Radiative equilibrium is the condition where the total
thermal radiation
Thermal radiation is electromagnetic radiation generated by the thermal motion of particles in matter. Thermal radiation is generated when heat from the movement of charges in the material (electrons and protons in common forms of matter) is ...
leaving an object is equal to the total thermal radiation entering it. It is one of the several requirements for
thermodynamic equilibrium
Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermod ...
, but it can occur in the absence of thermodynamic equilibrium. There are various types of radiative equilibrium, which is itself a kind of
dynamic equilibrium
In chemistry, a dynamic equilibrium exists once a reversible reaction occurs. Substances transition between the reactants and products at equal rates, meaning there is no net change. Reactants and products are formed at such a rate that the conc ...
.
Definitions
Equilibrium, in general, is a state in which opposing forces are balanced, and hence a system does not change in time. Radiative equilibrium is the specific case of
thermal equilibrium
Two physical systems are in thermal equilibrium if there is no net flow of thermal energy between them when they are connected by a path permeable to heat. Thermal equilibrium obeys the zeroth law of thermodynamics. A system is said to be in ...
, for the case in which the exchange of heat is done by
radiative heat transfer
Thermal radiation is electromagnetic radiation generated by the thermal motion of particles in matter. Thermal radiation is generated when heat from the movement of charges in the material (electrons and protons in common forms of matter) is ...
.
There are several types of radiative equilibrium.
Prevost's definitions
An important early contribution was made by
Pierre Prevost in 1791.
Prevost considered that what is nowadays called the
photon gas
In physics, a photon gas is a gas-like collection of photons, which has many of the same properties of a conventional gas like hydrogen or neon – including pressure, temperature, and entropy. The most common example of a photon gas in equilibr ...
or
electromagnetic radiation
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, inf ...
was a fluid that he called "free heat". 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 theory of exchanges 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.
Prevost in 1791 offered the following definitions (translated):
''Absolute equilibrium'' of free heat is the state of this fluid in a portion of space which receives as much of it as it lets escape.
''Relative equilibrium'' of free heat is the state of this fluid in two portions of space which receive from each other equal quantities of heat, and which moreover are in absolute equilibrium, or experience precisely equal changes.
Prevost went on to comment that "The heat of several portions of space at the same temperature, and next to one another, is at the same time in the two species of equilibrium."
Pointwise radiative equilibrium
Following Planck (1914),
a radiative field is often described in terms of
specific radiative intensity In radiometry, spectral radiance or specific intensity is the radiance of a surface per unit frequency or wavelength, depending on whether the Spectral radiometric quantity, spectrum is taken as a function of frequency or of wavelength. The Internat ...
, which is a function of each geometrical point in a space region, at an instant of time.
[Mihalas, D., Weibel-Mihalas, B. (1984). ''Foundations of Radiation Hydrodynamics'', Oxford University Press, New York](_blank)
.[Goody, R.M., Yung, Y.L. (1989). ''Atmospheric Radiation. Theoretical Basis'', second edition, Oxford University Press, New York, 1989, .] This is slightly different from Prevost's mode of definition, which was for regions of space. It is also slightly conceptually different from Prevost's definition: Prevost thought in terms of bound and free heat while today we think in terms of heat in kinetic and other dynamic energy of molecules, that is to say heat in matter, and the thermal
photon gas
In physics, a photon gas is a gas-like collection of photons, which has many of the same properties of a conventional gas like hydrogen or neon – including pressure, temperature, and entropy. The most common example of a photon gas in equilibr ...
. 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
In physics, the Poynting vector (or Umov–Poynting vector) represents the directional energy flux (the energy transfer per unit area per unit time) or '' power flow'' of an electromagnetic field. The SI unit of the Poynting vector is the watt ...
at that point (Mihalas 1978
[Mihalas, D. (1978). ''Stellar Atmospheres'', 2nd edition, Freeman, San Francisco, .] 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(zero). Pointwise radiative equilibrium is closely related to Prevost's absolute radiative equilibrium.
Mihalas and Weibel-Mihalas (1984)
emphasise that this definition applies to a static medium, in which the matter is not moving. They also consider moving media.
Approximate pointwise radiative equilibrium
Karl Schwarzschild
Karl Schwarzschild (; 9 October 1873 – 11 May 1916) was a German physicist and astronomer.
Schwarzschild provided the first exact solution to the Einstein field equations of general relativity, for the limited case of a single spherical non-r ...
in 1906 considered a system in which
convection
Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the convec ...
and
radiation
In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium. This includes:
* ''electromagnetic radiation'', such as radio waves, microwaves, infrared, visi ...
both operated but radiation was so much more efficient than convection that convection could be, as an approximation, neglected, and radiation could be considered predominant. This applies when the temperature is very high, as for example in a star, but not in a planet's atmosphere.
