Evolution of molecular abundances in proto-planetary disks with accretion flow

We investigate the evolution of molecular abundances in a protoplanetary disk in which matter is accreting toward the central star by solving numerically the reaction equations of molecules as an initial-value problem. We obtain the abundances of molecules, both in the gas phase and in ice mantles of grains, as functions of time and position in the disk. In the region of surface density less than 10(2) g cm(-2) (distance from the star greater than or similar to 10 AU for the mass accretion rate 10(-8) M. yr(-1)), cosmic rays are barely attenuated even on the midplane: of the disk and produce chemically active ions such as H-3(+) and He+. We find that through reactions with these ions considerable amounts of CO and N-2, which are initially the dominant species in the disk, are transformed into CO2, CH4, NH3, and HCN. In the regions where the temperature is low enough for these products to freeze onto grains, they accumulate in ice mantles. As the matter migrates toward inner warmer regions of the disk, some of the molecules in the ice mantles evaporate. It is found that most of the molecules desorbed in this way are transformed into less volatile molecules by the gas-phase reactions, which then freeze out. Molecular abundances both in the gas phase and in ice mantles crucially depend on the temperature and thus vary significantly with the distance from the central star. although molecular evolution proceeds in protoplanetary disks, our model also shows that significant amount of interstellar ice, especially water ice, survives and is included in ice mantles in the outer region of the disks. We also find that the timescale of molecular evolution is dependent on the ionization rate and the grain size in the disk. If the ionization rate and the grain size are the same as those in molecular clouds, the timescale of the molecular evolution, in which CO and N-2 are transformed into other molecules, is about 10(6) yr, which is slightly smaller than the lifetime of the disk. The timescale for molecular evolution is larger (smaller) in the case of lower (higher) ionization rate or larger (smaller) grain size. We compare our results with the molecular composition of comets, which are considered to be the most primitive bodies in our solar system. The molecular abundances derived from our model naturally explain the coexistence of oxidized ice and reduced ice in the observed comets. Our model also suggests that comets formed in different regions of the disk have different molecular compositions. Finally, we give some predictions for future millimeter-wave and sub-millimeter-wave observations of protoplanetary disks.