We discuss the correlation between the dark matter content of elliptical galaxies and their ellipticities. We then explore a mechanism for which the correlation would emerge naturally. Such mechanism leads to identifying the dark matter particles to gravitons. A similar mechanism is known in Quantum Chromodynamics (QCD) and is essential to our understanding of the mass and structure of baryonic matter.

Alexandre Deur, "A correlation between the amount of dark matter in elliptical galaxies and their shape" (28 Jul 2014).

Every now and then there is a paper that suggests that the phenomena described as dark matter is really implied by General Relativity, or a trivial variant of General Relativity, and that the discrepancy between theory and observation that astronomers observe is because they inappropriately conclude that in systems like galaxies and galactic clusters that Newtonian gravity is a reasonably accurate approximation of General Relativity.

This is one of the stronger arguments that I have seen for that position.

Most of those papers argue basically that what a Newtonian gravitational approximation (mediated through a stylized approximation of a galaxy's structure or a numerical many body simulation much like those of lattice QCD) is missing is the gravitational effects of the coherent angular momentum of the many bodies in a galaxy as they rotate around a central black hole. On balance, I've found that the argument that this contribution is tiny is stronger than the argument that this is the main source of dark matter phenomena.

Put another way, they focus on the additional degrees of freedom (i.e. additional amount of information necessary to describe) the behavior of General Relativity (which requires a spin-2 tensor field graviton), rather than the spin-0 scalar field gravitons of Newtonian gravity.

This paper focuses on a different distinction between Newtonian gravitons and General Relativistic ones. Newtonian gravitons, like real world photons, don't interact with each other. They couple only to mass and electric charge, respectively. In contrast, in General Relativity, gravity is a function of both mass and energy. Thus, gravity can influence particles that have zero rest mass (i.e. photons and gluons), and in principle, gravity may even influence other gravitons. In this respect gravitons are more like gluons, which interact both with quarks and with each other, and less like photons.

Focusing on this self-interaction of gravitons suggests an effect of approximately the right order of magnitude to account for differences in the amount of "dark matter" effects seen in ellipical galaxies of different sizes. A previous paper from 2009 argues that the effect is on the right order of magnitude to account for the rotation curves of galaxies and the Tully-Fisher relation, and may also explain, or at least help to explain, dark matter phenomena in galaxy clusters.

I haven't had the time to rigorously review the accuracy of the analysis, but the approach does look like a fruitful one to explore that is understudied. Deur basically claims to have derived a versions of MOND (Milgrom's modified gravity theory) from first principles using a toy model approximation of GR that preserves the essentials of General Relativity in a symmetric and homogeneous case, while proving much more accurate for galactic clusters and that can explain the Bullet Cluster.

An interesting analysis of what would distinguish MOND from MOND-like theories is found in another 2009 paper by another author.

If he's right, he deserves the Nobel prize for physics. If this approach really works, of course, it would also eliminate the phenomenological need for any beyond the Standard Model particles other than the graviton, which is by far the best empirically supported hypothetical particle. Given our failure to discovery any other dark matter candidates, this increasingly looks like a feature rather than a bug.

Deur's approach was also discussed recently at the Physics Forums.

## 9 comments:

The locations of dark matter are not 100% correlated with non-dark-matter. Recent calculations put the cross-correlation between dark matter and galaxies to be only around 1-10%. (If I'm reading Figure 8 correctly.)

http://phys.org/news/2014-07-large-dark-peaks-gravitational-lensing.html

Plus, there are a number of dwarf galaxies that are nearly 100% dark matter, and with virtually no baryonic matter.

This means that dark matter is not MOND, or similar modification.

It's a fermion particle with a rest mass likely between 2 keV and 10 keV, and that doesn't interact with the strong force or E&M.

What MOND and theories like this one suppose is effects attributed to dark matter are attributable to distributions of ordinary Standard Model/GR matter energy. MOND and its relativistic approximations of it like TeVeS assume that the weak fields are stronger than one might otherwise suppose. MOND accurately approximates dark matter effects in the vicinity of galaxies of all kinds and predicted before observations were made that dwarf galaxies would appear to be dark matter dominated.

The self-interaction of graviton theory proposes that in the presence of highly massive objects that are not spherically symmetric that gravity is made stronger and more directional by virtue of the self-interaction of gravitons.

Both of these theories predict the same observables as traditional dark matter theories, but with only one new experimentally measured parameter in the case of the first, and zero new experimentally measured parameters (in principle anyway) in the second (self-interaction should be a function of the general relativity gravitational constant G).

MOND has always underestimated dark matter phenomena in galactic clusters, and is arguably a poor fit for the bullet cluster. But, the self-interaction of the graviton theory scales up dark matter phenomena in galactic clusters to just about the right amount and naturally explains the Bullet Cluster observations, since the interacting gas of the colliding galaxies is homogeneous and the symmetry defuses the self-interaction of graviton effects.

This dispatch summarizes pretty well Deur's paper but I don't know if we should say that the paper derived a version of MOND from first principles. MOND postulates that at below some given acceleration, the laws of acceleration change. Deur's point is that above some mass scale, the non-linearity of General Relativity kicks in (if it's not cancelled by symmetry). That's not equivalent. A big consequence is that MOND cannot explain the Bullet cluster observation while Deur's calculations can. Although from the fundamental point of view, it is not the same to postulate some ad-hoc phenomenology, as MOND does, to explain something and to use fairly solid theoretical arguments, as Deur's does. The leading DM candidates such WIMP or axions are too based on fairly reasonable theoretical grounds. Maybe that's why they are more attractive than MOND (no pun intended).

