The very early afterglow powered by ultra-relativistic mildly magnetized outflows

In the Poynting Flux-dominated outflow (the initial ratio of the electromagnetic energy flux to the particle energy flux $\sigma_0\gg1$) model for gamma-ray bursts, particularly the γ-ray emission phase, nearly half of the internally dissipated magnetic energy is converted into the γ-ray energy emission and the rest is converted into the kinetic energy of the outflow. Consequently, at the end of the γ-ray burst, σ decreases significantly ($\sigma\sim 1$ or even smaller). We numerically investigate the very early reverse shock emission powered by such mildly magnetized outflows interacting with medium–uniform interstellar medium (ISM) or stellar wind (WIND). We show that for $\sigma\sim0.05{-}1$ and typical parameters of gamma-ray bursts, both the ISM-ejecta interaction and the WIND-ejecta interaction can power very strong optical emission ($m_{R}\sim 10{-}12{\rm th}$ mag or even brighter). Similar to the very early afterglow powered by the non-magnetized ejecta interacting with the external medium, the main difference between the ISM-ejecta interaction case and the WIND-ejecta interaction case is that, before the reverse shock crosses the ejecta, the R-band emission flux increases rapidly for the former, but for the latter it increases only slightly. At the very early stage, the ejecta are ultra-relativistic. Due to the beaming effect, the random magnetic field generated in shocks contained in the viewing area is axisymmetric, unless the line of sight is very near the edge of ejecta. The formula $\Pi_{\rm net}\approx 0.60b^2/(1+b^2)$ (where b is the ratio of the ordered magnetic field strength to that of random one) has been proposed to describe the net linear polarization of the synchrotron radiation coming from the viewing area. For $\sigma\sim 0.05{-}1$, the ordered magnetic field dominates over the random one generated in the reverse shock (As usual, we assume that a fraction $\epsilon_{\rm B}\sim 0.01$ of the thermal energy of the reverse shock has been converted into the magnetic energy), the high linear polarization is expected. We suggest that the linear polarization detection of the early multi-wavelength afterglow is required to see whether the outflows powering GRBs are magnetized or not.