 Finite-age planetary scattering regimes

At fixed stellar mass $M_{\star }$, planetary mass density ${\rho }_p$, age $t_{\star }$ and initial ratio $\kappa =a_0/a_p$, the order-unity Safronov number comparison and comet energy diffusion give boundariesTheir logarithmic slopes in planetary mass versus radius are $-3/2$ and $3/4$. Above both, strong kicks and a short estimated diffusion time favour ejection; below the escape boundary, repeated weak encounters favour collision statistically. Below the age boundary, the stated diffusion mechanism has not completed on its characteristic clock. Collision lifetimes require additional cross-section and encounter-rate information, so this map alone cannot establish retention or accretion within the age.