Coherent synchrotron radiation can be emitted by relativistic electromagnetic subcycle solitons dwelling in a low-temperature collisionless plasma. Using three-dimensional particle-in-cell simulations we show that solitons, left in a wake of a relativistically intense short circularly polarized laser pulse in the plasma, emit spiral electromagnetic wave, as a result of charge density oscillations in the wall of the soliton cavity. This high-frequency afterglow persists for tens of Langmuir periods.