A radiation zone, or radiative region is a layer of a star's interior where energy is primarily transported toward the exterior by means of radiative diffusion and thermal conduction, rather than by convection.[1] Energy travels through the radiation zone in the form of electromagnetic radiation as photons.
Matter in a radiation zone is so dense that photons can travel only a short distance before they are absorbed or scattered by another particle, gradually shifting to longer wavelength as they do so. For this reason, it takes an average of 171,000 years for gamma rays from the core of the Sun to leave the radiation zone. Over this range, the temperature of the plasma drops from 15 million K near the core down to 1.5 million K at the base of the convection zone.[2]
Temperature gradient
In a radiative zone, the temperature gradient—the change in temperature (T) as a function of radius (r)—is given by:
\( {\displaystyle {\frac {{\text{d}}T(r)}{{\text{d}}r}}\ =\ -{\frac {3\kappa (r)\rho (r)L(r)}{(4\pi r^{2})(16\sigma _{B})T^{3}(r)}}} \)
where κ(r) is the opacity, ρ(r) is the matter density, L(r) is the luminosity, and σB is the Stefan–Boltzmann constant.[1] Hence the opacity (κ) and radiation flux (L) within a given layer of a star are important factors in determining how effective radiative diffusion is at transporting energy. A high opacity or high luminosity can cause a high temperature gradient, which results from a slow flow of energy. Those layers where convection is more effective than radiative diffusion at transporting energy, thereby creating a lower temperature gradient, will become convection zones.[3]
This relation can be derived by integrating Fick's first law over the surface of some radius r, giving the total outgoing energy flux which is equal to the luminosity by conservation of energy:
\( {\displaystyle L=-4\pi \,r^{2}D{\frac {\partial u}{\partial r}}} \)
Where D is the photons diffusion coefficient, and u is the energy density.
The energy density is related to the temperature by Stefan-Boltzmann law by:
\( {\displaystyle U={\frac {4}{c}}\,\sigma _{B}\,T^{4}} \)
Finally, as in the elementary theory of diffusion coefficient in gases, the diffusion coefficient D approximately satisfies:
\( {\displaystyle D={\frac {1}{3}}c\,\lambda } \)
where λ is the photon mean free path, and is the reciprocal of the opacity κ.
Eddington stellar model
Eddington assumed the pressure P in a star is a combination of an ideal gas pressure and radiation pressure, and that there is a constant ratio, β, of the gas pressure to the total pressure. Therefore, by the ideal gas law:
\)
\( {\displaystyle \beta P=k_{B}{\frac {\rho }{\mu }}T}
where kB is Boltzmann constant and μ the mass of a single atom (actually, an ion since matter is ionized; usually a hydrogen ion, i.e. a proton). While the radiation pressure satisfies:
\( {\displaystyle 1-\beta ={\frac {P_{\text{radiation}}}{P}}={\frac {u}{3P}}={\frac {4\sigma _{B}}{3c}}{\frac {T^{4}}{P}}} \)
so that T4 is proportional to P throughout the star.
This gives the polytropic equation (with n=3):[4]
\( {\displaystyle P=\left({\frac {3ck_{B}^{4}}{4\sigma _{B}\mu ^{4}}}{\frac {1-\beta }{\beta ^{4}}}\right)^{1/3}\rho ^{4/3}} \)
Using the hydrostatic equilibrium equation, the second equation becomes equivalent to:
\( {\displaystyle -{\frac {GM\rho }{r^{2}}}={\frac {{\text{d}}P}{{\text{d}}r}}={\frac {16\sigma _{B}}{3c(1-\beta )}}T^{3}{\frac {{\text{d}}T}{{\text{d}}r}}} \)
For energy transmission by radiation only, we may use the equation for the temperature gradient (presented in the previous subsection) for the right-hand side and get
\( {\displaystyle GM={\frac {\kappa L}{4\pi c(1-\beta )}}} \)
Thus the Eddington model is a good approximation in the radiation zone as long as κL/M is approximately constant, which is often the case.[4]
Stability against convection
See also: Natural convection
The radiation zone is stable against formation of convection cells if the density gradient is high enough, so that an element moving upwards has its density lowered (due to adiabatic expansion) less than the drop in density of its surrounding, so that it will experience a net buoyancy force downwards.
The criterion for this is:
\( {\displaystyle {\frac {{\text{d}}\,log\,\rho }{{\text{d}}\,log\,P}}>{\frac {1}{\gamma _{ad}}}} \)
where P is the pressure, ρ the density and \( {\displaystyle \gamma _{ad}} \) is the heat capacity ratio.
