Efficiency of planetesimal ablation in giant planetary envelopes

Observations of exoplanetary spectra are leading to unprecedented constraints on their atmospheric elemental abundances, particularly O/H, C/H, and C/O ratios. Recent studies suggest that elemental ratios could provide important constraints on formation and migration mechanisms of giant exoplanets. A fundamental assumption in such studies is that the chemical composition of the planetary envelope represents the sum-total of compositions of the accreted gas and solids during the formation history of the planet. We investigate the efficiency with which accreted planetesimals ablate in a giant planetary envelope thereby contributing to its composition rather than sinking to the core. From considerations of aerodynamic drag causing 'frictional ablation' and the envelope temperature structure causing 'thermal ablation', we compute mass ablations for impacting planetesimals of radii 30 m to 1 km for different compositions (ice to iron) and a wide range of velocities and impact angles, assuming spherical symmetry. Icy impactors are fully ablated in the outer envelope for a wide range of parameters. Even for Fe impactors substantial ablation occurs in the envelope for a wide range of sizes and velocities. For example, iron impactors of sizes below similar to 0.5 km and velocities above similar to 30 km s(-1) are found to ablate by similar to 60-80 per cent within the outer envelope at pressures below 103 bar due to frictional ablation alone. For deeper pressures (similar to 10(7) bar), substantial ablation happens over a wider range of parameters. Therefore, our exploratory study suggests that atmospheric abundances of volatile elements in giant planets reflect their accretion history during formation.