Constraints on Dark Matter in the Solar System

[Buzz Bloom]

I wonder if someone can tell me if I have interpreted the cited article correctly.

https://arxiv.org/abs/1306.5534​

The article seems to have calculated upper bounds on the density of DM for different parts of our solar system.

We have found that
ρ_dm is less than 1.1⋅10⁻²⁰ g cm⁻³ at the orbital distance of Saturn,
ρ_dm<1.4⋅10⁻²⁰ g cm⁻³ at the orbital distance of Mars, and
ρ_dm<1.4⋅10⁻¹⁹ g cm⁻³ at the orbital distance of the Earth.​

These three values are all orders of magnitude greater than the standard average value for the universe given in various forms in various references.

ρ_dm = 2.3 10^-24 g cm⁻³​

The article dos not provide any lower bound for these ρ_dm values, but says:

Our estimates of the dark matter density and mass at various distances from the Sun are generally overridden by their errors (σ).​

My interpretation is that the study described in the article failed to find what they were looking for. In particular:
1. This study found no evidence for any DM present in the solar system.
2. This study found no evidence contradicting the following:

IF there is any DM in the solar system, THEN it is just as likely to have the standard value for the average density, 2.3 10^-24 g cm⁻³, as any other value less than the upper bound they found.​

Now, I actually think it is generally very beneficial for failed research to have published results explaining the failure. What disappointed me in this article was I could find no discussion of the shape of the likely distribution function of possible values. Just having an upper bound seems to me to be not particularly useful.

 

[Orodruin]

I would not call this failed research. They were looking to put a bound on the amount of dark matter in the solar system and it is exactly what they did. Regardless of what other bounds come from other sources, you can now go to this paper and say that this is the bound coming from observations of this type.

IF there is any DM in the solar system, THEN it is just as likely to have the standard value for the average density, 2.3 10-24 g cm−3, as any other value less than the upper bound they found.

You cannot say this. Assigning something as likely implies assigning a probability distribution.

Now, I actually think it is generally very beneficial for failed research to have published results explaining the failure. What disappointed me in this article was I could find no discussion of the shape of the likely distribution function of possible values. Just having an upper bound seems to me to be not particularly useful.

How do you expect a study with a sensitivity much weaker than the expected signal to provide you with a distribution? Upper bounds are often very useful in restricting theoretical possibilities and limits what theorists may cook up.

 

[Chronos]

The Milky Way is absolutely ginormous compared to the solar system. So you can fulfill the dark matter mass estimate for the entire galaxy with a crazy low DM density in our microscopic neighborhood. As noted on p12 of the paper the expected DM density in the solar system was already miniscule as depicted in Table 1, so their results are not really surprising.

 

[Buzz Bloom]

The Milky Way is absolutely ginormous compared to the solar system. So you can fulfill the dark matter mass estimate for the entire galaxy with a crazy low DM density in our microscopic neighborhood.

Hi @Chronos:
Thank you for your response.

What confuses me is that I have not been able to find any reference that explains any mechanism which would cause particular places within a large volume of almost uniform DM density to have locally significant differences in density from the common background. I have also been unable to find any sources presenting definitive evidence that small volumes, for example the solar system, actually have significant differences in DM density from the density of a large volume containing the small volume. The Table 1 in cited article is also a list of previous estimates of upper bounds rather than of any actual density values. By any chance, can you cite a reference that can help me?

Regards,
Buzz

 

[Buzz Bloom]

Hi @Orudruin:
Thank you for your response.

Regarding you comment

I would not call this failed research.

