Changes between Version 3 and Version 4 of u/BonnorEbertModule
 Timestamp:
 10/03/12 16:03:21 (12 years ago)
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u/BonnorEbertModule
v3 v4 1 1 == 1. The Quick and Dirty == 2 2 === Big Picture === 3 4 The Bonnor Ebert density profile is coded into astrobear using an approximate analytic solution to the LaneEmden equation. This function solves for the density contrast of the sphere from center to outer edge, as a function of the nondimensional radius, \xi , where 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 LaneEmden equation. This function solves for the density contrast of the sphere from center to outer edge, as a function of the nondimensional radius,xi, where xi is given by: 5 4 6 5 {{{#!latex … … 8 7 }}} 9 8 9 Where r is dimensional radius of the sphere, Cs is isothermal sound speed (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. 10 11 Now, that all explains the clump object itself, but there is an additional "object" in the BE problem module that controls the ambient medium in which the clump resides. This ambient object is by default set to have a uniform density, equal to the density at the sphere's outer most edge, rho(Rbe). Additionally, it is also in pressure equilibrium with the sphere. That is, Pamb=P(Rbe). Now, since the simulation is isothermal, this condition means the temperature is discontinuous at the sphereambient interface, given by P/n = KT, where n is the numberdensity of the gas. 12 13 To summarize, the BE sphere is a clump object that is intialized with the BE density profile. It is placed in an ambient medium object. How to control the different parameters of these objects is described next. 10 14 11 15 … … 20 24 These 3 parameters uniquely and completely specify a sphere in hydrostatic equilibrium as given by the Lane Emden equation (see). They are '''userspecified''' in problem.data. 21 25 26 Now, to recap, the BE sphere is actually a clump object. It is completely controlled external to problem.f90 by the input parameters in physics.data that all explains the initiation of the BE sphere, or clump object. 27 28 22 29 === Units === 23