Dark matter and keplerian revolution

[TrickyDicky]

Dark matter is believed to have a more homogenous distribution than normal matter, a bias of at least 2 is used in models of large-scale structure in order to justify large voids and superclusters in a homogenous universe.
If Dark matter is so evenly distributed I have some difficulties to understand why it does alter the rotation curves of galaxies but it doesn't disturb the revolution orbits of the solar system. I would guess that if Dark matter is all around us it should affect the dynamics of the planetary orbits in asimilar way it affects the stars revolving around the galaxies.

 

[zhermes]

I would guess that if Dark matter is all around us it should affect the dynamics of the planetary orbits in asimilar way it affects the stars revolving around the galaxies.

Dark matter certainly has some effect on the solar system; its just that these effects are entirely negligible given our observational/computational abilities. Galaxies are the smallest structures which noticeably effected by the presence of dark matter.

I think the reasoning behind this conclusion is exactly your initial point: the difference in homogeneity between baryonic and dark matters. Because, on a small scale, baryonic matter is much less homogeneous, those smaller scales (e.g. solar systems) are dominated by the baryonic over-densities (e.g. stars). On larger scales (e.g. galaxies), where the homogeneity of baryonic and dark matter become more comparable, the effects are similarly more comparable.

 

[TrickyDicky]

I think the reasoning behind this conclusion is exactly your initial point: the difference in homogeneity between baryonic and dark matters. Because, on a small scale, baryonic matter is much less homogeneous, those smaller scales (e.g. solar systems) are dominated by the baryonic over-densities

I don't think this witty reasoning works really, what counts gravitationally more is Dark matter since it's much more abundant than Baryonic, and if it is homogenously distributed in solar system scales, according to gravitational fields superposition principle the homogenous dark matter field should influence the orbit velocities of the outer planets, the fact that the system has baryonic over-densities shouldn't affect this.

So either the distribution at small scales of Dark matter follows the baryonic distribution, or I can't see how it doesn't affect the planetary orbits.

 

[Ich]

So either the distribution at small scales of Dark matter follows the baryonic distribution, or I can't see how it doesn't affect the planetary orbits.

This doesn't make sense. The more dark matter in the SS, the more effect on planetary orbits.

To understand what's happening, you have to understand how Newtonian gravity works in a homogeneous ball of dust. Sun and planets accelerate at the exact same rates to the galaxy's center, so there is no measurable effect of the big DM blob in our Milky Way.
Except for the small corrections due to DM inside the solar system. It is obvious that this amount is very small, and the smaller it is, the less measurable effect.
Try to do the calculations, this is easier to calculate than to explain.

 

[TrickyDicky]

This doesn't make sense. The more dark matter in the SS, the more effect on planetary orbits.

To understand what's happening, you have to understand how Newtonian gravity works in a homogeneous ball of dust. Sun and planets accelerate at the exact same rates to the galaxy's center, so there is no measurable effect of the big DM blob in our Milky Way.
Except for the small corrections due to DM inside the solar system. It is obvious that this amount is very small, and the smaller it is, the less measurable effect.
Try to do the calculations, this is easier to calculate than to explain.

Read the first post, we are not talking about the big DM blob here, I started with the assumption that the DM is distributed homogenously also inside the solar system and therefore it should have a gravitational influence on the orbiting velocities.
So if what you are saying is that DM is all concentrated in a big blob in the halo of the galaxy that is a different scenario, but if that is the case that creates a serious problem for the large-scale structure of the universe if we want to maintain that it is homogenous.

 

[zhermes]

So if what you are saying is that DM is all concentrated in a big blob in the halo of the galaxy that is a different scenario, but if that is the case that creates a serious problem for the large-scale structure of the universe if we want to maintain that it is homogenous.