Although you make a good point, I still have some reservations. The following is a quote from the article:

The goal of this paper is an attempt to detect the gravitational manifestation of dark matter or to give a constraining upper limit for the dark matter density and mass in the Solar system using a new version of the planetary ephemerides, EPM2011, and new observations of planets and spacecraft .​

The underlining is mine for convenient reference. The first stated goal was not achieved. The second goal did achieve approximately a one-third reduction in the upper bound from previous research. In particular, the article's new results in Table 6 gives a value of

1.1 × 10⁻²⁰​

compared with a 2006 value of

4 × 10⁻¹⁹​

in Table 1. In my post #1 I compared this new value with the average universe DM density of

2.26 × 10^-24.​

After 10 years, a reduction of 3 compared with a needed additional reduction of 60,000 to get close to a plausible target of ρ_c value seems to me to be not close to what the researches were likely hoping for. (The DM values are for g/cm³ units.)

In considering your comment, I looked up an estimated DM density for the sun's location in the Milky Way:

6.2 ×10⁻²⁵.​

If this value has a good theoretical basis as an estimate of the actual density near the sun (I have no opinion or references about that), then an additional factor of 27 will be needed to get close to confirming this theoretical value with direct observational data.

Regarding another comment

How do you expect a study with a sensitivity much weaker than the expected signal to provide you with a distribution? Upper bounds are often very useful in restricting theoretical possibilities and limits what theorists may cook up.

I agree that "upper bounds are often very useful".
I do not have adequate math skills to answer your question as I would like to. One thing that may have been helpful in specifying a probability distribution is a specification of a confidence limit for the upper bound. I made a search for this in the article text and also scanned the article, but I found none. Such a confidence limit would correspond to the distribution's tail size. I would hope that a probability and/or statistics expert might be able to suggest a likely plausible shape for the distribution. Although I had a flat distribution in mind when I said,

it is just as likely to have the standard value for the average density

I actually do not think that a flat distribution is likely to be close to correct. My best guess is the distribution might be something like an exponential or a Poisson distribution.

Regards,
Buzz

 

[Orodruin]

One thing that may have been helpful in specifying a probability distribution is a specification of a confidence limit for the upper bound.

No, this is in fact not a good way to establish a probability distribution.

Such a confidence limit would correspond to the distribution's tail size.

No it would not. The confidence limit tells you about how likely a result would be given that a certain hypothesis was true. It tells you nothing of the probability distribution of the relevant parameter.

 

[Buzz Bloom]

Hi @Orudruin:

Thank you very much for correcting me.

Regards,
Buzz

 

[Orodruin]

A classical example of where this becomes apparent:

Imagine you are screened for some horrible disease, the test gives no false negatives (i.e., always detects the disease when you have it) but has a false positive rate of 1% (says you have it in 1% of the cases if you do not have it). You know that one out of $10^6$ people have the disease. Your test is positive. How worried should you be? The test would give you a confidence level of 99%. If the null hypothesis that you do not have the disease is true, the result is among the 1% most extreme outcomes. In reality, you are more likely one out of the 10000 people testing positive by chance.

 

[Buzz Bloom]

Please show me definitive proof of Black Matter.

Hi @rgaknwdpohm:

I think you may have a different concept of what "proof" means than I do. Physics is not mathematics. Mathematicians prove theorems. Physicists (and other scientists) create theories that lead to predictions which in principle may be validated or not. Validated predictions strengthens the usefulness of the theory.

I suggest you look for things to read that explain the predictions about dark matter (DM) that have been validated. Wikipedia is very useful, but sometimes not quite right. Many threads here on the Physics Forums are about DM and may be helpful to you. Do a search on "dark matter" in the title of threads.

Hope this helps.

Regards,
Buzz

 

[Buzz Bloom]

I have done the math...?

Hi @rgaknwdpohm:
I don't get what you mean. What math have you done?

Regards,
Buzz

 

[snorkack]

Ask it this way:
dark matter appears to be concentrated in Milky Way, in preference to intergalactic space.
How exactly is dark matter distributed within Milky Way?
Is dark matter distributed evenly, or is it significantly concentrated near Sun (and other stars)?

 

[Buzz Bloom]

How exactly is dark matter distributed within Milky Way?

