Density wave theory
Encyclopedia
Chia-Chiao Lin
Chia-Chiao Lin is an American applied mathematician and Institute Professor emeritus at the Massachusetts Institute of Technology.-Biography:...
and Frank Shu
Frank Shu
Frank Shu , is an astrophysicist, author and professor of astronomy at the University of California, Berkeley and University of California, San Diego and the university president of the National Tsing Hua University....
in the mid-1960s to explain spiral arm structure 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...
. Their theory introduces the idea of long-lived quasistatic
Quasistatic
Quasistatic can refer to:* Quasistatic process* Quasistatic equilibrium* Quasistatic loading* Quasistatic approximation...
density waves (also called heavy sound), which are sections of the galactic disk that have greater mass density (about 10–20% greater). The theory has also been successfully applied to Saturn's rings
Rings of Saturn
The rings of Saturn are the most extensive planetary ring system of any planet in the Solar System. They consist of countless small particles, ranging in size from micrometres to metres, that form clumps that in turn orbit about Saturn...
.
Galactic spiral arms
Lin and Shu proposed in 1964 that the arms were not material in nature, but instead made up of areas of greater density, similar to a traffic jam on a highway. The cars move through the traffic jam: the density of cars increases in the middle of it. The traffic jam itself, however, does not move (or not a great deal, in comparison to the cars). In the galaxy, stars, gas, dust, and other components move through the density waves, are compressed, and then move out of them.
More specifically, the density wave theory argues that the "gravitational attraction between stars at different radii" prevents the so-called winding problem, and actually maintains the spiral pattern.
The rotation speed of the arms is defined to be
, the global pattern speed. (Thus, within a certain non-inertial reference frameNon-inertial reference frame
A non-inertial reference frame is a frame of reference that is under acceleration. The laws of physics in such a frame do not take on their most simple form, as required by the theory of special relativity...
, which is rotating at
, the spiral arms appear to be at rest). The stars within the arms are not necessarily stationary, though at a certain distance from the center, 
, the corotation radius, the stars and the density waves move together. Inside that radius, stars move more quickly (
) than the spiral arms, and outside, stars move more slowly (
). It is easy to see that for an m-armed spiral, a star at radius R from the center will move through the structure with a frequency 
. So, the gravitational attraction between stars can only maintain the spiral structure if the frequency at which a star passes through the arms is less than the epicyclic frequencyEpicyclic frequency
In astrophysics, particularly the study of accretion disks, the epicyclic frequency is the frequency at which a radially displaced fluid parcel will oscillate. It can be referred to as a "Rayleigh discriminant"...
,
, of the star. This means that a long-lived spiral structure will only exist between the inner and outer Lindblad resonanceLindblad resonance
A Lindblad resonance, named for the Swedish galactic astronomer Bertil Lindblad, is an orbital resonance in which an object's epicyclic frequency is a simple multiple of some forcing frequency...
(ILR, OLR, respectively), which are defined as the radii such that:
and 
, respectively. Past the OLR and within the ILR, the extra density in the spiral arms pulls more often than the epicyclic rate of the stars, and the stars are thus unable to react and move in such a way as to "reinforce the spiral density enhancement".Further implications
H I region
An H I region is an interstellar cloud composed of neutral atomic hydrogen , in addition to the local abundance of helium and other elements. These regions are non-luminous, save for emission of the 21-cm region spectral line. This line has a very low transition probability, so requires large...
and dust bands on the inner edges of spiral arms, the existence of young, massive stars and H II region
H II region
An H II region is a large, low-density cloud of partially ionized gas in which star formation has recently taken place. The short-lived, blue stars forged in these regions emit copious amounts of ultraviolet light, ionizing the surrounding gas...
s throughout the arms, and an abundance of old, red stars in the remainder of the disk". Basically, when clouds of gas and dust
Cosmic dust
Cosmic dust is a type of dust composed of particles in space which are a few molecules to 0.1 µm in size. Cosmic dust can be further distinguished by its astronomical location; for example: intergalactic dust, interstellar dust, interplanetary dust and circumplanetary dust .In our own Solar...
enter into a density wave and are compressed the rate of star formation increases as some clouds meet the Jeans criterion
Jeans instability
In physics, the Jeans instability causes the collapse of interstellar gas clouds and subsequent star formation. It occurs when the internal gas pressure is not strong enough to prevent gravitational collapse of a region filled with matter...