Subrahmanyan Chandrasekhar
Subrahmanyan Chandrasekhar (; ) (19 October 1910 – 21 August 1995) was an Indian-American theoretical physicist who spent his professional life in the United States. He shared the 1983 Nobel Prize for Physics with William A. Fowler for "... ...
(1950, page 290) writes of a model of a
stellar atmosphere
The stellar atmosphere is the outer region of the volume of a star, lying above the stellar core, radiation zone and convection zone.
Overview
The stellar atmosphere is divided into several regions of distinct character:
* The photosphere, which ...
in which "there are no mechanisms, other than radiation, for transporting heat within the atmosphere ...
ndthere are no sources of heat in the surrounding" This is hardly different from Schwarzschild's 1906 approximate concept, but is more precisely stated.
Radiative exchange equilibrium
Planck
Max Karl Ernst Ludwig Planck (, ; 23 April 1858 – 4 October 1947) was a German theoretical physicist whose discovery of energy quanta won him the Nobel Prize in Physics in 1918.
Planck made many substantial contributions to theoretical p ...
(1914, page 40)
[Planck, M. (1914). ''The Theory of Heat Radiation'', second edition translated by M. Masius, P. Blakiston's Son and Co., Philadelphia, 1914.] refers to a condition of
thermodynamic equilibrium
Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermod ...
, 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
Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermod ...
, but is one in which some sub-processes include net transport of matter or energy including radiation). Radiative exchange equilibrium is very nearly the same as Prevost's relative radiative equilibrium.
Approximate radiative exchange equilibrium
To a first approximation, an example of radiative exchange equilibrium is in the exchange of non-
window
A window is an opening in a wall, door, roof, or vehicle that allows the exchange of light and may also allow the passage of sound and sometimes air. Modern windows are usually glazed or covered in some other transparent or translucent materia ...
wavelength thermal radiation between the land-and-sea surface and the lowest atmosphere, when there is a clear sky. As a first approximation (Swinbank 1963,
[Swinbank, W.C. (963). Long-wave radiation from clear skies, ''Quarterly Journal of the Royal Meteorological Society'', 89: 339–348.] Paltridge and Platt 1976, pages 139–140
[Paltridge, G.W., Platt, C.M.R., (1976). ''Radiative Processes in Meteorology and Climatology'', Elsevier, Amsterdam, .]), in the non-window
wavenumber
In the physical sciences, the wavenumber (also wave number or repetency) is the ''spatial frequency'' of a wave, measured in cycles per unit distance (ordinary wavenumber) or radians per unit distance (angular wavenumber). It is analogous to temp ...
s, there is zero net exchange between the surface and the atmosphere, while, in the window wavenumbers, there is simply direct radiation from the land-sea surface to space. A like situation occurs between adjacent layers in the turbulently mixed
boundary layer
In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a no-slip boundary condi ...
of the lower
troposphere
The troposphere is the first and lowest layer of the atmosphere of the Earth, and contains 75% of the total mass of the planetary atmosphere, 99% of the total mass of water vapour and aerosols, and is where most weather phenomena occur. From ...
, expressed in the so-called "cooling to space approximation", first noted by Rodgers and Walshaw (1966).
[Rodgers, C.D., Walshaw, C.D. (1966). The computation of infrared cooling rate in planetary atmospheres, ''Quarterly Journal of the Royal Meteorological Society'', 92: 67–92.][Paltridge, G.W., Platt, C.M.R., (1976). ''Radiative Processes in Meteorology and Climatology'', Elsevier, Amsterdam, , page 172.][Goody, R.M., Yung, Y.L. (1989). ''Atmospheric Radiation: Theoretical Basis'', 2nd edition, Oxford University Press, Oxford, New York, 1989, , page 250.][Wallace, J.M., Hobbs, P.V. (2006). ''Atmospheric Science: An Introductory Survey'', 2nd edition, Elsevier, Amsterdam, , page 138.]
In astronomy and planetary science
Global radiative equilibrium
Global radiative equilibrium can be defined for an entire passive celestial system that does not supply its own energy, such as a planet.
Liou (2002, page 459) and other authors use the term global radiative equilibrium to refer to radiative exchange equilibrium globally between Earth and extraterrestrial space; such authors intend to mean that, in the theoretical, incoming
solar radiation
Solar irradiance is the power per unit area (surface power density) received from the Sun in the form of electromagnetic radiation in the wavelength range of the measuring instrument.
