Why is there no DM halo around the solar system?

[Buzz Bloom]

If anyone knows a reference that discusses this question, please post a citation.

Naively it seems that any central mass would attract DM from the mass's general vicinity so that an approximately spherically symmetric accumulation would develop over time about the central mass. This seems to be accepted as the explanation of why the velocities of stars (or gas) within spiral galaxies do not exhibit a Newtonian pattern. Since the planets of our solar system DO have a Newtonian pattern, there must not be any such DM halo. But, why not?

 

[newjerseyrunner]

It's there, it's just not very big. The distribution of DM seems fairly uniform within the galaxy, but that density is so low that in places where mass is fairly densely concentrated (like a solar system) it's gravity is negligible. DM's gravity comes from the fact that there is so much empty space in the galaxy, and it's got just as much DM as the solar system.

Think about it like this: a cloud in the sky can weigh over a million pounds. That's a million pounds of water, which is a very large amount, but when the cloud comes down to Earth and you run through it as fog, you barely notice it's mass.

Also, matter conglomerates because matter sticks to other matter. Atoms collide with each other and lose some of their energy to friction, slowing them down and allowing fast clouds to cool and condense. Dark matter does not seem to interact with anything, including itself, so there is nothing to slow it down, disperse it's energy, and make it form dense areas, only clouds the size of galaxies.

 

[Janus]

It's not that the Solar system doesn't contain DM, it's a matter of the relativity density of the solar system with respect to a galaxy. The density of DM in the vicinity of the Sun is ~5e-13 kg per cubic km. So let's take the volume inside the radius of Pluto's orbit and work out how much DM would be contained in that volume. It works out to be ~5e17 kg, or something like the mass of a small asteroid. Since the Sun has a mass of 2e30 kg, its is no wonder that the DM in the solar system has no noticeable effect on the planet's orbits.

Now, let's calculate the amount of DM at the same density, enclosed in the volume inside a radius equal to the Sun's distance from the center of the Galaxy. We are ~27,000 light years from the center so that is ~2.6e17 km, for a volume of ~7e52 cubic km, which give us a DM mass of 19 billion suns. Since the total estimated mass of the stars in our galaxy is ~64 billion solar masses, this amounts to a good fraction of the mass effecting the Sun's orbit around the galaxy, and we would expect it to have a significant effect.

 

[Buzz Bloom]

Hi Janus and newjerseyrunner:

Thank you both for your posts. I have a sense that your explanations regarding the thread's question missed an important aspect of the question, but I am not an expert in this subject, so I may be wrong.

any central mass would attract DM from the mass's general vicinity so that an approximately spherically symmetric accumulation would develop over time about the central mass.

I think that making a calculation based the current average density of DM in the universe,

ρ_DM = ρ_c x Ω_DM,​

fails to consider that a central mass of Baryonic matter of mass M would pull all DM within some distance D towards the mass's center of gravity, which over a period of time will concentrate the DM into densities much greater than ρ_DM. One can get a rough estimate of D by considering the distance at which the escape velocity equals the Hubble velocity:

√(2 G M / D) = h D → D = (2 G M / h²)^1/3​

Then the "captured" DM mass would be

M_DM = (4/3) π D³ ρ_DM​

I know this is an oversimplification, since one needs to consider how H and ρ_c change over time. However, I think it will be OK as a very rough approximation.

I suggest doing two calculations, one for the solar system, and one for some spiral galaxy (perhaps the Milky Way) where a reasonable estimate of the mass of its baryonic matter is known. My guess is that the ratio, M_DM/M, of of "captured" DM mass to each system's original baryonic mass will be comparable. If my guess is right, then my "Why" question would remain a mystery.

My skills at making such calculations are marginal at best, but I plan to do what I can, although I expect it will take me at least several days.

Regards,
Buzz

 

[Jonathan Scott]

Capturing DM is not like capturing baryonic matter, because of the lack of non-gravitational interaction or anything like "friction" (apart from gravitational tidal effects). It isn't easy to understand how galaxies can capture it, and the DM passing through the solar system would probably barely notice it.

 

[Buzz Bloom]

Capturing DM is not like capturing baryonic matter

Hi Jonathan:

Thanks for your post.

