Fig. C.4

Left panel: timescales for the 5-M♃ example of Sect. 4 studied in this appendix. The timescales are, from top to bottom in the legend, the accretion timescale τacc = M/ (ṀXY + ṀZ); Kelvin-Helmholtz time τKH = Etot/Lint; local impact timescale from Eq. (C.28), using the geometric mean of ℓρ and ℓSedov; global and eddy mixing times given by Eq. (C.21); global impact timescale given by Eq. (C.24); and cooling time of the region affected by one impact, τcool = Eimpact/Lint. Right panel: relevant lengthscales: from top to bottom, total radius R; (outer) radiative-convective boundary; radius of maximal energy deposition RmaxE; core radius Rcore; size of a convective eddy at RmaxE, which is equal to the pressure scale height since αMLT = 1; size of the Sedov blast wave estimate ℓSedov; size of the density-contrast estimate ℓρ; and the size (diameter) of the planetesimals.
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