The rotation curve of a galaxy can be represented by a graph that plots the orbital velocity of the stars or gas in the galaxy on the y-axis against the distance from the center of the galaxy on the x-axis.
A general rule or law of particle disk rotation can be stated as: Galaxies with uniform distribution of mass have a rotation curve sloping up from the center to edge. Galaxies with a central bulge in the disk (line B in illustration) have a rotation curve sloping horizontally flat from center to edge, whereas systems with most of their mass concentrated in the center of their rotation disk (dotted line A in illustration), such as the Solar System of planets or the Jovian System of moons, have a rotation curve that slopes down from the center to the edge.
Stars are observed to revolve around the center of some galaxies at a constant speed over a large range of distances from the center of the galaxy. Therefore it can be calculated that they are revolving around a disk of matter with a central bulge. Most Low surface Brightness (LSB) galaxies rotate with a rotation curve that slopes up from center, indicating little core bulge.
The galaxy rotation problem is a discrepancy between the interpretation of the observed luminance to mass ratio of matter in the disk portions of spiral galaxies and the luminance to mass ratio of matter in the cores of galaxies. This discrepancy is currently thought to betray the presence of dark matter that permeates the galaxy and extends into the galaxy's halo. An alternative explanation is a modification of the laws of gravity, such as MOND (Modified Newtonian Dynamics).[2] A less controversial solution to the luminance to mass ratio problem is; due to the greater density of matter in cores there is a greater probability that a higher ratio of core matter is in stars undergoing fusion than in the disk therefore a higher luminance to mass ratio in core matter than in the disk.
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In 1959, Louise Volders demonstrated that spiral galaxy M33 does not spin as expected according to Keplerian dynamics,[3] a result which was extended to many other spiral galaxies during the seventies.[4] Based on this model, matter (such as stars and gas) in the disk portion of a spiral should orbit the center of the galaxy similar to the way in which planets in the solar system orbit the sun, that is, according to Newtonian mechanics. Based on this, it would be expected that the average orbital speed of an object at a specified distance away from the majority of the mass distribution would decrease inversely with the square root of the radius of the orbit (the dashed line in Fig. 1). At the time of the discovery of the discrepancy, it was thought that most of the mass of the galaxy had to be in the galactic bulge, near the center. The rotation direction is based on how the galaxy was formed.
Observations of the rotation curve of spirals, however, do not bear this out. Rather, the curves do not decrease in the expected inverse square root relationship but are "flat" – outside of the central bulge the speed is nearly a constant (the solid line Fig. 1). The explanation that requires the least adjustment to the physical laws of the universe is that there is a substantial amount of matter far from the center of the galaxy that is not emitting light in the mass-to-light ratio of the central bulge. This extra mass is proposed by astronomers to be due to dark matter within the galactic halo, the existence of which was first posited by Fritz Zwicky some 40 years earlier in his studies of the masses of galaxy clusters. Presently, there are a large number of pieces of observational evidence that point to the presence of cold dark matter, and its existence is a major feature of the present Lambda-CDM model that describes the cosmology of the universe.
Having been important in convincing people of the existence of dark matter, recent work on galaxy rotation curves provides some of its greatest challenges. Detailed investigations of the rotation curves of low surface brightness galaxies (LSB galaxies) in the 1990s[5] and of their position on the Tully-Fisher relation[6] showed that these did not behave as expected. These galaxies had to be dominated by dark matter in a surprising fashion. However, such dark matter-dominated dwarf galaxies may hold the key to solving the dwarf galaxy problem of structure formation.
Further challenges to dark matter theory, or at least its most popular form - cold dark matter (CDM), came from analysis of the centres of low surface brightness galaxies. Numerical simulations based on CDM gave predictions of the shape of the rotation curves in the centre of dark-matter dominated systems, such as these galaxies. Observations of the actual rotation curves did not show the predicted shape.[7] This so-called cuspy halo problem of cold dark matter is considered an intractable issue by theoretical cosmologists.
That dark matter theory continues to be supported as an explanation for galaxy rotation curves is because the evidence for dark matter is not solely derived from these curves. It has been uniquely successful in simulating the formation of the large scale structure seen in the distribution of galaxies and in explaining the dynamics of groups and clusters of galaxies (as originally proposed by Zwicky). Dark matter also correctly predicts the results of gravitational lensing observations.
There are a limited number of attempts to find alternative explanations to dark matter to explain galaxy rotation curves. One of the most discussed alternatives is MOND (Modified Newtonian Dynamics), originally proposed as a phenomenological explanation back in 1983 but which has been seen to have predictive power in the rotation curves of LSB galaxies. This posits that the physics of gravity changes at large scale but, until recently, was not a relativistic theory. However, this changed with the development of the tensor–vector–scalar gravity (TeVeS) theory.[8] A more successful alternative is the modified gravity (MOG) theory of Moffat such as scalar–tensor–vector gravity (STVG).[9] Brownstein and Moffat (astro-ph/0506370) applied MOG to the question of galaxy rotation curves, and presented the fits to a large sample of over 100 low surface brightness (LSB), high surface brightness (HSB) and dwarf galaxies.[10] Each galaxy rotation curve was fit without dark matter using only the available photometric data (stellar matter and visible gas) and alternatively a two-parameter mass distribution model which made no assumption regarding the mass to light ratio. The results were compared to MOND and were nearly indistinguishably right out to the edge of the rotation curve data, where MOND predicts a forever flat rotation curve, but MOG predicts an eventual return to the familiar inverse-square gravitational force law. Although these alternatives are not yet considered by the astronomical community to be as convincing as the dark matter model,[11] gravitational lensing studies may provide the means to separate the predictions of alternative gravity theories from the dark matter explanation.