جینز Jeans
*Fr.: Jeans*
Sir James Hopwood Jeans (1877-1946), English mathematical physicist,
astrophysicist, and popularizer of science. He made important contributions
to theoretical astrophysics, especially to the theory of stellar formation.
→ *Jeans escape*,
→ *Jeans instability*,
→ *Jeans length*,
→ *Jeans mass*,
→ *Jeans scale*,
→ *Rayleigh-Jeans law*,
→ *Rayleigh-Jeans spectrum*,
→ *thermal Jeans mass*,
→ *turbulent Jeans mass*,
→ *Jeans escape*. |

گریز ِ جینز goriz-e Jeans
*Fr.: échappement de Jeans*
A → *thermal escape*
process by which the atmosphere of a planet loses gases to outer space.
This form of thermal escape occurs because some molecules, especially low mass ones,
are within the higher-velocity
end of the → *Maxwell-Boltzmann distribution*.
The possibility for the gases to escape occurs when
the thermal energy of air molecules becomes
greater than the → *gravitational potential energy*
of the planet:
(3/2)*kT* = (1/2)*mv*^{2} > *GmM*/*R* where *v*
is upward velocity of a molecule of mass
*m*, *M* is the mass of the planet, and *R* is the radius of the planet
at which thermal escape occurs.
The minimum velocity for which this can work is called the
→ *escape velocity* is:
*v*_{e} = (2*MG*/*R*)^{1/2}.
Hydrogen molecules (H_{2}) and helium, or their ions tend to
have velocities high enough so that they are not bound by Earth's
gravitational field and are lost to space from the top of the
atmosphere.
This process is important for the loss of hydrogen, a low-mass
species that more easily attains escape speed at a given
temperature, because *v* ~ (2*kT*/*m*)^{1/2}.
As such, Jeans' escape was likely influential in the
atmospheric evolution of all the early terrestrial planets. Jeans'
escape currently accounts for a non-negligible fraction of hydrogen
escaping from Earth, Mars, and Titan, but it is negligible for Venus
because of a cold upper atmosphere combined with relatively high
gravity
(see, e.g., Catling, D. C. and Kasting, J. F., 2017, Escape of Atmospheres to
Space, pp.
129-167. Cambridge University Press). → *Jeans*; → *escape*. |

ناپایداری ِ جینز nâpâydâri-ye Jeans
*Fr.: instabilité de Jeans*
An instability that occurs in a → *self-gravitating*
→ *interstellar cloud* which is in
→ *hydrostatic equilibrium*.
Density fluctuations caused by a perturbation may condense the material
leading to the domination of gravitational force
and the cloud collapse. The advent of instability involves a threshold called
the → *Jeans length* or the → *Jeans mass*. → *Jeans*; → *instability*. |

درازای ِ جینز derâzâ-ye Jeans (#)
*Fr.: longueur de Jeans*
The critical size of a homogeneous and isothermal interstellar
cloud above which the cloud is unstable and must collapse under its own gravity.
Below this size the cloud's internal pressure is sufficient to resist collapse.
The Jeans length is defined by:
*λ*_{J} = (π c_{s}^{2}/Gρ)^{1/2}
= 0.2 pc (*T*/10 K)^{1/2}(*n*_{H2}/10^{4}
cm^{-3})^{-1/2},
where *c*_{s} is the → *sound speed*, *G* is the
→ *gravitational constant*, ρ is the gas density,
*T* is the gas temperature, and *n*_{H2} is the
molecular hydrogen density. → *Jeans*; → *length*. |

جرم ِ جینز jerm-e Jeans (#)
*Fr.: masse de Jeans*
The → *minimum*
mass for an → *interstellar* cloud below which the
→ *thermal pressure* of the gas prevents its
→ *collapse*
under the force of its own → *gravity*.
It is given by the formula *M*_{J} =
(π^{5/2} / 6) *G*^{ -3/2}ρ_{0}^{-1/2}*c*_{s}^{3}, where *G* is the
→ *gravitational constant*, ρ_{0} the
initial → *density*,
and *c*_{s} the isothermal → *sound speed*.
It can be approximated to *M*_{J}
~ 45 (*T*_{K}) ^{3/2} (*n*_{cm-3})^{ -1/2}
in units of solar masses, where *T*_{K} is the temperature in
→ *Kelvin*, and
*n*_{cm-3} the gas density per cm^{3}. High density favors
collapse, while high temperature favors larger Jeans mass. See also:
→ *thermal Jeans mass*,
→ *turbulent Jeans mass*. → *Jeans*; → * mass*. |

مرپل ِ جینز marpel-e Jeans
*Fr.: échelle de Jeans*
Same as → *Jeans length*. → *Jeans*; → *scale*. |

قانون ِ ریلی-جینز qânun-e Rayleigh-Jeans(#)
*Fr.: loi de Rayleigh-Jeans*
A classical law approximately describing the intensity of radiation
emitted by a → *blackbody*. It states that this intensity is
proportional to the temperature divided by the fourth power of the wavelength
(8π*kT*/λ^{4}). The Rayleigh-Jeans law is a good approximation
to the experimentally verified Planck radiation formula only at long wavelengths.
At short wavelengths it runs into a paradox named the
→ *ultraviolet catastrophe*. → *Rayleigh*; → *Jeans*;
→ *law*. |

بیناب ِ ریلی-جینز binâb-e Rayleigh-Jeans
*Fr.: spectre Rayleigh-Jeans*
The part of → *electromagnetic spectrum* approximated by the
→ *Rayleigh-Jeans law*. → *Rayleigh*; → *Jeans*;
→ *spectrum*. |

جرم ِ جینز ِ گرمایی jerme-e Jeans-e garmâyi
*Fr.: masse de Jeans thermique*
The → *Jeans mass* when → *turbulence*
is insignificant. → *thermal*;
→ *Jeans*; → *mass*. |

جرم ِ جینز ِ آشوبناک jerm-e Jeans-e âšubnâk
*Fr.: masse de Jeans turbulente*
The characteristic mass for → *cloud fragmentation*
in a → *turbulent* medium. While the standard
→ *Jeans mass*
depends simply on the gas mean → *density* and
→ *temperature*, and
fragmentation is purely gravitational, turbulent Jeans mass depends
strongly also on the → *Mach number*
(Chabrier et al. 2014, arXiv:1409.8466). → *turbulent*;
→ *Jeans*; → *mass*. |