This paper was presented as part of the subject "Great Debates in Astronomy" and was the second speaker for the negative on the subject "Dark Matter - Fact or Fiction".   The paper focuses on Modified Newtonian Dymantics (MOND) as an alternate explanation for phenomenon requiring Dark Matter solutions. I do not have permission to publish the work of the other participants, which may make this paper somewhat more difficult to follow.  However, I have made a few amendments to the original to allow it to more easily stand-alone.

Introduction

When Einstein’s theory of General Relativity was published, it offered a new perspective on our understanding of gravity.  However, in most instances the predictions of Newton’s less complete theory of gravity were still valid.  Despite this historical precedent (one of many), it seems to be generally held that General Relativity offers a complete picture of the mechanisms of gravitation, and where observations depart from its predictions, we must seek additional physical phenomenon to bring our observations into line with General Relativity.  Dark Matter is just such a postulate.

However, whilst a great many scientists are involved in searching for this mystery matter (and the sheer number of candidates highlights the uncertainty of any clear winner emerging under present circumstances), others have taken the less popular route of examining our understanding of gravity, and its application to the problems that seem to call for a ‘Dark Matter solution’. General Relativity is only called into play for extremes of mass and velocity, and thus our observations are limited by the vast scale of the universe, and our planet’s need to be away from such phenomenon.  This means we are observing and correlating phenomenon at great distances, with resultant losses of accuracy.  Distortion of gravitational fields by high density objects is not something to be studied in the lab.  This means that any growth in our knowledge of gravitation is likely to come from observations of extreme conditions, and just as extreme conditions overcame Newtonian gravitational theory, so they may well best Einstein.

MOND (MOdified Newtonian Dynamics)

Whilst the subject of much denigration, MOND (an extension of Newtonian gravity in conditions of very low acceleration, as outlined by speaker 1) has a large number of predictive successes under its belt, and more importantly, has made these predictions whilst maintaining its structural integrity.  Dark Matter on the other hand makes piecemeal predictions, and Dark Matter models that produce a supportive set of results for one phenomenon often produce predictions at odds with observations for others. Specifically, MOND has made successful predictions in the following areas, where the predictions of Dark Matter models have been unsuccessful (McGaugh 2002):

• M/L-Surface Brightness Relation
• Mass Surface Densities
• Disk-Halo Conspiracy
• Rotation Curve Shapes
• Rotation Curve Rate of Rise
• Rotation Curve Fits
• Thin Low Surface Brightness Disks

Similarly, MOND has made successful predictions in a number of areas that Dark Matter theories are unable to offer predictions, or for which Dark Matter solutions are not promising:

• LSBG Tully-Fisher Relation
• Stellar Mass to Light Ratios
• Local M/L
• Transition Radii
• Characteristic Accelerations
• Dwarf Spheroidal Galaxies

Moti Milgrom, the father of MOND, has never shied away from the fact that MOND requires additional unseen mass from its observations, but the ratio to visible mass is much lower (roughly 1:1 – Milgrom 2006) than Dark Matter theories suggest, and can readily be accounted for by discoveries of hitherto unseen mass of standard baryonic constitution.  As Oort said “light is not always a reliable trace of matter”.  Brown dwarves, neutron stars and black holes, as well as cold gas clouds are all candidates.  Applying the figures of Dark Matter proponents that only 4% of the universes mass is baryonic, we have only found about a tenth of this, so missing baryonic mass is a problem for both camps. Supporters of MOND are the first to agree that it is not a complete description of gravity that can be applied to all scenarios.  In this area they share much in common with theorists in the areas of super-symmetry and indeed dark matter - as evidenced by the goldilocks-like array of dark matter temperatures (too-hot, too-cold, just-right dark matter).  However, as a starting point for examining our understanding of gravitational theory, it has had much success, particularly at galactic-scale levels.  It has also acted as a platform for the development of enhanced theories, such as TeVeS (Tensor-Vector-Scalar covariant field theory), that incorporate General Relativity, and address many of the initial short-fallings of MOND. Some features of TeVeS include (Bekenstein 2005):

• a Newtonian limit for non-relativistic dynamics with significant acceleration
• a MOND limit when accelerations are small
• β and γ PPN coefficients in agreement with solar system measurements
• lensing predictions  by visible matter in agreement with general relativity's predictions made with a dynamically successful dark halo model
• cosmological models are consistent with general relativity in predicting slow evolution of the scalar field.

Brownstein and Moffat (2005) achieved similar success with their metric-skew-tensor gravity (MSTG) theory and the scalar-tensor vector gravity (STVG) theory, which as well as predicting galactic rotational velocity curve data, have addressed the issue of the Pioneer 10/11 trajectory anomaly.

MED (Modified Einstein Dynamics)

In some instances, it may be that we do not need to extend our description of gravity, but rather reconsider the problem.  Galactic rotational curves adopt a Newtonian view of the galaxy, but because of the large number of simultaneously interacting object moving at high speeds, a general relativistic perspective may be more correct, and work done by Cooperstock and Tieu (2005) has shown that treating the problem in this manner can allow a descriptive and predictive model to be developed that is consistent with general relativity, but does not require exotic Dark Matter. Cooperstock and Tieu developed General Relativity galactic models, deviating from standard Newtonian models by incorporating the combined rotating mass of all freely-gravitating elements into the gravitational field.  These models predicted correct galactic velocity curves over a number of galaxies without the need to incorporate exotic Dark Matter.  The results show a concentrated mass-density disk, without requiring an extended dark matter halo, implying that unseen matters is concentrated in the disk, and is therefore most likely to be baryonic in nature. Although the work only addressed one aspect of the Dark Matter, future work in applying this general relativistic approach to other problems currently championing Dark Matter as a solution may well yield equally compelling data, and the combination of a general relativistic analysis with extended models of gravitation (as is being pursued by TeVeS) may well give us a framework that encompasses all of our observations. It should be noted that the success of this method using General Relativity alone does not invalidate or conflict with extended gravitational models, as any proposed model must deliver results consistent with General Relativity where these problem spaces overlap.  Relativity is what happens as v -> c; MOND is what happens as a -> 0, so they are called on under very different circumstances, and do not butt heads.  Indeed, consistency with General Relativity is the foremost requirement of any extended theory.

