Galaxy rotation curve
Encyclopedia
The rotation curve of a galaxy
Galaxy
A galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The word galaxy is derived from the Greek galaxias , literally "milky", a...

can be represented by a graph
Graph of a function
In mathematics, the graph of a function f is the collection of all ordered pairs . In particular, if x is a real number, graph means the graphical representation of this collection, in the form of a curve on a Cartesian plane, together with Cartesian axes, etc. Graphing on a Cartesian plane is...

that plots the orbital velocity
Orbital velocity
Orbital velocity can refer to the following:* The orbital speed of a body in a gravitational field.* The velocity of particles due to wave motion, in particular in wind waves....

of the star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...

s or gas
Gas
Gas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...

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
Spiral galaxy
A spiral galaxy is a certain kind of galaxy originally described by Edwin Hubble in his 1936 work The Realm of the Nebulae and, as such, forms part of the Hubble sequence. Spiral galaxies consist of a flat, rotating disk containing stars, gas and dust, and a central concentration of stars known as...

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
Dark matter
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...

that permeates the galaxy and extends into the galaxy's halo
Dark matter halo
A dark matter halo is a hypothetical component of a galaxy, which extends beyond the edge of the visible galaxy and dominates the total mass. Since they consist of dark matter, halos cannot be observed directly, but their existence is inferred through their effects on the motions of stars and gas...

. An alternative explanation is a modification of the laws of gravity, such as MOND
Mond
Mond may refer to:* MOND - Modified Newtonian Dynamics. A proposed adjustment to the classical inverse-square law of gravity.* Der Mond, an opera in one act* Mond Nickel Company, a defunct mining company...

(Modified Newtonian Dynamics). 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.

## History and description of the problem

In 1959,
Louise Volders demonstrated
that spiral galaxy M33
Triangulum Galaxy
The Triangulum Galaxy is a spiral galaxy approximately 3 million light years from Earth in the constellation Triangulum. It is catalogued as Messier 33 or NGC 598, and is sometimes informally referred to as the Pinwheel Galaxy, a nickname it shares with Messier 101...

does not spin
as expected according to Keplerian dynamics
Kepler's laws of planetary motion
In astronomy, Kepler's laws give a description of the motion of planets around the Sun.Kepler's laws are:#The orbit of every planet is an ellipse with the Sun at one of the two foci....

,
a result which was extended to many other spiral galaxies
during the seventies. Based on this model, matter
Matter
Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...

(such as star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...

s and gas) in the disk portion of a spiral should orbit
Orbit
In physics, an orbit is the gravitationally curved path of an object around a point in space, for example the orbit of a planet around the center of a star system, such as the Solar System...

the center of the galaxy similar to the way in which planets in the solar system
Solar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...

orbit the sun, that is, according to Newtonian mechanics. Based on this, it would be expected that the average orbital speed
Orbital speed
The orbital speed of a body, generally a planet, a natural satellite, an artificial satellite, or a multiple star, is the speed at which it orbits around the barycenter of a system, usually around a more massive body...

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
Occam's razor
Occam's razor, also known as Ockham's razor, and sometimes expressed in Latin as lex parsimoniae , is a principle that generally recommends from among competing hypotheses selecting the one that makes the fewest new assumptions.-Overview:The principle is often summarized as "simpler explanations...

to the physical laws of the universe
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

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
Dark matter
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...

within the galactic halo
Dark matter halo
A dark matter halo is a hypothetical component of a galaxy, which extends beyond the edge of the visible galaxy and dominates the total mass. Since they consist of dark matter, halos cannot be observed directly, but their existence is inferred through their effects on the motions of stars and gas...

, the existence of which was first posited by Fritz Zwicky
Fritz Zwicky
Fritz Zwicky was a Swiss astronomer. He worked most of his life at the California Institute of Technology in the United States of America, where he made many important contributions in theoretical and observational astronomy.- Biography :Fritz Zwicky was born in Varna, Bulgaria to a Swiss father....

some 40 years earlier in his studies of the masses of galaxy cluster
Galaxy cluster
A galaxy cluster is a compact cluster of galaxies. Basic difference between a galaxy group and a galaxy cluster is that there are many more galaxies in a cluster than in a group. Also, galaxies in a cluster are more compact and have higher velocity dispersion. One of the key features of cluster is...

s. Presently, there are a large number of pieces of observational evidence that point to the presence of cold dark matter
Cold dark matter
Cold dark matter is the improvement of the big bang theory that contains the additional assumption that most of the matter in the Universe consists of material that cannot be observed by its electromagnetic radiation and whose constituent particles move slowly...

