It very much depends on where you are! Dark matter as we understand it must be some kind of particle, or at least act like some kind of particle. We’re not exactly clear on what the exact nature of that particle would be, or what its individual mass is, or what kind of interactions it ought to have either with itself or with the matter that makes up our planet and all the stars.
But it certainly does seem that dark matter isn’t spread evenly throughout the entire universe. It’s clustered in lumps, and those lumps become the homes to galaxies. Small gatherings of dark matter are generally assumed to be roundish, since that’s the easiest shape for a three dimensional object to form under the influence of gravity.
For galaxy clusters, we can actually map out the shape of the dark matter surrounding these thousands of galaxies by looking at the way that light bends around that part of the Universe. Not all clusters have particularly spherical dark matter surroundings, and we can see the irregularities because the light from galaxies behind the cluster is not bent in the same way along all of the cluster’s edges.
Within any of these collections of dark matter (technically called halos) surrounding a galaxy or a collection of galaxies, the dark matter is densest at the center, and becomes gradually more diffuse the further out you go. For our own Milky Way, that means that the dark matter density is the highest towards the very center of the galaxy, and out near our solar system, the dark matter density is significantly lower.
Most galaxies contain significantly more mass in dark matter than in luminous matter, but this isn’t because it’s more dense -- the dark matter halo is simply much larger. In the case of the dark matter surrounding our Milky Way, it’s also spherical and not effectively flat, like the bright part of the galaxy is. You can pack a lot more material in a sphere than you can in a circle, so the combination of the dark matter halo being physically larger and a sphere means you wind up with a lot more mass.
The dark matter density near the solar system, from what I could find, sits at around 0.006 solar masses per cubic parsec, which is a set of units that’s not going to make much sense unless you’re a professional astrophysicist. This is extremely low density. Six-thousandths of a solar mass is approximately the same as six Jupiter mass planets, and a parsec is a 75% of the distance from the Sun to the nearest star. So this means if you wanted to reproduce the dark matter density with the luminous matter that planets are made of, you’d have to clear out a cube of space that’s three light years to a side of absolutely everything. No dust, no gas, no stars, no planets. You get six Jupiters in that box, and you’ll have to spread those Jupiters around, since we don’t have any indication that dark matter comes in chunks.
We can scale this metaphor down a bit; if you wanted to get the same kind of density but in a cubic kilometer, you’d have to evacuate that square kilometer of absolutely every single atom of material. A single grain of birch pollen floating in that cubic kilometer would contain 20 times more mass than there would be in dark matter in that same volume.
At the center of the galaxy, the dark matter should be more than 150 times more concentrated, but this is very difficult to measure within our own galaxy. So far, our observations seem to line up with the models we’ve developed, but there’s definitely room to improve. In any case, 150 times the density of the solar neighborhood is still not very dense! That gets us all of about eight grains of pollen.
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