The correct answer is A) opens the burner circuit upon sensing a flame failure. A photoelectric cell installed in an automatically fired auxiliary boiler burner management system is designed to detect the presence of a flame and open the burner circuit if the flame is lost. This is a safety feature to prevent unburned fuel from accumulating, which could lead to a dangerous explosion. Option A accurately describes the function of the photoelectric cell in this system. The other options are incorrect because: B) the photoelectric cell does not directly detect radiant heat, C) the photoelectric cell does not require mechanical linkage, and D) the photoelectric cell is not bypassed at low firing rates, as it must remain active to detect flame failure at all times.