Numerical models and results

Kang and Jones (2005a) considered a supernova explosion with Eo = 1051 ergs

and Msn = 10M$un in a uniform medium with nH = 3 X10 cm . The physical quantities are normalized, both in the numerical code and in the plots below, by the following constants:

po = 7.0X10——3, to = 6.1x103yr, ro = 28.5pc, uo = 4.6X103km.sec—1, Po = 1.5x10——3, Ko = 4.0X 1028cm2sec—1. (4.26.6)

It was assumed a Bohm type diffusion coefficient, k= (3 X 1022cm2sec—1/p/B^ , (4.27.7)

where B^ = 5 is the interstellar magnetic field strength in units of 10—6Gs and p is the particle momentum in units of mc. The pressure of the background gas is set to be Pgo = 10—12 erg/cm3 (To ~ 106 K), and the Mach number of the initial shock is go

13. In the code units Pgo = 1.67X10—4 and K(p/ = 1.5X10—7p. It is assumed that there exits a pre-exiting CR population f (p)<* p—4 5, corresponding to an upstream CR pressure, Pco = 0.5Pgo. The simulation is initialized at t/to = 1 by the Sedov-

Taylor similarity solutions which are characterized by the shock position rs/ro =4 ((/to )/5 and speed, us/uo = (2/5)4 (Ao )—35 with 4 = 1.15167. The spatial grid resolution in the code unit is Aro = 6.0 x 10-4 at the base grid and Ars = 2.3 x 10-6 at the 8-th refined grid, which is the finest refined grid for this simulation. When the simulation is repeated with 10 levels of refined grids, Pc increases less than 0.5 %, indicating true convergence in the simulation with 8

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