= Solution
For a steady spherical wind, <conservation of mass> gives
$$
\dot M_w=4\pi r^2\rho(r)v(r)
=4\pi R_e^2m_Hn_e\sqrt{\frac{2GM_*}{R_e}}.
$$
Thus
$$
\boxed{\dot M_w=4\pi m_Hn_e\sqrt{2GM_*}\,R_e^{3/2}
\simeq7.99\times10^9\,\mathrm{kg\,s^{-1}}
\simeq1.27\times10^{-13}M_\odot\,\mathrm{yr^{-1}}.}
$$
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 $v_e\simeq4.22\times10^4\,\mathrm{m\,s^{-1}}$. This boundary flux remains fixed even if pressure changes the subsequent radial velocity profile.
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