Paper: Constraints on Dark Matter in the Solar System

[inflector]

Any comments on the recent N. P. Pitjev and E. V. Pitjeva paper:

Constraints on Dark Matter in the Solar System
arXiv: http://arxiv.org/abs/1306.5534

MIT Technology Review article:
http://www.technologyreview.com/view/516681/the-incredible-dark-matter-mystery-why-astronomers-say-it-is-missing-in-action/

If I understand it correctly, the gist of the article is that they examined the effects of potential dark matter on solar system dynamics and found that if present if can't be more than the mass of a large asteroid.

 

[D H]

That's what the article is saying. The Russian Institute for Applied Astronomy is one of the three leading organizations that develop solar system ephemerides. (The other two are JPL and the French IMCCE.) All three use general relativity to model the behaviors of the bodies that comprise the solar system. Thanks to vastly improved measurements and vastly improved models, there appears to be very little leeway in any of these ephemerides for dark matter in the solar system.

 

[Chalnoth]

If I understand it correctly, the gist of the article is that they examined the effects of potential dark matter on solar system dynamics and found that if present if can't be more than the mass of a large asteroid.

Well, the limit for the dark matter within the orbit of Saturn is about a third the mass of Ceres, which is a dwarf planet. But yeah.

 

[Vanadium 50]

Isn't their limit thousands (perhaps even a million) of times larger than the average DM density?

 

[mfb]

It is a limit independent of galactic models, so it is a nice cross-check. In addition, it rules out that sun-like stars accumulate significant amounts of dark matter.

$$M_{Earth}/M_{Moon} = 81.3005676 \pm 0.00000006$$
$$AU = (149597870695.88 \pm 0.14) m$$

The digits for the ratio not match, but that is an incredible precision. In particular, the relative masses are known better than the absolute masses by several orders of magnitude.

 

[mrspeedybob]

Equation 1 on page 4 seems unjustified to me. If DM is homogenous on scales much larger then the solar system then any acceleration due to it's gravity should affect all bodies in the solar system alike. For example, it will accelerate the Sun and Saturn in the same direction by the same amount but make no net contribution to Saturn's acceleration toward the sun.

 

[mfb]

A uniform distribution leads to a net attractive force - this is easier to see if you consider the field inside earth, for example: Independent of their position, freely falling objects would approach each other. They don't have to be in the center.
This is based on Newtonian gravity, but I don't think GR fundamentally changes this for mass densities and accelerations in the solar system.

 

[D H]

Equation 1 on page 4 seems unjustified to me. If DM is homogenous on scales much larger then the solar system then any acceleration due to it's gravity should affect all bodies in the solar system alike.

Not relative to the solar system barycenter or relative to the sun, and that is what is being investigated. The galactic gravity gradient across the solar system is so very, very tiny that tidal effects resulting from gravitational acceleration toward nearby stars and toward the center of the galaxy can safely be ignored. By means of both measurements and models of behaviors, a barycentric frame is indistinguishable from an inertial frame within the context of solar system.

That equation yields the sunward acceleration toward for any spherical mass distribution about the Sun. A uniform distribution is the simplest case of a spherical mass distribution. That's the baseline assumption for dark matter. Dark matter might be more concentrated in the vicinity of the solar system thanks to the mass of the solar system, and if that's the case it's the Sun that is going to be the primary culprit. Assuming some kind of a Sun-centered spherical mass distribution for dark matter (but not necessarily a uniform distribution) makes sense.