| 19 | | which describes the luminosity due to gas falling in from a distance r away (instead of infinity). However, as these plots show, using this equation for different values of the kinetic energy at r (ke(r)), i.e. ke(r)=1/2 mv^2^(r), does not produce wildly differing accretion energies until you move to the far left on the x-axis. In fact, in all but the most extreme cases |
| | 19 | which describes the luminosity due to gas falling in from a distance r away (instead of infinity). However, as these plots show, using this equation for different values of the kinetic energy at r (ke(r)), i.e. ke(r)=1/2 mv^2^(r), does not produce wildly differing accretion energies until you move to the far left on the x-axis. In fact, in all but the most extreme cases, the degree of error is negligible (<1%), even at a distance of 1/100,000 of a parsec (i.e. much less than a typical cell size). At that distance, it doesn't matter whether the gas parcel is starting from rest, moving slowly (less than freefall speed), or moving fast (up to 10x freefall speed), the accretion energy that parcel will release at the stellar surface ''is the same''. This is a statement that ''most'' of the energy gained from gravitational infall occurs in the final legs of the journey. Therefore under most circumstances, using the simpler equation (the first one listed) should be a *great* approximation. |
