## [astro-ph/0608675] Gravitational Lensing in Modified Gravity and the Lensing of Merging Clusters without Dark Matter

 Authors: J. W. Moffat Abstract: Gravitational lensing in a modified gravity (MOG) is derived and shown to describe lensing without postulating dark matter. The recent data for merging clusters identified with the interacting cluster 1E0657-56 is shown to be consistent with a weak lensing construction based on MOG without exotic dark matter. [PDF]  [PS]  [BibTex]  [Bookmark]

Discussion related to specific recent arXiv papers
Aseem Paranjape
Posts: 7
Joined: December 23 2005
Affiliation: IUCAA, Pune, India

### [astro-ph/0608675] Gravitational Lensing in Modified Gravity

This paper claims to explain the observations of the cluster 1E0657-56 which was studied by Clowe et al astro-ph/0608407, using modified gravity (MOG).
If I've understood correctly, the main cluster is treated as spherically symmetric and its convergence $\kappa$ distribution is shown to have a peak away from the center (Fig 1). (There's some ambiguity about whether it's the main cluster or the \emph{total} system that is assumed to have spherical symmetry.) I also don't understand how a peak in a radial profile explains the localized lensing peaks offset from the plasma in the cluster.

Tommy Anderberg
Posts: 47
Joined: November 24 2005
Affiliation: independent

### Re: [astro-ph/0608675] Gravitational Lensing in Modified Gra

Aseem Paranjape wrote:(There's some ambiguity about whether it's the main cluster or the \emph{total} system that is assumed to have spherical symmetry.)
Looks like the total. Reminescent of the classic spherical chicken joke, but it serves the intended purpose: to show qualitatively that offset peaks can be achieved without dark matter, so we shouldn't jump to conclusions before a more realistic analysis is performed, presumably numerically.

Douglas Clowe
Posts: 11
Joined: November 05 2005
Affiliation: Ohio University

### [astro-ph/0608675] Gravitational Lensing in Modified Gravity

While some might consider me biased, I can't see how his conclusions are supported by the paper, and think that he actually managed to disprove his theory in this paper.

He took a spherical model, using an exponential profile for the gas and a spherical tophat for the galaxies, then showed that putting these into his lensing equations from his model resulted in a kappa profile which looks a lot like a spiral galaxy rotation curve.

A couple problems with this (ignoring the idea of approximating the bullet cluster as a sphere and not offseting the positions of the gas and galaxies):
1) His kappa signal never decreases, but stays roughly constant at large radius, while every cluster ever measured with weak gravitational lensing, the bullet cluster included, follows a ~r^{-1} fall off in kappa over a range of a 500-1500 kpc (and faster at larger radii) when you do azimuthal averaging of the signal.
2) In normal clusters, where the galaxies and gas are spatially coincident and do follow a mass profile qualitatively similar (in that it's peaked in the center and decreases with radius) to what he shows in figure 1 (the red curve), kappa also peaks in the center and decreases with radius.

Basically in this paper he's showing that using his theory, he generates a much larger lensing signal than the same mass would in Newtonian gravity (which is good, it's exactly what you need), but the actual profile he gets out is unphysical and has never been observed, and can be ruled out at very high confidence levels from all the normal clusters in the literature.

Even if he can somehow show that having both the gas and the galaxies centrally peaked results in a centrally peaked kappa profile while having the gas centrally peaked and the galaxies not gets this decrease in kappa at small radius and finds a way to correct the large radius behaviour so that kappa decreases with radius like the observations, it's still a huge leap to go from this 1-D model to say that his theory can reproduce the bullet cluster observations in 2-D.

