Changes between Version 9 and Version 10 of u/erica/angularmomentumoutflows


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Timestamp:
08/01/16 16:41:16 (9 years ago)
Author:
Erica Kaminski
Comment:

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  • u/erica/angularmomentumoutflows

    v9 v10  
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    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:
     27That 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:
    2828
    2929[[latex($\bold{L}'+\bold{S}'=(\bold{L}+\bold{S})+\bold{L}_{acc}$)]]
    3030
    31 and thus, we can define the spin vector using:
     31Thus, the spin vector is given by:
    3232
    3333[[latex($\bold{S}'=\bold{S}+\bold{L}-\bold{L}'+\bold{L}_{acc}$)]]
    3434
    35 Thus, we can say the conserved accreted angular momentum per time step is:
     35And we can say the conserved accreted angular momentum per time step is:
    3636
    3737[[latex($\bold{S}'-\bold{S}=(\bold{L}-\bold{L}')+\bold{L}_{acc}$)]]
    3838
    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:
     39Next, 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:
    4040
    4141[[latex($\bold{L}_{out}=f_a (\bold{S}'-\bold{S})\cdot\hat{\bold{S}'} ~\hat{\bold{S}'}$)]]