Constraining The Magnetic Field in Gamma Ray Burst Blast Waves

We point out that already existing literature on relativistic collisionless MHD shocks show that the parameter σ ≡ upstream proper magnetic energy density/upstream rest mass energy density, plays an important role in determining the structure and accelerating properties of such shocks. By adopting the value of σ ≈ 0.002 which corresponds to the relativistic shock associated with the Crab nebula, and by using appropriate relativistic shock jump conditions, we obtain here a generous upper-limit on the value of (proper) magnetic field, Bsh ≈ 1.5× 10ηn 1/2 1 G, for gamma ray burst (GRB) blast wave. Here, η ≡ E/Mc, where E is the energy and M is the mass of the baryons entrained in the original fireball (FB), and n1 is the proper number density of the ambient medium. Further, we point out that, in realistic cases, the actual value Bsh could be as low as ∼ 5× 10ηn 1/2 1 G. realistic cases. Subject headings: gamma rays: burstshydrodynamics-relativity shock waves