Lindblad resonance
Encyclopedia
A Lindblad resonance, named for the Swedish galactic astronomer Bertil Lindblad
, is an orbital resonance
in which an object's epicyclic frequency
(the rate at which one periapse follows another) is a simple multiple of some forcing frequency
. Resonances of this kind tend to increase the object's orbital eccentricity
and to cause its longitude of periapse to line up in phase with the forcing. Lindblad resonances drive spiral density waves
both in galaxies (where stars are subject to forcing by the spiral arms themselves) and in Saturn's rings
(where ring particles are subject to forcing by Saturn's moons).
Lindblad resonances affect stars at such distances from a disc galaxy
's centre where the natural frequency of the radial component of a star's orbital velocity is close to the frequency of the gravitational potential maxima encountered during its course through the spiral arms. If a star's orbital speed around the galactic centre is greater than that of the part of the spiral arm through which it is passing, then an inner Lindblad resonance occurs - if smaller, then an outer Lindblad resonance. At an inner resonance, a star's orbital speed is increased, moving the star outwards, and decreased for an outer resonance causing inward movement.
Bertil Lindblad
Bertil Lindblad Bertil Lindblad Bertil Lindblad (Örebro, 26 November 1895 – Saltsjöbaden (outside Stockholm, 25 June 1965) was a Swedish astronomer.After finishing his secondary education at Örebro högre allmänna läroverk, Lindblad matriculated at Uppsala University in 1914...
, is an orbital resonance
Orbital resonance
In celestial mechanics, an orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital periods being related by a ratio of two small integers. Orbital resonances greatly enhance the mutual gravitational influence of...
in which an object's epicyclic frequency
Epicyclic 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"...
(the rate at which one periapse follows another) is a simple multiple of some forcing frequency
Harmonic oscillator
In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x: \vec F = -k \vec x \, where k is a positive constant....
. Resonances of this kind tend to increase the object's orbital eccentricity
Orbital eccentricity
The orbital eccentricity of an astronomical body is the amount by which its orbit deviates from a perfect circle, where 0 is perfectly circular, and 1.0 is a parabola, and no longer a closed orbit...
and to cause its longitude of periapse to line up in phase with the forcing. Lindblad resonances drive spiral density waves
Density wave theory
Density wave theory or the Lin-Shu density wave theory is a theory proposed by C.C. Lin and Frank Shu in the mid-1960s to explain spiral arm structure of spiral galaxies. Their theory introduces the idea of long-lived quasistatic density waves , which are sections of the galactic disk that have...
both in galaxies (where stars are subject to forcing by the spiral arms themselves) and in 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...
(where ring particles are subject to forcing by Saturn's moons).
Lindblad resonances affect stars at such distances from a disc galaxy
Disc galaxy
Disc galaxies are galaxies which have discs, a flattened circular volume of stars. These galaxies may, or may not include a central non-disc-like region .Disc galaxy types include* spiral galaxies** barless spiral galaxies...
's centre where the natural frequency of the radial component of a star's orbital velocity is close to the frequency of the gravitational potential maxima encountered during its course through the spiral arms. If a star's orbital speed around the galactic centre is greater than that of the part of the spiral arm through which it is passing, then an inner Lindblad resonance occurs - if smaller, then an outer Lindblad resonance. At an inner resonance, a star's orbital speed is increased, moving the star outwards, and decreased for an outer resonance causing inward movement.