Title:
The Mass-Luminosity Relation for Spiral Galaxies.
Authors:
Genkina, L. M.
Publication:
Soviet Astronomy, Vol. 14, p.732
Publication Date:
02/1971
Origin:
ADS
Bibliographic Code:
1971SvA....14..732G
Around the time this paper was published a fairly accurate mass-luminosity relation existed for both elliptical and lenticular galaxies. There were a few suggestions for the mass-luminosity relation of spiral galaxies, however they were different and had a quite large dispersion.
One of the suggestions was that of Holmberg who proposed that the color index be introduced as a supplementary parameter. The author determined that for statistical mass determinations the "mass-luminosity-color" relation had no essential advantage over the ordinary mass-luminosity relation. He then tried dividing spiral galaxies into subtypes and concluded that the introduction of new parameters did not appear to reduce the dispersion in the mass-luminosity relation.
Genkin and the author of this paper derived a mass-luminosity relation for spiral galaxies based on a catalog of masses compiled from data published prior to 1967. Radio astronomy became a popular way to determine the masses of galaxies at this time(right around the time Jocelyn Bell Burnell made her discovery). He notes that Vorontsov-Vel'yaminov pointed out a systematic disparity between the masses determined from radio and optical observations and advised to consider the data separately(the optical observations had two disadvantages).
At this point he goes on to show mass-luminosity relations using at first optical observations, and then only radio observations. He concludes that the closeness of the lines in these relations suggests that a mass-luminosity relation for spiral galaxies can be established within reasonable accuracy. Combining Burbidges' and Roberts' galaxies he found that the regression line is very close to the equation determined by Vorontsov-Vel'vaminov for spiral and irregular galaxies. However, in the 16 Type Ir I galaxies the author worked on, the slope was slightly smaller due to the exclusion of irregular galaxies.
I did not see any posts over this topic and figured I would choose one that was very early in the process of investigating spiral galaxies. It also shows the impact of improved methods such as radio vs. optical observations.
Monday, May 9, 2011
Saturday, May 7, 2011
Tully-Fisher Relation
For our last blog post, given the option of MOND, Mass-Luminosity, and Tully-Fisher it seems that MOND has been the most popular. I figured I'd mix things up just a bit. After scouring through at least a solar mass worth of articles of both Mass-Luminosity and Tully-Fisher, I picked out this one from a few years back.
The full article can be accessed here.
The data they're using here comes from AEGIS. The All-wavelength Extended Groth strip International Survey was an international collaboration between scientists and observatories in order to bring together larger data sets than any one had access to. The NRAO's, Very Large Array radio telescope from New Mexico, NASA's infrared Spitzer Space Telescope, Caltech's Palomar Observatory telescopes, the three imaging processors at the aptly-named Canada-France-Hawaii Telescope on Mauna Kea, the optical telescope at Keck Observatory also on Mauna Kea, NASA's Hubble Space Telescope, NASA's ultraviolet GALEX satellite, and NASA's Chandra X-ray Observatory satellite. Data taken from various spots on Earth as well as from orbit in a multitude of wavelengths and methodologies allowed for a rather varied data set from AEGIS.
We've learned that there is a good relationship between the rotation velocity and the luminosity of a galaxy. To be more precise, there is a relationship between rotation velocity and mass but there is also a relationship between mass and luminosity; hence, there is a relationship between rotation velocity and luminosity as well.
This diagram shows us the basic idea behind the relationship, its measurements, and how we've used it to determine the Hubble constant. As we all experienced in our own rotational velocity curves and trying to best fit the graphs, not all methods were equally successful. This articles provides a closer-fit line because they're using measurements for baryonic mass instead of using luminosity alone to infer the mass. Furthermore, they're considering more than pure rotation velocity by adding in the velocity dispersion. The velocity dispersion is what all the σ measurements refer to and allows a more accurate assessment of the true energies involved. As they slowly modify their constants, re-define their data, more and more evidence is added to the relationship and the best-fit line becomes increasingly more precise. I am curious as to how they were able to estimate the baryonic mass. It seems like they did achieve a greater level of precision given their ability to fit their data appropriately, but the article itself claims that this is beyond the scope of their publication.
This relationship and this data set has also been a part of the development of the current understanding of galaxy evolution and predicting mergers. As a lot of this data came from Mauna Kea observatories, the University of Hawaii's observatory also put together some of the information. That website can be found here but the most interesting video is below.
The full article can be accessed here.
