The Case for Modified Newtonian Dyanimcs

It seems that many researchers are taking up the Modified Newtonian Dynamics (MOND) battle standard against supporters of Dark Matter halos to explain galactic rotation curves and other astronomical phenomena. I myself am partial to the belief that MOND is a more likely explanation than invisible matter that only interacts via gravitational forces. Stirring debate among these two groups is not my purpose though, it is to present an article that strongly supports MOND as a viable alternative to dark matter. The full article is as follows:

The MOND Fundamental Plane

The article itself is extremely technical with copious amounts of mathematics interjected into its paragraphs, but the introduction and conclusion are worth noting. The authors begin by briefly reviewing the current models of galactic properties such as rotation curves and Mass-Luminosity relations. They draw attention to the problems inherent in these models such as mass anisotropic degeneracies and systematic biases. They then propose that MOND can fit the models of elliptical galaxies, and even Early-Type and Spiral galaxies. The conclusions of their findings are that, statistically speaking, MOND fits over 9000 galaxies taken from the NYU Value added Galaxy Catalog. They admit that some aspects of their model have as much as a 10% error, but counter that this is due to the statistical analysis of 9000 galaxies simultaneously as opposed to fitting the model to each galaxy individually.

Radius-Luminosity and Mass-Luminosity Relationships for Active Galactic Nuclei; Koratkar and Gaskell

Radius-Luminosity and Mass-Luminosity Relationships for Active Galactic Nuclei
Koratkar and Gaskell
The Astrophysical Journal, 370:L61-L64, 1991 April 1

In this paper, Koratkar and Gaskell study ten active galactic nuclei in an attempt to find a independant direct relationship between mass and bolometric luminosity of interior objects, i.e. the central black hole. Given any trend or solution is simple and calculable, they could then find a way to discern properties of distant galaxies based on a single observable. Though the paper touches lightly on raiud-luminosity relationships, I will focus more on the development of a mass-luminosity relationship and the verification of previous derivations in existence.

This paper centers around data collected by the authors regarding the active galactic nuclei, herein referred to as AGNs, of ten individual galaxies. These AGNs represent the core element of each galaxy and are expected to produce and radiate the majority of energy of the galaxy over most, if not all wavelengths of our observable range. The accepted model physics at that time of publishing favored the idea that any energy radiated would be the result of accretion from the Broad-Line Region onto the central object, or black hole. if we accept this model as correct, then it would make sense that the bolometric luminosity, a measure of the expected energy generation across all measurable wavelenghts, would correlate to the total mass of this region, the core AGN.

To produce working data for the mass is familiar and quite simple. Analyzing the Doppler width of the emission spectra provides velocity information for the gasses of the broad-line region surrounding the core. If we assume that the movement of gasses is dominated by gravitational forces, then we can calculate a value for the mass of the AGN by integrating over the core radius. Calculation can be done using any number of available methods, but was done using Monte Carlo methods for this paper.

This study resulted in producing a tested relationship between the bolometric luminosity and a calculated mass of AGNs. Since real astronomical data was used, this paper was a big step on the side of observational astronomy. In addition, it proved to solidify belief in the previously derived theoretical relationship suggested by previous researchers like Dibai, Joly, and Reshetnikov years earlier.

Simulation of Colliding Galaxies

A couple of years ago, I did a project for a Parallel Processing course that utilized a computer simulation of colliding galaxies. I adapted an existing program to my computer cluster running Pelican HPC. The program utilizes a simulation tool called GADGET-2 and it computes gravitational forces with a Tree-SPH (Smooth Particle Hydrodynamics) algorithm. The tree is used for short-range gravitational forces, while long-range forces are computed with a Fast Fourier Transform particle mesh method. The program was written and refined over the years by Volker Springel of the Max Planck Institute for Astrophysics and is freely available on the internet at http://www.mpa-garching.mpg.de/galform/gadget/index.shtml.

