Why is there no DM halo around the solar system?

[Buzz Bloom]

I am not aware of any obsevational evidence suggesting clouds of dark matter exist on scales as small as a star.

H i Chronos:

Thanks for your post.

If my calculations in my post #23 are correct, it is not likely that any measurable DM would be farther from the sun than roughly RM_DM.test = 2 ×D_esc wh

(5) D_esc = V_sun² / 2 G M_sun = 5.04 x 10⁹ m

.​

R_DM.test would be about 20% of Mercury's orbit radius. However, from this calculation it seems plausible that there may be some DM within radius R_DM.test. I intend to make an effort at calculating an estimate of how much DM might be there. So far no observations have been made of an orbiting body this close to the sun.

The closest vehicle to the sum \was Helios 2.
https://en.wikipedia.org/wiki/Helios_( spacecraft )#Launch_and_trajectory

(I think Helios 2 was also called Helios II and Helios B.) If calculations indicate that there is plausibly an observable amount of DM inside the R_DM.test radius, then presumably observing the orbit of a vehicle passing closer to the sun than R_DM.test might show some DM is there. A vehicle transit even closer to the sun would improve chances of finding DM.

Regards,
Buzz

 

[my2cts]

@Buzz Bloom You yet have to show that any DM would be captured at all. The escape velocity is irrelevant.
DM will just describe hyperbolic orbitals and have higher than or equal to escape velocity at the Sun's position. This is why a DM halo is not expected to exist.

 

[Buzz Bloom]

The escape velocity is irrelevant. DM will just describe hyperbolic orbitals and have higher than or equal to escape velocity at the Sun's position.

Hi @my2cts:

Thanks for your post.

I don't understand why escape velocity is irrelevant. Can you explain that in more detail?

If relative to the sun,

a DM particle P approaches the sun and passes the sun at a distance R from the sun's center
at a velocity V_DM, and
the sun's escape velocity at distance R is V(R), and
V_DM < V(R),​

why won't P go into an orbit about the sun?

Regards,
Buzz

 

[Buzz Bloom]

I have just calculated an optimistic value for the total amount of DM that could have possibly been gravitationally captured into orbits around the sun during the sun's lifetime, and that it is way much too small a mass for it to be measurable. The volume of space possible occupied is roughly equivalent to a sphere with a radius of about 20% of Mercury's radius. The value I calculated is:

M_max.captured = 1.26 x 10²¹ kg.​

This is 9 orders of magnitude less than the mass of the sun,

M_sun = 3 x 10³⁰ kg.​

If anyone is interested, I will post the details of my calculation.

I want to thank everyone for participating in this thread, and thereby helping me understand the question with which I started this thread.

Regards to all,
Buzz

 

[Jonathan Scott]

Hi @my2cts:

Thanks for your post.

I don't understand why escape velocity is irrelevant. Can you explain that in more detail?

If relative to the sun,

a DM particle P approaches the sun and passes the sun at a distance R from the sun's center
at a velocity V_DM, and
the sun's escape velocity at distance R is V(R), and
V_DM < V(R),​

why won't P go into an orbit about the sun?

Regards,
Buzz

There's no "friction" mechanism to get rid of the kinetic energy which the DM would have gained during its approach towards the sun in the first case, so it would always be traveling faster than escape velocity and would simply pass by on a hyperbolic trajectory.

 

[HarryusualS]

