of all Lindblad resonances up to the torque cutoff. A similar statement to (\[eqn:momentum\]), dropping the viscous term local to the planet, was made by @fsc_2014. Given $B$, (\[eqn:momentum\]) can be solved for the gap contrast with the inner disc: $$\begin{aligned}
\frac{\Sigma_{\rm p}}{\Sigma_-} \sim \frac{1}{1 + B/\nu} 
\label{eqn:oom1}\end{aligned}$$ (see also @dm_2013; @kmt_2015; @gs_2018). Combining mass conservation (\[eqn:mass\]) with momentum conservation (\[eqn:momentum\]) yields the gap contrast with the outer disc: $$\begin{aligned}
\frac{\Sigma_{\rm p}}{\Sigma_+} \sim \frac{1}{1 + (A + B)/\nu} \,.
\label{eqn:oom2}\end{aligned}$$ An equivalent equation is derived by @tt_2016 [their appendix B] and @tmt_2020 [their equation 26]. Equations (\[eqn:oom1\]) and (\[eqn:oom2\]) inform us that planetary consumption ($A \neq 0$) leads to asymmetric gap contrasts: a deeper gap relative to the outer disc than to the inner disc. The outer gap contrast is the more important insofar as the outer disc controls surface densities everywhere downstream; in other words, $\Sigma_+$ is the independent variable while $\Sigma_{\rm p}$ and $\Sigma_-$ are dependent variables. Equation (\[eqn:oom2\]) states that, given $\Sigma_+$, the effects of accretion ($A$) and repulsion ($B$) in setting the gap depth $\Sigma_{\rm p}$ are additive (not multiplicative). If $A > B$, then consumption dominates.

For $A=A_{\rm Bondi}$ and $B$ given by (\[eqn:B\]), $$\label{eqn:ab}