Responses to Speaker 2

1. Cosmic Background Radiation - Search for Dark Matter

WMAP data (WMAP Working Group 2006) has been recently updated and revised, as of March 2006.  Rather than clearly supporting Dark Matter, the picture has become somewhat murkier, with the power law curve actually falling between the predictions of CDM and MOND.  The results are inconclusive to either side, but cannot be trumpeted as ‘requiring’ Dark Matter, as suggested by the affirmative case.  It should also be noted, that as with CDM and rotational curves, MOND makes no falsifiable predictions for CDM, so cannot be dismissed on the basis of this data.  Also, CDM fits to the first two peak predictions required additional baryon density, whereas they are predicted by MOND without alteration.  Going beyond MOND, TeVeS actually accounts for the oscillations that produce density fluctuations via the inherent scalar field – a component that is a natural product of the theorem, rather than an additional variable (McGaugh 2006).

2. X-ray Observations of Dark Matter Distribution

Gravitational lensing and the CMB results depend not on mass but on the level of gravitational energy.  If, as we argued, our understanding of gravitational functioning is incomplete, then gravitational flux cannot be accurately determined from mass alone. The Bullet Cluster observations reaffirm the need for greater mass in rich clusters, but in no way dictates the nature of that mass.  As discussed previously, both MOND and DM require additional baryonic mass, and within MOND the mass requirements are much more modest that CDM.  These results simply imply that the mass is not collisional, which rules out gas, but not any number of other baryonic candidates.  Indeed, Angus, Famaey, & Zhao examined the bullet cluster using TeVeS, and were able to “generate a multi-centred baryonic system with a weak lensing signal resembling that of the merging galaxy cluster 1E 0657-56 with a bullet-like light distribution.".  Thus the “smoking gun” for Dark Matter can also claimed as evidence for modified gravity theories. Also, no gravity laws currently account for the acceleration of H0, and this needs to be explained if Dark Matter is not to be considered a result of errors in our understanding of gravity at the extremes.

General response to affirmative case

The chief problem with the various Dark Matter candidates cited (neutralinos, sterile neutrinos, axions, photinos and other WIMPS) is that we don’t know any properties, particularly mass.  Thus, assembling any usable and predictive framework is problematic, and cuts its proponents a lot of scope to arbitrarily construct models that fit the data, but which are unable to be scrutinized.  This present incapability to construct models does not rule out Dark Matter, but does provide a lot of latitude, thereby blunting its ability to demonstrate a persuasive case.  As McGaugh has noted “Once invoked, dark matter can be distributed in any way necessary to explain just about anything.” By comparison, once a modified force law has been specified, it is unable to adjust its predictions.  MOND is coupled to the mass distribution observed in a system - you cannot adjust MOND to suit any rotation curve you like.  McGaugh again “I find it remarkable that of the infinite variety of things rotation curves might plausibly do were they caused by a Newtonian disk [and a] dark matter halo, they in fact do the one (and only one) thing allowed by MOND”.

Conclusion

Were the evidence for MOND (or indeed Dark Matter) conclusive, then we would not need to be having this debate.  Questions still remain over modified gravitational theories, but their predictive success (which is heavily understated by the Dark Matter camp) demonstrate that by re-examining our somewhat slavish devotion to the Newton/Einstein models, a potentially viable model of gravitational manifestations across a broad number of phenomenon can be developed, without resorting to the arbitrary world of Dark Matter, and the Pandora’s box of questions that it opens.

References

Angus, G., Famaey, B., Zhao, H.  “Can MOND take a bullet? Analytical comparisons of three versions of MOND beyond spherical symmetry” 2006 http://arxiv.org/abs/astro-ph/0606216 Bekenstein, J. “Relativistic gravitation theory for the MOND paradigm” 2005 http://arxiv.org/abs/astro-ph/0403694 Brownstein, J., Moffat , J. “Galaxy Rotation Curves Without Non-Baryonic Dark Matter” 2005 http://arxiv.org/abs/astro-ph/0506370 Brownstein, J., Moffat , J. “Gravitational solution to the Pioneer 10/11 anomaly” 2006 http://arxiv.org/PS_cache/gr-qc/pdf/0511/0511026.pdf Cooperstock, F., Tieu, S. “General Relativity Resolves Galactic Rotation Without Exotic Dark Matter”, 2005 http://xxx.lanl.gov/PS_cache/astro-ph/pdf/0507/0507619.pdf Cooperstock, F., Tieu, S. “Perspectives on Galactic Dynamics via General Relativity”, 2005 http://arxiv.org/PS_cache/astro-ph/pdf/0512/0512048.pdf Milgrom, M., “Milgrom's perspective on the Bullet Cluster”, 2006 http://www.astro.umd.edu/~ssm/mond/moti_bullet.html McGaugh, S. http://www.astro.umd.edu/~ssm/mond/CMB5.html 2006 http://www.astro.umd.edu/~ssm/mond/faq.html http://www.astro.umd.edu/~ssm/mond/bullet_comments.html WMAP Science Working Group “Wilkinson Microwave Anisotropy Probe (WMAP):Three–Year Explanatory Supplement” March 16, 2006 http://lambda.gsfc.nasa.gov/product/map/current/pub_papers/threeyear/supplement/wmap_3yr_supplement.pdf