Jonathon Scott, well put.
This discussion of DM is interesting and got me thinking. I am not a physicist but would like to learn more here. We have a poor understanding of interactions of particles that do not collide. Imagine a DM particle in the outer halo of the MW. It is in a low density medium of DM with no net gravitational force. But the DM halo pulls like a point mass. Two point masses defile an elliptic path around the MW that the DM could follow forever. However, as the DM approaches the center of the MW, the pull of the MW becomes weaker as it now pulls from all directions. Near the center, the DM is moving very fast but almost free of net gravity. As it bends and emerges, the opposite happens. When the DM leaves the DM halo at less than the exit velocity, it orbits and returns to repeat the journey. As the DM approaches the Sun at high speed, the gravity of the Solar System dominates within 2 ly. Approximated as an elliptic orbit for 2 masses, the DM bends around the Sun and keeps going. As it moves 10 ly away, other stars offset the pull of the Solar System and the DM continues toward the center, speeding up and bending near stars. So the DM is captured by the Sun if their paths cross, but the defined elliptic orbit takes the DM out among other stars and the orbit around the Sun is neutralized. The key is that the DM is generally moving faster than an orbit around the Sun that would be contained in the region where the Solar System gravity dominates over other stars. If Buzz Bloom has calculated that a few DM are captured and are insignificant mass, then this has been insightful. Thank you.

 

[Buzz Bloom]

There's no "friction" mechanism to get rid of the kinetic energy which the DM would have gained during its approach towards the sun in the first case, so it would always be traveling faster than escape velocity and would simply pass by on a hyperbolic trajectory.

Hi Jonathan:

Thank you for your post.

I think I understand the point you are making.

If a DM particle P is moving from a great distance towards the sun S with a velocity V, and it later passes the sun at distance D, and the sun's escape velocity for D is V_esc, and V < V_esc, then P will still not be captured by S because while traveling towards S, P will have been accelerated by falling towards S, so when it passes S it will have an increased velocity V* > V_esc.

Have I understood you correctly?

Regards,
Buzz

 

[Jonathan Scott]

Hi Jonathan:

Thank you for your post.

I think I understand the point you are making.

If a DM particle P is moving from a great distance towards the sun S with a velocity V, and it later passes the sun at distance D, and the sun's escape velocity for D is V_esc, and V < V_esc, then P will still not be captured by S because while traveling towards S, P will have been accelerated by falling towards S, so when it passes S it will have an increased velocity V* > V_esc.

Have I understood you correctly?

Regards,
Buzz

Yes, exactly.

For gravitational capture to occur, there has to be a way for the falling particle to lose energy. DM is not subject to friction with normal matter, so it is very difficult to capture. There are various ways in which close gravitational interactions with multiple bodies can be arranged to cause transfer of energy (for example as used for gravitational assist of solar system probes) but that would be very unlikely to have any significant effect on random particles.

 

[Buzz Bloom]

Hi Jonathan:

Thanks for confirming my understanding.

There are various ways in which close gravitational interactions with multiple bodies can be arranged to cause transfer of energy

I thought of this multi-body possibility, and also decided, as you did, that it would happen so rarely that no measurable DM could be captured that way. I think this is the final answer to my original question.

However, I now am uncertain about how a galaxy could collect very large amounts of DM. For example, the density of DM given in the literature for the MW space near the sun is about 70,000 times the average DM density in the universe. Do you think that the fact that a galaxy has a very large number of bodies in it might allow for a frequent multi-body capturing mechanism?

Regards,
Buzz

 

[Jonathan Scott]

Hi Jonathan:

Thanks for confirming my understanding.I thought of this multi-body possibility, and also decided, as you did, that it would happen so rarely that no measurable DM could be captured that way. I think this is the final answer to my original question.

However, I now am uncertain about how a galaxy could collect very large amounts of DM. For example, the density of DM given in the literature for the MW space near the sun is about 70,000 times the average DM density in the universe. Do you think that the fact that a galaxy has a very large number of bodies in it might allow for a frequent multi-body capturing mechanism?

Regards,
Buzz

On a large enough scale, there is sufficient time and distance for density variations to cause gravitational effects (more like a dynamic fluid than multiple individual bodies) which lead to clumping of both ordinary matter and dark matter. The ordinary matter can form denser clouds and stars, but dark matter doesn't stick together so it remains diffuse.

I don't know much beyond that about dark matter. Different theories of dark matter lead to different predictions of how it would be distributed which can then be matched up with experimental observations of stellar motion and galactic rotation curves. Although it is possible to match almost any observation by a suitable choice of dark matter distribution, it is not so easy to explain why dark matter should end up being distributed in exactly that way.

