New one by Moffat (comparing fit to rotation curves)

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marcus

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in case if might be of interest

http://arxiv.org/abs/astro-ph/0506370
Galaxy Rotation Curves Without Non-Baryonic Dark Matter
J. R. Brownstein, J. W. Moffat
Submitted to ApJ, June 20, 2005. 43 pages, 7 figures, 4 tables, 101 galaxies

"We apply the modified acceleration law obtained from Einstein gravity coupled to a massive skew symmetric field F_{\mu\nu\lambda} to the problem of explaining galaxy rotation curves without exotic dark matter. Our sample of galaxies includes low surface brightness (LSB) and high surface brightness (HSB) galaxies, and an elliptical galaxy. In those cases where photometric data are available, a best fit via the single parameter (M/L)_{stars} to the luminosity of the gaseous (HI plus He) and luminous stellar disks is obtained. Additionally, a best fit to the rotation curves of galaxies is obtained in terms of a parametric mass distribution (independent of luminosity observations) -- a two parameter fit to the total galactic mass, (or mass-to-light ratio M/L), and a core radius associated with a model of the galaxy cores using a nonlinear least-squares fitting routine including estimated errors. The fits are compared to those obtained using Milgrom's phenomenological MOND model and to the predictions of the Newtonian-Kepler acceleration law."
 

marcus

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I had a look. judging by the graphs, Moffat "metric skew tensor" gravity law gets about same good fit to the observed rotation curves as Milgrom MOND.

does Moffat's version have an advantage in some other department?

the pictures look impressive to someone without special knowledge of MOND----several of the figures, like figure 1, are actually composed of many separate plots for many different galaxies and in nearly every case the two modified laws seem to fit remarkably well
 

ohwilleke

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Moffat has been the other game in town for modified gravity for a long time. His formula is different, but as the graphs show, they work out to produce similar results in practice.

The downside of Moffat's formula is that it has more parameters to fine tune with. This is a particular concern because his results are post-dicts, while MONDs results are in many cases predicts.

The upside, not proven in this paper or any paper I've seen yet, but at least claimed in this paper near the end of the text, is that it does better in clusters, which is a big deal, as that is the big problem with MOND. Also, Moffat has a specific formula, while Bekenstein, at least, only has a toy model formula, although the toy model formula choice doesn't have an impact in areas where we have empirical data.

Moffat's formula predicts a significant fall off in modified gravity effects in the fringe areas of the galactic disk compared to MOND. The data in the charts doesn't strongly support that conclusion. He doesn't do a least square analysis to compare the two theories to the data, but eyeballing it, MOND does better (on both this and Tulley-Fischer margins of error), particularly at the galactic fringes where Moffat's theory has velocities falling off more rapidly than they do. But, Moffat, to his credit in this regard, cites Prada for the claim that "satellite" stars around galaxies show Newtonian behavior in a 6,000 data point study.

He also notes that he has followed the example of Sanders and Bekenstein and come up with a relativistic version of this theory.

The theories really all go at the same idea, one I tend to endorse, which is that a modified gravity formula can explain DM and that DM has serious issues that it leaves unexplained (like why is DM distributed as it is) that are unanswered.

I'd like to see a good galactic cluster paper from Moffat. If he could fit the micro-lensing results that would be a real accomplishment.

The Prada paper is very significant and so I'll cite it here:
http://arxiv.org/abs/astro-ph/0301360

Observing the dark matter density profile of isolated galaxies
Authors: Francisco Prada, Mayrita Vitvitska, Anatoly Klypin, Jon A. Holtzman, David J. Schlegel, Eva K. Grebel, H.-W. Rix, J. Brinkmann, T.A. McKay, I. Csabai
Comments: 15 pages, 10 figures, submitted to ApJ
Journal-ref: Astrophys.J. 598 (2003) 260-271

