Sanders Final Post

Final Exam Paper for Astronomy 561

My Subject for this paper is Possibility of Settlement between Modification of Newtonian Mechanics versus Dark Matter and Dark Energy. While I wish to produce a scholarly paper, I would also like my high school students to read this article and begin to understand what the nature of science and the nature of scientist are all about. Even when experienced scientist and engineers are on the trail of understanding, they sometimes forget that for every question they answer two new questions seem to appear. It seems the more we learn, the less we know. Also no student or professional should forget the pursuit of knowledge can be fun and exciting, not boring.

Before we have an argument between MOND versus Dark Matter and Dark Energy, maybe we should observe the disagreements between MOND believers. When I read any single paper, I am lead by reason to believe a solution is at hand. However, the next paper always points out some problem with the new adjustment to Newton’s modified law. In this paper I have quoted:

Astronomy Abstract Service and provide the
Bibliographic Code: 2010MNRAS.407.1128S
for that particular Abstract

The idea is to allow each reader to make a judgment about several modified theories and the weakness of each. My judgment is that each adjustment seems reasonable but with thirteen adjustments we have one monster formula not ready for use in our own homes.

Title: The Universal Faber-Jackson relation by Sanders, R. H. #1
Bibliographic Code: 2010MNRAS.407.1128S

Abstract
In the context of modified Newtonian dynamics, the Fundamental Plane, as the observational signature of the Newtonian viral theorem, is defined by high-surface-brightness objects that deviate from being purely isothermal: the line-of-sight velocity dispersion should slowly decline with radius as observed in luminous elliptical galaxies. All high-surface-brightness objects (e.g. globular clusters, ultra-compact dwarfs) will lie, more or less, on the Fundamental Plane defined by elliptical galaxies, but low-surface-brightness objects (dwarf spheroidals) would be expected to deviate from this relation. This is borne out by observations. With Milgrom's modified Newtonian dynamics (MOND), the Faber-Jackson relation (L ~ σ4), ranging from globular clusters to clusters of galaxies and including both high- and low-surface-brightness objects, is the more fundamental and universal scaling relation in spite of its larger scatter. The Faber-Jackson relation reflects the presence of an additional dimensional constant (the MOND acceleration a0) in the structure equation.


Title: Exact Solutions and Approximations of Mond Fields of Disk Galaxies #2
Author: Brada, R and Milgrom, M
Bibliographic Code: 1994astro.ph.7071B

Abstract
We consider models of thin disks (with and without bulges) in the Bekenstein-Milgrom formulation of MOND as a modification of Newtonian gravity. Analytic solutions are found for the full gravitational fields of Kuzmin disks, and of disk-plus-bulge generalizations of them. For all these models a simple algebraic relation between the MOND potential field and the Newtonian potential holds everywhere outside the disk. We give exact expressions for the rotation curves for these models. We also find that the algebraic relation is a very good approximation for exponential disks. The algebraic relation outside the disk is then extended into the disk to derive an improved approximation for the MOND rotation curve of disk galaxies that requires only knowledge of the Newtonian curve and the surface density.


Title: MOND in the early universe #3
Author: McGaugh, Stacy
Bibliographic Code: 1999AIPC..470…72M

Abstract
I explore some consequences of Milgrom's modified dynamics for cosmology. There appear to be two promising tests for distinguishing MOND from CDM: (1) the rate of growth of structure and (2) the baryon fraction. These should be testable with observations of clusters at high redshift and the microwave background, respectively.


Title: Modified Newtonian dynamics and its implications #4
Author: Sanders, R. H.
Bibliographic Code: 2001astro.ph..6558S

Abstract
Milgrom has proposed that the appearance of discrepancies between the Newtonian dynamical mass and the directly observable mass in astronomical systems could be due to a breakdown of Newtonian dynamics in the limit of low accelerations rather than the presence of unseen matter. Milgrom's hypothesis, modified Newtonian dynamics or MOND, has been remarkably successful in explaining systematic properties of spiral and elliptical galaxies and predicting in detail the observed rotation curves of spiral galaxies with only one additional parameter-- a critical acceleration which is on the order of the cosmologically interesting value of $cH_o$. Here I review the empirical successes of this idea and discuss its possible extension to cosmology and structure formation.



Title: Modified Newtonian dynamics and its implications #5
Author: Sanders, R. H.; McGaugh, Stacy S.
Bibliographic Code: 2002ARA&A..40..263S

Abstract
Modified Newtonian dynamics (MOND) is an empirically motivated modification of Newtonian gravity or inertia suggested by Milgrom as an alternative to cosmic dark matter. The basic idea is that at accelerations below ao ~ 10-8 cm/s2 ~ cHo/6 the effective gravitational attraction approaches √(gnao), where gn is the usual Newtonian acceleration. This simple algorithm yields flat rotation curves for spiral galaxies and a mass-rotation velocity relation of the form M ∝ V4 that forms the basis for the observed luminosity-rotation velocity relation-the Tully-Fisher law. We review the phenomenological success of MOND on scales ranging from dwarf spheroidal galaxies to super clusters and demonstrate that the evidence for dark matter can be equally well interpreted as evidence for MOND. We discuss the possible physical basis for an acceleration-based modification of Newtonian dynamics as well as the extension of MOND to cosmology and structure formation.