I understand that there are EM interactions among baryonic particles that cause their kinetic energy reduction due to photons created in the interactions radiating the energy away. (See https://www.physicsforums.com/threads/the-dark-sky-ahead.836784 post #7.) However, if we assume that DM is like dust, imagine a sphere of DM of non-rotating dust with uniform density ρ and radius R in a locally otherwise empty universe. That is, assume an empty shell of outer radius R_v and inner radius R, and R_v >> R.

If we think of this DM sphere in terms of radially symmetric shells of zero thickness separated from each other by dR, the shell at radius D is attracted towards the center by a mass

(1) M(D) = (4/3) π D³ ρ.​

The acceleration towards the center acting on this shell is

(2) A(D) = G M(D) / D² - h² D (1+(3/2) Ω_mass).​

This assumes that Ω_radiation << 1. From this we calculate that

(3) A(R) = 0 for R = (G M(R) / (h² D (1+(3/2) Ω_mass))^1/3​

Let this value of R be called R_limit, and assume that the sphere radius

(4) R < R_limit.​

I am not sure that the following assumption is correct, but for this discussion, I am assuming it anyway to keep the math simple. Assume that as the nested shells move towards the center, that the shells do not pass each other. If we assume that the sphere has uniform density at time T₀, then, one can calculate where each shell will be at a later time T > T₀.

My guess is that a current DM halo around a galaxy will be more centrally concentrated than a halo around the solar system since the galaxy's halo has been contracting for about 13 Gy, while the solar system halo has been contracting for only 5 Gy. However, I am doubtful that this will be an explanation for why no halo is detectable around the solar system.

Regards,
Buzz

 

[phinds]

My guess is that a current DM halo around a galaxy will be more centrally concentrated than a halo around the solar system since the galaxy's halo has been contracting for about 13 Gy, while the solar system halo has been contracting for only 5 Gy. However, I am doubtful that this will be an explanation for why no halo is detectable around the solar system.

Bad guess, as it turns out. DM spends more time in the halo around a galaxy than in the center. This is a direct result of the fact that it only interacts gravitationally and so is not slowed as it passes through the center and out to the other side and back again.

 

[newjerseyrunner]

Dark matter is affected by the galaxy far less than the galaxy is affected by the dark matter. I don't like thinking about the universe as a bunch of galaxies with DM halos around them. I prefer to think of the universe as clouds of dark matter that have little galaxies bobbing around inside of them.

Here is a nice visual:
https://qph.is.quoracdn.net/main-qimg-1ad964633d3fb229579f9a1f9d8ecf8b?convert_to_webp=true
In this analogy, the galaxy is the bubble, the DM halo is the water. The DM (water) is affected by the movement of the galaxy (bubble) inside, but who's really in charge?

 

[Buzz Bloom]

I now see I made a math error.

(1) M(D) = (4/3) π D³ ρ.​

The acceleration towards the center acting on this shell is

(2) A(D) = G M(D) / D² - h² D (1+(3/2) Ω_mass).
(3) A(R) = 0 for R = (G M(R) / (h^{2 D} (1+(3/2) Ω_mass))^1/3​

Let this value of R be called Rlimit, and assume that the sphere radius​

Substituting (1) into this (2) gives

(5) A(D) = G (4/3) π D³ ρ / D² - h2 D (1+(3/2) Ω_mass).

= (4/3) π G ρ D = h² D (1+(3/2) Ω_mass).​

Therefore (5) with A(D) = 0 cannot be solved for D.

I need to think about what this means. Any suggestions?

ADDED
I must have made a mistake in calculating the formula for the acceleration effect of the expanding universe.

A = h² D (1+(3/2) Ω_mass)​

I will look for that mistake.

Regards,
Buzz

 

[Buzz Bloom]

Bad guess, as it turns out. DM spends more time in the halo around a galaxy than in the center. This is a direct result of the fact that it only interacts gravitationally and so is not slowed as it passes through the center and out to the other side and back again.

Hi phinds:

Thank you for the excellent point in your post. I have never considered that before.

