Final Paper

Dark Matter & WIMPS picture are missing

The XENON100 dark matter detector recently released its data for the first one hundred days of operation. The detector failed to find evidence of dark matter. The XENON detector is a large tank of 161 kg of chilled xenon buried far beneath the ground. The tank is buried far underground in Italy with an average of about 1.4 kg of rock and ultra pure metal, to prevent cosmic rays from interacting with the xenon and giving a false reading. The hope was that a change in the spin coupling of a nucleon could be observed providing evidence that the xenon in the detector is reacting with WIMPs (Weakly Interacting Massive Particles). This experiment was a significant setback, although not a total refutation of the theory. Dark matter theorist once again failed to observe any interaction or evidence of “dark matter” although there are multiple possible candidates to look for.

In analyzing galactic rotation curves it was found that galaxies often fail to match the Keplerian prediction of motion. Observable galaxies tend to clump matter toward the center of each galaxy as shown in the picture below. According to Newton’s Law of Universal Gravitation there should be a significant reduction in rotation speed at the fringes of each galaxy. In the picture below the spiral arms should be moving significantly slower than the stars closer to the core of the galaxy.


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Newton’s Law of Universal Gravitation has worked extremely well and has been verified countless times with the exception of extremely high velocities in which case the general relativity correction is required. The expected and observed galactic rotation speeds are far below the threshold that requires relativistic correction and therefore the velocity should be reduced as a square of the distance away from the center.


This equation demonstrates the classical relationship between gravitational force and centripetal force. This relationship demonstrates that the velocity of an object is a function of its distance from the center of mass and the mass of the object itself.




The observational data of galactic rotation is contradictory to the theory expressed by combining Newton’s Law of Universal Gravitation with centripetal force for objects in circular motion. This relationship is demonstrated in the graph below: [9]


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This results in a problem that has yet to be resolved. Either Newton’s Law of Universal Gravitation needs modification for areas of low density as proposed by the MOND theory or there is an as yet unobserved form of matter, not predicted by the standard model that results in the gravitational effect seen. [6]

In order to obtain accurate information for a universal gravitation calculation a reasonable approximation for the distance must be made. Observing distance involved in galactic rotation is beyond the use of simple RADAR, parallax, and even using main sequence stars for exploiting the absolute v. apparent luminosity relationship. The distances are so great that we are required to use a combination of Cepheid variable stars and using Type 1A supernovae to obtain a reasonable approximation between the Earth and the galaxy of interest. [9]

Cepheid Variables are a class of stars that have a regular change in luminosity that is a function of its distance from where it is observed. The picture below shows the variation in luminosity in a time dependent sequence. [7]


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The variation in the luminosity of the Cepheid variable is very regular. A plot of the luminosity v. time for Cepheid variable star shows that the variation is harmonic and very regular.


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Cepheid variables within our galaxy were than standardized by comparing absolute luminosity with relative luminosity to generate a plot of luminosity v. period. A linear relationship was determined. This allows us to determine the absolute luminosity from the period of oscillation; astronomers can then compare the absolute luminosity to the relative luminosity and calculate distance.

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Distances greater than 10,000,000 parsecs require another method of distance calculation. The Tully-Fisher relation should not be used as it involves galactic rotation rates and would be a confounding variable in analysis. We can not use galactic rotation rates to determine distance and therefore measure galactic rotation rates. Using the periodicity of Cepheid variables and the luminosity as a function of distance of Type 1A supernovae the distance to the galaxy can be determined. Type 1A supernovae can be measured for brightness and the width of the curve can be used to determine the absolute brightness and therefore calculate distance. [7,9]


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This distance and the observation of the width of the galaxy based on observation allows for a reasonable approximation of the radius of the galaxy of interest.

