  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
one-dimensional 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's to star's mass ratio
$\mu$, the gas disc's aspect ratio $h$, and its Shakura & Sunyaev viscosity
parameter $\alpha$. Specifically, we focus on low-mass planets ($\mu<\mu_{\rm
th}\equiv h^3$) and identify a new low-viscosity regime, $\alpha<h(\mu/\mu_{\rm
th})^5$, in which the classical analytical scaling relations are invalid.
Equivalently, this low-viscosity regime applies to every gap that is depleted
by more than a factor of $(\mu_{\rm th}/\mu)^3$ relative to the unperturbed
density. We show that such gaps are significantly deeper and wider than
previously thought, and consequently take a longer time to reach equilibrium.