This computer simulation allows us to watch collisions that in nature take hundreds of millions of years. The model shows that a collision of two spiral galaxies can create elliptical galaxy. Although the animation appears rough and crude (windows media file, what else), the result you'll see resembles an elliptical galaxy. Lots of data (energy, etc) is generated, but I won't include that here. I hope to refine this program over the summer.

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.
http://www.blogger.com/img/blank.gif
Origin: WILEYhttp://www.blogger.com/img/blank.gif

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.

If You Could See Neutrinos...

...how far back into the universe could you see?

For the case of photons we look at the cosmic microwave background (CMB) and use it to construct an image of the so called 'surface of last scattering', which represents the moment when photons decoupled from and were able to escape the cosmic plasma. This corresponds to a t=380,000 years (with t=0 being the very beginning) in the current theory.

For the case of neutrinos we would look to the cosmic neutrino background (CNB) and try to use that to construct a surface of last scattering for the neutrinos. At what time did neutrinos decouple from the cosmic plasma? Current theories predict that this decoupling time occurred when the universe was less then a second old.

It would stand to reason then that one should be able to use neutrinos to 'look further back' into the universe. In other words, one would expect the last scattering surface for neutrinos to be further back than the last scattering surface for photons.

However, at least one paper finds the opposite to be true:

http://arxiv.org/abs/0907.2887

Somewhat counter-intuitively, the CNB last scattering surface turns out to be much closer and much thicker than the CMB surface--the paper suggests it has to do with the fact that neutrinos are able to have different velocities from each other.

So perhaps the neutrino's LSS is inside the CMB's, but where might the dark matter LSS be?

Dark Matter – Cosmic Glue?

Ever since mankind was able to get beyond his basic needs for survival and move to higher levels of thinking, he has always questioned the unknown. His basic powers of observation have answered many of the fundamental questions that were explained away by the presence of a God. The stars are no exception and have not escaped the observations of Man. The question, “ Is there more?’, is alive and well.

While researching topics for this paper, I came across a series of lectures and articles by Professor Kim Griest of the University of California at San Diego. His presentation style and simple manner of explanation allows for the general layman a basic understanding of the complex topic of dark matter. Is dark matter real and if so, what is its purpose for the universe?

When man began his observation of the stars, these were only points of light suspended in the night sky. They all moved across the night sky through the seasons. All except one, the North Star. They used the position of the stars to help them navigate across unknown oceans and return home. As time went on, Man became more curious about these points of light in the sky. In order for all of this to make sense to them, they placed the Earth as the center of the Universe.

It was not until men like Copernicus and Galileo said that the Earth was not the center of the Universe and that it revolved around the sun. Soon new speculations about the night sky began a much more intense observation of the stars. This, of course, was not without persecution of these ideas by the religious side. With the invention of the telescope, Man was now able to get a little closer to the stars. These telescopes could only see an occasional planet and the sun, but other stars were still only points of light.

As telescopes began to evolve, other artifacts began to be apparent. One such artifact was the Nebulae or cloud like smudges. For a while smudges were thought to be composed of gas until much bigger telescopes were developed that could give us a much closer look. It turns out that many of these smudges were clusters of stars. If we look at our own Milky Way Galaxy, we can see these smudges very prominently with our naked eye on very clear, dark nights. Yet, as we examine the smudges of our own galaxy, we can see that indeed they are clusters of millions of stars. The better the telescopes, the farther we could see and find that smudges beyond our own galaxy were galaxies themselves.