[In contrast, most galactic rotation curves seem to be a remarkably good fit for a pattern described by the MOND (MOdified Newtonian Dynamics) idea, which involves a modification to gravity but unfortunately isn't even self-consistent as a physical theory. The success of the fit suggests that there might be something in it, meaning either that there is somehow a physical reason why dark matter reproduces the MOND pattern or that the real answer is a modified gravity theory which gives similar results to MOND but has a sound and self-consistent physical basis. Various people have been attempting to construct such a theory, such as Moffat's STVG/MOG, which claims various successes, but unlike MOND it has more additional parameters that can be tweaked to fit observations, so it still seems somewhat arbitrary.]

 

[Buzz Bloom]

On a large enough scale, there is sufficient time and distance for density variations to cause gravitational effects (more like a dynamic fluid than multiple individual bodies) which lead to clumping of both ordinary matter and dark matter. The ordinary matter can form denser clouds and stars, but dark matter doesn't stick together so it remains diffuse.

Hi Jonathan:

Thank you very much for your post.

I very much like your discussion about DM. I wonder if there is any references about a theory of mechanisms for galactic aggregation of very large amounts of DM compared with the DM:baryonic cosmic ratio. I will start a new thread to explore this.

Regards,
Buzz

 

[Buzz Bloom]

the density of DM given in the literature for the MW space near the sun is about 70,000 times the average DM density in the universe.

Hi Jonathan:

Well I have to confess another senior moment: this time a very large error in my calculation related to the quote above. I do not remember where the 70,000 number came from. I was quoting it from memory. I guess the error involved making the conversion from 0.35 GeV/cm³ to kg/m³. But while preparing to create a thread about this number, I recalculated it. The correct value for the ratio of DM near the sun, to the universe's average DM density is: 0.28.

Note that instead of the MW collecting an enormous amount of DM, it seems likely that the DM available with the baryonic matter just got distributed radially so that the density near the sun's "orbit" radius was reduced, while at larger radii, it got larger. In order for the velocity profile to be roughly constant for sufficiently large radii, the density will be roughly proportional to 1/r².

My apologies for any confusion my error caused.

Regards,
Buzz

 

[nikkkom]

However, I now am uncertain about how a galaxy could collect very large amounts of DM.

It's almost the other way around: DM collects large amounts of matter.

Imagine the Universe some 500 thousand years after Big Bang. It is nearly uniformly filled with neutral hydrogen at about 2000K, and with much larger mass of invisible particles of DM, moving with some non-relativistic velocities.

The velocities (temperature) of both gas and DM particles is falling due to expansion of the Universe.

A moment is reached when random motion of all these particles is not fast enough to smear out random density fluctuations, and matter (both hydrogen and DM) starts contracting into gravitationally bound "clouds". Huge ones, on the order of galaxy cluster sizes.

DM particles in a cloud can't concentrate too much to the center - as each individual particle falls towards the center, it does not hit anything, whizzes through the center and ends up on the other side of the cloud. Not so for hydrogen gas: if it is sufficiently dense, it interacts non-gravitationally too. Viscous dissipation in the gas let's it shed some energy, form successively fragmenting small star-forming clouds and first stars. Collectively, these clouds and stars preferentially form close to the center of the DM cloud: they are the proto-galaxy.

 

[Buzz Bloom]

It's almost the other way around: DM collects large amounts of matter.

Thanks for your post.

I think I understand the scenario you describe. You are saying that when the stuff out of which a galaxy is formed began its contraction toward forming the galaxy, it already contained DM and baryonic matter in approximately the 5 to 1 ratio that has been calculated as the relative amount of these components in the universe as a whole. Is this correct?

Regards,
Buzz

 

[nikkkom]

You are saying that when the stuff out of which a galaxy is formed began its contraction toward forming the galaxy, it already contained DM and baryonic matter.

Yes.

