2022ApJ...938..155P

This work extends a contemporaneous effort to study the properties of the lower-energy counterpart synchrotron emission produced by the cooling of relativistic gamma-ray burst (GRB) electrons through radiation (synchrotron and self-Compton) emission and adiabatic losses. We derive the major characteristics (pulse duration, lag time after burst, and brightness relative to the burst) of the prompt optical counterpart (POC) occurring during or after the GRB. Depending on the magnetic field lifetime, duration of electron injection, and electron transit time Δt_o from hard X-ray (GRB) to optical-emitting energies, a POC may appear during the GRB pulse (of duration δt_γ) or after (delayed OC). The signature of counterparts arising from the cooling of GRB electrons is that POC pulses (Δt_o < δt_γ) last as long as the corresponding GRB pulse (δt_o ≃ δt_γ), while delayed OC pulses (Δt_o > δt_γ) last as long as the transit time (δt_o ≃ Δt_o). If OC variability can be measured, then another signature for this OC mechanism is that the GRB variability is passed on to POCs but not to delayed OCs. Within the GRB electron cooling model for counterparts, POCs should be on average dimmer than delayed ones (consistent with the data), and harder GRB low-energy slopes β_LE should be associated more often with the dimmer POCs. The latter sets an observational bias against detecting POCs from (the cooling of electrons in) GRBs with a hard slope β_LE, making it more likely that the detected POCs of such bursts arise from another mechanism.