Apparently you're a little unclear on the current view of the DM distribution. Try a good images search for dark matter---lots of good, informative stuff comes up. The halo of a galaxy is a dark matter blob, roughly homogeneous. The DM of lone galaxies are generally just that blob, in galaxy clusters (and similarly dense environments) each halo is a more-dense blob of DM in a larger DM blob ('blob' isn't the technical term). Clusters and large regions are generally connected by DM streams (that actually is the appropriate term)---which gives the large-scale universe a filamentary-like structure (which can be seen in SDSS etc).

The universe is NOT perfectly homogenous for dark matter: there is NOT a uniform sea of dark matter around everything. Dark matter is simply more homogeneous than baryonic matter, and its also homogeneous in a scale-invariant sense that certainly isn't true for baryonic matter.

 

[Ich]

Read the first post, we are not talking about the big DM blob here, I started with the assumption that the DM is distributed homogenously also inside the solar system and therefore it should have a gravitational influence on the orbiting velocities.

You don't understand. I'm talking about a scenario where DM is distributed homogeneously everywhere inside the galaxy. "Everywhere" definitely including our solar system.
Do the maths.

 

[BillSaltLake]

Expect ~5:1 ratio of DM to baryonic, so the galaxy contains ~10⁴² kg of DM distributed over 10¹⁶ ly³. The orbit out to Neptune contains ~10^-9 ly³, so the solar system contains ~10¹⁷ kg of DM, compared to 2x10³⁰ kg of baryonic matter. Small (dark) potatoes.

 

[Parlyne]

The gravitational force due to a (effectively) homogeneous material of (effectively) infinite extent is 0 to begin with. Even if there were significantly more dark matter in the solar system, its effect would not be noticeable unless it's mass distribution were not uniform.

 

[TrickyDicky]

The universe is NOT perfectly homogenous for dark matter: there is NOT a uniform sea of dark matter around everything. Dark matter is simply more homogeneous than baryonic matter, and its also homogeneous in a scale-invariant sense that certainly isn't true for baryonic matter.

I was assuming both that the uniformity was not perfect(I spoke about a bias of 2) and I can assume the scale-invariance of DM, still the difference in density for baryonic matter doesn't seem to be so big between star system and the galaxy rim to justify such a different effect of DM on orbit velocity of the star versus the planet, and we should expect some overdensities of DM at solar system scale, certainly not as pronounced as the baryonic matter ones.

 

[TrickyDicky]

I was assuming both that the uniformity was not perfect(I spoke about a bias of 2) and I can assume the scale-invariance of DM, still the difference in density for baryonic matter doesn't seem to be so big between star system and the galaxy rim to justify such a different effect of DM on orbit velocity of the star versus the planet, and we should expect some overdensities of DM at solar system scale, certainly not as pronounced as the baryonic matter ones.

Let's introduce some numbers to see where the problem might be, in our galaxy's spiral arms there are some stars with approximate mass of around 10^31 kg that are clearly affected by DM in their rotational velocity curve, if we wanted to extrapolate this to our solar system we need to consider that it's much smaller , we have to account for the relative size of our solar system compared with the distances between the stars. The distance to the farthest reaches of our solar system is measured in light hours or possibly one light day. whereas the stars are all light years away. This is a factor of around 1000 in linear distance while in volumes this represents 1000 cubed or on billion so there is a billion times as much "empty space" as solar systems in our region of the galaxy. So assuming the same density of DM in the solar system than in the galaxy, if it affects a mass of 10^31 kg star in a spiral arm, it makes sense that in a billion times smaller volume it would affect a mas of 10^22 kg like that of planet Pluto, but actually it doesn't.

Probably this is flawed somewhere and I would like to understand the exact reason why DM doesn't affect solar system orbits.

 

[George Jones]

You need to compute something like:

1) the fraction (dark matter mass)/(total mass) of stuff inside Pluto's orbit;

2) the fraction (dark matter mass)/(total mass) of stuff inside an outer galactic star's orbit.

There should be a huge difference.