Mass Estimate
Mass can be estimated using Newton’s law of universal gravitation. Astronomers may select an easily observable section of a galaxy and observe its movement through time. The observed stars should be fairly close to the core of the galaxy as that is where the Newton’s law of universal gravitation closely conforms to observed rates of galactic rotation rates. If the observed star were beyond a certain threshold the galaxy would appear to have much more mass than it actually does. This is the primary problem that must be sorted out using either the dark matter or MOND theory. [9]

Astronomers are required to correct the mass of galaxies using various forms of spectroscopy to account for factors that are not visible. The total amount of interstellar medium can be estimated using 21 cm radiation. This spectroscopy is used to detect gas clouds that are difficult to observe directly as they do not emit light and absorb very little. In addition to this the luminosity of the galaxies, corrected for distance, are used to calculate the mass of the observable galaxy, estimates are used to account for black holes and unobservable but evidence based phenomena. [9]

The two primary explanations for the difference in the observed galactic rotation and the calculated galactic rotation of Newton’s law of universal gravitation are cold dark matter (CDM) and Modified Newtonian Dynamics (MOND). Currently the majority of resources, time and personnel, are exploring CDM. [8, 11]

Fritz Zwicky originally postulated dark Matter in 1933. He was observing the motion of galaxies in the Coma cluster of galaxies and noticed a significant difference in the motion of the galaxies and their observable mass according to Kepler’s 3rd Law of motion. He suggested the presence of “dark matter” a type of matter that conveys the gravitational force of associated with mass but does not interact with light. Dark matter is believed to be the most likely source of difference in observed and theoretical rotation curves of galaxies. Current cosmological models of the universe have dark matter accounting for 23% of the universe while “dark energy” accounts for another 72% of the universe. Together our “observable” universe only accounts for 5 % of the total “stuff” in the universe. There are several different proposals for what could constitute dark matter including WIMPs, neutrinos, and axions, or some other super symmetric particle. There are several projects currently searching for these particles including the CERN Axion Solar Telescope looking for axions, Antarctic Muon And Neutrino Detector Array looking for neutrinos, the Large Hadron Collider looking for super symmetric particles, and the XENON100 detector looking for WIMPs. CDM is clearly the odds on favorite in terms of funding and manpower as a solution to galactic rotation curves. [3, 5, 9, 12, 13]

Current dark matter research is focusing on different candidates of dark matter specifically WIMPs, Weakly Interacting Massive Particles. These particles are considered to be prime targets to be “dark matter” if they can be detected. The XENON100 project was set up in an underground cave in Italy with the purpose being to detect WIMPs. A cave was filled with chilled Xenon and isolated with rock, concrete, iron, etc. This isolation is to prevent cosmic rays from interacting with Xenon. The WIMPs were postulated to be found by their interaction with Xenon, which in turn would cause the emission of a photon, which could be detected in an underground, shielded detector. The Xenon project released the first 100 days of data and detected a total of 6 interactions, 2 of which were proven to be electronic noise, 3 which matched the prediction of stray cosmic radiation, and 1 unaccounted for particle. This did not match the expectations of the researchers and has led researchers to throw out the one remaining detection as another electronic error. [3, 5, 12, 13]

The modified Newtonian gravity theory or MOND theory was originally proposed by Moti Milgrom to explain the galactic rotation curve. He proposed that in very low-density situations Newton’s law of gravity must be modified to account for the galactic rotation curve. The gravitational acceleration in "low gravity" areas can be modeled to fit the observational data. The gravitational acceleration is modified the term Mu(g/a0) where a0 is a new parameter and Mu is an asymptotic function which has yet to be finalized but there are three main candidates (1/x^2, 1/x, e^-x). The asymptotic nature of Mu allows the modification of Newtonian gravity to approach zero the stronger the gravitational field and therefore match the observational evidence for the inner part of galactic rotation curves. The MOND theory even accounts for pressure supported systems showing that they are finite with density falling rapidly as a function of 1/r^4. The most impressive part about the MOND theory is its ability to predict the galactic rotation curve based solely on observable evidence in the near infrared region of the spectrum. This is not just the general averaged rotational velocity but very specific values based on the clumping of observable matter. The MOND theory even accounts for variation in the M/L relationship of the T-F relation based on the color of galaxies. The MOND theory accounts for variation of surface brightness of the galaxy has a corresponding variation in the MOND curve and the observed rotational curve. The MOND theory is not without its problems, it fails to account for the motion in certain super clusters unless a much smaller amount of “dark matter” is considered. The Bullet Cluster provides and excellent example for the problems with the MOND. The “dark matter” effects, such as gravitational interaction seem to be centered far away from the observable mass indicating the presence of an undetectable form of matter. [6, 11]