If I understand your concept correctly, my assumption about the "dust" with no angular momentum slowly falling inward failed to consider that over time each dust particle would acquire sufficient radial velocity to become dynamically stable with a repeated motion that passes through the center and comes out the other side.

I will now need to think about the dynamics that brings that stability about, and its effect on the shell model.

I still don't understand why this phenomenon would lead to our solar system having no halo.

Regards,
Buzz

 

[DaveC426913]

Hi phinds:

Thank you for the excellent point in your post. I have never considered that before.

If I understand your concept correctly, my assumption about the "dust" with no angular momentum slowly falling inward failed to consider that over time each dust particle would acquire sufficient radial velocity to become dynamically stable with a repeated motion that passes through the center and comes out the other side.

I will now need to think about the dynamics that brings that stability about, and its effect on the shell model.

I still don't understand why this phenomenon would lead to our solar system having no halo.

Regards,
Buzz

You're over-thinking it.

Each particle starts with a random amount of angular momentum. It neither gains nor loses it as it gravitates inward. It simply orbits the CoM of the galaxy. Since it does not interact with nay bodies in it orbit, there is no need to apply some 'stability' factor.

 

[newjerseyrunner]

Think about a bunch of marbles on a sheet, they bend the sheet very slightly, you've seen this analogy before:

Now give those marbles random directions and velocities, they start hitting each other. click clack click clack. When two marbles hit each other head on, going 5mph relative to each other they hit and make a big CLICK, and then move away from each other it slightly less than 5mph of total velocity. Why? Because the collision caused them to lose some energy, it got converted to sound and heat. Now when you have a lot of marbles that get close to each other, there is a lot of collisions and they quickly disperse outwards, but they've lost enough energy that they now can't overcome the mutual pull of all of the other marbles, so they start falling back towards the center of mass, so eventually, you'll get clumps or marbles that have very little velocity relative to each other.

Now imagine those marbles can't hit each other, they just go straight through each other. They're still affected by the curve in the sheet caused by the other particles, but they don't collide. How would it act?

 

[Buzz Bloom]

You're over-thinking it.

Hi Dave:

Thanks for your post.

I wanted to avoid including angular momentum because it complicated calculations, and because I think it doesn't effect the overall conclusion about the difference in the DM in the vicinity of a galaxy or our solar system. If I ignore the value changes with time of h and dh/dt, in order to calculate M(R) I will still need to consider what the fraction of the time a particle with a given maximum distance D from the central mass spends at a distance d in the range [R,R+dR].

Regards,
Buzz

 

[Buzz Bloom]

Now imagine those marbles can't hit each other, they just go straight through each other. They're still affected by the curve in the sheet caused by the other particles, but they don't collide. How would it act?

Hi newjerseyrunner:

Thanks for your posts.

I think my posts #10 and #13 responding to phinds and Dave answer the quoted question you asked. If I am still missing something, please let me know.

Regards,
Buzz

 

[phinds]

If I understand your concept correctly, my assumption about the "dust" with no angular momentum slowly falling inward failed to consider that over time each dust particle would acquire sufficient radial velocity to become dynamically stable with a repeated motion that passes through the center and comes out the other side.

exactly

I still don't understand why this phenomenon would lead to our solar system having no halo.

most likely because the DM just passes through the solar system on the way to the center the same as it does through the galaxy center

 

[Buzz Bloom]

most likely because the DM just passes through the solar system on the way to the center the same as it does through the galaxy center

Hi phinds:

Thanks for your post.

This quote confuses me.

The gravitational acceleration by the maximum total estimated mass of the Milky Way (3 x 10⁴² kg), assumed to all be at the galaxy's center, on any location in the solar system (distance 2.57 x 10²¹ m) is 3 x 10^-11 m/s². The gravitational acceleration by the Sun's mass (2 x 10³⁰ kg) on Pluto (semi-major axis 1.5 x 10¹¹ m) is 6 x10^-3 m/s². That is, the Sun's gravitational influence on the solar system is greater than the Milky Way's gravity on the solar system by more than a factor of 10⁸.

Therefore, it seems most likely that the Sun's influence on local DM would gravitationally capture that DM rather than that DM passing by the solar system on it's way to or from the center of the Milky Way.

Regards,
Buzz

 

[phinds]

Hi phinds:

Thanks for your post.

