Changes between Version 12 and Version 13 of u/erica/RadFeedback


Ignore:
Timestamp:
11/19/15 13:49:30 (9 years ago)
Author:
Erica Kaminski
Comment:

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  • u/erica/RadFeedback

    v12 v13  
    1717However, in our simulations the gas parcel isn't falling into the sink from infinity, but rather from some distance r away from the sink. At this radius it has some kinetic and gravitational potential energy, as it does once it falls to the surface of the star. Energy conservation gives:
    1818
    19 [[latex($\frac{1}{2}m v(r)^2 - \frac{GmM_{enc}}{r} = \frac{1}{2}m v(R_{*})^2 - \frac{GmM_{*}}{R_{*}}$)]]
     19[[latex($\frac{1}{2}m v^2(r) - \frac{GmM_{r}}{r} = \frac{1}{2}m v^2(R_{*}) - \frac{GmM_{*}}{R_{*}}$)]]
     20
     21Rearranging for the accretion luminosity, we have:
     22
     23[[latex($L=\frac{1}{2} \dot{m}v^2(r)+G(\frac{M_{*}}{R_{*}}-\frac{M_{r}}{r})\dot{m}$)]]