Past exam of the astrophysical fluid dynamics course of the University of Cambridge / 2015 / Paper 1 / 4 / d

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- Solution d

Solution

For a steady spherical wind, conservation of mass gives

\dot{M}_{w} = 4 π r^{2} ρ (r) v (r) = 4 π R_{e}^{2} m_{H} n_{e} \frac{2 G M _{*}}{R _{e}} .

Thus

\dot{M}_{w} = 4 π m_{H} n_{e} 2 G M_{*} R_{e}^{3/2} ≃ 7.99 \times 1 0^{9} kg s^{- 1} ≃ 1.27 \times 1 0^{- 13} M_{⊙} y r^{- 1} .

Here

n_{e}

denotes the given number density at the escape radius, rather than electron density; the composition is atomic hydrogen. The reference speed is

v_{e} ≃ 4.22 \times 1 0^{4} m s^{- 1}

. This boundary flux remains fixed even if pressure changes the subsequent radial velocity profile.

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