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| | 1 | = Computing the Jeans Length = |
| | 2 | |
| | 3 | The first step in setting up this problem was to consider the Jeans Length for a given ambient density and temperature. Recall, |
| | 4 | |
| | 5 | [[latex($\lambda_J = C_s(\frac{\pi} { G \rho_0})^{1/2}$)]] |
| | 6 | |
| | 7 | I used the ambient density and temperature of the BP case for the Bonnor Ebert runs. This gave |
| | 8 | |
| | 9 | [[latex($\rho0 = 3.34 \times 10^{-23} g/cm^3$)]] |
| | 10 | |
| | 11 | [[latex($\ T = 100K $)]] |
| | 12 | |
| | 13 | Using the isothermal sound speed of, |
| | 14 | |
| | 15 | [[latex($C_s = (\frac{K_B*T}{m_H})^{1/2}$)]] |
| | 16 | |
| | 17 | where Kb is the boltzmann constant and mH is the mass of hydrogen, I calculated |
| | 18 | |
| | 19 | [[latex($\lambda_J = 1.08 \times 10^{20} cm \approx 35 pc $)]] |
| | 20 | |
| | 21 | = Setting up the problem domain = |
| | 22 | |
| | 23 | I decided on a 1D grid (a string of cells in x) that was much greater than the Jeans length: |
| | 24 | |
| | 25 | [[latex($L = 1550 ~ pc $)]] |
| | 26 | |
| | 27 | The Jeans Length needed to be resolved to prevent artificial fragmentation, so |
| | 28 | |
| | 29 | [[latex($\triangle x < \frac{1}{4} \lambda_J \Rightarrow $)]] |
| | 30 | |
| | 31 | [[latex($\triangle x < 9 ~pc $)]] |
| | 32 | |
| | 33 | Choosing 1550 cells in the x direction (small computational cost given 1D sim) satisfies this by having |
| | 34 | |
| | 35 | [[latex($\triangle x = 1~pc $)]] |
| | 36 | |
| | 37 | so there are about 35 cells/ Jeans length. |
| | 38 | |
| | 39 | = Seeding the perturbation, analytic solution = |
| | 40 | |
| | 41 | = The code = |