For a homogenic ideal gas, this is equivalent to:
\( {\displaystyle {\frac {{\text{d}}\,log\,T}{{\text{d}}\,log\,P}}<1-{\frac {1}{\gamma _{ad}}}} \)
We can calculate the left-hand side by dividing the equation for the temperature gradient by the equation relating the pressure gradient to the gravity acceleration g:
\( {\displaystyle {\frac {{\text{d}}P(r)}{{\text{d}}r}}\ =\ g\rho \ =\ {\frac {G\,M(r)\,\rho (r)}{r^{2}}}}
\)
M(r) being the mass within the sphere of radius r, and is approximately the whole star mass for large enough r.
This gives the following form of the Schwarzschild criterion for stability against convection:[4]
\( {\displaystyle {\frac {3}{64\pi \sigma _{B}\,G}}{\frac {\kappa \,L}{M}}{\frac {P}{T^{4}}}<1-{\frac {1}{\gamma _{ad}}}} \)
Note that for non-homogenic gas this criterion should be replaced by the Ledoux criterion, because the density gradient now also depends on concentration gradients.
For a polytrope solution with n=3 (as in the Eddington stellar model for radiation zone), P is proportional to T4 and the left-hand side is constant and equals 1/4, smaller than the ideal monoatomic gas approximation for the right-hand side giving \( {\displaystyle 1-1/\gamma _{ad}=2/5} \). This explains the stability of the radiation zone against convection.
However, at a large enough radius, the opacity κ increases due to the decrease in temperature (by Kramers' opacity law), and possibly also due to a smaller degree of ionization in the lower shells of heavy elements ions.[5] This leads to a violation of the stability criterion and to the creation of the convection zone; in the sun, opacity increases by more than a tenfold across the radiation zone, before the transition to the convection zone happens.[6]
Additional situations in which this stability criterion is not met are:
Large values of \( {\displaystyle L(r)/M(r)} \(, which may happen towards the star core's center, where M(r) is small, if nuclear energy production is strongly peaked at the center, as in relatively massive stars. Thus such stars have a convective core.
A smaller value of \( {\displaystyle \gamma _{ad}} \). For semi-ionized gas, where approximately half of the atoms are ionized, the effective value of \( {\displaystyle \gamma _{ad}} \)drops to 6/5,[7] giving \( {\displaystyle 1-1/\gamma _{ad}=1/6} \). Therefore, all stars have shallow convection zones near their surfaces, at low enough temperatures where ionization is only partial.
Main sequence stars
For main sequence stars—those stars that are generating energy through the thermonuclear fusion of hydrogen at the core, the presence and location of radiative regions depends on the star's mass. Main sequence stars below about 0.3 solar masses are entirely convective, meaning they do not have a radiative zone. From 0.3 to 1.2 solar masses, the region around the stellar core is a radiation zone, separated from the overlying convection zone by the tachocline. The radius of the radiative zone increases monotonically with mass, with stars around 1.2 solar masses being almost entirely radiative. Above 1.2 solar masses, the core region becomes a convection zone and the overlying region is a radiation zone, with the amount of mass within the convective zone increasing with the mass of the star.[8]
The Sun
In the Sun, the region between the solar core at 0.2 of the Sun's radius and the outer convection zone at 0.71 of the Sun's radius is referred to as the radiation zone, although the core is also a radiative region.[1] The convection zone and the radiation zone are divided by the tachocline, another part of the Sun.
Notes and references
Ryan, Sean G.; Norton, Andrew J. (2010), Stellar Evolution and Nucleosynthesis, Cambridge University Press, p. 19, ISBN 0-521-19609-4
Elkins-Tanton, Linda T. (2006), The Sun, Mercury, and Venus, Infobase Publishing, p. 24, ISBN 0-8160-5193-3
LeBlanc, Francis (2010), An Introduction to Stellar Astrophysics (1st ed.), John Wiley and Sons, p. 168, ISBN 1-119-96497-0
O.R. Pols (2011), Stellar Structure and Evolution, Astronomical Institute Utrecht, September 2011, pp. 64–68
Krief, M., Feigel, A., & Gazit, D. (2016). Solar opacity calculations using the super-transition-array method. The Astrophysical Journal, 821(1), 45.
Turck-Chieze, S., & Couvidat, S. (2011). Solar neutrinos, helioseismology and the solar internal dynamics. Reports on Progress in Physics, 74(8), 086901.
