Heavy-metal Jupiters by major mergers: metallicity vs. mass for giant planets

Some Jupiter-mass exoplanets contain $\sim$$100\, M_\oplus$ of metals, well above the $\sim$$10\, M_\oplus$ typically needed in a solid core to trigger giant planet formation by runaway gas accretion. We demonstrate that such `heavy-metal Jupiters' can result from planetary mergers near $\sim$10 au. Multiple cores accreting gas at runaway rates gravitationally perturb one another onto crossing orbits such that the average merger rate equals the gas accretion rate. Concurrent mergers and gas accretion implies the core mass scales with the total planet mass as $M_{\rm core} \propto M^{1/5}$ - heavier planets harbour heavier cores, in agreement with the observed mass-metallicity relation. While the average gas giant merges about once to double its core, others may merge multiple times, as merger trees grow chaotically. We show that the dispersion of outcomes inherent in mergers can reproduce the large scatter in observed planet metallicities, assuming $3-30\, M_\oplus$ pre-runaway cores. Mergers potentially correlate metallicity, eccentricity, and spin.