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Stellar Winds

Red: Radiation driven wind

Blue: Without driving force

Singularity of isothermal, radiation-dust driven wind

\frac{1}{v}\frac{dv}{dr}=\frac{\frac{2a^2}{r}-\frac{GM}{r^2}+\frac{A}{r^2}}{v^2-a^2}

Nature of dust driven wind - momentum coupling

Gas momentum equation

\rho_g(\frac{\partial u_g}{\partial t}+u_g\cdot\nabla u_g)=-\nabla p_g+\rho_g g+f_{drag}

Dust momentum equation

\rho_d(\frac{\partial u_d}{\partial t}+u_d\cdot\nabla u_d)=-\nabla p_d+\rho_g g-f_{drag}+f_{rad}

f_{drag}=\pi b^2\rho_g w_{dr}\sqrt{w_{dr}^2+a_g^2}

f_{drag}: Drag force on gas

w_{dr}=u_d-u_g: Drift velocity

b: Radius of dust grain

a_g: Sound speed of gas

We can argue that as dust grain moving through gas, drag force can "immediately" let dust velocity relax to a proper drift velocity with respect to gas. Therefore it is approximately quasi-static everywhere and drag force should be balanced by radiation force and any other forces. Usually radiation force and drag force can be balanced.

f_{drag}=f_{rad}=\frac{\pi b^2 Q_{rp} L_*}{4\pi r^2 c}

Where Q_{rp} is radiation pressure mean efficiency, it consist of Planck mean absorption efficiency and scattering mean efficiency and is dependent on the properties of light and dust grain. Such as radius and mass of dust grain, constituents of dust grain, wavelength of light and light spectroscopy. Further, formation of dust grain is relevant to the stage of the star.

L_* luminosity of the star

At last, equate drag force and radiation force will give:

w_{dr}=\sqrt{\frac{Q_{rp} L_*}{4\pi r^2 \rho_g c}}=\sqrt{\frac{Q_{rp} L_* u_g}{\dot{M}c}}

Posted: 11 years ago (Updated: 11 years ago)
Author: Zhuo Chen
Categories: (none)

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Stellar Winds

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