Version 1 (modified by 7 years ago) ( diff ) | ,
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2/7/18
Fryer sent progenitor data. The density, pressure, temperature, and velocity profiles of this progenitor look like:
The goal is to get these profiles initialized on an Eulerian grid in astrobear and to make sure the solution can be numerically stable over multiple dynamical times. The question of stability is interesting and something we will turn to next.
The pressure and density profiles of a polytropic sphere in hydrostatic equilibrium (HSE) are given by the Lane-Emden equation:
This equation is derived by combining the equation of HSE with Poisson’s equation for gravity and the pressure/density relationship of a polytrope:
where is the polytropic index. Note the polytropic index is related to the adiabatic index () through the equation:
Exact analytic solutions of the Lane-Emden equation exist only for certain values of . These are:
(exact solutions exist)
However, for other values of the Lane-Emden must be numerically integrated.
In astrobear, I have written a numerical solver for which corresponds to the Isothermal limit (). In principle, we would be able to initialize an isothermal sphere on the grid using the inner and outer density of the sphere and its radius, but given the density contrast here is >> than the critical value of 14.1, this sphere would be highly gravitationally unstable — I imagine its evolution would be close to that of the singular isothermal sphere.
Thus, we need an alternative solution to modeling the progenitor.
I could easily modify the algorithm I have for setting up a polytropic sphere in HSE for (which corresponds to an adiabatic sphere of ).
2/5/18
We would like to model the progenitor of a core collapse supernova in astrobear. The project will be a parameter study to explore the role of magnetic fields and turbulent perturbations on the collapsing core.
Attachments (25)
- progenitor_profiles.png (241.6 KB ) - added by 7 years ago.
- press_2D_lowres.png (203.3 KB ) - added by 7 years ago.
- rho_2D_lowres.png (215.5 KB ) - added by 7 years ago.
- 2D_rho_zoomin.png (244.0 KB ) - added by 7 years ago.
- 2D_press_zoomin.png (232.1 KB ) - added by 7 years ago.
- Screen Shot 2018-03-01 at 9.50.04 AM.png (44.8 KB ) - added by 7 years ago.
- problem.f90_mar15 (5.9 KB ) - added by 7 years ago.
- profile.out_mar15 (40.6 KB ) - added by 7 years ago.
- global.data_mar15 (7.9 KB ) - added by 7 years ago.
- profile_init.out_mar15 (40.6 KB ) - added by 7 years ago.
- progenitor_profiles.dat_mar15 (16.1 KB ) - added by 7 years ago.
- scales.data_mar15 (619 bytes ) - added by 7 years ago.
- physics.data_mar15 (9.8 KB ) - added by 7 years ago.
- problem.data_mar15 (207 bytes ) - added by 7 years ago.
- density_2D_higheres.png (192.8 KB ) - added by 7 years ago.
- density_2D_higheres_zoomin.png (177.4 KB ) - added by 7 years ago.
- highres_2D_tempColor.png (401.0 KB ) - added by 7 years ago.
- highres_2D_rhoColor.png (308.3 KB ) - added by 7 years ago.
- highres_2D_pressColor.png (291.7 KB ) - added by 7 years ago.
- mesh_octant_2tff.png (419.9 KB ) - added by 7 years ago.
- HSE_octant_2tffs.gif (2.4 MB ) - added by 7 years ago.
- vzmach_octant_2tffs.gif (2.2 MB ) - added by 7 years ago.
- rho_octant_2tffs.gif (2.3 MB ) - added by 7 years ago.
- press_octant_2tffs.gif (2.3 MB ) - added by 7 years ago.
- HSE_octant_resolutionStudy.png (64.2 KB ) - added by 7 years ago.