Deep and wide gaps by super Earths in low-viscosity discs

Abstract

Planets can open cavities (gaps) in the protoplanetary gaseous discs in which they are born by exerting gravitational torques. Viscosity counters these torques and limits the depletion of the gaps. We present a simple 1D scheme to calculate the gas density profile inside gaps by balancing the gravitational and viscous torques. By generalizing the results of Goodman & Rafikov (2001), our scheme properly accounts for the propagation of angular momentum by density waves. This method allows us to easily study low-viscosity discs, which are challenging for full hydrodynamical simulations. We complement our numerical integration by analytical equations for the gap's steady-state depth and width as a function of the planet'sto- star's mass ratio μ, the gas disc's aspect ratio h, and its Shakura & Sunyaev viscosity parameter a. Specifically, we focus on low-mass planets (μ < μth = h3) and identify a new low-viscosity regime, α