Solar irradiance is measured in watts per square metre (W/m ...
absorbed by Earth's surface and its atmosphere would be equal to
outgoing longwave radiation
Outgoing Long-wave Radiation (OLR) is electromagnetic radiation of wavelengths from 3–100 μm emitted from Earth and its atmosphere out to space in the form of thermal radiation. It is also referred to as up-welling long-wave radiation an ...
from Earth's surface and its atmosphere. Prevost
would say then that the Earth's surface and its atmosphere regarded as a whole were in absolute radiative equilibrium. Some texts, for example Satoh (2004),
[Satoh, M. (2004). ''Atmospheric Circulation Dynamics and General Circulation Models'', Springer-Praxis, Chichester UK, , page 370.] simply refer to "radiative equilibrium" in referring to global exchange radiative equilibrium.
Planetary equilibrium temperature
The various global temperatures that may be theoretically conceived for any planet in general can be computed. Such temperatures include the ''planetary equilibrium temperature'', ''equivalent blackbody temperature'' or ''effective radiation emission temperature'' of the planet. This is related to (but not identical to) the measured
global-mean surface air temperature, which additionally incorporates the presence of an atmosphere.
A radiative equilibrium temperature is calculated for the case that the supply of energy from within the planet (for example, from
chemical
A chemical substance is a form of matter having constant chemical composition and characteristic properties. Some references add that chemical substance cannot be separated into its constituent elements by physical separation methods, i.e., wi ...
or
nuclear
Nuclear may refer to:
Physics
Relating to the nucleus of the atom:
* Nuclear engineering
*Nuclear physics
*Nuclear power
*Nuclear reactor
*Nuclear weapon
*Nuclear medicine
*Radiation therapy
*Nuclear warfare
Mathematics
*Nuclear space
*Nuclear ...
sources) is negligibly small; this assumption is reasonable for Earth, but fails, for example, for calculating the temperature of
Jupiter
Jupiter is the fifth planet from the Sun and the List of Solar System objects by size, largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but ...
, for which internal energy sources are larger than the incident solar radiation,
[Aumann, H. H.; Gillespie, C. M., Jr.; and Low, F. J. (July 1969)]
The Internal Powers and Effective Temperatures of Jupiter and Saturn
, ''Astrophysical Journal,'' 157 p. L69. DOI: 10.1086/180388. Retrieved 2019-06-19. and hence the actual temperature is higher than the theoretical radiative equilibrium.
Stellar equilibrium
A star supplies its own energy from nuclear sources, and hence the temperature equilibrium cannot be defined in terms of incident energy only.
Cox and Giuli (1968/1984)
[Cox, J.P. with Giuli, R.T. (1968, reprint 1984). ''Principles of Stellar Structure'', Gordon and Breach, New York, {{ISBN, 0-677-01950-5, page 134.] define 'radiative equilibrium' for a
star
A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...
, taken as a whole and not confining attention only to its atmosphere, when the rate of transfer as heat of energy from nuclear reactions plus
viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the inte ...
to the microscopic motions of the material particles of the star is just balanced by the transfer of energy by electromagnetic radiation from the star to space. Note that this radiative equilibrium is slightly different from the previous usage. They note that a star that is radiating energy to space cannot be in a steady state of temperature distribution unless there is a supply of energy, in this case, energy from nuclear reactions within the star, to support the radiation to space. Likewise the condition that is used for the above definition of pointwise radiative equilibrium cannot hold throughout a star that is radiating: internally, the star is in a
steady state
In systems theory, a system or a Process theory, process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those p ...
of temperature distribution, not internal thermodynamic equilibrium. Cox and Giuli's definition allows them to say at the same time that a star is in a steady state of temperature distribution and is in 'radiative equilibrium'; they are assuming that all the radiative energy to space comes from within the star.
Mechanisms of radiative equilibrium
When there is enough matter in a region to allow molecular collisions to occur very much more often than creation or annihilation of photons, for radiation one speaks of local thermodynamic equilibrium. In this case,
Kirchhoff's law of equality of radiative absorptivity and emissivity holds.
[Milne, E.A. (1928). The effect of collisions on monochromatic radiative equilibrium](_blank)
''Monthly Notices of the Royal Astronomical Society'' 88: 493–502
Two bodies in radiative exchange equilibrium, each in its own local thermodynamic equilibrium, have the same temperature and their radiative exchange complies with the
Stokes-Helmholtz reciprocity principle.
References
Thermodynamics