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The primary issued that I have with the theory of dark matter is epistemological. The MOND theory requires modification of a human-created law of explaining natural phenomena. As new information, such as galactic rotation curves, comes into play we will most likely modify the theory to incorporate the new information as MOND does. CDM requires us to postulate the existence of a particle that has never been observed, is not part of the standard model, and continually shows null results from increasingly more precise, and expensive, measurement. CDM may end up being the answer to the question of galactic rotation curves but it is the responsibility of the scientific community to act on falsifiable theories. MOND is falsifiable within our own solar system. There exist points within our solar system where the gravitational field is essentially canceled out between the sun and some other massive body such as Jupiter. In this very small region gravity can be assessed and determined to be a function of Newton’s law of gravity or the MOND. This can be done for less than the cost spent on one of the four experiments currently searching for dark matter particles listed earlier.

The problem with searching for dark matter is that you may be searching for something that isn’t there, similar to Michelson in his search for ether. Michelson spent years refining the accuracy of his detector, sorting through data in order to measure something that wasn’t there. The propagation of a wave required a medium at the time based on all observational evidence. The question of when to change direction and seek a new explanation for observation remains a key, and yet unsolved aspect of the scientific process.

References
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[2] Cepheid Variable Stars. (n.d.). Cepheid Variable Stars (figure ). Retrieved May 3, 2011, from http://www.optcorp.com/edu/articleDetailEDU.aspx?aid=1646
[3] Cown, Science News, R. (n.d.). Underground Experiment Fails to Find Dark Matter. Retrieved April 27, 2011, from Science News website: http://www.wired.com/wiredscience/2011/04/xenon100-dark-matter/
[4] FORS1. (2004). Spiral Galaxy NGC 1232 [Data file]. Retrieved from http://apod.nasa.gov/apod/ap040125.html
[5] How does AMANDA work? (n.d.). Public Information on AMANDA. Retrieved May 4, 2011, from Barwick Group, School of Physical Sciences, University of California Irvine website: http://amanda.uci.edu/public_info.html
[6] McGaugh, S. (n.d.). The MOND Page. Retrieved May 3, 2011, from University of Maryland website: http://www.astro.umd.edu/~ssm/mond/
[7] Nave, C. R. (n.d.). Cepheid Vairables. Retrieved May 4, 2011, from Georgia State University website: http://hyperphysics.phy-astr.gsu.edu/hbase/astro/cepheid.html
[8] Newton, W. (2011, Spring). Astronomy 561 Notes. Powerpoint Presention presented at PHYS561, Mesquite Tx.
[9] Newman/NASA, P. (2010, April 19). Dark Matter. Retrieved May 5, 2011, from NASA
website: http://imagine.gsfc.nasa.gov/docs/science/know_l1/dark_matter.html
[10] Sanders, R. H. (2009). Modified Newtonian Dynamics: A Falsification of Cold Dark Matter. Advances in Astronomy, 2009, article id 752439.
[11] Schilling, G. (2007, April). Battlefield Galactica: Dark Matter vs. MOND. Sky & Telescope. Retrieved from http://www.allesoversterrenkunde.nl/artikelen/617-Battlefield-Galactica-Dark-Matter-vs-MOND.html
[12] Schumann, M. (2011, May 5). Xenon 100. In XENON 100 releases first Results. Retrieved May 3, 2011, from Rice University website: http://xenon.physics.rice.edu/
[13] Sugarbaker, A. (2007, December 2). Figure #1. In Early Evidence for Dark Matter:
The Virial Theorem and Rotation Curves [Figure #1]. Retrieved May 4, 2011, from Stanford University website: http://large.stanford.edu/courses/2007/ph210/sugarbaker2/