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Unfortunately, all new discoveries were limited by visual observation. This limitation was based on the fact that if it is to be seen, we must have light. Knowing the speed of light, we were able to calculate luminosity of stars and that of whole galaxies. This allowed us to determine distances far greater than anyone could imagine. But any discovery of new information was limited only by our technology. Now we are able to determine whether stars were traveling closer towards us or moving farther away. By the use of Doppler techniques were we able to find if a star was coming towards us or in fact, moving away from us. The shorter the wavelength, the more compressed the wave of light would be thus moving it closer to the blue spectrum of light. The longer the wavelength, the more it would move towards the red spectrum of light, thus the star was moving away. Today, we use more advanced techniques that allow us to “see” into the electromagnetic spectrum that we can not see with our own eyes moving us into radio signals, microwave, infrared, ultra violet, x-ray and even gamma rays. We are also able, through the use of spectrometry, to determine the composition of many stars with Hydrogen being the main fuel of a star. Regardless of what we used, we were still looking at light as our main source of information.

Since stars and star systems could be found in specific regions of the sky, it was thought that the Universe was static. In 1910, Albert Einstein said that the Universe was expanding and contracting. (Ronald W. Clark; Einstein – The Life and Times: 1971) Einstein’s General Theory of Relativity was the first theory to be applied to the whole Universe. Yet, Einstein himself thought that his theory was wrong. His theory depended upon 2 numbers: Hubble’s constant which addressed the expansion rate and the Omega which involved the density of the amount of the mass in the Universe. (Kim Griest, “Dark Matter and the Fate of the Universe”, Feb. 22, 2000) Whatever he did with these numbers, the Universe was either expanding or contracting. This was not good enough for him so he added a third number, the cosmological constant. By using this number, he could then balance the other numbers thus making the Universe static.

But Hubble showed that the Universe was expanding causing Einstein to call his cosmological constant his “greatest blunder”. We have found that there is expansion going on, but the galaxies and stars are not moving away from each other and are fixed in positions relative to each other. So astronomers began looking not at the stars and galaxies but at the darkness of space in between them. If this is so, then there must be something that makes up this space. The best way to describe this is the Raisin Bread Theory which states that the raisins in the dough are all located in positions relative to each other and as the bread is baked, it is the bread that is expanding with the raisins maintaining their positions within the bread. So space now was thought to have substance.

Another observation that supports this theory is the fact that galaxies are rotating at tremendous speeds and even with such speeds, the galaxies remain intact instead of being flung outwards into space. By measuring the total luminosity of the galaxy, we can estimate somewhat accurately,

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the total number of stars in that galaxy. What we find is that there is not nearly enough mass to keep the galaxy intact. There are not enough stars for the total gravity to keep the stars bound in their rotations around the galaxy because of the speed of their rotation. So in order for there to be enough mass, it must be coming from something else at least by a factor of 10 or more. (Kim Griest, Feb.22, 2000). This “something else” then forms a “halo” that surrounds the entire galaxy. This “something else” is what is completely dominating the gravity. It is suspected that it is matter that we can not see, hence the term “dark matter”. Illustration 1 is an artist rendition of what a galaxy may really look like if we could see this dark matter.


Illustration 1
(Zebu.uoregon.ed)

So when trying to calculate the total mass, we find that the mass of the disk is not enough as shown in the curve labeled “disk” below. If we add the mass of the gas in the galaxy, we find that plus the mass of the stars is still not enough. Therefore, there is another curve that is produced when we calculate a new curve with the proper masses to sustain that rotation. (See rotational curve graphs below.) This graph is based on a well studied galaxy know as NGC 3198.

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So the race is on to find out what this “stuff” is, how much there is and what is its basic form. Two basic particles that are being researched are MACHOs (Massive Astrophysical Compact Halo Objects) and WIMPS (Weakly Interacting Massive Particles). WIMPS seem to be attracting the most attention. These particles are so small that they can pass through mass with no interaction. They can slip through the space of atoms.

The problem is that with all the research and millions of dollars invested, we are yet to find a particle that fits the picture that astronomers and physicists are looking for. The main culprit is the background noise or radiation coming from space itself. We are still looking for a signal that can be labeled to the illusive particle. So great laboratory facilities with massive instruments to collect these particles have been built deep into the Earth to eliminate the background noise. Even so, the particle remains a mystery. So the question remains. Is dark matter real? The math says it is. Theories that galaxies would otherwise fling their contents into space say it is. So what is it?

