Ultra-relativistic double explosions

Abstract

We consider fluid dynamics of relativistic double explosion—when a point explosion with energy E1 is followed by a second explosion with energy E2 after time td (the second explosion could be in a form of a long lasting wind). The primary explosion creates a self-similar relativistic blast wave propagating with Lorentz factor Γ1(t). A sufficiently strong second explosion, with total energy E2≥10−2E1, creates a fast second shock in the external fluid previously shocked by the primary shock. At times longer than the interval between the explosions td, yet short compared with the time when the second shock catches up the primary shock at ∼tdΓ12, the structure of the second shock is approximately self-similar. The self-similar structure of the second shock exists for the case of constant external density (in this case Γ2∝t−7/3), but not for the wind environment. At early times, the Lorentz factor of the second shock may exceed that of the primary shock and may boost the synchrotron emission of locally accelerated electrons into the Fermi Large Area Telescope range.