In physics, radiative equilibrium is the condition where
a steady
state system is in dynamic equilibrium, with equal incoming and
outgoing radiative heat flux
and negligible heat transfer by conduction and convection.
In atmospheric physics, under conditions of
radiative equilibrium, total flux is constant with depth. In astrophysics,
radiative equilibrium is used to determine atmospheric radiation of stars. In climate
science, the net change in the tropopause
after temperatures readjust to radiative equilibrium in the stratosphere,
is used to determine the radiative
forcing, as part of an assessment of natural and anthropogenic climate
change.
Definitions
History
In 1791 Pierre Prevost showed that all bodies radiate heat
and concluded, Radiation will exactly compensate absorption. He used the
terms absolute and relative equilibrium to describe changes. Prevost considered
that what is nowadays called the photon gas
or electromagnetic radiation was a fluid
that he called "free heat" (French:
le feu). Prevost
proposed that free radiant heat is a very rare fluid, rays of which, like light
rays, pass through each other without detectable disturbance of their passage.
Prevost's called his theory movable equilibrium of heat, now designated
as the theory of exchanges, which stated that each body radiates to, and
receives radiation from, other bodies. The radiation from each body is emitted
regardless of the presence or absence of other bodies.
In 1906 Karl Schwarzschild postulated the radiative
equilibrium (German: Strahlungsgleichgewicht) dependent on Kirchhoff's law of thermal
radiation, when he studied the sun.
Pointwise radiative equilibrium
Following Planck (1914), a radiative field is often described in
terms of specific radiative intensity, which is
a function of each geometrical point in a space region, at an instant of time.
A detailed definition is given by Goody and Yung (1989). They think of the
interconversion between thermal radiation and heat in matter. From the specific
radiative intensity they derive
, the monochromatic vector flux density of radiation at each
point in a region of space, which is equal to the time averaged monochromatic Poynting
vector at that point (Mihalas 1978 on pages 9–11). They define the
monochromatic volume-specific rate of gain of heat by matter from radiation as
the negative of the divergence of the monochromatic flux density vector; it is
a scalar function of the position of the point:
.
They define (pointwise) monochromatic radiative
equilibrium by
at every point of the region that is in radiative
equilibrium.
They define (pointwise) radiative equilibrium by
at every point of the region that is in radiative
equilibrium.
This means that, at every point of the region of space that
is in (pointwise) radiative equilibrium, the total, for all frequencies of
radiation, interconversion of energy between thermal radiation and energy
content in matter is nil.
Approximate pointwise radiative equilibrium
Chandrasekhar writes of a model of a stellar atmosphere in which "there are no
mechanisms, other than radiation, for transporting heat within the atmosphere
... [and] there are no sources of heat in the atmosphere." This is hardly
different from Schwarzschild's 1906 approximate concept, but is more precisely
stated.
Exchange equilibrium between systems
Radiative exchange equilibrium occurs with thermodynamic
systems. Planck
(1914) refers to a condition of thermodynamic equilibrium, in which
"any two bodies or elements of bodies selected at random exchange by
radiation equal amounts of heat with each other."
The term radiative exchange equilibrium can also be
used to refer to two specified regions of space that exchange equal amounts of
radiation by emission and absorption (even when the steady state is not one of
thermodynamic equilibrium, but is one in which some sub-processes include net
transport of matter or energy including radiation).
Radiative equilibrium in astrophysics
Radiative equilibrium for a star, is taken as a
whole and not confining attention only to its atmosphere. And when the rate of
heat transfer from nuclear reactions plus viscosity to
the microscopic motions of the material particles of the star is balanced
by the transfer of energy by electromagnetic radiation from the star to space.
A star that is radiating energy to space cannot be in a
steady state of temperature distribution unless there is a steady supply of
energy from nuclear reactions within the star, to support the radiation to
space.
Planetary equilibrium temperature
is the theoretical temperature for a blackbody,
which does not consider a radiative atmosphere.
Radiative equilibrium in Earth sciences
Radiative equilibrium or radiative balance or
just energy balance, describe a steady
state net change of infrared radiation from Earth and shortwave radiation from outer space.
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