Effects of Collisions with Rocky Planets on the Properties of Hot   Jupiters
  Observed Hot Jupiters exhibit a wide range of physical properties. For a given mass, many planets have inflated radii, while others are surprisingly compact and may harbor large central cores. Motivated by the observational sample, this paper considers possible effects from collisions of smaller rocky planets with gas giant planets. In this scenario, the Jovian planets migrate first and enter into (approximately) 4 day orbits, whereas rocky planets (mass = 0.1-20 that of Earth) migrate later and then encounter the gaseous giants. Previous work indicates that the collision rates are high for such systems. This paper calculates the trajectories of incoming rocky planets as they orbit within the gaseous planets and are subjected to gravitational, frictional, and tidal forces. These collisions always increase the metallicity of the Jovian planets. If the incoming rocky bodies survive tidal destruction and reach the central regions, they provide a means of producing large planetary cores. Both the added metallicity and larger cores act to decrease the radii of the gas giants at fixed mass. The energy released during these collisions provides the Jovian planet with an additional heat source; here we determine the radial layers where kinetic energy of the colliding body is dissipated, including the energy remaining upon impact with the existing core. This process could have long-term effects if the colliding body deposits significant energy deep in the interior, in regions of high opacity. Both Hot Jupiters and newly formed gas giants have inflated radii, large enough to allow incoming rocky planets to survive tidal disruption, enhance the central core mass, and deposit significant energy (in contrast, denser giant planets with the mass and radius of Jupiter are expected to tidally destroy incoming rocky bodies). 
Kassandra R. Anderson and Fred C. Adams
astro-ph.EP