Short answer: 10^-18 as much as the mass of the sun, 1 proton-mass per 3 cubic centimeters. Not enough to be detected gravitationally - it just gets swamped.
Moreover, locally, it is expected to be approximately uniform in density, which makes any gravitational interaction negligible.
Nevertheless, our gravitational experiments can say things about the properties of dark matter (it generally obeys the Equivalence Principle): https://arxiv.org/abs/1207.2442
Furthermore, for certain classes of ultra-light dark matter, gravitational and spin-coupled searches can have something to say, e.g.: https://arxiv.org/abs/1512.06165
Dark matter doesn't physically interact with itself or regular matter, so it doesn't "clump" the way regular matter does. A particle of dark matter will fall towards the Sun or Earth, but it doesn't stop when it gets there - it just carries right on through, with just as much energy as it had before. We expect there to be a dark matter "wind" passing through the solar system at galactic speeds, so it doesn't stick around.
But! There may be seasonal variations in the amount of dark matter reaching Earth due to a solar "lensing" effect. Attempts have been made to find this signal, and an annual modulation has been found, but the debate as to its cause is ongoing.
The galaxy's dark matter is largely rotating with the bulk of the visible galaxy. However, the solar system's peculiar motion through the dark matter (DM[a]) does perturb the DM, and some DM will entrain to solar system objects (mostly the sun) leading to small overdensities.
However, remember that within the orbit of Neptune there is only about ten Phobos-masses worth of dark matter, or barely more than Jupiter's small moons Lysithea (disc. 1938) or Sinope (disc. 1914, until 2000 the outermost known moon of Jupiter).
Moreover, Jupiter can't really gravitationally entrain anything beyond 0.35 astronomical units away from it (otherwise the sun dominates), and gas (whether dark matter or electrically neutral atoms or light molecules[b]) is too low-mass to be drawn into a orbit around Jupiter with such a small radius.
There is likely a small overdensity of DM within the sun, but that's really a focusing of dark matter gas through gravitational lensing rather than dark matter gas staying trapped within the sun. It may help understanding if you hold the sun stationary and blow a wind of dark matter gas past (and through) it -- the gravitation of the sun pinches some of the gas inwards. Since on timescales of small numbers of years the sun has roughly constant velocity against the gas (or the wind blows with constant strength from a constant direction), the pinched wind is at a constant location and constant density deep within the sun.
Whether any of the less-massive bodies of the solar system have overdensities within them (or possibly tails[1]) depends on the mass of dark matter particles, and right now that's not well-enough constrained to answer with any confidence.
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[a] here I mean specifically cold dark matter (from the standard cosmology) rather than neutrinos. Solar neutrinos and (relativistic) neutrinos from far away sources are "hot" and so run away from the galaxy too quickly to account for much of its non-visible mass; cosmic neutrinos (the neutrino analogue of the cosmic microwave background) are cold and dark, but individually they're too low-mass to form galaxy or even galaxy-cluster size halos. The total mass of the cosmic neutrino background is also small.
[b] of course, ionization of neutral atoms and gas molecules is pretty likely in the solar system, and Jupiter has an enormous magnetotail. Dark matter doesn't feel magnetism (and isn't ionized by UV or X-rays), otherwise it wouldn't be dark. So while gases can be drawn around Jupiter electromagnetically, dark matter cannot.
What do you think of the possibility of 'dark sector' interactions?[1]
The idea that dark matter might consist of a class of self-interacting particles, and that we might be embedded in a universe full of hidden phenomena as rich as the ordinary-matter phenomena that are visible to us (e.g. dark 'planets', dark 'stars', dark 'galaxies', or something very different) was always intriguing to me, but it seems that a consensus is emerging, based on observations of large-scale distribution, that dark matter is dominated by a single type of particle incapable of self-interaction.
Is it still possible that some fraction of the dark matter in the universe is self-interacting, capable of 'clumping' and exhibiting physics similar to ordinary condensed matter, or are all the indications now pointing strongly towards a single non self-interacting particle?
> What do you think of the possibility of 'dark sector' interactions?
It remains a possibility. It does not seem to be required by observation, though. Worse, if you move away from parsimonious non-interacting quantum field theories to more complex models, you have to suppress a lot of symmetries that inevitably produce observables which are not seen. Most people working with general relativity just use non-interacting scalar fields, but specific ideas about dark matter have to consider the ins and outs of gauge theory (e.g. does DM only feel gravitons and Higgs or does it also feel one or more of the other non-photon gauge bosons? if it feels the weak force, what goes on at electroweak scales? and so on...). The microscopic details of the microscopic alternatives within the broad family of QFT dark matter get hairy quickly, and there's very little astrophysical evidence to prefer one over the other (people favour axions or sterile neutrinos for reasons from within particle physics, and are looking for such things to complete their extensions to the standard model, they have to be very weakly interacting for particle-physics-in-laboratories reasons, but oh by the way as a side effect dark matter could be wholly or at least partially these proposed standard-model-problem-slaying particles).
> [what if we propose dark photons, dark atoms, etc.?]
