Some useful facts about dark matter

We live in the middle of a cloud of dark matter, one that provides sufficient mass to keep the Milky Way Galaxy from flying apart. A tweeted question from @stanltaaf inspired me to put together some useful facts about the dark matter halo in which we live. Useful of course is a relative term.

First, let's get a sense of scale. We measure distances in space in either light-years or parsecs (1 parsec = 3.26 lightyears). The nearest stars are on the order of parsecs away. We measure Galactic scales on kiloparsecs (1kpc = 1000 parsecs); our Sun is about 8 kpc from the Galactic Center. Below is a picture of the visible part of a spiral galaxy; the stars and glowing gas that we can see. If this spiral was our own Milky Way, we'd be embedded in one of the arms about halfway out. The arm of stars forms the actual glowing Milky Way which can be seen on clear nights. On Earth, the Galactic Center is towards the constellation Sagittarius, but is only overhead in the Southern hemisphere. There are somewhere around 100-400 billion stars in the Milky Way, we are in fact a rather large galaxy. Most of these stars are smaller, cooler, and redder than our Sun. 

NGC 1232 via APOD Image Credit: FORS, 8.2-meter VLT Antu, ESO

NGC 1232 via APOD
Image Credit: FORS8.2-meter VLT AntuESO

Now, this is what we can see in a Milky Way-like galaxy. The actual mass of the galaxy is dominated overall by the dark matter halo. Unlike stars and gas, dark matter doesn't live in a pancake-like disk, it is a big fluffy halo, looking something like this:

Image credit: ESO/L Calçada.

Image credit: ESO/L Calçada.

The halo itself extends much further away from the center of the galaxy than the thick visible disk of stars. Right where we live is around the point where the density of visible matter is larger than the density of dark matter. Averaged over parsec-scale distances, locally there is about 1 hydrogen atom per cubic centimeter, or about 1 GeV of energy per cm3. Of course, very locally (around the Sun or here on Earth, densities are a lot higher). Dark matter density locally is about 0.3-0.4 GeV/cm3.

If dark matter is a WIMP (weakly interacting massive particle, where Weak means the weak nuclear force), then very roughly there is 1 dark matter particle per coffee mug around here. Which is a useful thing to know.

It'd be nice to see both dark matter and visible matter together, which of course we can't in reality. If we could see dark matter directly, it wouldn't be dark. While we can see dark matter indirectly through its gravitational effects (through lensing), we can also use computer simulations of galaxy formations to get an idea of what galaxies and their dark matter should look like. Here's one such simulation from Andrew Pontzen and the N-Body Shop

Given that we live in the middle of a cloud of dark matter, how much is passing through us? Well, the Sun orbits the center of the Galaxy in 100-200 million years (the Galactic Year), implying that it is moving at something like 200 km/s. Anything gravitationally bound to the Galaxy (like dark matter) at our distance from the Galactic Center is also moving at something like 200 km/s. Some are moving slower, some faster, but on average, dark matter is passing through you right now at relative speeds higher than anything humanity has ever achieved. The New Horizons probe to Pluto, for example, reached 16.3 km/s, and was the fastest space probe ever launched.

So that single dark matter particle in your coffee mug isn't sticking around very long. Another will be along soon, however.

Interestingly, these local speeds for dark matter is independent of what the dark matter is. If it's a WIMP or something much heavier or lighter, the fact that dark matter makes that sort of fluffy halo means that dark matter must be moving at around 200 km/s local to the Earth. Only by assuming new interactions of dark matter with itself or with the visible matter could we postulate different speeds of dark matter locally (though the average is still about 200 km/s). Some of my research involves such novel physics, and how we might look for it.

As the Sun swings through the Galaxy, it sweeps through dark matter. Now, some of that dark matter might, very rarely, hit an atom in the Sun, lose energy and get trapped in the Sun. This could lead to dark matter annihilating in the core of the Sun. Could this do anything interesting?

Well, let's ask how much dark matter the Sun could possible scoop up. Imagine that all the dark matter that ever passed through the Sun was trapped. Over the last 5 billion years, the Sun has passed through about 2x1018 kg of dark matter. That sounds like a lot, but it's only one trillionth the mass of the Sun. So even in this crazy maximal case, the dark matter is a small perturbation on the Sun's mass.

That doesn't mean this can't be interesting. If dark matter gets trapped at the Sun's core, then it might hit other dark matter and annihilate. After all, it doesn't have much else to do. If that annihilation results in high energy neutrinos, we might see that in our neutrino detectors on Earth. We look, but we haven't seen anything yet.

For small cool stars, or stellar remnants like white dwarfs, brown dwarfs, and neutron stars, this trapping and annihilation could lead to unusual heating mechanisms. This would be irrelevant in the Sun, but important in these other types of stars. So we can place limits on certain kinds of dark matter this way.

How many dark matter particles hit you?

This is a highly model-dependent answer (theorist for "it depends"). Again, assuming dark matter is a WIMP, current experimental results indicate that dark matter can scatter off nuclei at most about once per kilogram per year. So over an average lifetime, one might expect a few thousand dark matter particles to ricochet off of atoms in your body.

Nothing bad will happen to you when this happens. The energies are small, and for comparison, a few thousand potassium atoms in your body decay every second, releasing comparable amounts of energy. Damn those bananas.