The data they're using here comes from AEGIS. The All-wavelength Extended Groth strip International Survey was an international collaboration between scientists and observatories in order to bring together larger data sets than any one had access to. The NRAO's, Very Large Array radio telescope from New Mexico, NASA's infrared Spitzer Space Telescope, Caltech's Palomar Observatory telescopes, the three imaging processors at the aptly-named Canada-France-Hawaii Telescope on Mauna Kea, the optical telescope at Keck Observatory also on Mauna Kea, NASA's Hubble Space Telescope, NASA's ultraviolet GALEX satellite, and NASA's Chandra X-ray Observatory satellite. Data taken from various spots on Earth as well as from orbit in a multitude of wavelengths and methodologies allowed for a rather varied data set from AEGIS.
We've learned that there is a good relationship between the rotation velocity and the luminosity of a galaxy. To be more precise, there is a relationship between rotation velocity and mass but there is also a relationship between mass and luminosity; hence, there is a relationship between rotation velocity and luminosity as well.
This diagram shows us the basic idea behind the relationship, its measurements, and how we've used it to determine the Hubble constant. As we all experienced in our own rotational velocity curves and trying to best fit the graphs, not all methods were equally successful. This articles provides a closer-fit line because they're using measurements for baryonic mass instead of using luminosity alone to infer the mass. Furthermore, they're considering more than pure rotation velocity by adding in the velocity dispersion. The velocity dispersion is what all the σ measurements refer to and allows a more accurate assessment of the true energies involved. As they slowly modify their constants, re-define their data, more and more evidence is added to the relationship and the best-fit line becomes increasingly more precise. I am curious as to how they were able to estimate the baryonic mass. It seems like they did achieve a greater level of precision given their ability to fit their data appropriately, but the article itself claims that this is beyond the scope of their publication.
This relationship and this data set has also been a part of the development of the current understanding of galaxy evolution and predicting mergers. As a lot of this data came from Mauna Kea observatories, the University of Hawaii's observatory also put together some of the information. That website can be found here but the most interesting video is below.
Thursday, May 5, 2011
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.
[4]
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]
[12]
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]
[2]
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.
[8]
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.
[7]
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]
[9]
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]
[4]
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
[1] Baez, J. (2006, August 16). This Weeks Finds In Mathematical Physics [Figure]. Retrieved May 4, 2011, from http://math.ucr.edu/home/baez/week238.html
[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/
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.
[4]
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]
[12]
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]
[2]
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.
[8]
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.
[7]
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]
[9]
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]
[4]
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
[1] Baez, J. (2006, August 16). This Weeks Finds In Mathematical Physics [Figure]. Retrieved May 4, 2011, from http://math.ucr.edu/home/baez/week238.html
[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/
Tuesday, May 3, 2011
Cosmological observations in a modified theory of gravity (MOG)
Cosmological observations in a modified theory of gravity (MOG)
J.W. Moffat a,b , V.T. Toth a April 14, 2011
a Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
b Department of Physics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
The paper in question tells of the modified gravity theory or MOG as a theory devoid of exotic dark matter and that the authors have used the MOG to model galaxy cluster mass, rotational curves and lensing. They agree that adiabatic cold dark matter (ACDM) does indeed provide explanation cosmological phenomenon but in their opinion creates a massive discrepancy or hole in the universe. This hole or omission contends that roughly 95% of the matter in the universe is undetectable to us at this time. The authors claim that they can use their MOG to answer the problems encountered from the standard gravitational theory.
The modified theory of gravity is a theory full based on scalar, tensor and vector fields and it has evolved into Scalar-Tensor-Vector Gravity (STVG) theory. This in principle has stated that the dampened structure growth at low values of k and using a lesser effect of the Silk damping, a process which creates a more uniform density of the universe as well as Cosmic Microwave Background (CMB), are very similar to the calculations determined by the adiabatic cold dark matter theory. Though the do differ.
The MOG calculations are jagged than the predicted graphs of the ACDM. This is believed to have occurred due to the fact that much more data is required to fill and smooth the data series, as more and more galaxies are surveyed this is predicted to make the curve a better fit. There is also the problem of the dampened power spectrum at both high and low values of k as sub galactic distance scales are used. Over the MOG and CMB spectrum a change in the value of the Mukhanov’s constant produces similar results as the dark matter curves.
The authors are convinced that their Modified theory of Gravity (MOG) can indeed explain the discrepancies of Newtonian mechanics. It seems that just varying constants in the equations can indeed fit the observable data. As we, ourselves, have found out through our own homework calculations. Only time will tell.