Hi @snorkack:
I think you are suggesting I ask this question rather than the question I originally asked:

I wonder if someone can tell me if I have interpreted the cited article correctly.

Am I correct that this is what you meant?

I also think you were suggesting I ask this question:

Is dark matter distributed evenly, or is it significantly concentrated near Sun (and other stars)?

I believe I have already answered that question:

In considering your comment, I looked up an estimated DM density for the sun's location in the Milky Way:
6.2 ×10−25.If this value has a good theoretical basis as an estimate of the actual density near the sun (I have no opinion or references about that), then an additional factor of 27 will be needed to get close to confirming this theoretical value with direct observational data.

That is the DM density near the sun is about 1/27 of ρ_c, the average density in the universe, and the average density in the Milky Way halo should be greater than ρ_c.

The question I am still trying to find an answer to is WHY might the density near the sun be so small?.

Regards,
Buzz

 

[Buzz Bloom]

These three values are all orders of magnitude greater than the standard average value for the universe given in various forms in various references.
ρ_dm = 2.3 × 10^-24 g cm⁻³

I apologize for the above error.
The correct value is

ρ_dm = 2.3 × 10^-30 g cm⁻³ .​

Therefore a correct comparison of the smallest maximum

1.1×10⁻²⁰ g cm⁻³​

to the estimated value

6.2(4) ×10⁻²⁵ g cm^-3​

for the DM density near the sun would be a ratio of about 18,000.

Regards,
Buzz

 

[eachus]

Does dark matter gravitationally attract other DM? Does ordinary matter attract DM? If either of these were false, it would maximally falsify general relativity. It would also put significant dents in the standard model of particle physics. So in what follows, I will assume that DM is ordinary from a gravitational perspective.

So why doesn't DM cluster within galaxies, instead of on their fringes? There are two possible mechanisms. One is that DM is charged in some non-electromagnetic sense (call it hypercharge), and all DM has the same hypercharge. Possible, but we are still reaching way outside the standard model if we postulate a new force. The other possibility is that while DM does not interact with ordinary matter electromagnetically, it interacts through some other known force. The usual suspect here is the weak force. If we use Ockham's razor, then we get after a lot of steps to DM particles with a non-zero Y_W. Since DM particles are not charged and Y_W = -2(Q-T₃), DM particles would have an integer (and probably non-zero) weak hypercharge (Y_W). Fancy that.

Assuming that similar weak hypercharges repel, then if DM is all of one charge, DM particles will repel at short range but can pile up into not very dense clouds of DM as detected by astronomers.

Does DM interact with neutrinos? It is possible. Most or all such collisions would exchange nothing but momentum (with Z₀ being the mediating particle). If so, neutrinos flowing out from the sun will push DM out of the solar system, and galaxies will collectively push DM out of their centers. So it seems to fit with the data.

One last question: Does the existence of DM explain the matter-antimatter balance? It is a trick question in that any complete theory of creation has to explain both. But it does seem as though DM all having hypercharge of the same sign would likely come from the same mechanism.

 

[nikkkom]

Does dark matter gravitationally attract other DM? Does ordinary matter attract DM? If either of these were false, it would maximally falsify general relativity. It would also put significant dents in the standard model of particle physics. So in what follows, I will assume that DM is ordinary from a gravitational perspective.

So why doesn't DM cluster within galaxies, instead of on their fringes?

Because in order to "sink" closer to the center of a galaxy, orbiting object (be it a DM particle, or a star) needs to lose energy. Both DM particles and stars usually fail to do so, since they interact with the rest of the matter mostly via gravity. (Heavy particles, statistically, still sink to the center a bit, by scattering lighter ones. So stars do concentrate somewhat by this mechanism, DM particles don't).

Dust and gas are different, they have significant additional interactions and much more efficiently lose their kinetic energy. In spiral galaxies, this results in gas/dust sinking into the plane of rotation - and then forming new stars there. Now there new stars _are_ concentrated in this galaxy, because they are formed in it.