, and collapse to form new stars. Since star formation does not happen immediately, the stars are slightly behind the density waves. The hot OB star
OB star
OB stars are hot, massive stars of spectral types O or B which form in loosely organized groups called OB associations. They are short lived, and thus don't move very far from where they were formed within their life. During their lifetime, they will emit copious amounts of ultraviolet radiation...
s that are created ionize the gas of the interstellar medium
Interstellar medium
In astronomy, the interstellar medium is the matter that exists in the space between the star systems in a galaxy. This matter includes gas in ionic, atomic, and molecular form, dust, and cosmic rays. It fills interstellar space and blends smoothly into the surrounding intergalactic space...
, and form H II regions. These stars have relatively short lifetimes, however, and expire before fully leaving the density wave. The smaller, redder stars do leave the wave, and become distributed throughout the galactic disk.
Application to Saturn's rings
Beginning in the late 1970s, Peter GoldreichPeter Goldreich
Peter Goldreich is an American astrophysicist whose research focuses on celestial mechanics, planetary rings, helioseismology and neutron stars. He is currently the Lee DuBridge Professor of Astrophysics and Planetary Physics at California Institute of Technology. Since 2005 he has also been a...
, Frank Shu
Frank Shu
Frank Shu , is an astrophysicist, author and professor of astronomy at the University of California, Berkeley and University of California, San Diego and the university president of the National Tsing Hua University....
, and others applied density wave theory to the rings of Saturn
Rings of Saturn
The rings of Saturn are the most extensive planetary ring system of any planet in the Solar System. They consist of countless small particles, ranging in size from micrometres to metres, that form clumps that in turn orbit about Saturn...
. Saturn's rings (particularly the A Ring) contain a great many spiral density waves and spiral bending waves excited by Lindblad resonances and vertical resonances (respectively) with Saturn's moons. The physics are largely the same as with galaxies, though spiral waves in Saturn's rings are much more tightly wound (extending a few hundred kilometers at most) due to the very large central mass (Saturn itself) compared to the mass of the disk. The Cassini mission
Cassini-Huygens
Cassini–Huygens is a joint NASA/ESA/ASI spacecraft mission studying the planet Saturn and its many natural satellites since 2004. Launched in 1997 after nearly two decades of gestation, it includes a Saturn orbiter and an atmospheric probe/lander for the moon Titan, although it has also returned...
has revealed very small density waves excited by the ring-moons Pan
Pan (moon)
Pan is the innermost moon of Saturn. It is a walnut-shaped small moon about 35 kilometres across and 23 km high that orbits within the Encke Gap in Saturn's A Ring. Pan acts as a ring shepherd and is responsible for keeping the Encke Gap free of ring particles.It was discovered by Mark R...
and Atlas
Atlas (moon)
Atlas is an inner satellite of Saturn.Atlas was discovered by Richard Terrile in 1980 from Voyager photos and was designated '. In 1983 it was officially named after Atlas of Greek mythology, because it "holds the rings on its shoulders" like the Titan Atlas held the sky up above the Earth...
and by high-order resonances with the larger moons, as well as waves whose form changes with time due to the varying orbits of Janus
Janus (moon)
Janus is an inner satellite of Saturn. It is also known as Saturn X . It is named after the mythological Janus.-Discovery and orbit:Janus occupies practically the same orbit as the moon Epimetheus...
and Epimetheus
Epimetheus (moon)
Epimetheus is an inner satellite of Saturn. It is also known as Saturn XI. It is named after the mythological Epimetheus, brother of Prometheus.-Discovery:Epimetheus occupies essentially the same orbit as the moon Janus...
.
External sources
- Bertin, Giuseppe. 2000. Dynamics of Galaxies. Cambridge: Cambridge University Press.
- Bertin, G. and C.C. Lin. 1996. Spiral Structure in Galaxies: A Density Wave Theory. Cambridge: MIT Press.
- C.C. Lin, Yuan, C., and F.H. Shu, "On the Spiral Structure of Disk i Galaxies III. Comparison with Observations", Ap.J. 155, 721 (1969). (SCI)
- Yuan, C.,"Application of Density-Wave Theory to the Spiral Structure of the Milky Way System I. Systematic Motion of Neutral Hydrogen", Ap.J., 158, 871 (1969). (SCI)
External links
- Britannica.com: Density Wave Theory (galactic structure)
- Internet Encyclopedia of Science: Density Wave
- UOttawa FactGuru: Density Wave Theory
See also
- Magellanic spiral galaxy
- Barred spiral galaxyBarred spiral galaxyA barred spiral galaxy is a spiral galaxy with a central bar-shaped structure composed of stars. Bars are found in approximately two-thirds of all spiral galaxies...
- Spiral galaxySpiral galaxyA 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...
- GalaxyGalaxyA 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...