The Impact of Ambipolar Diffusion on the Rossby Wave Instability in a Protoplanetary Disk

Recent observational and simulation studies have revealed that ambipolar diffusion is an important phenomenon in the outer regions of a protoplanetary disk (PPD). However, numerous simulation studies have found that ambipolar diffusion suppresses the turbulence caused by the magnetorotational instability (MRI) in these regions of a PPD. The aim of this study is to investigate the impact of ambipolar diffusion on the Rossby wave instability (RWI) at large radii of a PPD. To accomplish this, we examine the occurrence of the RWI in a PPD threaded by the magnetic field in the presence of ambipolar diffusion. Additionally, we scale the ambipolar diffusivity with respect to both the toroidal magnetic field and an important parameter known as the Elsässer number. We obtain the growth rate of unstable RWI modes in the outer regions of a PPD using linear perturbation analysis. In our nonaxisymmetric perturbation analysis, we find that the amplitude of the toroidal field oscillates in various modes for small values of the Elsässer numbers. For small Elsässer numbers, the growth rate of unstable modes associated with the RWI decreases. In other words, ambipolar diffusion suppresses the perturbation caused by the RWI. This effect is similar to the effect of ambipolar diffusion on the MRI. In contrast to the MRI, where there is a range around 1 for the Elsässer numbers, the existence of ambipolar diffusion supports the occurrence of RWI. Finally, we compare our findings with those of simulation studies to emphasize the importance of RWI in the outer regions of a PPD.