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A Strömgren sphere and neutral time

  1. May 15, 2009 #1

    TFM

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    1. The problem statement, all variables and given/known data

    A Strömgren sphere is the ionized region surrounding a strong ionizing source. Its size is determined by there being a balance between the rate of ionization and the rate of recombination. Consider such a sphere of radius [tex]R_S[/tex] = 10 pc and internal density [tex]n_e = 10^6 m^{-3}[/tex], and with a central ionizing source of [tex]10^{49} photons s^{−1}[/tex].

    a)

    How long will it take to become neutral once the ionising star has switched off?

    b)

    Suppose that the sphere expands at a rate equal to the sound speed in a 10^4 K gas. How long will it take to expand to a radius of 100 pc? ([tex]v_s^2\approx 3kT/m_H[/tex])


    2. Relevant equations



    3. The attempt at a solution

    Okay I have done part b), getting an answer of about 5.6 million years, but I have a small query regarding part a).

    I know that the charge loss will be [tex]10^49 atoms s^{-1} [/tex]
    because this is the photon rate when it is in equilibrium, which means this rate is equal to the rate at which atoms become neutral. I also know that I need to work out the volume of the sphere, and thus the number of particles in it.

    However, i am slightly uncertain how to work out how many particles are actually ionised before the star is turned off.

    ?

    Thanks in advanced,

    TFM
     
    Last edited: May 15, 2009
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