An Etymological Dictionary of Astronomy and Astrophysics
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The evolution over time of a gravitationally → bound system consisting of N components because of encounters between the components, as studied in → stellar dynamics. Due to this process, in a → star cluster, → low-mass stars may acquire larger random velocities, and consequently occupy a larger volume than → high-mass stars. As a result, massive stars sink to the cluster centre on a time-scale that is inversely proportional to their mass. See also → mass segregation.

→ dynamical; → relaxation.

The process by which a magnetic system relaxes to its minimum energy state over time.

→ magnetic; → relaxation.

A process in which a molecule relaxes without emitting a → photon.

→ radiation; → -less; → relaxation.

To lessen the force, strength or intensity of something.

m M.E., from O.Fr. relaxer from L. relaxare "relax, loosen, open," from → re- "back" + laxare "loosen," from laxus "loose."

Vâhelidan, from vâ-, → re-, + helidan, heštan "to place, put" from Mid.Pers. hištan, hilidan "to let, set, leave, abandon;" Parthian Mid.Pers. hyrz; O.Pers. hard- "to send forth," ava.hard- "to abandon;" Av. harəz- "to discharge, send out; to filter," hərəzaiti "releases, shoots;" cf. Skt. srj- "to let go or fly, throw, cast, emit, put forth;" Pali sajati "to let loose, send forth."

1) The evolution of the properties of a physical system which has been disturbed and which regains its equilibrium condition once the disturbing action has ceased. Relaxation is the response of the system to the perturbation. The time required by the system to regain its condition of minimum energy is called the → relaxation time.
2) Math.: In numerical analysis, a method of solving equations in which the errors, or residuals, resulting from an initial approximation are reduced by succeeding approximations until finally all are within the toleration limit.

Verbal noun of → relax.

The characteristic length of time that is required for a system undergoing → relaxation to move to its equilibrium state. If the system follows an exponential law G = G₀ exp(-t / τ), the relaxation time is the time required for G to obtain the fraction 1/e of its initial value G₀.

→ relaxation; → time.

A → dynamical system that has regained its → equilibrium. Especially a system in which the kinetic and potential energies obey a specific relationship known as the → virial theorem.

P.p. from relax, → relaxation.

A process whereby stellar orbit relaxation can be dramatically enhanced in orbits in a nearly Keplerian star cluster close to a → massive black hole (MBH). This process can modify the angular momentum distribution and affect the interaction rates of the stars with the MBH more efficiently than non-resonant relaxation. In the standard relaxation picture, each encounter is random and uncorrelated, so stars undergo a random walk. Relaxation is driven by the diffusion of energy which then leads to angular momentum transfer. However, in a stellar cluster around a MBH, each star will be on a Keplerian orbit, which is a fixed ellipse in space. The orbits of two nearby stars will thus exert correlated torques on one another, which can lead to a direct resonant evolution of the angular momentum. Since resonant relaxation increases the rate of angular momentum scattering, stars reach highly eccentric orbits more rapidly where they can become → extreme mass ratio inspiral (EMRI)s (Rauch, K.P., Tremaine, S., 1996, arXiv:astro-ph/9603018; Gair J.R. et al. 2013, Living Rev. Relativity, 16, (2013), 7 http://www.livingreviews.org/lrr-2013-7, doi:10.12942/lrr-2013-7).

→ resonant; → relaxation.

A process in which a dynamical system made up of many objects (star cluster, galaxy cluster) rapidly relaxes from a chaotic initial state to a quasi-equilibrium.

→ violent; → relaxation.