Q: How likely is it that there’s dark matter in me right now?

Physicist: Probably very likely!  Probably!

When we look out into the universe we find that on galactic scales and up that most of the mass in the universe is “dark”.  Based on how galaxies form, move, collide, and bend light we can infer that the large majority of the matter creating gravity out there interacts with everything, including itself, only through gravity.

Like all the other matter, the Milky Way’s dark matter is zipping around at a fair clip.  Our solar system (and all the stars close enough to see with the naked eye) are orbiting the galaxy at about 220 km per second.  Around here we’re all orbiting in more or less the same way so, like cars on a highway, relative to each other we’re traveling much slower; a mere few dozen km per second.  But dark matter doesn’t have to “stay in its lane”.  Like cars driving across a highway, matter in a random orbit tends to find itself in an unfortunate situation sooner than later, so orbiting in formation is just something that normal matter does.  Or rather what it does after a violent process of elimination (and that’s why Saturn’s rings, the solar system, and the entire galaxy are all roughly flat).

An unfortunate situation.

Not interacting means that dark matter orbits galaxies in puffy, roughly spherical “dark matter halos”; a cloud of randomly orbiting stuff that barely notices all of the stars it passes by/through.  We can expect any individual bit of dark matter around us to be moving at on the order of hundreds of km per second.

All this to say, “having dark matter in your body” doesn’t mean you’ve come down with a bad case of WIMP-iness.  You’re not slowly collecting dark matter in your thyroid.  Even if you could detect dark matter (which has proven to be tricky) in your body, by the time you realized it was there it would already be long gone.  Literally.  The best human reaction times of any kind are around a tenth of a second, so any dark matter you find in your body is likely to be dozens of km away by the time you are physiologically able to know about it.  Which is… useful knowledge?

We can see that dark matter is there and we can pontificate about what it’s like, but we’ve never once seen it do anything other than simply exist in extremely large quantities.  We think it’s matter, because it produces gravity.  From the way it arranges itself around galaxies, we don’t think it ever interacts, slows down, or changes direction except through gravity.  We’re standing in an extremely thin, omni-directional rain of invisible, intactile stuff that passes through us at stupefying speeds, and that’s about all we can say about the dark matter around us it.  Unfortunately, for this question, we have no idea how much mass particles of dark matter have, or even if dark matter takes the form of particles at all (although, if it didn’t, quantum mechanics would have a lot of explaining to do).

So here’s a wild estimate.  The radius of our galaxy is about 129,000 light years and the total amount of dark matter is in the neighborhood of 10¹² solar masses, or about 2×10⁴² kg of mass.  Assuming that’s evenly and spherically distributed around the galaxy (which is a rough, but not terrible, estimate), that’s a density of about 2.6x10^-22 kg/m³.  So if you gathered up all of the dark matter in the Earth (or an empty Earth-sized volume, for all that dark matter cares) you’d have a bit less than 1 kg.

If each dark matter particle was as massive as a bowling ball (which… maybe?), then there’s no dark matter in you right now.  At any moment there’d be one place within a few Earth radii that had any dark matter, and that wouldn’t happen to be where you are.  There just isn’t enough luck.  But for the same reason that it’s easier to dodge water balloons than rain, you’re more likely to have dark matter in you if it’s made up of more particles with less mass each.

We can measure how dense dark matter is on galactic scales, but we have no idea how big a single particle of dark matter is.  Bigger particles are less likely to be inside of you (or any other particular place) and smaller particles with the same total mass are more likely to be everywhere.

The average adult (human) mass is 62 kg, which implies a volume of 0.062 m³ because, conveniently, people have the same density as water (which is why you can comfortably swim under water) and water is exactly one metric ton per cubic meter (which is not a coincidence).  So given that rough dark matter density and that average person-volume, your share is about 1.6x10^-23 kg.  That doesn’t sound like a lot, because it isn’t.  A single red blood cell is more than a billion times bigger (about 2.7x10^-14 kg).  But particles are really small.  The most massive verified particle is the Higgs boson, which weighs in at a hefty 2.2x10^-25 kg.  If dark matter particles are equally as massive, then you should have about 7oish of them in your body at all times; zipping through you at colossal speeds.  At the other end of the scale are neutrinos, with a mass of no more than 2.14x10^-37 kg.  If dark matter particles are neutrino-sized, then you presently overlap with at least 75 trillion of them.

So if dark matter is made of particles that are not-a-hell-of-a-lot-bigger than every other known particle, then if you took a snapshot of yourself right now, the chance that you have dark matter in your body is as close to 100% as you’d care to imagine.  That drops suddenly as the masses of those particles gets close to around 10-100 times more massive than the most massive known particle (being more specific is a little silly considering how rough the density estimate is).

But don’t get too excited.  The ten or so yoctograms of extra matter in your body is a long way from producing enough gravity to ruin your day, and gravity is the only tool dark matter has to work with.  “There’s dark matter in me right now!” is a great conversation starter and ender, but that’s about the extent of its personal relevance.

The colliding planets picture is from here.