<p>The DM halo of a galaxy is expected to have a smooth density profile: highest at the center, with density increasingly smoothly outward.[*] At the approximate radius of the Sun's orbit, the DM density is estimated to be <span class="math-container">$\sim 0.1$</span> solar masses per cubic parsec, which is <span class="math-container">$\sim 7 \times 10^{-22}$</span> kg/m<span class="math-container">$^{3}$</span> (see, e.g., the references in <a href="https://physics.stackexchange.com/a/170513/67614">this physics.stackexchange answer by ProfRob</a>). On scales as small as the Solar System, this local DM distribution is <em>uniform</em>.</p>
<p>The DM particles are assumed to be on predominantly radial orbits (moving inwards towards the galactic center or outwards away from it), while the Sun is on an approximately circular orbit with an azimuthal velocity of <span class="math-container">$\sim 200$</span> km/s. So DM particles passing through the Solar System will have velocities relative to the Solar System of a few hundred km/s and will thus not be captured. You can think of the Sun and the Solar System as moving in its orbit through a locally uniform background medium of DM particles, which are themselves whizzing about on mostly radial orbits.</p>
<p>It's not clear from that PBS video how they came up with &quot;<span class="math-container">$10^{18}$</span> kg&quot;, but presumably it was just (density of DM) <span class="math-container">$\times$</span> (volume of Solar System). The latter, of course, is ambiguous, since it depends on what you decide is the size of the Solar System (out to Jupiter's orbit? out to Neptune's orbit? out to the outer edge of the Kuiper belt?). If we take the DM density mentioned above, then the corresponding volume implies a radius of <span class="math-container">$\sim 50$</span> astronomical units as their definition of &quot;within the Solar System&quot;.</p>
<p>[*] Note that the name &quot;DM halo&quot; is perhaps a bit misleading, since it might be taken as implying something like a shell of DM surrounding an inner, DM-free galaxy -- I suspect this is guiding your thinking when you say, &quot;I assume that smattering of dark matter is in some distant halo -- if yes, how far away is that halo from the Sun?&quot;. But this is not the case.</p>

CC BY-SA 4.0
2024-06-18T11:46:11.423Z
Great answer, but note that DM halos _can_ have non-zero angular momenta. In fact, [Obreja+ 22](https://ui.adsabs.harvard.edu/abs/2022A%26A...657A..15O) argue that the MW has a rather large spin, although they later issued an erratum saying that they over-interpreted _how_ extreme the MW is. Whether or not a sufficiently large co-spin would make enable DM to clump around solar systems, I don't know.
pela
CC BY-SA 4.0
2024-06-19T18:07:24.297Z
@ScienceSnake We don't have positive evidence, but there is a lot of theoretical guidance. If DM is a particle, then we expect the dominant component to be smooth, just because DM "sub-structures" so deep in the galaxy would be severely tidally stripped. But if the DM was primordial cold enough to make structures much smaller than the solar system, there should still be a local sub-structure component. Alternatively, it remains possible that the DM is primordial black holes, in which case the local mass distribution would be quite non-uniform.
Sten
CC BY-SA 4.0
2024-06-24T17:52:26.647Z
If I understand all this correctly, you're saying that probably the majority of the DM within our solar system is not gravitationally bound to our system, but is merely transiting our neighborhood in its dance around & through the Milky Way. Is that fair?
Tom
CC BY-SA 4.0
2024-06-25T19:35:05.197Z
@Tom Yes, exactly.
Peter Erwin
CC BY-SA 4.0
2024-06-18T11:33:16.753Z
2024-06-18T11:33:16.753Z
Peter Erwin
<p>In <a href="https://youtu.be/AK44wAvv2E4?si=g2eiM1Pp6PFWl1mX&amp;t=241" rel="nofollow noreferrer">this episode of PBS Space Time</a>, it's claimed that our solar system contains on the order of 10<sup>18</sup> kg of dark matter.</p>
<p>As a point of comparison, Mt. Everest is estimated to have roughly the same mass: 1.75 x 10<sup>18</sup> kg. (source: <a href="https://mounteverest.info/mount-everest-weigh-mass-volume/" rel="nofollow noreferrer">mounteverest.info</a>)</p>
<p>That's a lot by human scale, but practically nothing compared to the whole Earth, to say nothing of our system's other major bodies and structures.</p>
<p>I assume that smattering of dark matter is in some distant halo -- if yes, how far away is that halo from the Sun?</p>
<p>I imagine the furthest extent of any permanent dark matter halo would be determined by the Sun's Hill sphere, because anything further would be pulled away eventually. Wikipedia says that all the stable orbits around the Sun are within 1/2 or 1/3 of the Hill radius, but I wonder if the range of stability would be different for dark matter.</p>
<p>If indeed it is expected to be a halo, I'm hoping for concrete units.</p>

