Changes between Version 12 and Version 13 of u/erica/RadFeedback
- Timestamp:
- 11/19/15 13:49:30 (9 years ago)
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u/erica/RadFeedback
v12 v13 17 17 However, 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: 18 18 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 21 Rearranging for the accretion luminosity, we have: 22 23 [[latex($L=\frac{1}{2} \dot{m}v^2(r)+G(\frac{M_{*}}{R_{*}}-\frac{M_{r}}{r})\dot{m}$)]]