Using the Sloan Digital Sky Survey (SDSS), we probe the halo mass distribution by studying the velocities of satellites orbiting isolated galaxies. In a subsample that covers 2500 sq. degrees on the sky, we detect about 3000 satellites with absolute blue magnitudes going down to M_B = -14; most of the satellites have M_B=-16 to -18, comparable to the magnitudes of M32 and the Magellanic Clouds. After a careful, model-independent removal of interlopers, we find that the line-of-sight velocity dispersion of satellites declines with distance to the primary. For an L* galaxy the r.m.s. line-of-sight velocity changes from ~120 km/s at 20 kpc to ~60 km/s at 350 kpc. This decline agrees remarkably well with theoretical expectations, as all modern cosmological models predict that the density of dark matter in the peripheral parts of galaxies declines as rho_DM propto r^{-3}. Thus, for the first time we find direct observational evidence of the density decline predicted by cosmological models; we also note that this result contradicts alternative theories of gravity such as MOND. We also find that the velocity dispersion of satellites within 100 kpc scales with the absolute magnitude of the central galaxy as sigma propto L^{0.3}; this is very close to the Tully-Fisher relation for normal spiral galaxies.
 
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wolram

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Of all the constants, gravity is the only one we have actually measured, ok
these measurments are in our solar system, but to vary gravity in the standard
model would require, variable curvature, or an interaction between gravity and
mass that is dynamic, "communication".
Neither the higgs field nor the graviton have been found, and have been constrained to ever tighter limits, so is there a possibility that these two
have any part to play?
 

ohwilleke

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I'm sorry wolfram, but I don't follow what you are saying at all.

Certainly we have measured other constants like those of QED and particle masses. The gravity is the least accurately known fundamental physical constant of them all.

Now, I'm with you to the extent that Moffat is arguing for changing constants over time. His use of the term "running constant" is actually pretty sloppy. But, there is nothing too profound which is necessary to get what he calls a gravitational constant that runs with distance. This is really just a way of saying that the gravitational force varies with distance (something we knew already) according to a different formula than generally accepted.

As far as the parameters that Moffat uses in his theory, I think lack of measurement is not really the problem with them. The problem is too many measurements. They are essentially all measured values and this allows for fine tuning.

It isn't really hard to get formulas like these out of the standard model. Indeed, there are strong anaologies at a quantum level between QCD and gravity. There are some hints (rumors from Motl about weaker than Newtonian effects at the sub 0.1mm scale) that both may exhibit asymptotic freedom (i.e. uncharacteristic weakness) at very small scales, and increasing strength at very large scales (galactic dynamics, e.g.).

One interesting aspect of some versions of Moffat's theory in particular is that unlike ordinary GR which features rank-2 tensors, his theory involves a rank-3 tensor. This might suggest a spin-3 graviton.

Moffat's theory is set forth from scratch here: http://arxiv.org/abs/astro-ph/0412195

Gravitational Theory, Galaxy Rotation Curves and Cosmology without Dark Matter
Authors: J. W. Moffat
Comments: 33 pages, 20 figures, 1 table. Latex file. Additional text and references. Corrections. To be published in Journal of Cosmology and Astroparticle Physics (JCAP)
Journal-ref: JCAP 0505 (2005) 003

Einstein gravity coupled to a massive skew symmetric field F_{\mu\nu\lambda} leads to an acceleration law that modifies the Newtonian law of attraction between particles. We use a framework of non-perturbative renormalization group equations as well as observational input to characterize special renormalization group trajectories to allow for the running of the effective gravitational coupling G and the coupling of the skew field to matter. The latter lead to an increase of Newton's constant at large galactic and cosmological distances. For weak fields a fit to the flat rotation curves of galaxies is obtained in terms of the mass (mass-to-light ratio M/L) of galaxies. The fits assume that the galaxies are not dominated by exotic dark matter and that the effective gravitational constant G runs with distance scale. The equations of motion for test particles yield predictions for the solar system and the binary pulsar PSR 1913+16 that agree with the observations. The gravitational lensing of clusters of galaxies can be explained without exotic dark matter. An FLRW cosmological model with an effective G=G(t) running with time can lead to consistent fits to cosmological data without assuming the existence of exotic cold dark matter.
The best argument for a gravitational constant that did run from time, if you were to make that argument would be that gravity is an emergent machian consequence of the distribution of matter in the universe that as a result the expansion of the universe changes the effective gravitational constant.

