2011ApJ...727..108W

Dwarf stars are believed to have a small protostar disk where planets may grow up. During the planet formation stage, embryos undergoing type I migration are expected to be stalled at an inner edge of the magnetically inactive disk (a_crit∼ 0.2-0.3 AU). This mechanism makes the location around a_crit a "sweet spot" for forming planets. In dwarf stars with masses ∼0.5 M_☉, a_crit is roughly inside the habitable zone of the system. In this paper, we study the formation of habitable planets due to this mechanism using model system OGLE-06-109L, which has a 0.51 M_☉ dwarf star with two giant planets in 2.3 and 4.6 AU observed by microlensing. We model the embryos undergoing type I migration in the gas disk with a constant disk-accretion rate (). Giant planets in outside orbits affect the formation of habitable planets through secular perturbations at the early stage and secular resonance at the late stage. We find that the existence and the masses of the habitable planets in the OGLE-06-109L system depend on both and the speed of type I migration. If planets are formed earlier, so that is larger (∼10^–7 M_☉/yr), terrestrial planets cannot survive unless the type I migration rate is an order of magnitude less. If planets are formed later, so that is smaller (∼10^–8 M_☉/yr), single and high-mass terrestrial planets with high water contents (∼5%) will be formed by inward migration of outer planet cores. A slower-speed migration will result in several planets via collisions of embryos, and thus their water contents will be low (∼2%). Mean motion resonances or apsidal resonances among planets may be observed if multiple planets survive in the inner system.