, and its existence is a major feature of the present Lambda-CDM model
Lambda-CDM model
ΛCDM or Lambda-CDM is an abbreviation for Lambda-Cold Dark Matter, which is also known as the cold dark matter model with dark energy...

that describes the cosmology
Physical cosmology
Physical cosmology, as a branch of astronomy, is the study of the largest-scale structures and dynamics of the universe and is concerned with fundamental questions about its formation and evolution. For most of human history, it was a branch of metaphysics and religion...

of the universe
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...

.

## Further investigations

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 and of their position on the Tully-Fisher relation
Tully-Fisher relation
In astronomy, the Tully–Fisher relation, published by astronomers R. Brent Tully and J. Richard Fisher in 1977, is an empirical relationship between the intrinsic luminosity of a spiral galaxy and its velocity width...

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
Dwarf galaxy problem
The dwarf galaxy problem is one that arises from numerical cosmological simulations that predict the evolution of the distribution of matter in the universe. Dark matter seems to cluster hierarchically and in ever increasing number counts for smaller and smaller sized halos...

of structure formation
Structure formation
Structure formation refers to a fundamental problem in physical cosmology. The universe, as is now known from observations of the cosmic microwave background radiation, began in a hot, dense, nearly uniform state approximately 13.7 Gyr ago...

.

Further challenges to dark matter theory, or at least its most popular form - cold dark matter
Cold dark matter
Cold dark matter is the improvement of the big bang theory that contains the additional assumption that most of the matter in the Universe consists of material that cannot be observed by its electromagnetic radiation and whose constituent particles move slowly...

(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. This so-called cuspy halo problem
Cuspy halo problem
The cuspy halo problem arises from cosmological simulations that seem to indicate cold dark matter would form cuspy distributions — that is, increasing sharply to a high value at a central point — in the most dense areas of the universe. This would imply that the center of our galaxy,...

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 lens
Gravitational lens
A gravitational lens refers to a distribution of matter between a distant source and an observer, that is capable of bending the light from the source, as it travels towards the observer...

ing observations.

## Alternatives to dark matter

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
Mond
Mond may refer to:* MOND - Modified Newtonian Dynamics. A proposed adjustment to the classical inverse-square law of gravity.* Der Mond, an opera in one act* Mond Nickel Company, a defunct mining company...

(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. A more successful alternative is the modified gravity (MOG) theory of Moffat such as scalar–tensor–vector gravity (STVG). 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. 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
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...

community
Scientific community
The scientific community consists of the total body of scientists, its relationships and interactions. It is normally divided into "sub-communities" each working on a particular field within science. Objectivity is expected to be achieved by the scientific method...

to be as convincing as the dark matter model, gravitational lensing studies may provide the means to separate the predictions of alternative gravity theories from the dark matter explanation.

• Vera Rubin
Vera Rubin
Vera Rubin is an American astronomer who pioneered work on galaxy rotation rates. She is famous for uncovering the discrepancy between the predicted angular motion of galaxies and the observed motion, by studying galactic rotation curves...

• Unsolved problems in physics
Unsolved problems in physics
This is a list of some of the major unsolved problems in physics. Some of these problems are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result...

• Nonsymmetric gravitational theory
Nonsymmetric gravitational theory
In theoretical physics, the nonsymmetric gravitational theory of John Moffat is a classical theory of gravitation which tries to explain the observation of the flat rotation curves of galaxies....

• Dark matter
Dark matter
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...

• Long-slit spectroscopy
Long-slit spectroscopy
In astronomy, Long-slit spectroscopy involves observing an elongated celestial object through an elongated slit aperture, and refracting this light with a prism or diffraction grating...