Early GRB afterglows from reverse shocks in ultra-relativistic long-lasting winds

We develop a model of early GRB afterglows with the dominant $X$-ray contribution from the reverse shock (RS) propagating in highly relativistic (Lorentz factor $\gamma_w \sim 10^6$) magnetized wind of a long-lasting central engine. The model reproduces, in a fairly natural way, the overall trends and yet allows for variations in the temporal and spectral evolution of early optical and $X$-ray afterglows. The high energy and the optical synchrotron emission from the RS particles occurs in the fast cooling regime; the resulting synchrotron power $L_s$ is a large fraction of the wind luminosity, $L_s \approx L_w/\sqrt{1+\sigma_w}$ ($L_w$ and $\sigma_w$ are wind power and magnetization). Thus, plateaus - parts of afterglow light curves that show slowly decreasing spectral power - are a natural consequence of the RS emission. Contribution from the forward shock (FS) is negligible in the $X$-rays, but in the optical both FS and RS contribute similarly: the FS optical emission is in the slow cooling regime, producing smooth components, while the RS optical emission is in the fast cooling regime, and thus can both produce optical plateaus and account for fast optical variability correlated with the $X$-rays, e.g., due to changes in the wind properties. We discuss how the RS emission in the $X$-rays and combined FS and RS emission in the optical can explain many of puzzling properties of early GRB afterglows.