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The Eddington luminosity, also referred to as the Eddington limit, is the maximum luminosity a body (such as a star) can achieve when there is balance between the force of radiation acting outward and the gravitational force acting inward. The state of balance is called hydrostatic equilibrium. When a star exceeds the Eddington luminosity, it will initiate a very intense radiation-driven stellar wind from its outer layers. Since most massive stars have luminosities far below the Eddington luminosity, their winds are mostly driven by the less intense line absorption. The Eddington limit is invoked to explain the observed luminosity of accreting black holes such as quasars. Originally, Sir Arthur Stanley Eddington took only the electron scattering into account when calculating this limit, something that now is called the classical Eddington limit. Nowadays, the modified Eddington limit also counts on other radiation processes such as bound-free and free-free radiation (see Bremsstrahlung) interaction. ==Derivation== The limit is obtained by setting the outward radiation pressure equal to the inward gravitational force. Both forces decrease by inverse square laws, so once equality is reached, the hydrodynamic flow is different throughout the star. From Euler's equation in hydrostatic equilibrium, the mean acceleration is zero, : where is the velocity, is the pressure, is the density, and is the gravitational potential. If the pressure is dominated by radiation pressure associated with a radiation flux , : Here is the opacity of the stellar material. For ionized hydrogen , where is the Thomson scattering cross-section for the electron and is the mass of a proton. The luminosity of a source bounded by a surface is : Now assuming that the opacity is a constant, it can be brought outside of the integral. Using Gauss's theorem and Poisson's equation gives : where is the mass of the central object. This is called the Eddington Luminosity.〔Rybicki, G.B., Lightman, A.P.: ''Radiative Processes in Astrophysics'', New York: J. Wiley & Sons 1979.〕 For pure ionized hydrogen : where ☉ the mass of the Sun and ☉ the luminosity of the Sun. The maximum luminosity of a source in hydrostatic equilibrium is the Eddington luminosity. If the luminosity exceeds the Eddington limit, then the radiation pressure drives an outflow. The mass of the proton appears because, in the typical environment for the outer layers of a star, the radiation pressure acts on electrons, which are driven away from the center. Because protons are negligibly pressured by the analog of Thomson scattering, due to their larger mass, the result is to create a slight charge separation and therefore a radially directed electric field, acting to lift the positive charges, which are typically free protons under the conditions in stellar atmospheres. When the outward electric field is sufficient to levitate the protons against gravity, both electrons and protons are expelled together. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Eddington luminosity」の詳細全文を読む スポンサード リンク
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