At the risk of sounding foolish, as most novices to this subject matter are, I venture to use the old saying, “can’t see the forest for the trees.” I would love to see dark matter discovered and solidly identified. But is it possible that dark matter is not a particle at all but a “soup of particles” and what we are doing is trying to identify tomatoe soup by trying to isolate a single sugar? This is like trying to identify water in an ocean by attempting to isolate a hydrogen neutron. There isn’t one! The blame for this failure is the background noise one gets. Is it possible that all of the background noise put together is in fact the dark matter we have been searching for. If so, it becomes the forest that we can’t see.

Regardless, the subject of dark matter is a facinating one as it seems to be the glue that holds everything together. It has stretching ability which accounts for the fixed relative position of all the observable objects in space. If that is so, then it should reach a point where it can not stretch any further and begin to contract again towards “the big crunch” and if this is true, then the universe really does expand and contract. Maybe Einstein was not really wrong after all when he first said so.

Bibliography

Clark, Ronald W.; Einstein The Life and Times; World Publishing Corp.; 1971, 1984; pg 266-271

Griest, Kim Professor; University of California at San Diego; “Dark Matter and the Fate of the Universe”; February 22, 2000

Griest, Kim Professor; University of California at San Diego; “Mystery of Empty Space”; March 7, 2010

Tully-Fisher Method for Determining Distances to Galaxies

Previous methods for measuring distances to galaxies include parallax angles and standard candles. However, accurate parallax angles are limited to stars within about 500 pc. Beyond that distance, the angles become too small to measure. Standard candles are based on astronomical objects of known luminosity. By measuring the brightness of standard candles, observers can calculate the object’s distance using the inverse-square law. However, a problem with standard candles is in determining the absolute magnitude of the object. The challenge is finding objects that are good candidates for standard candles – that is objects that are luminous, easily identifiable, and relatively common. The more confident we know a star’s luminosity, the more certainty in determining its distance.

An alternative to the aforementioned techniques is the Tully-Fisher Relation. The attached paper published in Astronomy and Astrophysics in 1977 describes a method for determining the distances to galaxies. R. Brent Tully and J. Richard Fisher determined that the variability of light emitted from netral hydrogen in a galaxy is related to the luminosity of the galaxy. Also, the more variability in the light emitted by netral hydrogen, the more luminous the galaxy. Radiation from the approaching side of a rotating galaxy is changes to shorter wavelengths of light while the light from the receding side of the galaxy changes to longer wavelengths. The variability in light increases by an amount proportional to the rotating speed of the galaxy.

I found a visual to illustrate this point at http://lifeng.lamost.org/courses/astrotoday/CHAISSON/AT324/HTML/AT32402.HTM

Figure 24.11 A galaxy's rotation causes some of the radiation it emits to be blueshifted and some to be redshifted (relative to what the emission would be from a nonrotating source). From a distance, when the radiation from the galaxy is combined into a single beam and analyzed spectroscopically, the redshifted and blueshifted components combine to produce a broadening of the galaxy's spectral lines. The amount of broadening is a direct measure of the rotation speed of the galaxy.

The more massive the galaxy, the faster the stars move in their orbits at the galaxy’s edge. The paper summarizes the relationship between gravitational and centrifugal forces: v² = GM/R and that luminosity is proportional to mass as well as the area of the disk. Tully and Fisher used this method to calibrate the distances of galaxies in excess of 100Mpc.

Recent Studies: Since its introduction, there have been continued research in this area. Another paper, Evolution of the Tully-Fisher Relation up to z=1.4 published last year in Astronomy and Astrophysics, is a study that focuses on Tully Fisher relation at high redshift in the B,V, R, I, and K₅ . I will review this paper and submit a follow-up to this blog.