An Etymological Dictionary of Astronomy and Astrophysics
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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.

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)mv²  >  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 = (2MG/R)^1/2. Hydrogen molecules (H₂) 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 ~ (2kT/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.

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.

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_s²/Gρ)^1/2 = 0.2 pc (T/10 K)^1/2(n_H2/10⁴ 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.

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 ^-3/2ρ₀^-1/2c_s³, where G is the → gravitational constant, ρ₀ 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 cm³. High density favors collapse, while high temperature favors larger Jeans mass. See also: → thermal Jeans mass, → turbulent Jeans mass.

→ Jeans; → mass.

Same as → Jeans length.

→ Jeans; → scale.

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 (8πkT/λ⁴). 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.

The part of → electromagnetic spectrum approximated by the → Rayleigh-Jeans law.

→ Rayleigh; → Jeans; → spectrum.

The → Jeans mass when → turbulence is insignificant.

→ thermal; → Jeans; → mass.

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.