might be accommodated. Alternatively, much higher planet masses can be viable if the orbits are stabilized by resonant lock. The configuration of the HR 8799 planet orbits appear to be consistent with a 1:2:4:8 resonance [e.g. @reidemeister09; @konopacky16].

The truncation of the inner edge of the planetesimal disk by the gravity of the outermost planet b offers another form of dynamical mass constraint. The separation of the planet from the disk is sensitive to the planet mass, as the planet clears a chaotic zone around itself due to resonance overlap [e.g. @quillen06a; @chiang09]. For the simple case of circular and coplanar orbits, @wisdom80 derived an analytic formula for the width of the chaotic zone exterior to the planetary orbit, $\Delta a = Ca_\text{pl}(M_\text{pl}/M_{*})^{2/7}$, where $C$ is a scaling coefficient of 1.3, $a_{pl}$ is the semi-major axis of the planet, and $M_{pl}$ and $M_{*}$ are the mass of the planet and the star, respectively. Other work that adopts a slightly different definition of resonance width gives a different scaling factor [e.g. 1.4, @malhotra98]. The width of the chaotic zone for more complex configurations has been the subject of numerous investigations, considering additional factors like the eccentricity of the planet orbit [@quillen06b; 