Cosmological observations in a modified theory of gravity (MOG)
J.W. Moffat a,b , V.T. Toth a April 14, 2011
a Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
b Department of Physics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
The paper in question tells of the modified gravity theory or MOG as a theory devoid of exotic dark matter and that the authors have used the MOG to model galaxy cluster mass, rotational curves and lensing. They agree that adiabatic cold dark matter (ACDM) does indeed provide explanation cosmological phenomenon but in their opinion creates a massive discrepancy or hole in the universe. This hole or omission contends that roughly 95% of the matter in the universe is undetectable to us at this time. The authors claim that they can use their MOG to answer the problems encountered from the standard gravitational theory.
The modified theory of gravity is a theory full based on scalar, tensor and vector fields and it has evolved into Scalar-Tensor-Vector Gravity (STVG) theory. This in principle has stated that the dampened structure growth at low values of k and using a lesser effect of the Silk damping, a process which creates a more uniform density of the universe as well as Cosmic Microwave Background (CMB), are very similar to the calculations determined by the adiabatic cold dark matter theory. Though the do differ.
The MOG calculations are jagged than the predicted graphs of the ACDM. This is believed to have occurred due to the fact that much more data is required to fill and smooth the data series, as more and more galaxies are surveyed this is predicted to make the curve a better fit. There is also the problem of the dampened power spectrum at both high and low values of k as sub galactic distance scales are used. Over the MOG and CMB spectrum a change in the value of the Mukhanov’s constant produces similar results as the dark matter curves.
The authors are convinced that their Modified theory of Gravity (MOG) can indeed explain the discrepancies of Newtonian mechanics. It seems that just varying constants in the equations can indeed fit the observable data. As we, ourselves, have found out through our own homework calculations. Only time will tell.
Wednesday, April 27, 2011
Galaxy Evolution I: Galaxy spectra, and how we know what we know part I
To understand how we've built up our picture of galaxy evolution, let's have a look at what galaxy spectra look like.
The coninuum part of a galaxy's spectrum is the sum of the billions of stars' black body spectra:
The 400nm (4000 Angstom) break pointed out by the arrow is caused by (i) the absorption of small wavelength (high energy) photons by metals (non-H, He) in the atmospheres of stars and a lack of hot, blue stars. From what we know, the 400nm break should be weak in spiral galaxies (lots of luminous, hot blue stars) and strong in elliptical galaxies (very few blue stars). But we're getting ahead of ourselves...
Lets's look at some actual spectra of galaxies:
From top left to bottom right, here are the optical images of these galaxies:
NGC4889:
NGC 2775
The coninuum part of a galaxy's spectrum is the sum of the billions of stars' black body spectra:
The 400nm (4000 Angstom) break pointed out by the arrow is caused by (i) the absorption of small wavelength (high energy) photons by metals (non-H, He) in the atmospheres of stars and a lack of hot, blue stars. From what we know, the 400nm break should be weak in spiral galaxies (lots of luminous, hot blue stars) and strong in elliptical galaxies (very few blue stars). But we're getting ahead of ourselves...
Lets's look at some actual spectra of galaxies:
From top left to bottom right, here are the optical images of these galaxies:
NGC4889:
NGC 2775
NGC 6181
NGC 4449
The first two are elliptical galaxies, the third a spiral, and the fourth an irregular galaxy. Notice that the elliptical spectra have notcieable absorption lines and the spiral and irregular emission lines. Absorption lines indicate metals in stellar atmospheres or cold gas in the interstellar medium. Emission lines indicate hot gas, likely heated by hot, blue stars. We can conclude that ellipticals have very few hot, blue stars, leaving only an older population of stars. Spirals and irregulars, on the other hand, appear to have many young, blue stars.
Stay tuned...
Sunday, April 24, 2011
Collisionless Nature of Dark Matter
As I was researching articles to review to post to the blog, I came across a title that caught my curiosity. "Quantifying The Collisionless Nature Of Dark Matter And Galaxies In A 1689";(Doron Lemze, Yoel Rephaeli, Rennan Barkana, Tom Broadhurst, Rick Wagner & Mike L. Norman). I found this while searching Worldwidescience.org on topics of surface profile of galaxies and densities.
The word "collisionless" caught my attention because when we think of collisions we think of two or more masses making contact and either combining into one mass or bouncing off each other into different directions from their original trajectory. So I quickly assumed that collisionless refers to the lack of contact between the masses indicated as dark matter.