To abuse the rubber sheet analogy, you might expect that local deviations in the rubber sheet typography might come more easily when it is nearly flat, than they would when it is tightly rolled up.
 
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wolram

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Ohwilleke

I'm sorry wolfram, but I don't follow what you are saying at all.
----------------------------------------------------------------------------
Thats ok, not many do, i seem to look to side or the back.

I have been cosidering the unique relationship of the Higgs field and the
graviton, if these exist, One is the mass giver, the other the atractor.
Maybe you think about the same things?
But if constraints get much tighter, then we have to narrow the possibilities
in cosmology.
 

ohwilleke

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It is interesting that so many of the open questions in physics from grand unification, to the numerous constants of the standard model, to dark matter, to dark energy, to the missing Higgs, to neutrino mass seem to involve gravity and mass.
 

turbo

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ohwilleke said:
The best argument for a gravitational constant that did run from time, if you were to make that argument would be that gravity is an emergent machian consequence of the distribution of matter in the universe that as a result the expansion of the universe changes the effective gravitational constant.
Wolram said:
I have been cosidering the unique relationship of the Higgs field and the
graviton, if these exist, One is the mass giver, the other the atractor.
Maybe you think about the same things?
ohwilleke said:
It is interesting that so many of the open questions in physics from grand unification, to the numerous constants of the standard model, to dark matter, to dark energy, to the missing Higgs, to neutrino mass seem to involve gravity and mass.
Yes to all of these comments. There is a logical extension that must be made - namely that mass is conferred by the same field that mediates gravitational attraction. If this were not true, we would not see objects acting consistently (in terms of gravitational effects) all around us in every direction at every distance. If these two fields were not balanced to the nth degree all over the universe at all times, the universe would look pretty darned strange. Any slight incongruities in the fields that convey mass (Higgs field) and gravitational attraction (gravitational field) would cause the universe to behave quite badly, and we do not see this. Does this leave us any slight possibility that mass and gravitation arise from two different fields?

The non-detections of the Higgs and the graviton do not prove that their respective fields do not exist, but it should prompt a little epistemology amongst the faithful of standard cosmology (a valuable pursuit more honored in the breach these days, I fear). Two separate fields that are remarkably congruent across all observable space and time - hmm, what does that suggest?
 
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Chronos

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I don't think mass and gravitational attraction can be distinguished, but that is merely a conjecture. It looks to me they are equivalent in every reference frame. How would you suggest we tell them apart?
 

Garth

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ohwilleke said:
It is interesting that so many of the open questions in physics from grand unification, to the numerous constants of the standard model, to dark matter, to dark energy, to the missing Higgs, to neutrino mass seem to involve gravity and mass.
If gravity and inertial mass were inversely proportional to each other
G ~ 1/M then GM = constant and the theory would be concordant with Newtonian experiment.

Garth
 

turbo

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Chronos said:
I don't think mass and gravitational attraction can be distinguished, but that is merely a conjecture. It looks to me they are equivalent in every reference frame. How would you suggest we tell them apart?
In the standard model: 1) mass is a property of matter conferred upon it through its interaction with the Higgs field and 2) massive bodies curve space-time (GR model of the gravitational field) resulting in mutual attraction. The problem is not how to tell mass and gravitation apart (they are very different things, by the way - one is an "intrinsic" physical property and the other is a force), the problem is how to unify them properly to explain what we observe everywhere in the universe.
 

ohwilleke

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I think that if you wanted to look at distinctions between gravity and inertial mass you'd have to look to energy. Energy gravitates. Energy does not have inertia.

For example, consider a superconducting loop carrying vast amounts of energy. It would seem to be that under GR this would gravite more strongly than a superconducting loop with no current. Yet, it isn't at all obvious that it would take more force to move the energized superconducting loop than it would to move the non-energized superconducting loop.

Am I wrong?
 

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