Observations of pre-transitional disks show a narrow inner dust ring and a larger outer one. They are separated by a cavity with no or only little dust. We propose an efficient recycling mechanism for the inner dust ring which keeps it in a steady state. No major particle sources are needed for replenishment. Dust particles and pebbles drift outwards by radiation pressure and photophoresis. The pebbles grow during outward drift until they reach a balanced position where residual gravity compensates photophoresis. While still growing larger they reverse their motion and drift inward. Eventually, their speed is fast enough for them to be destroyed in collisions with other pebbles and drift outward again. We quantify the force balance and drift velocities for the disks LkCa15 and HD 135344B. We simulate single-particle evolution and show that this scenario is viable. Growth and drift timescales are on the same order and a steady state can be established in the inner dust ring.
Small, illuminated aerosol particles embedded in a gas experience a photophoretic force. Most approximations assume the mean particle surface temperature to be effectively the gas temperature. This might not always be the case. If the particle temperature or the thermal radiation field strongly differs from the gas temperature (optically thin gases), given approximations for the free molecule regime overestimate the photophoretic force by an order of magnitude on average and for individual configurations up to three magnitudes. We apply the radiative equilibrium condition from the previous paper (Paper 1) -where photophoresis in the free molecular flow regime was treated -to the slip flow regime. The slip-flow model accounts for thermal creep, frictional and thermal stress gas slippage and temperature jump at the gas-particle interface. In the limiting case for vanishing Knudsen numbers -the continuum limit -our derived formula has a mean error of only 4 % compared to numerical values. Eventually, we propose an equation for photophoretic forces for all Knudsen numbers following the basic idea from Rohatschek by interpolating between the free molecular flow and the continuum limit.
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