O.R. Pols (2011), Stellar Structure and Evolution, Astronomical Institute Utrecht, September 2011, p. 37
Padmanabhan, Thanu (2001), Theoretical Astrophysics: Stars and stellar systems, Theoretical Astrophysics, 2, Cambridge University Press, p. 80, ISBN 0-521-56631-2
External links
SOHO ... Solar and Heliospheric Observatory — official site of this NASA and ESA joint project.
Animated explanation of the Radiation zone (University of South Wales).
Animated explanation of the temperature and density of the Radiation zone (University of South Wales).
vte
The Sun
Internal structure
Core Radiation zone Tachocline Convection zone
The Sun by the Atmospheric Imaging Assembly of NASA's Solar Dynamics Observatory - 20100819.jpg
Atmosphere
Photosphere
Supergranulation Granule Faculae Sunspot
Chromosphere
Plage Spicule Moreton wave
Corona
Transition region Coronal hole Coronal loop Coronal mass ejection Prominence Helmet streamer Supra-arcade downflows
Variation
Solar cycle
List of solar cycles Solar maximum Solar minimum Wolf number Solar wind Flare Helioseismology
Heliosphere
Current sheet Termination shock Heliosheath Heliopause Bow shock
Related
Eclipse Heliophysics In culture
solar deities Solar activity Solar astronomy Solar dynamo Solar energy Solar neutrino Solar observation Solar phenomena Solar physics Solar System Solar telescope Solar time Space climate Space weather Standard solar model Star Sunlight radiation
Spectral class: G-type main-sequence star
vte
Accretion Molecular cloud Bok globule Young stellar object
Protostar Pre-main-sequence Herbig Ae/Be T Tauri FU Orionis Herbig–Haro object Hayashi track Henyey track
Main sequence Red-giant branch Horizontal branch
Red clump Asymptotic giant branch
super-AGB Blue loop Protoplanetary nebula Planetary nebula PG1159 Dredge-up OH/IR Instability strip Luminous blue variable Blue straggler Stellar population Supernova Superluminous supernova / Hypernova
Early Late Main sequence
O B A F G K M Brown dwarf WR OB Subdwarf
O B Subgiant Giant
Blue Red Yellow Bright giant Supergiant
Blue Red Yellow Hypergiant
Yellow Carbon
S CN CH White dwarf Chemically peculiar
Am Ap/Bp HgMn Helium-weak Barium Extreme helium Lambda Boötis Lead Technetium Be
Shell B[e]
White dwarf
Helium planet Black dwarf Neutron
Radio-quiet Pulsar
Binary X-ray Magnetar Stellar black hole X-ray binary
Burster
Hypothetical
Blue dwarf Green Black dwarf Exotic
Boson Electroweak Strange Preon Planck Dark Dark-energy Quark Q Black Gravastar Frozen Quasi-star Thorne–Żytkow object Iron Blitzar
Deuterium burning Lithium burning Proton–proton chain CNO cycle Helium flash Triple-alpha process Alpha process Carbon burning Neon burning Oxygen burning Silicon burning S-process R-process Fusor Nova
Symbiotic Remnant Luminous red nova
Structure
Core Convection zone
Microturbulence Oscillations Radiation zone Atmosphere
Photosphere Starspot Chromosphere Stellar corona Stellar wind
Bubble Bipolar outflow Accretion disk Asteroseismology
Helioseismology Eddington luminosity Kelvin–Helmholtz mechanism
Properties
Designation Dynamics Effective temperature Luminosity Kinematics Magnetic field Absolute magnitude Mass Metallicity Rotation Starlight Variable Photometric system Color index Hertzsprung–Russell diagram Color–color diagram
Star systems
Binary
Contact Common envelope Eclipsing Symbiotic Multiple Cluster
Open Globular Super Planetary system
Earth-centric
observations
Sun
Solar System Sunlight Pole star Circumpolar Constellation Asterism Magnitude
Apparent Extinction Photographic Radial velocity Proper motion Parallax Photometric-standard
Lists
Proper names
Arabic Chinese Extremes Most massive Highest temperature Lowest temperature Largest volume Smallest volume Brightest
Historical Most luminous Nearest
Nearest bright With exoplanets Brown dwarfs White dwarfs Milky Way novae Supernovae
Candidates Remnants Planetary nebulae Timeline of stellar astronomy
Related articles
Substellar object
Brown dwarf Sub-brown dwarf Planet Galactic year Galaxy Guest Gravity Intergalactic Planet-hosting stars Tidal disruption event
Hellenica World - Scientific Library
Retrieved from "http://en.wikipedia.org/"
All text is available under the terms of the GNU Free Documentation License