Title: General Relativity and Quantum Cosmology, Astrophysics #6
Origin: ARXIV
Bibliographic Code: 2006gr.qc…..4047F

Abstract
Empirical implications of a teleparallel displacement of momentum between initial and final quantum states, using conformally flat quantum coordinates are investigated. An exact formulation is possible in an FRW cosmology in which cosmological redshift is given by 1+z=a_0^2/a^2(t). This is consistent with current observation for a universe expanding at half the rate and twice as old as indicated by a linear law, and, in consequence, requiring a quarter of the critical density for closure. A no CDM teleconnection model resolves inconsistencies between galactic profiles found from lensing data, rotation curves and analytic models of galaxy evolution. The teleconnection model favors a closed no Lambda cosmology. After rescaling Omega so that Omega=1 is critical density, for 225 supernovae, the best fit teleconnection no Lambda model with Omega=1.89 is marginally preferred to the best fit standard flat space Lambda model with Omega=0.284. It will require many observations of supernovae at z>1.5 to eliminate either the standard or teleconnection magnitude-redshift relation. In quantum coordinates the anomalous Pioneer blueshift and the flattening of galaxies' rotation curves appear as optical effects, not as modifications to classical motions. An exact form of Milgrom's phenomenological law (MOND) is shown.


Title: Are Dark Matter and Dark Energy the Residue of the Expansion-Reaction to the Big Bang? #7
Author: Ringermacher, Harry I.;Mead, Lawrence R.
Bibliographic Code: 2006gr.qc….10083R

Abstract
We derive the phenomenological Milgrom square-law acceleration, describing the apparent behavior of dark matter, as the reaction to the Big Bang from a model based on the Lorentz-Dirac equation of motion traditionally describing radiation reaction in electromagnetism but proven applicable to expansion reaction in cosmology. The model is applied within the Robertson-Walker hypersphere, and suggests that the Hubble expansion exactly cancels the classical reaction imparted to matter following the Big Bang, leaving behind a residue proportional to the square of the acceleration. The model further suggests that the energy density associated with the reaction acceleration is precisely the critical density for flattening the universe thus providing a potential explanation of dark energy as well. A test of this model is proposed.


Title: Modified Gravity Without Dark Matter #8
Author: Sanders, Robert
Bibliographic Code: 2007LNP…720..375S

Abstract
On an empirical level, the most successful alternative to dark matter in bound gravitational systems is the modified Newtonian dynamics, or MOND, proposed by Milgrom. Here I discuss the attempts to formulate MOND as a modification of General Relativity. I begin with a summary of the phenomenological successes of MOND and then discuss the various covariant theories that have been proposed as a basis for the idea. I show why these proposals have led inevitably to a multi-field theory. I describe in some detail TeVeS, the tensor-vector-scalar theory proposed by Bekenstein, and discuss its successes and shortcomings. This lecture is primarily pedagogical and directed to those with some, but not a deep, background in General Relativity.


Title: Modified gravity and the phantom of dark matter #9
Author: Brownstein, Joel Richard
Bibliographic Code: 2009PhDT….…172B

Abstract
Astrophysical data analysis of the weak-field predictions support the claim that modified gravity (MOG) theories provide a self-consistent, scale-invariant, universal description of galaxy rotation curves, without the need of non-baryonic dark matter. Comparison to the predictions of Milgrom's modified dynamics (MOND) provides a best-fit and experimentally determined universal value of the MOND acceleration parameter. The predictions of the modified gravity theories are compared to the predictions of cold non-baryonic dark matter (CDM), including a constant density core-modified fitting formula, which produces excellent fits to galaxy rotation curves including the low surface brightness and dwarf galaxies. Upon analyzing the mass profiles of clusters of galaxies inferred from X-ray luminosity measurements, from the smallest nearby clusters to the largest of the clusters of galaxies, it is shown that while MOG provides consistent fits, MOND does not fit the observed shape of cluster mass profiles for any value of the MOND acceleration parameter. Comparison to the predictions of CDM confirm that whereas the Navarro-Frenk-White (NFW) fitting formula does not fit the observed shape of galaxy cluster mass profiles, the core-modified dark matter fitting formula provides excellent best-fits, supporting the hypothesis that baryons are dynamically important in the distribution of dark matter halos.
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MNRAS Keywords: galaxies: kinematics and dynamics, cosmology: theory, dark matter
DOI: 10.1111/j.1365-2966.2009.16184.x

Bibliographic Code: http://adsabs.harvard.edu/abs/2010MNRAS.403..886M

The above link should access all the Bibliographic Code.
Abstract
A new formulation of modified Newtonian dynamics (MOND) as a modified-potential theory of gravity is propounded. In effect, the theory dictates that the MOND potential φ produced by a mass distribution ρ is a solution of the Poisson equation for the modified source density, where g = ν(|gN|/a0)gN, and gN is the Newtonian acceleration field of ρ. This makes φ simply the scalar potential of the algebraic acceleration field g. The theory thus involves solving only linear-differential equations, with one non-linear, algebraic step. It is derivable from an action, satisfies all the usual conservation laws, and gives the correct centre-of-mass acceleration to composite bodies. The theory is akin in some respects to the non-linear Poisson formulation of Bekenstein and Milgrom, but it is different from it, and is obviously easier to apply. The two theories are shown to emerge as natural modifications of a Palatini-type formulation of Newtonian gravity, and are members in a larger class of bi-potential theories.

I hope these articles of scholarly research give readers some idea of the many views of fellow scientists who agree in their pursuit of MOND theory. I know as a trained scientist and engineer, I have tried to make astute observations.

I have attempted, with earnest effort, to avert all feelings from my youth while I lived across the street from a Pentecostal Church. This period of time was before TV. On Saturday night neighbors from far and near would arrive at my parent’s front porch to watch the “Holy Rollers” in action!! At times when I review some of this “Science Debate,” that “Old Time Feeling” returns. I may be watching “Scientist Holy Rollers” in a MOND versus Dark Matter debate.