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

Some Jupiter-mass exoplanets contain similar to 100 M-circle plus of metals, well above the similar to 10 M-circle plus 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 similar to 10 au. Multiple cores accreting gas at runaway rates gravitationally perturb one another on to 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-core proportional to M-1/5 - heavier planets harbour heavier cores, in agreement with the observed relation between total mass and metal mass. 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-circle plus pre-runaway cores. Mergers potentially correlate metallicity, eccentricity, and spin.