CC BY-SA 4.0
2024-06-16T05:46:27.597Z
see https://physics.stackexchange.com/questions/194107/is-dark-matter-expected-to-be-equally-distributed-in-our-solar-system  "Dark matter is pretty uniformly distributed on Solar System scales." so no halo. It is moving too fast, relative to the solar system, to be in orbit. It just falls in, and then falls out again.
James K
CC BY-SA 4.0
2024-06-16T05:56:33.247Z
but also https://physics.stackexchange.com/questions/102605/mass-density-of-dark-matter-in-solar-system-near-us, which gives some numbers
James K
CC BY-SA 4.0
2024-06-16T06:05:06.197Z
According to my skim of the recent paper [arXiv:2206.08535](https://arxiv.org/abs/2206.08535) there is a small contribution from temporarily captured dark matter, which makes a power-law density profile $\rho\propto r^{-3/2}$.
Sten
CC BY-SA 4.0
2024-06-16T06:57:55.113Z
Because dark matter has (almost) no other interactions apart from gravity, a ball of pure dark matter can't collapse. See https://physics.stackexchange.com/q/214950/123208 But a ball of DM in the vicinity of normal baryonic matter can collapse (to an extent) by exchanging kinetic energy with the normal matter.
PM 2Ring
CC BY-SA 4.0
2024-06-16T06:59:59.027Z
ObXKCD: https://xkcd.com/2186/
PM 2Ring
CC BY-SA 4.0
2024-06-17T22:50:44.750Z
@PM2Ring “Balls” of dark matter *can* collapse (that’s how you get DM halos and the cosmic web); just not as much as baryonic matter can. See for example the videos of evolving pure DM simulations [here](http://www.benediktdiemer.com/visualization/movies/).
Peter Erwin
CC BY-SA 4.0
2024-06-18T01:54:25.710Z
These are all useful comments, but as this question is absolutely on-topic for our site, it therefore deserves an *answer*. It could be as simple as a summary of each of the linked pages. Anyone? [PS the xkcd link is an essential addition!]
Chappo Hasn't Forgotten
<dark-matter>
How is dark matter distributed within our solar system?
Tom
# How is dark matter distributed within our solar system?

(Asked by: username_0 on 2024-06-16)

In [this episode of PBS Space Time](https://youtu.be/AK44wAvv2E4?si=g2eiM1Pp6PFWl1mX&t=241), it's claimed that our solar system contains on the order of 1018 kg of dark matter.

As a point of comparison, Mt. Everest is estimated to have roughly the same mass: 1.75 x 1018 kg. (source: [mounteverest.info](https://mounteverest.info/mount-everest-weigh-mass-volume/))

That's a lot by human scale, but practically nothing compared to the whole Earth, to say nothing of our system's other major bodies and structures.

I assume that smattering of dark matter is in some distant halo -- if yes, how far away is that halo from the Sun?

I imagine the furthest extent of any permanent dark matter halo would be determined by the Sun's Hill sphere, because anything further would be pulled away eventually. Wikipedia says that all the stable orbits around the Sun are within 1/2 or 1/3 of the Hill radius, but I wonder if the range of stability would be different for dark matter.

If indeed it is expected to be a halo, I'm hoping for concrete units.

