An implicit advection scheme for modeling relativistic shocks with high Lorentz factors

A. A. Hujeirat; S. Fehlmann

paper

An implicit advection scheme for modeling relativistic shocks with high Lorentz factors

arXiv:0903.3025

Abstract

Jet-plasmas emanating from the vicinity of relativistic objects and in gamma-ray bursts have been observed to propagate with Lorentz factors laying in the range between one and several hundreds. On the other hand, the numerical studies of such flows have been focussed so far mainly on the lowest possible range of Lorentz factors $Γ,$ specifically, on the regime $1 \leq Γ \leq 5.$ Therefore, relativistic flows with high $Γ -$ factors have poorly studied, as most numerical methods are found to encounter severe numerical difficulties or even become numerically unstable for $Γ ≫ 1. I n t hi s p a p er w e p r ese n t anim pl i c i t n u m er i c a l a d v ec t i o n sc h e m e f or m o d e l in g t h e p r o p a g a t i o n o f r e l a t i v i s t i c pl a s ma s w i t h s h oc k s, d i sc u ss i t sco n s i s t e n cy w i t h r es p ec tt o b o t h t h e in t er na l an d t o t a l e n er g y f or m u l a t i o nin g e n er a l r e l a t i v i t y . U s in g t h e t o t a l e n er g y f or m u l a t i o n, t h esc h e m e i s f o u n d t o b e v iab l e f or m o d e l in g m o v in g s h oc k s w i t hm o d er a t e L or e n t z f a c t or s, t h o ug h w i t h r e l a t i v e l y s ma l l C o u r an t n u mb er s . I n t h e l imi t o f hi g h L or e n t z f a c t or s, t h e in t er na l e n er g y f or m u l a t i o nin co mbina t i o n w i t ha f in e - t u n e d a r t i f i c ia l v i scos i t y i s m u c hm or er o b u s t an d e f f i c i e n t . W eco n f i r m o u r co n c l u s i o n s b y p er f or min g t es t c a l c u l a t i o n s an d co m p a r e t h er es u l t s w i t hana l y t i c a l so l u t i o n so f t h er e l a t i v i s t i cs h oc k t u b e p r o b l e m . T h e aim o f t h e p r ese n t m o d i f i c a t i o ni s t oe nhan ce t h er o b u s t n esso f t h e g e n er a l r e l a t i v i s t i c im pl i c i t r a d ia t i v e M H D so l v er : GR - I - R M H D (h ttp : // w w w 1. i w r . u ni - h e i d e l b er g . d e / g r o u p s / co m p a s t r o / h o m e / g r - i - mh d - so l v er) an d e x t e n d i t sr an g eo f a ppl i c a t i o n s in t o t h e hi g h$ Γ-$regime.}

9 pages, 14 figures