This quote confuses me.

The gravitational acceleration by the maximum total estimated mass of the Milky Way (3 x 10⁴² kg), assumed to all be at the galaxy's center, on any location in the solar system (distance 2.57 x 10²¹ m) is 3 x 10^-11 m/s². The gravitational acceleration by the Sun's mass (2 x 10³⁰ kg) on Pluto (semi-major axis 1.5 x 10¹¹ m) is 6 x10^-3 m/s². That is, the Sun's gravitational influence on the solar system is greater than the Milky Way's gravity on the solar system by more than a factor of 10⁸.

Therefore, it seems most likely that the Sun's influence on local DM would gravitationally capture that DM rather than that DM passing by the solar system on it's way to or from the center of the Milky Way.

Regards,
Buzz

Your logic/math seems sound to me. I wasn't sure, which is why I said "most likely". Must be something we're both missing. I think it probably has to do with the speed of the DM "particles" as they pass through the solar system. They are probably traveling faster than the escape velocity of the solar system.

 

[Buzz Bloom]

I think it probably has to do with the speed of the DM "particles" as they pass through the solar system. They are probably traveling faster than the escape velocity of the solar system.

Hi phinds:

Thanks for your post.

My guess is that your suggestion above won't work either. I will have to some math (a slow process for me) to check it out. This is what I plan.

Consider an extended line through the Sun and the center of the Milky Way. Assume a DM particle P on this line with a maximal distance D_m from the center of the Milky Way, D_M equal to some multiple of the radius of the Milky Way. Calculate P's velocity when it passes near the Sun. At some point, distance D from the Sun, this velocity will be less than the escape velocity at the radius D.

Now, consider all possible radial paths of a particle P through the center of the Milky Way. If P were to pass within a distance D of the Sun, it would be captured. I could possibly then calculate what fraction of such particles moving from a distance D_m through the Milky Way's center would pass within D of the Sun. This would then be an approximate estimate of the fraction of the Milky Way's DM that would be captured by the Sun.

Regards,
Buzz

 

[Buzz Bloom]

I have been thinking hard about the scenario from my previous post. I have decided that it might produce an interesting result, but I am now thinking it will not be very relevant for reasons I will discuss later. Here are some beginning results.

I decided to chose for D_m the distance from the Milky Way (MW) center, P_MW, at which the escape velocity equals the Hubble velocity.

V_esc = √(2 G M_MW / D_m)
V_h = h D_m
G = M_MW = 6.69 x 10^-11 m³ kg^-1 s^-2
M_MW = 1.4 x 10⁴² kg
h^-1 = 5.45 x 10¹⁷ s
D_m = (2 G M_MW / h²)^3/2 = 3.82 x 10²² m​

I assumed all of the MW mass is at the galaxy's center, and at time t = 0, a DM particle is at distance y₀ = D_m with zero velocity. The particle falls radially toward the center on a radial line that passes through the sun. The time t at which the particle is at distance y is given by:

where μ = G M_MW.
(See https://en.wikipedia.org/wiki/Free_fall Inverse-square law gravitational field.)

The time at which the test particle reaches P_MW is

t(0) = 8.56 x 10¹⁷ s = 27.2 Gy.​

The distance between the sun and P_MW is

y_sun = 2.57 x 10²¹ m.​

The time at which the test particle reaches the sun is

t(y_sun) = 1.37 x 10¹⁷ s = 4.34 Gy.​

I will add in a later post calculations for the velocity of the test particle at y = 0 and y = y_sun.

My reasons for expecting the results this scenario to not be very relevant are the following.
I think that the way DM in the MW halo actually passes by the sun is not radially. Also the time frame for the particle to fall is too long for the scenario to have much relevance.

I think a scenario closer to reality is to consider that the DM halo is (1) more-or-less on the average not moving, and (2) it has a density ρ(y) that varies with the distance y from P_MW. Also, at the time the sun and it's system was being formed, (3) the baryonic material that was to become the solar system was passing through the halo DM at an approximate radial distance y_sun with the DM density being ρ_DM(y_sun), and (4) this proto-solar system material having in it's orbit with respect to P_MW a velocity through the DM. This velocity can be compared with the MW's escape velocity at y_sun.