 

[Buzz Bloom]

HI All:

In spite of the arguments discussed in this thread explainin why there is no measurable amount of DM in our solar system, apparently some recent computer simulations have produced a different answer.

http://phys.org/news/2015-11-earth-hairy-dark.html​

I would be curious to see some comments about this.

Regards,
Buzz

 

[nikkkom]

HI All:

In spite of the arguments discussed in this thread explainin why there is no measurable amount of DM in our solar system, apparently some recent computer simulations have produced a different answer.

http://phys.org/news/2015-11-earth-hairy-dark.html​

I would be curious to see some comments about this.

http://arxiv.org/pdf/1507.07009v2.pdf

Frankly, despite having lots of math, it looks like nonsense to me. Just plain old common sense wasn't applied in a number of places. They model a completely smooth stream of DM particles traveling on parallel lines flowing through a spherical body, and arrive to a conclusion that gravity will bend the stream so that it will focus into a much tighter "hair".

- How such completely smooth stream of DM particles is supposed to form and survive for billions of years not disturbed?
- Any, even small non-uniformity of the body will ruin the focusing.
- If somehow it gets focused to a small focus, it will not stay that way. After passing the focus, DM particles will disperse (similar to optical lens).
- Table 1 column 2 lists stream velocity low enough for focus to be not at billions of kms away, but at the planet surface. For Earth, it lists 14 and 18 km/s (for different internal models). Well, even a stationary particle acquires 11 km/s falling from infinity to Earth. Add to this the velocity acquired by falling from infinity into Solar System. Basically, *very nearly all* DM particles passing through Earth have velocities higher than this.

 

[newjerseyrunner]

I saw that article today too, seemed strange.

 

[Buzz Bloom]

If somehow it gets focused to a small focus, it will not stay that way. After passing the focus, DM particles will disperse (similar to optical lens).

I saw that article today too, seemed strange.

Hi nikkkom and newjerseyrunner:

I tried to read the article, but I found it to be unintelligible. Have either of you looked at it sufficiently to be sure it says, or does not say, the following:

DM streams whose shapes the simulation shows to be altered by bodies of the solar system are also shown to remain bound to the solar system.​

If you can find a clear statement one way or the other, I would much appreciate it if you could post a short quote, and cite the page number for the quote.

Regards,
Buzz

 

[Buzz Bloom]

Hi @nikkkom and @newjerseyrunner:

I confess that I still find the article unintelligible, but after scanning through it a few times, looking for sections I could more-or-less understand, I have formed a strong impression that the the intensified density regions formed as "hairs" are not gravitationally bound to the solar system, although I failed to find an explicit statement saying that. My interpretation is that the hairs are more-or-less stable, in that they are continuously formed from the input streams of DM, while the DM in the hairs continues to flow through and out of the solar system. Do you think that this interpretation is physically possible?

Regards,
Buzz

 

[nikkkom]

Hi @nikkkom and @newjerseyrunner:

I confess that I still find the article unintelligible, but after scanning through it a few times, looking for sections I could more-or-less understand, I have formed a strong impression that the the intensified density regions formed as "hairs" are not gravitationally bound to the solar system, although I failed to find an explicit statement saying that. My interpretation is that the hairs are more-or-less stable, in that they are continuously formed from the input streams of DM, while the DM in the hairs continues to flow through and out of the solar system. Do you think that this interpretation is physically possible?

Hairs won't form, there is nothing to stop DM particles from dispersing after passing the focus.
Take ordinary lens and let parallel rays of light be focused with it. Do you see "light hair" forming when rays of light get focused?

 

[Buzz Bloom]

Hairs won't form, there is nothing to stop DM particles from dispersing after passing the focus.
Take ordinary lens and let parallel rays of light be focused with it. Do you see "light hair" forming when rays of light get focused?

Hi nikkkom:

Thanks for you post.

I think we are not on the same page here.

Regarding

"Do you see "light hair" forming when rays of light get focused?"​

do you think that it might be possible that the phenomenon of (1) gravitational lensing of a stream of DM particles being bent gravitationally while moving through a massive body, might be sufficiently different than (2) light paths being bent by the change of index of refraction at the surface of a lens, so that (1) could produce "hairs" while (2) doesn't?

