Vorticity and Magnetic Field Generation from Initial Anisotropy in Ultrarelativistic Gamma-Ray Burst Blastwaves

Because conical segments of quasispherical ultrarelativistic blastwaves are causally disconnected on angular scales larger than the blastwave inverse Lorentz factor, astrophysical blastwaves can sustain initial anisotropy, imprinted by the process that drives the explosion, while they remain relativistic. We show that initial angular energy fluctuations in ultrarelativistic blastwaves imply a production of vorticity in the blastwave, and calculate the vortical energy production rate. In gamma-ray burst (GRB) afterglows, the number of vortical eddy turnovers as the shocked fluid crosses the blastwave shell is about unity for marginally nonlinear anisotropy. Thus the anisotropy must be nonlinear to explain the magnetic energy density inferred in measured GRB spectra.