**Tags:** dark-matter
> **Comments:**
> **username_1**: see https://physics.stackexchange.com/questions/194107/is-dark-matter-expected-to-be-equally-distributed-in-our-solar-system  "Dark matter is pretty uniformly distributed on Solar System scales." so no halo. It is moving too fast, relative to the solar system, to be in orbit. It just falls in, and then falls out again.  
> **username_1**: but also https://physics.stackexchange.com/questions/102605/mass-density-of-dark-matter-in-solar-system-near-us, which gives some numbers  
> **username_2**: According to my skim of the recent paper [arXiv:2206.08535](https://arxiv.org/abs/2206.08535) there is a small contribution from temporarily captured dark matter, which makes a power-law density profile $\rho\propto r^{-3/2}$.  
> **username_3**: Because dark matter has (almost) no other interactions apart from gravity, a ball of pure dark matter can't collapse. See https://physics.stackexchange.com/q/214950/123208 But a ball of DM in the vicinity of normal baryonic matter can collapse (to an extent) by exchanging kinetic energy with the normal matter.  
> **username_3**: ObXKCD: https://xkcd.com/2186/  
> **username_4**: @PM2Ring “Balls” of dark matter *can* collapse (that’s how you get DM halos and the cosmic web); just not as much as baryonic matter can. See for example the videos of evolving pure DM simulations [here](http://www.benediktdiemer.com/visualization/movies/).  
> **username_5**: These are all useful comments, but as this question is absolutely on-topic for our site, it therefore deserves an *answer*. It could be as simple as a summary of each of the linked pages. Anyone? [PS the xkcd link is an essential addition!]  

---

## 1 answers

### Answer by username_4 on 2024-06-18. Score: 6 | Accepted answer

The DM halo of a galaxy is expected to have a smooth density profile: highest at the center, with density increasingly smoothly outward.[\*] At the approximate radius of the Sun's orbit, the DM density is estimated to be $\sim 0.1$ solar masses per cubic parsec, which is $\sim 7 \times 10^{-22}$ kg/m$^{3}$ (see, e.g., the references in [this physics.stackexchange answer by ProfRob](https://physics.stackexchange.com/a/170513/67614)). On scales as small as the Solar System, this local DM distribution is *uniform*.

The DM particles are assumed to be on predominantly radial orbits (moving inwards towards the galactic center or outwards away from it), while the Sun is on an approximately circular orbit with an azimuthal velocity of $\sim 200$ km/s. So DM particles passing through the Solar System will have velocities relative to the Solar System of a few hundred km/s and will thus not be captured. You can think of the Sun and the Solar System as moving in its orbit through a locally uniform background medium of DM particles, which are themselves whizzing about on mostly radial orbits.

It's not clear from that PBS video how they came up with "$10^{18}$ kg", but presumably it was just (density of DM) $\times$ (volume of Solar System). The latter, of course, is ambiguous, since it depends on what you decide is the size of the Solar System (out to Jupiter's orbit? out to Neptune's orbit? out to the outer edge of the Kuiper belt?). If we take the DM density mentioned above, then the corresponding volume implies a radius of $\sim 50$ astronomical units as their definition of "within the Solar System".

[\*] Note that the name "DM halo" is perhaps a bit misleading, since it might be taken as implying something like a shell of DM surrounding an inner, DM-free galaxy -- I suspect this is guiding your thinking when you say, "I assume that smattering of dark matter is in some distant halo -- if yes, how far away is that halo from the Sun?". But this is not the case.

> **Comments:**
> **username_6**: Great answer, but note that DM halos _can_ have non-zero angular momenta. In fact, [Obreja+ 22](https://ui.adsabs.harvard.edu/abs/2022A%26A...657A..15O) argue that the MW has a rather large spin, although they later issued an erratum saying that they over-interpreted _how_ extreme the MW is. Whether or not a sufficiently large co-spin would make enable DM to clump around solar systems, I don't know.  
> **username_2**: @ScienceSnake We don't have positive evidence, but there is a lot of theoretical guidance. If DM is a particle, then we expect the dominant component to be smooth, just because DM "sub-structures" so deep in the galaxy would be severely tidally stripped. But if the DM was primordial cold enough to make structures much smaller than the solar system, there should still be a local sub-structure component. Alternatively, it remains possible that the DM is primordial black holes, in which case the local mass distribution would be quite non-uniform.  
> **username_0**: If I understand all this correctly, you're saying that probably the majority of the DM within our solar system is not gravitationally bound to our system, but is merely transiting our neighborhood in its dance around & through the Milky Way. Is that fair?  
> **username_4**: @Tom Yes, exactly.  

---

