Auroral roar emissions are commonly interpreted as Z (or upper hybrid) mode naturally excited by precipitating auroral electrons. Subsequent conversion to escaping radiation makes it possible for these emissions to be detected on the ground. Most emissions are detected as having left-hand (L) circular (or ordinary O) polarization, but the companion paper presents a systematic experimental study on the rare occurrence of the right-hand polarized, or equivalently, extraordinary (X) mode 4fce emission. A similar observation was reported earlier by Sato et al. (2015). The suggested emission mechanism is the nonlinear coalescence of two upper hybrid roars at 2fce. The present paper formulates a detailed theory for such an emission mechanism