One problem you run into is that if you can form composite dark particles analogous to atoms, or dark molecules, what prevents them from forming larger structures that collapse gravitationally? Likewise, if you can emit dark photons, you're removing momentum-energy from a particle in an orbit, and you would then expect the particle to fall into a closer orbit. Again, how do you prevent gravitational collapse? You might fix that by feeding back (squash DM together in galactic cores, release enormous "dark shine" dark-photon-analogues which then kick the massive DM particles into wider orbits, but it's like balancing a pencil on its tip; this is called DMAF (dark matter annihilation feedback), and is speculative. On the other hand baryon-flow feedback is a thing in solving e.g. the core/cusp density problem in particle dark matter, and that's a lot less speculative, because we know things like galactic jets are practically mandatory.
You're generally stuck with appealing to rareness, which is in conflict with Copernican principles which work really remarkably well in cosmology (and astrophysics too), or slowing down dark chemistry so much that it basically doesn't have to enter into equations anyway.
Carroll blogged about this a decade (!) ago (how to feel old: remember reading his cosmic variance blogpostings and making the discovery, pardon the pun, of how many years it's been since he stopped blogging there...) here : http://www.preposterousuniverse.com/blog/2008/10/29/dark-pho...
In astrophysics instead of using base-ten for enumerating interesting things in the sky, the counting system goes roughly: forbidden-everywhere, unique, mandatory-everywhere. If you introduce dark matter stars, you would expect there to be so many of them that you could not miss the Einstein lenses they generate. (Similar to MACHO hunting). Dark matter galaxies, being much more massive, would be even harder to miss. You will struggle to find a deep-field image that isn't filled with background galaxies (or clusters) lensing even more background ones. If there are dark galaxies, surely they would be in the foreground of some of the visible galaxies -- otherwise what prevents that?
Finally, we do have some gravitational structuring of dark matter; the standard description of structure formation requires it, and it's hard to get the late-time structures we see without dark matter filaments.
This is exactly the comprehensive reply I was hoping for, thanks. I dug up a Carroll post on the arrow of time and the big bang for this thread which turned out to be from 2004, so I know the feeling.
If there are any other non-experts like me this far down this reply chain who are interested in dark sector speculation, in addition to raattgift's excellent links I'd recommend the Wikipedia page on the Lightest Supersymmetric Particle [1] and Rob Reid's recent podcast with dark matter researcher Priya Natarajan [2].
Dark matter is a supersolid that fills 'empty' space, strongly interacts with ordinary matter and is displaced by ordinary matter. What is referred to geometrically as curved spacetime physically exists in nature as the state of displacement of the supersolid dark matter. The state of displacement of the supersolid dark matter is gravity.
The supersolid dark matter displaced by a galaxy pushes back, causing the stars in the outer arms of the galaxy to orbit the galactic center at the rate in which they do.
Displaced supersolid dark matter is curved spacetime
Yeah, we get it. You believe in the ether. Perhaps you would prefer to call it "the firmament." The only people who believe this are certain fringe (read that pseudoscience) speculators who will never be taken seriously because they ignore the actual data, and have only a rudimentary understanding of the rigorously verified physics involved.
> "the empty vacuum of space … is filled with 'stuff' ... The modern concept of the vacuum of space, confirmed every day by experiment, is a relativistic ether."
Laughlin’s ‘stuff’ is the smoothly distributed, strongly interacting, supersolid dark matter that fills ‘empty’ space and is displaced by ordinary matter.
No. You proved my point by demonstrating that you have no idea what they are talking about.
You could educate yourself. Go study quantum mechanics and the Heisenberg uncertainty principle. Learn about particle fields, vacuum fluctuations, virtual particle pairs, and the Casimir effect. Find out what this "boiling sea of vacuum energy" actually is, and why one might call it ether, and in what sense that would be true.
> What else has approximately uniform local density
Vacuum.
Cool-phase neutral atomic gas in interstellar settings.
Cool-phase neutral molecular gas ditto.
What breaks the uniformity of the latter two is mainly electromagnetic interactions. UV or X-rays will ionize them, and the freed electrons will cause secondary ionizations. This is the main pathway for heating neutral interstellar gases. Subsequent cooling is by photon emission. This drives dust-grain-forming chemistry; these grains are more dense than gas, and so have different gravitational observables as well as different emission/absorption characteristics. Very roughly, the dust grains can collide and stick to one another chemically, leading to further density non-uniformities.
Cold dark matter doesn't feel UV or X-Rays or it wouldn't be dark, and if it is collisionless (as in the standard model of cosmology) then there is no dark chemistry that can locally densify dark matter.
> What else has approximately uniform local density of distribution?
Really, anything that approaches an ideal classical gas. "Local" is an important qualifier.
A cubic centimetre of taken from near the middle of a small jar of water inside your household refrigerator or a cm^3 of gas taken from near the middle of a helium-filled balloon.
The middle, because the density differs at the boundary of the material in the container. Likewise, the density changes sharply at the edges dark matter clouds, but is fairly uniform in large volumes far from the boundary.
The overdensity in the jar's contents compared to the contents of the fridge overall and the underdensity of helium in a balloon in a room at sea level compared to the whole room are very roughly analogous to overensities and underdensities of dark matter at scales much larger than solar systems.
Short answer: 10^-18 as much as the mass of the sun, 1 proton-mass per 3 cubic centimeters. Not enough to be detected gravitationally - it just gets swamped.