It may be that (a) the orbital velocity of the sun about P_MW is too fast for the sun to accumulate enough DM around it to effect planet orbits, and (b) without the sun being able to capture DM, the ρ_DM(y_sun) density might be too small to effect the orbits of the sun's planets. I think this scenario would be more relevant than the one in my previous post for answering the thread's question.

Any comments or questions?

 

[newjerseyrunner]

I think the assumption that DM moves in a similar speed to the matter is not correct. I was under the impression that DM is traveling every which way. It only interacts gravitationally, so it'd be difficult for it to transfer energy around and all end up the same way, only the tidal force of gravity would even slightly pull on the DM.

You meant that you would expect the DM near the solar system to travel more or less together, sort of like how the other stars near us are all traveling more or less the same direction and speed?

 

[phinds]

As for your statement:

We assume that the DM material in the MW halo has more-or-less approximately zero velocity component in the plane of the sun's orbit

I'm not clear on what you mean, but it doesn't not sound right. DM moves in and out of the center of the galaxy in the plane of the suns orbit, so clearly cannot have zero velocity in that plane.

Oh ... are you talking about the DM halo of the solar system (if there even is one?). The total amount of dark matter in the solar system has been estimated to be about the same as a modest-sized asteroid. Negligible in terms of having any gravitational effect regardless of its kinematics.

 

[Buzz Bloom]

Hi @newjerseyrunner, @Janus, @Jonathan Scott, @phinds, @DaveC426913:

Thanks to all of you for helping me better understand the question I asked to start this thread. I think I have now learned enough to understand a plausible reason why the solar system might have acquired some DM which might affect orbits in the solar system. I hope you will look at my explanation below, and respond with comments agreeing or disagreeing with my analysis.

First a summary:
The sun has a (near) circular orbit around the center of the Milky Way (MW). Assumptions:

(a) I think that most of the DM material in the MW halo has approximately zero velocity component in the plane of the sun's orbit, V_DM. For the purpose of this analysis, I assume V_DM = 0.
(b) I assume sufficient DM exists near the sun's orbit so that the DM that is close enough to the sun to be captured by the sun's gravity will be able to affect solar orbits.​

I calculate the distance from the sun, D_esc, at which its escape velocity V_esc equals the sun's velocity, V_sun, in it's orbit. The only DM that can be captured by the sun's gravitation must come within the distance D from the sun's center as the sun moves through the DM. Below I show the calculation of D.

The answer I got is D = 5.04 x 10⁶ km. This is less than to the radius of Mercury's orbit, 5.7 x10¹⁰ km. (I would much appreciate someone checking my math.)

Calculation

(1) V_sun = 8.28 x 10⁸ km/h = 2.3 x 10⁵ m/s

https://en.wikipedia.org/wiki/Galactic_year​

(2) G = 6.67 x 10^-11 m³ s^-2 kg^-1

https://en.wikipedia.org/wiki/Physical_constant#Table_of_universal_constants​

(3) M_sun = 1.99 x 10³⁰ kg

http://nineplanets.org/data1.html​

(4) V_esc² = 2 G M_sun / D = 2.66 x 10²⁰ m³/s²
(5) D_esc = V_sun² / 2 G M_sun = 5.04 x 10⁹ m​

This calculation (if I did it correctly) depends on several assumptions.

The (a) assumption has positive and negative possible affects. If V_DM > 0 then only some of the DM closer to the sun than D_esc would be captured. On the other hand, some of the DM further than D_esc from the sun would also be captured.

Given the result of the calculation, I think that the (b) assumption may need further investigation, but for now I need to think about the implications of the small value of D_esc.
​

ADDED
I just thought of another possibility that might reduce the effectiveness of the captured DM to affect orbits. Each captured particle would have an elliptical orbit with its perihelion being the distance it passed closest to the sun at the velocity V_sun. The particle's aphelion is likely to be be most of the time much further away from the sun, where it would have less (or maybe negligible) effect on orbits. I need to look into this possibility also.