Regarding

Hairs won't form, there is nothing to stop DM particles from dispersing after passing the focus.​

Why do you think it is impossible for hairs to form continuously, AND then these DM in these hairs disperse and move pass the focal point and on through the solar system into interstellar space?

Regards,
Buzz

 

[nikkkom]

Regarding

"Do you see "light hair" forming when rays of light get focused?"​

do you think that it might be possible that the phenomenon of (1) gravitational lensing of a stream of DM particles being bent gravitationally while moving through a massive body, might be sufficiently different than (2) light paths being bent by the change of index of refraction at the surface of a lens, so that (1) could produce "hairs" while (2) doesn't?

No, I don't think so. In both cases, we have non-interacting particles converging nearly to a point, passing through it and dispersing. (A beam of *electrons* would be different.)

 

[Buzz Bloom]

No, I don't think so. In both cases, we have non-interacting particles converging nearly to a point, passing through it and dispersing. (A beam of *electrons* would be different.)

Hi nikkkom:

Thanks again for your prompt post.

I think we have different interpretations of what a "hair" is.

I believe that you are thinking that a "hair" consists of a specific collection of DM stuff in the shape described in the article as a "hair". I agree that this interpretation of "hair" is impossible.

I am thinking of a "hair" as an oddly hairlike shaped region of space (which may slowly move over time in the general region of the gravitating body), and that there is a continuous flow of DM through (in and then out of) this shape. What makes the shape distinctive is that the density of DM inside this shape is very much larger than the density of the incoming stream of DM.

Regards,
Buzz

 

[nikkkom]

I am thinking of a "hair" as an oddly hairlike shaped region of space (which may slowly move over time in the general region of the gravitating body), and that there is a continuous flow of DM through (in and then out of) this shape.

Yes. And I'm saying that's not going to happen. No "hair", no "tube" and no "cylinder".

 

[nikkkom]

DM particles would have approximately these trajectories:

 

[Buzz Bloom]

DM particles would have approximately these trajectories:

Hi nikkkom:

The following is Figure 1 from the article.

Why do you think the DM paths produced by the gravitational lensing from the article's simulations are impossible?

Regards,
Buzz

 

[nikkkom]

Why do you think the DM paths produced by the gravitational lensing from the article's simulations are impossible?

Gosh.

Because in the picture you posted, something inexplicable bends DM particles' path (where the small box is) and they somehow stop moving sideways. This should not be possible, as DM particles do not interact with themselves.

 

[Buzz Bloom]

Because in the picture you posted, something inexplicable bends DM particles' path and they somehow stop moving sideways.

Hi nikkkom:

As I discussed previously, the DM is not assumed to stop moving.

I am thinking of a "hair" as an oddly hairlike shaped region of space (which may slowly move over time in the general region of the gravitating body), and that there is a continuous flow of DM through (in and then out of) this shape. What makes the shape distinctive is that the density of DM inside this shape is very much larger than the density of the incoming stream of DM.

The focusing just continuously moves a stream of DM through a smaller region of space, so that the density of DM in that smaller region is much increased compared with the input stream. The figure does not show the stream exiting the hair, just entering it, but the interpretation I am describing includes exiting as well, and I think this interpretation is what the article intended.

I apologize that I don't seem to be able to describe this interpretation in a way that communicates clearly.

Regards,
Buzz

 

[Jonathan Scott]

It's not true that DM doesn't interact at all; it's that it only interacts gravitationally.

It seems at least theoretically possible that if some effect causes it to focus into a narrower stream, then the self-gravitational attraction of that stream would refocus it weakly again later, possibly with a sort of diffraction pattern where directional oscillations reinforce and cancel, until it disperses back to a random flow. However, I very much doubt that a sufficiently coherent uniform flow could exist to start that effect in the first place, and I suspect that you'd require very special (physically implausible) conditions to focus the flow sufficiently accurately for the self-gravity to have enough effect to be noticeable.