Tommy Anderberg
Posts: 47
Joined: November 24 2005
Affiliation: independent

### Re: [astro-ph/0608675] Gravitational Lensing in Modified Gra

Douglas Clowe wrote:While some might consider me biased
:) Since Moffat also gets accelerated expansion out of his MOG, I am really pushing the diabolical advocacy here... so you may want to keep my own infamous bias in mind when I say that you make a good point here:
Douglas Clowe wrote: the actual profile he gets out is unphysical and has never been observed, and can be ruled out at very high confidence levels from all the normal clusters in the literature
On the other hand, as in your critique of astro-ph/0606216 in http://cosmocoffee.info/viewtopic.php?p=1949#1949
Douglas Clowe wrote:Also, the Angus paper used a perfectly symmetric system which had dark matter in the outer peaks already (claimed it could be neutrinos, but had it peaked into cusps), just not as much dark matter as you'd need with Newtonian gravity. If you look at the figures in our papers, you'll see 1E0657 is not even close to being symmetric
you seem to be demanding too much of simple examples which are primarily meant as proofs of concept, not as realistic models.

What these examples show is that lensing maps and mass distributions need not coincide in TeVeS and MSTG. With that proof of concept in hand you have a reason to try and create a realistic model without the unnatural symmetries required for analytic tractability. Everybody probably agrees that
Douglas Clowe wrote:it's still a huge leap to go from this 1-D model to say that his theory can reproduce the bullet cluster observations in 2-D

but at this stage it would also be a great leap to claim that it definitely can not. To find out, you just have to try it. Lots of computer modeling work ahead for MOG proponents, I think.

John Moffat
Posts: 2
Joined: September 02 2006
Affiliation: Perimeter Institute for Theoretical Physics

### [astro-ph/0608675] Gravitational Lensing in Modified Gravity

In response to Douglas Clowe's comments about my paper: astro-ph/0608675, I did not set out in this paper to produce a "realistic" model of the interacting cluster 1E0657-56. I wanted to get across the message that my relativistic modified gravity (MOG) can describe the basic features of the "bullet" cluster, namely, that the convergence field kappa(R) can show a pronounced peaking in the regions containing visible galaxies, even though the matter associated with the galaxies is unable in Einstein's and Newton's gravity theories to produce sufficient lensing and image distortion of light from distant background galaxies. The reason my MOG convergence curve looks like a galaxy rotational velocity curve is because the same underlying MOG physics is taking place: By solving the field equations obtained from the MOG action principle, one arrives at a modification of Newtonian gravity that is not an inverse square law, but has a distance range-dependence that increases the strength of gravity as the distance increases from a matter source. Eventually well beyond the fixed distance range the gravitational potential becomes Newtonian. This leads to excellent fits to the rotational velocity data and fits to the mass profiles of X-ray clusters without dark matter. Since MOG is a relativistic gravity theory, it can make definite predictions about the lensing of light rays.

I assume that the total interactiing cluster is spherically symmetrical (which may not be the case for 1E0567-56) in order to obtain an analytical description of the gravitational physics using MOG. The simple model I use for the densities of the separated surface X-ray plasma and galaxies is also chosen so as to illustrate the essential physics. On page 6 of my paper, I state: "We are required in a realistic model to cut off the surface density Sigma at the edges of the interacting cluster." On page 7, I say: "A more detailed study of the MOG prediction for the interacting cluster based on a fitting to published data will be considered in a future paper." Using a simple phenomenological model for the structure of 1E0567-56 hardly justifies Clowe's comment that "...I can't see how his conclusions are supported by the paper, and think that he actually manages to disprove his theory in this paper."

I believe that I have shown in a qualitatively convincing way that MOG can explain the lensing data for 1E0567-56 without dark matter. A more realistic model for the structure of the interacting cluster should remove any possible doubt that this is true. As I state in my conclusions: "...*one should not draw premature conclusions about the existence of dark matter* without a careful analysis of alternative gravity theories... ."

Tommy Anderberg's comments are right on.