 

[Ich]

Probably this is flawed somewhere

Yes: Bodies of different weight experience the same acceleration. That's not exactly the latest news in physics, but still not outdated.
So this:

if it affects a mass of 10^31 kg star in a spiral arm, it makes sense that in a billion times smaller volume it would affect a mas of 10^22 kg like that of planet Pluto

makes no sense. Pluto's acceleration is simply 10^-9 times the star's acceleration.

 

[BillSaltLake]

From my earlier post, there's about 10¹⁷ kg of dark matter within a sphere at Neptune's radius. This means that the outer planets (where the effect of DM is strongest) would experience a fractional increase of 10¹⁷/2x10³¹ = 5x10^-15 in gravitational pull due to DM. This is probably unmeasurable with current technology. The extra pull would certainly be real however, because the halo of DM around the galaxy is like a heavy dust sphere, which pulls everything inward as long as it's roughly in equilibrium.

 

[TrickyDicky]

Yes: Bodies of different weight experience the same acceleration. That's not exactly the latest news in physics, but still not outdated.
So this:

makes no sense. Pluto's acceleration is simply 10^-9 times the star's acceleration.

I know trolling is basically what you usually do around the forums, but it's not nice. It's up to you but I'd ask you to choose some other thread to exercise your wits.

 

[TrickyDicky]

You need to compute something like:

1) the fraction (dark matter mass)/(total mass) of stuff inside Pluto's orbit;

2) the fraction (dark matter mass)/(total mass) of stuff inside an outer galactic star's orbit.

There should be a huge difference.

Hmmm.. So I guess the 5:1 ratio DM/BM that BillSaltLake mentioned doesn't apply at different scales.

 

[George Jones]

Hmmm.. So I guess the 5:1 ratio DM/BM that BillSaltLake mentioned doesn't apply at different scales.

Right.

From my earlier post, there's about 10¹⁷ kg of dark matter within a sphere at Neptune's radius. This means that the outer planets (where the effect of DM is strongest) would experience a fractional increase of 10¹⁷/2x10³¹ = 5x10^-15 in gravitational pull due to DM. This is probably unmeasurable with current technology. The extra pull would certainly be real however, because the halo of DM around the galaxy is like a heavy dust sphere, which pulls everything inward as long as it's roughly in equilibrium.

 

[TrickyDicky]

Here is an answer by a professional astrophysicist (Richard Massey fro Edimburgh R.O.):

"Dark matter is much more spread out than luminous matter and on the scales that we are used to, there is the same amount of dark matter in every direction, and its net effect is to do nothing."

This doesn't seem to have a lot to do with what has been responded here, but anyway, I can't understand it either. In gravitational systems I thought what mattered in a certain orbit was the amount of mass inwards to the center of mass, and by the superposition principle it doesn't matter if the mass is clumped in over-densities or uniformly spread.

Is there some professional astronomer around here that could explain this? Obviously it's not as simple as it seems.

 

[George Jones]

Assume that the density of dark matter is constant in space. Then, the different relative influences of dark matter comes down to the differences in

(normal matter mass enclosed)/volume.

For Pluto's orbit, this is approximately (Sun's mass)/(volume enclosed by Pluto's orbit).

Compare this to (normal matter mass enclosed)/volume for an outer galactic star.

I don't have the numbers at my at finger tips, but there is a huge difference.

 

[TrickyDicky]

Assume that the density of dark matter is constant in space. Then, the different relative influences of dark matter comes down to the differences in

(normal matter mass enclosed)/volume.

For Pluto's orbit, this is approximately (Sun's mass)/(volume enclosed by Pluto's orbit).

Compare this to (normal matter mass enclosed)/volume for an outer galactic star.

I don't have the numbers at my at finger tips, but there is a huge difference.

Ok, I see the difference, so all comes down to the fact that baryionic matter is much denser in the solar system scale than in the galaxy scale (actually as zhermes said in the first answer), I was just fixed at the 5:1 ratio and also didn't consider the volume factor, I was thinking of areas. Thanks for the patient answers.