TYCHO: physics sources

Macroscopic physics derived from:

Dynamics and Gravity

General Relativistic dynamics may be used (Van Riper 1979 ApJ 232, 558, with slightly more accurate differences). Explicit hydrodynamics or implicit (hence damped) hydrodynamics (Arnett 1977 ApJS 35, 145) are options at runtime. TYCHO can do stellar evolution, pulsations, and explosions (in 1D).

Mass loss

For temperatures above 7,500 Kelvin, the mass loss is computed from subroutines provided by Rolf Kudritzki (1998).

For lower temperatures, expressions given in Dupree, A. K. Reimers, D. 1987, or the De Jager expression given in Chiosi and Maeder, 1986, ARAA 24, 336. have been used. The mass loss algorithms are being updated.

Envelope

The surface layers are constructed by Bulirsch-Stoer integration of the hydrostatic equations, ignoring nuclear burning. New integrations are done at each time step in order to consistently include changes due to mass loss and mixing. A five-point stencil in luminosity and in radius is used for interpolation for the boundary condition for the interior grid, with the middle point corresponding to the last converged model. Mass loss occurs by modifying the envelope mass. For the physics of the envelope see Kippenhahn and Weigert 1994, and for the mathematics Numerical Recipes 1992.

Atmosphere

An Eddington grey atmosphere is used for optical depths tau below 2/3; Dimitri Mihalas, 1978, Stellar Atmospheres, 2nd Edition, W. H. Freeman and Company: San Francisco, see eq. 3-16.

Radiative Transfer

Equilibrium diffusion of a Black-body gas of photons is used for the radiation transfer for the implicit hydrostatic mode, i.e., standard stellar evolution, and for the explicit hydrodynamic mode (stellar pulsations, explosion, or collapse). A gamma-ray and x-ray module is in preparation for calculation of supernova light curves.

Nonequilibrium diffusion of a Bose-Einstein gas of photons (parameterized by a radiation temperature and a possibly nonzero radiation chemical potential) may be added for the explicit hydrodynamic case, with flux limiting to insure a causal rate of flow in optically thin regions.

Convection and Mixing

The default treatment is standard mixing length (MLT), as defined in Kippenhahn and Weigert 1994, Stellar Structure and Evolution.

Several modifications are to be implemented to make more realistic the description of heat flow, and of the microscopic mixing of composition; see Meakin, C. & Arnett, D., 2007, ApJ 667, 448 and work in preparation. Both conventional MLT and more realistic turbulent convection are runtime options.

Return to main TYCHO page.

E-mail:darnett@as.arizona.edu

TYCHO is not public domain software, but is freely available for non-commercial purposes. Absolutely no guarantee is given; use at your own risk...