A Self-similar Solution for the Propagation of a Relativistic Shock in an Exponential Atmosphere | Zendy

Rosalba Perna | Zendy; M. Vietri | Zendy

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A Self-similar Solution for the Propagation of a Relativistic Shock in an Exponential Atmosphere

Author(s) -

Rosalba Perna,

M. Vietri

Publication year - 2002

Publication title -

the astrophysical journal

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.376

H-Index - 489

eISSN - 1538-4357

pISSN - 0004-637X

DOI - 10.1086/340667

Subject(s) - physics , atmosphere (unit) , lorentz factor , acceleration , shock (circulatory) , exponential function , limit (mathematics) , planar , lorentz transformation , astrophysics , shock wave , range (aeronautics) , classical mechanics , mechanics , mathematical analysis , mathematics , meteorology , materials science , medicine , computer graphics (images) , computer science , composite material

We derive a fully relativistic, self-similar solution to describe thepropagation of a shock along an exponentially decreasing atmosphere, in thelimit of very large Lorentz factor. We solve the problem in planar symmetry andcompute the acceleration of the shock in terms of the density gradient crossedduring its evolution. We apply our solution to the acceleration of shockswithin the atmosphere of a HyperNova, and show that velocities consistent withthe requirements of GRB models can be achieved with exponential atmospheresspanning a wide density range.Comment: ApJL in pres

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