161 | | Given these timescales, the diffusion wave probably won't be strongly peaked, yet will be broad -- traveling close to the speed of light. If my 'assumptions' were correct about a pre-stellar core (their average size and mass), then given their 'average density' and the rosseland mean opacity, we see that they are in the optically thin limit for diffusion. Given cores are not optically thin, this means that either the density assumption is way off (they should be centrally concentrated), or setting the scale height = box radius is off (perhaps for an optically thick core the scale height should be greater than the core size (so that the energy is roughly constant throughout the core). |
162 | | |
163 | | Tackling this slightly differently could be like confining the core to a smaller dimension so that we were ensuring we would be in the optically thick limit. That is, beginning by constraining [[latex($\lambda\approx 1/3$)]]. Then, we should be able to predict the timescale over which we would see a well-defined 'diffusion wave' propagate through the grid. |
164 | | |
165 | | ''' Coupling time estimate ''' |
| 161 | Given these timescales, the diffusion wave probably won't be strongly peaked, but will be broad -- traveling close to the speed of light. If my 'assumptions' were correct about a pre-stellar core (their average size and mass), then given their 'average density' and the rosseland mean opacity, we see that they are in the optically thin limit for diffusion. Given cores are not optically thin, this means that either the density assumption is way off (they should be centrally concentrated), or setting the scale height = box radius is off (perhaps for an optically thick core the scale height should be greater than the core size, so that the energy is roughly constant throughout the core). |
| 162 | |
| 163 | Tackling this slightly differently could be starting from the optically thick limit, [[latex($\lambda\approx 1/3$)]]. Then, we should be able to predict the timescale over which we would see a well-defined 'diffusion wave' propagate through the grid. |
| 164 | |
| 165 | = Diffusion estimate for optically thick 1 solar mass core = |
| 166 | |
| 167 | If we let, |
| 168 | |
| 169 | [[latex($R=1$)]], then we have |
| 170 | |
| 171 | [[latex($l=\frac{1}{\kappa_R \rho}=h$)]] |
| 172 | |
| 173 | and from before, |
| 174 | |
| 175 | [[latex($M=\rho l^3$)]] |
| 176 | |
| 177 | Solving these two equations gives: |
| 178 | |
| 179 | [[latex($h=$)]] |
| 180 | |
| 181 | [[latex($l=$)]] |
| 182 | |
| 183 | |
| 184 | = Coupling time estimate = |