A VLA Study of High-redshift GRBs II - The Complex Radio Afterglow of GRB 140304A: Shell Collisions and Two Reverse Shocks

We present detailed multi-frequency, multi-epoch radio observations of GRB 140304A at $z=5.283$ from 1 to 86 GHz and 0.45 d to 89 d. The radio and mm data exhibit unusual multiple spectral components, which cannot be simply explained by standard forward and reverse shock scenarios. Through detailed multi-wavelength analysis spanning radio to X-rays, we constrain the forward shock parameters to $E_{\rm K, iso}\approx4.9\times10^{54}\,$erg, $A_* \approx 2.6\times10^{-2}$, $\epsilon_{\rm e}\approx2.5\times10^{-2}$, $\epsilon_{\rm B}\approx5.9\times10^{-2}$, $p\approx2.6$, and $\theta_{\rm jet}\approx1.1^{\circ}$, yielding a beaming corrected $\gamma$-ray and kinetic energy, $E_{\gamma}\approx2.3\times10^{49}\,$erg and $E_{\rm K}\approx9.5\times10^{50}\,$erg, respectively. We model the excess radio emission as due to a combination of a late-time reverse shock (RS) launched by a shell collision, which also produces a re-brightening in the X-rays at $\approx0.26\,$d, and either a standard RS or diffractive interstellar scintillation. Under the standard RS interpretation, we invoke consistency arguments between the forward and reverse shocks to derive a deceleration time, $t_{\rm dec}\approx100\,$s, the ejecta Lorentz factor, $\Gamma(t_{\rm dec})\approx300$, and a low RS magnetization, $R_{\rm B}\approx0.6$. Our observations highlight both the power of radio observations in capturing RS emission and thus constraining the properties of GRB ejecta and central engines, and the challenge presented by interstellar scintillation in conclusively identifying RS emission in GRB radio afterglows.