To Eddie Devere: The locations of dark matter peaks are well correlated with non-dark-matter. Otherwise, the formation theory of large scale structure in the Lambda-CDM model would be in troubles. What's important for a cross-correlation function is its slope, not its value. See the gamma parameter in Eq. 7. The cross-correlation for the weak lensing peaks and CMASS galaxies has a slope (0.78) close to the slope of the CMASS galaxy autocorrelation (0.73). The peaks clearly above the noise are very well correlated, as it is stated in the conclusion of Shan's paper (end of 3rd paragraph).

If the correlation seen in the fig. of the news blurb (or Fig. 3 in Shan's paper) is not impressive, it's because of large noise, see the comment page 3 of Shan's paper. See also the weaker correlation for peaks without strong signal/noise ration (red line of Fig. 7) and the statement in the paper than half of the weak signal/noise peaks are just noise.

Dwarf galaxies harbor about the same amount of dark matter, relative to luminous content, than clusters, which are well reproduced in Deur's paper. So there does not seem to be a problem there.

"This dispatch summarizes pretty well Deur's paper but I don't know if we should say that the paper derived a version of MOND from first principles."

What I mean when I say that is that Deur derives a theory that reproduces dark matter phenomena such as the 1/r force law in the weak field and 1/r^2 force law in the strong field, from first principles without resorting to non-baryonic dark matter to explain them. MOND simply applies a 1/r^2 force law in one part of a galaxy, and a 1/r force law in another part of a galaxy by fiat and interpolates between the two with an arbitrarily chosen function chosen on the basis of fit to the data, while Deur finds a rather elegant way to derive a form for his force law equation from the equations of GR itself approximated in a novel way (in practice, all numerical GR work and most analytical conclusions are done with approximations of some kind or another, but different simplifying assumptions that mask the non-linear effects that Deur preserves are conventionally made).

Deur basically establishes that the most important non-linear effects in these systems take the form of a Yukawa interaction.

I would also call attention to work linked in a later post at this blog by Nikolic construction a true energy-momentum tensor for gravitational energy, rather than a mere pseudo-tensor which the conventional analysis supposes is the only possible solution to that issue, and by Juan Ramón González Álvarez arguing that while a spin-2 graviton in Minkowski space is not equivalent to GR, that it is sufficiently close to be an attractive alternative that is indistinguishable from GR through the empirical tests of GR that have been conducted to date (and hence making a particle based theory of quantum gravity that isn't quite GR possible).

I suspect that one or both of these insights would be necessary to turn Deur's essential insight about graviton self-interaction into a rigorous full fledged explanation of non-linear GR effects that can explain dark matter phenomena.

"a later post at this blog by Nikolic construction a true energy-momentum tensor"

This should read: "a later post at this blog by Nikolic constructing a true energy-momentum tensor"

Andrew: yes, you are right. Deur's work gives a (welcome) General Relativity basis to the MOND phenomenology, but only in the special case of disks. For the rest, it's quite different.

Your point on approximations is good too. Most of the GR work I know off (apart from the rare exact Schwarzchild or Kerr solutions) are done using the Einstein–Infeld–Hoffmann equations or higher order PPN approximation. The EIF eq. usually assume a spherical symmetry which is bad according to the argument in Deur's paper that the strong non-linear effects cancel out when there is a spherical symmetry. EIF eq. uals assume weak fields and we know from QCD that we would miss all the strong non-linear effects in the perturbative QCD approximation. So their is little chance that EIF formalism or higher order PPN could produce strong linearities. Full GR calculations in Numerical Relativity are being done but I don't know what approximations are made there.

I am missing your point when you say that Deur's work establish a Yukawa interaction. A linear (1D system) or log (2D system) potential doesn't look like e^(-mr)/r. Unless one says that everything is as if gravitons, in 2D system, acquire an effective mass that goes a -log[rlog(r)]/r. But it's not really interesting.

The discussion of the Yukawa potential component of gravitational potential in a system that is not spherically symmetric appears at the bottom of page four in the first paper linked above.

It is relevant because (1) it derives a Yukawa potential in GR from first principles, and (2) there is a fair amount of literature out there discussing the implications of gravitational equations with a Yukawa potential in addition to the 1/r Newtonian potential which generates MOND-like results in a variety of settings.

Essentially what you do is decompose a system into a spherically symmetric one where the Yukawa potential vanishes due to symmetrical cancellation, and a non-spherically symmetric system where it does not, and then scale the strength of the potential by the mass of the system.

The application of this analysis in this paper to elipitcal galaxies shows that it is not limited to spiral galaxies but can instead be applied to both classes of galaxies, although more detailed treatments of the dwarf galaxy, cluster and Bullet cluster cases are left to other sources referred to in the linked paper.

The paper also discusses how the self-interaction between gravitons in galaxies should weaken the gravitonal field between galaxies in an amount equal to the enhancement reflected in dark matter phenomena, by analogy to QCD and cites a 2004 paper discussing this analogy:

http://arxiv.org/pdf/hep-th/0410119v2.pdf

A weaker gravitational field outside galaxies looks like a repulsive force. Thus, pure GR may explain at least a third of dark energy.

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