The authors state that despite a recent collision of two massive clusters, the spatial distribution of dark matter and galaxies are quite similar. A conical shaped shock front is visible indicating two clusters have passed through each other with an obvious collisionally merged gas distribution, but the galaxies and the lensing mass are largely intact, implying straightforwardly that dark matter and galaxies are collisionless (Markevitch et al. 2002; clowe et al. 204; Bradac de al, 2006). It implied that once hydrostatic equilibrium is reached, dark matter and galaxies should have the same mean specific kinectic energy. The total specific kinectic energy of dark matter is proportional to that of the gas which was evident through X-ray and optical observations of groups and clusters using mean emission-weighted gas temperature scales.
The paper was very technical in nature and hard to follow as to their methodologies (probably due to my limited understanding of the processes used). It goes in detail in the use of calculated velocities of dark matter and galaxies as well as galaxies surface number densities and projected velocities dispersions.The paper is a continuing comprehensive study of the dynamical properties of dark matter, galaxies and the hydrodynamics in cluster A 1689. It assumes that if dark matter and galaxies are fully collisionless, they should have the same average specific kinectic energy.
The one thing that the paper does not do is exam the electromagnetic aspect of a "collisionless" particle. that is attraction versus repulsion forces. In my simple mind, I would expect the simple nature of chemistry and physics to come into play. If the gas particles are ionic in nature, would these tend to be more positive thus repulsive as they approach each other therefore, never actually colliding? I guess that is why I am taking this course turning my simple understanding into more highly complex confusion.
The word "collisionless" caught my attention because when we think of collisions we think of two or more masses making contact and either combining into one mass or bouncing off each other into different directions from their original trajectory. So I quickly assumed that collisionless refers to the lack of contact between the masses indicated as dark matter.
The authors state that despite a recent collision of two massive clusters, the spatial distribution of dark matter and galaxies are quite similar. A conical shaped shock front is visible indicating two clusters have passed through each other with an obvious collisionally merged gas distribution, but the galaxies and the lensing mass are largely intact, implying straightforwardly that dark matter and galaxies are collisionless (Markevitch et al. 2002; clowe et al. 204; Bradac de al, 2006). It implied that once hydrostatic equilibrium is reached, dark matter and galaxies should have the same mean specific kinectic energy. The total specific kinectic energy of dark matter is proportional to that of the gas which was evident through X-ray and optical observations of groups and clusters using mean emission-weighted gas temperature scales.
The paper was very technical in nature and hard to follow as to their methodologies (probably due to my limited understanding of the processes used). It goes in detail in the use of calculated velocities of dark matter and galaxies as well as galaxies surface number densities and projected velocities dispersions.The paper is a continuing comprehensive study of the dynamical properties of dark matter, galaxies and the hydrodynamics in cluster A 1689. It assumes that if dark matter and galaxies are fully collisionless, they should have the same average specific kinectic energy.
The one thing that the paper does not do is exam the electromagnetic aspect of a "collisionless" particle. that is attraction versus repulsion forces. In my simple mind, I would expect the simple nature of chemistry and physics to come into play. If the gas particles are ionic in nature, would these tend to be more positive thus repulsive as they approach each other therefore, never actually colliding? I guess that is why I am taking this course turning my simple understanding into more highly complex confusion.
Modified Newtonian Dynamics as an Alternative to Dark Matter
MODIFIED NEWTONIAN DYNAMICS AS AN
ALTERNATIVE TO DARK MATTER
Robert H. Sanders1 & Stacy S. McGaugh2
1Kapteyn Astronomical Institute, University of Groningen, Groningen, The Netherlands
2Department of Astronomy, University of Maryland, College Park, MD, USA
KEYWORDS: dark matter, galaxy dynamics, gravitational theory, cosmology
MODIFIED NEWTONIAN DYNAMICS AS AN
ALTERNATIVE TO DARK MATTER
Robert H. Sanders1 & Stacy S. McGaugh2
1Kapteyn Astronomical Institute, University of Groningen, Groningen, The Netherlands
2Department of Astronomy, University of Maryland, College Park, MD, USA
KEYWORDS: dark matter, galaxy dynamics, gravitational theory, cosmology
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 pgnao where gn is the usual Newtonian acceleration. This simple algorithm yields flat rotation curves for spiral galaxies and amass-rotation velocity relation of the form M / V 4 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 superclusters, 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.
These two authors discuss and compare math solutions and their accuracy using observed data in our known universe. The incomplete MOND theory cannot be extended to problems of cosmology and structure formation. However by making reasonable assumptions one may speculate on the form of a MOND cosmology.
The authors show equations relating the force of gravity to the force of charge particles as:
F = (GM/ r^2 ) x f (r/ro)
Scientist Milgrom (1983a) realized that this length in kpc law was incompatible with observed TF law, L is proportional to v^4. Moreover any modification of a length scale would imply that larger galaxies should exhibit a larger discrepancy. (Sanders 1986) This is contrary to observed data.
