Changes between Version 9 and Version 10 of u/erica/angularmomentumoutflows
- Timestamp:
- 08/01/16 16:41:16 (9 years ago)
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u/erica/angularmomentumoutflows
v9 v10 25 25 26 26 27 That is, the cross product of the particle's post-accretion com and velocity. Given this may be a slight over (or under) shoot of the actual post-accretion angular momentum, due to the fact that the particle may have lost (or gained) some angular momentum over the accretion time step, we create a new vector to absorb this difference, the 'spin' vector (S). We want the total angular momentum (L+S) to maintain conservation over the accretion time step. That is, we want:27 That is, the cross product of the particle's post-accretion com and velocity. Given this may be a slight over (or under) shoot of the actual post-accretion angular momentum, due to the fact that the particle may have lost (or gained) some angular momentum over the accretion time step, we create a new vector to absorb this difference, the 'spin' vector (S). This vector is created such that the ''total'' angular momentum (L+S) maintains conservation over the accretion time step. That is: 28 28 29 29 [[latex($\bold{L}'+\bold{S}'=(\bold{L}+\bold{S})+\bold{L}_{acc}$)]] 30 30 31 and thus, we can define the spin vector using:31 Thus, the spin vector is given by: 32 32 33 33 [[latex($\bold{S}'=\bold{S}+\bold{L}-\bold{L}'+\bold{L}_{acc}$)]] 34 34 35 Thus,we can say the conserved accreted angular momentum per time step is:35 And we can say the conserved accreted angular momentum per time step is: 36 36 37 37 [[latex($\bold{S}'-\bold{S}=(\bold{L}-\bold{L}')+\bold{L}_{acc}$)]] 38 38 39 Next, we would like to launch a fraction of the accreted angular momentum back along the spin axis of the particle, into the jets. To do this, we want to select only those components that are parallel to the jet, so we have the following prescription for the angular momentum for the outflow:39 Next, we would like to launch a fraction of the accreted angular momentum back along the spin axis of the particle, into the outflow cones. To do this, we want to select only those components that are parallel to the outflows. Thus, we have the following prescription for the angular momenta of the outflows: 40 40 41 41 [[latex($\bold{L}_{out}=f_a (\bold{S}'-\bold{S})\cdot\hat{\bold{S}'} ~\hat{\bold{S}'}$)]]