Changes between Version 16 and Version 17 of u/BonnorEbertModule
- Timestamp:
- 06/26/13 10:47:05 (12 years ago)
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u/BonnorEbertModule
v16 v17 3 3 A Bonnor Ebert sphere is just a clump "object" with a Bonnor Ebert density profile. The Bonnor Ebert density profile is coded into astrobear using an approximate analytic solution to the Lane-Emden equation. This function solves for the density contrast of the sphere from center to outer edge, as a function of the non-dimensional radius,xi, where xi is given by: 4 4 5 {{{#!latex 6 \xi ~=~ (\frac{4 \pi G \rho_c}{C_s^2})^\frac{1}{2}~r 7 }}} 5 [[latex($\xi ~=~ (\frac{4 \pi G \rho_c}{C_s^2})^\frac{1}{2}~r$)]] 8 6 9 7 , r is the dimensional radius of the sphere, Cs is the isothermal sound speed of the sphere (function of the temperature), and rho_c is the central density of the sphere. Once the user specifies r, rho_c, and xi for the sphere (see next section), astrobear sets both a) the temperature of the sphere using the above equation, and b) the outer density of the sphere. One can then use the ideal EOS in physics.data with a gamma = 1.0001 to approximate the grid as isothermal. Given P = nKT, the pressure of the sphere then drops away from the center of the sphere with the same gradient as rho.