Douglas Clowe
Posts: 11
Joined: November 05 2005
Affiliation: Ohio University

### [astro-ph/0608675] Gravitational Lensing in Modified Gravity

John -

my primary critism of your paper, is that if I apply your solution (from figure 1 in your paper) in 2-D, you would see a plane of high $\kappa$ everywhere except in the center of the gas clouds, and that is not what we observe ($\kappa$ decreases at r>500 kpc). This might be solved by an alteration of your baryonic profiles used in your model, but it is not clear in your paper if this is the case.

It is a huge step go to from 1-D models to 2-D models, and there are 2 problems with trying to model the system using non-Newtonian gravity in 2-D:
1) The system is not symmetric (the gas clouds are not centered on the line between the two centers of galaxy distributions, the 2 gas clouds and the 2 centers of galaxies are best described by a rhombus), and for both merging clusters you would need to either suppress the lensing by the gas peaks or displace them ontop of the galaxy peaks (which are not directly opposite in a line from the other galaxy peaks). It is not clear from your paper that the 1-D suppresion of the central peak would correpond to a 2-d shifting of the peaks in exactly the directions they need to shift.
2) The $\bar{\kappa}$ to optical light and X-ray gas mass ratios for this system are consistent with those in normal clusters with the same optical light total where the gas and galaxies are spatially coincident (and therefore have the baryons centered on the lensing peak 10 times higher than the bullet cluster), and 10 time higher than systems which have total baryonic masses (gas + galaxies) equal to the galactic masses of this system. So you not only have to get the $\kappa$ clouds to center near the galaxies. you also have to preserve the total lensing strength of the system relative to the total baryonic mass, despite 90% of the baryons being offset from the center of the lensing system.

In our paper, we tried to stress that we could not prove that gravity was Newtonian on these scales, but that we simply could not find anyway to solve those problems without the majority of the mass of the system being non-luminous matter with a center of mass being roughly around the position of the galaxies (and gravitational lensing doesn't care about what type of matter it is, we have to use BBN and similar arguments to say it can't be baryons). We're not disproving MOG or MOND or any type of modified gravity, we're simply saying that regardless of how you modify gravity, you're going to need the majority of mass of these systems, and by inference the universe (as clusters should be a representitive sample of the matter in the universe), to be some form of non-luminous matter. By using non-Newtonian gravity, you allow yourself to use less dark matter, but you will still need most of the mass to be dark matter (and as I mention in the thread on my paper that my estimates are a minimum of twice the gas mass in dark matter).

In your paper you showed that you can get a 1-d lensing profile which doesn't follow the baryonic mass distribution. But to go from that to a statement that your theory can explain the bullet cluster is simply not supported by the models in your paper (which is what you claim in the second sentence of the abstract).

doug

John Moffat
Posts: 2
Joined: September 02 2006
Affiliation: Perimeter Institute for Theoretical Physics

### [astro-ph/0608675] Gravitational Lensing in Modified Gravity

Doug -

The next step in my study of 1E0657-56 is to go from my 1-D lensing profile to a 2-D (or even a 3-D) lensing profile model using the fact that MOG doesn't follow a baryonic mass distribution. This requires using a more sophisticated model of the gas plasma and galaxy density profiles that displays the observed decrease of kappa for r > 500 kpc.

In my recent paper: gr-qc/0608074, I showed how MOG can describe a reasonable fit to the WMAP small angle acoustical oscillations peaks without dark matter using an analytical method for calculating the peaks. I need to also show that MOG can produce the increased amplitude that fits data for the CMB power spectrum without dark matter. As described in this paper, I have a possible interpretation of "dark energy" that follows from the theory.

Your comments about normal clusters are interesting. Joel Brownstein and I (MNRAS 2006, 367, 527, astro-ph/0507222) fitted the mass profiles of 106 X-ray clusters without dark matter with approximately the same two parameters alpha and lambda I used to produce my 1-D lensing profile for 1E0657-56. We used an isothermal model for all the fits. Naturally, non-isothermal corrections are needed to obtain better fitting accuracy for some of the X-ray cluster data.

I feel that at present you are not in a position to claim on the basis of your papers that "these results are direct proof that dark matter exists."

John