A most interesting question for me concerning gravity and dark matter was investigated directly by “dark halos” with an acceleration scale can the phenomenology of MOND be reproduced by dark halos– specifically the kind of dark halos that emerge from cosmological N-body simulations with an initial fluctuation spectrum given by cold dark matter (CDM)? This is an important question because the phenomenological success of MOND may be telling us something about the universal distribution of dark matter rather than anything about the law of gravity or inertia at low accelerations.
This question was first considered by Begeman et al. (1991) who attempted to devise disk-halo coupling rules that could yield a one-parameter fit to rotation curves (M/L of the visible disk) similar to modified Newtonian dynamics (MOND). Without any physical justification the core radius and asymptotic circular velocity of an isothermal halo were adjusted to the scale length and maximum rotation velocity of the disk to yield a characteristic acceleration. With such coupling rules, the fits to galaxy rotation curves were of lower quality than the MOND fits (particularly for the dwarf systems), and there were numerous ambiguities (e.g., in gas dominated galaxies, what is the proper disk length scale?). Similar ad hoc coupling rules between visible and dark components have also been considered by Giraud (2000).
While this disagrement between scientist has been intense for over thirty years this is a short period for science history. The disagreement leads scientist to follow their own intuitive judgment about how to apply science money and methods. I do not know of any other group better qualified to make such decisions. ( Like maybe politicians, actors, or news anchors??)
ALTERNATIVE TO DARK MATTER
Robert H. Sanders1 & Stacy S. McGaugh2
1Kapteyn Astronomical Institute, University of Groningen, Groningen, The Netherlands
2Department of Astronomy, University of Maryland, College Park, MD, USA
KEYWORDS: dark matter, galaxy dynamics, gravitational theory, cosmology
MODIFIED NEWTONIAN DYNAMICS AS AN
ALTERNATIVE TO DARK MATTER
Robert H. Sanders1 & Stacy S. McGaugh2
1Kapteyn Astronomical Institute, University of Groningen, Groningen, The Netherlands
2Department of Astronomy, University of Maryland, College Park, MD, USA
KEYWORDS: dark matter, galaxy dynamics, gravitational theory, cosmology
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 pgnao where gn is the usual Newtonian acceleration. This simple algorithm yields flat rotation curves for spiral galaxies and amass-rotation velocity relation of the form M / V 4 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 superclusters, 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.
These two authors discuss and compare math solutions and their accuracy using observed data in our known universe. The incomplete MOND theory cannot be extended to problems of cosmology and structure formation. However by making reasonable assumptions one may speculate on the form of a MOND cosmology.
The authors show equations relating the force of gravity to the force of charge particles as:
F = (GM/ r^2 ) x f (r/ro)
Scientist Milgrom (1983a) realized that this length in kpc law was incompatible with observed TF law, L is proportional to v^4. Moreover any modification of a length scale would imply that larger galaxies should exhibit a larger discrepancy. (Sanders 1986) This is contrary to observed data.
A most interesting question for me concerning gravity and dark matter was investigated directly by “dark halos” with an acceleration scale can the phenomenology of MOND be reproduced by dark halos– specifically the kind of dark halos that emerge from cosmological N-body simulations with an initial fluctuation spectrum given by cold dark matter (CDM)? This is an important question because the phenomenological success of MOND may be telling us something about the universal distribution of dark matter rather than anything about the law of gravity or inertia at low accelerations.
This question was first considered by Begeman et al. (1991) who attempted to devise disk-halo coupling rules that could yield a one-parameter fit to rotation curves (M/L of the visible disk) similar to modified Newtonian dynamics (MOND). Without any physical justification the core radius and asymptotic circular velocity of an isothermal halo were adjusted to the scale length and maximum rotation velocity of the disk to yield a characteristic acceleration. With such coupling rules, the fits to galaxy rotation curves were of lower quality than the MOND fits (particularly for the dwarf systems), and there were numerous ambiguities (e.g., in gas dominated galaxies, what is the proper disk length scale?). Similar ad hoc coupling rules between visible and dark components have also been considered by Giraud (2000).
While this disagrement between scientist has been intense for over thirty years this is a short period for science history. The disagreement leads scientist to follow their own intuitive judgment about how to apply science money and methods. I do not know of any other group better qualified to make such decisions. ( Like maybe politicians, actors, or news anchors??)
Subscribe to:
Posts (Atom)