicists, however, know that converting between energy and mass is so easy (via E=mc2) that they will very often, especially when talking about fundamental particles, cite masses in energy units. Divide by the speed of light squared to figure out that this is a density of 6.9×10-25 grams per cubic centimeter.

Second, "local" means "in our area of the Galaxy". Dark Matter clumps on scales of hundreds of light-years, at the smallest, so if you're looking on a scale smaller than that, it's going to look smooth. It's similar to our atmosphere; if you climb a mountain and get five miles above sea level, the air will be noticably thinner. But, if you go up just a few meters, you're not going to notice any difference in the density of air.

What is the density of air? Well, if you believe Wikipedia's Answer (and you should in this case), it's about 0.075 lbm/ft3... or, in more reasonable units, 0.0012 grams per cubic centimeter. (That's at room temperature and standard sea level pressure.)

And, while we're at it: the density of Dark Energy in the Universe is about 75% of the critical density, the critical density being 3H02/8πG, or 9.7×10-30 grams per cubic centimeter (for a Hubble constant of 72 km/s/Mpc).

Right.

So let's put this all together. Cup your hands. That makes a box roughly 5cm on a side, or 125 cubic centimeters in size. In your hands, you are holding:

  • 0.15 grams of air
  • 8.7×10-23 grams of Dark Matter
  • 9.1×10-28 grams equivalent of Dark Energy

Strictly speaking, "holding" isn't the right term, because the Dark Matter particles are passing right through your hands as if they weren't there... but at any one moment, that's how much Dark Matter is on average within the box you make by cupping your hands. (Air is coming in and out as well, because you probably have cracks in the box you make, but it doesn't pass through your hands.) And, it's hard to say whether Dark Energy is passing through your hands, or is a property of the vacuum and as such it is just how much energy density is there as a result of the volume you've cupped, but you get my drift.

Oh, and I suppose I should mention that every second, about 140 million neutrinos from the Sun pass through your cupped hands (based on the neutrino flux cited at this page from HyperPhysics). However, they're going so bloody fast (very close to the speed of light) that at any moment, there's only about a 2% chance that one of those neutrinos is right then within your hands.  (A similar consideration is probably true with Dark Matter particles, but I'd need to know the mass of said Dark Matter particles (nobody does), and I'd need to know their velocity (there are estimates, but I haven't tracked them down) to actually give you numbers.)

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