Regards,
Buzz

 

[Buzz Bloom]

OK. I made a big error about the semimajor axis of Pluto's orbit! I just corrected it in my previous post.
It is 5.87 x10⁹ km.
The value of D_esc = 5.04 x 10⁹ m = 5.04 x 10⁶ km
is less than Mercury's orbit of 57 x 10⁶ km.

Back to the drawing boards.

 

[Buzz Bloom]

I think the assumption that DM moves in a similar speed to the matter is not correct.

Hi @newjerseyrunner:

I am not sure what in particular I said that suggested I was assuming "DM moves in a similar speed to the matter". Can you quote from my text so I can explain what I intended to say?

Regards,
Buzz

 

[Buzz Bloom]

I'm not clear on what you mean, but it doesn't not sound right. DM moves in and out of the center of the galaxy in the plane of the suns orbit, so clearly cannot have zero velocity in that plane.

Hi @phinds:

Thanks for your post.

I assume that the DM has all kinds of different orbits with respect to the center of the MW. Relative to the MW, let

Π_sun be the plane of the sun's orbit, and
Π_DM. be the plane of a DM particle's orbit.​

Also, let

V_DM be the speed of the DM particle.​

Let

θ be the angle between Π_sun and Π_DM.​

When θ is close to π/2, the DM particle's velocity has only a small component in Π_sun. For every DM orbit with angle θ, its speed component in Π_sun is

V_DM.sun = V_DM sin θ.
Let V_DM.sun be the velocity of the particle relative the sun's motion.​

Half the time, the sign of the velocity of the particle relative the sun's motion will be positive and half negative.

(1) When it is positive, the velocity that is relevant to the particle's being captured (that is to be compared with V_sun), is

V_sun - V_DM.sun.​

This means that value of R_esc for this particle will be greater than for the case when θ = π/2.

(2) When it is positive, the velocity that is relevant is

V_sun + V_DM.sun.​

This means This means that value of R_esc for this particle will be less than for the case when θ = π/2.​

My guess is that these two case more-or-less will balance out. That is what I means by

The (a) assumption has positive and negative possible affects. If VDM > 0 then only some of the DM closer to the sun than Desc would be captured. On the other hand, some of the DM further than Desc from the sun would also be captured.

I hope this adequately clarifies my intention. Please let me know if I misunderstood your post.

Regards,
Buzz

 

[Buzz Bloom]

I think the assumption that DM moves in a similar speed to the matter is not correct. I was under the impression that DM is traveling every which way.

Hi @newjerseyrunner:

Thanks for your post. I gather from your post that you had a similar misunderstanding of my intention as did phines. I think my response post #26 to his post is also likely to clarify your misunderstanding. Please let me know if there is more that I need to clarify.

Regards,
Buzz

 

[Buzz Bloom]

(2) When it is positive, the velocity that is relevant is
Vsun + VDM.sun.

I just noticed a typo in my post #25. The text should be:
(2) When it is negative, the velocity that is relevant is

Vsun + VDM.sun.​

 

[ogg]

This stuff is over my head. That said, shouldn't neutrinos be treated in the same way as dark matter - with respect to halos and orbits? I guess only a small fraction of them won't be relativistic, even primadorial BB ones with their subsequent velocity reduction (red-shift). I wonder: its been said that there are no stable orbits, but does that include point-particles? Does the answer to that depend on the still puzzling/unknown way gravitational energy may (or may not) be 'lost'? binary pulsar orbital decay vs failure to see gravitational waves (so far). We live in interesting times...

 

[Chronos]

Dark matter clouds that are observationally evident are larger than galaxies. I am not aware of any obsevational evidence suggesting clouds of dark matter exist on scales as small as a star.

 

[Buzz Bloom]

Hi ogg:

Thanks for your post.

shouldn't neutrinos be treated in the same way as dark matter

I have been puzzled about the primordial neutrinos. They were relativistic and mostly non-interactive with anything long before the the universe became transparent. I have not yet been able to find any definitive statement about whether are still relativistic. If they are, they could not be captured gravitationally. If not, they could be part of the dark matter.

its been said that there are no stable orbits, but does that include point-particles?

I don't understand what you mean by this. What does not have stable orbits about a gravitating body? About what are there no stable orbits?

Regards,
Buzz

 

[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