The Influence Of The Opacity On The Structure Of The Protoplanetary Disks

The current theories suggest that the planets form from theprotoplanetary disks. The formation and evolution of the protoplanetarydisks have important effect on the planet formation and are hot topics.As a molecular cloud core collapses, the materials do not fall into thecentral star completely because of the angular momentum and a flat diskforms around the central star. The protoplanetary disks are composedmainly of gas, the angular momentum redistributes caused by the viscosity.The material flow into the central star, while a little of them transportoutward to conserve the angular momentum.For thin disks around the sun-like central stars, the surfacedensities are always used to describe the evolution of the disks. Thereare other physical quantities, such as temperatures, disk thickness,viscosities, and stabilities. When the surface densities are fixed,others quantities can be expressed as functions of the surface densities.An important physical quantity is viscosity, which is related to thetemperature and the temperature is related to the opacity. Therefore theeffect of the opacity on the disks is very important.The research on the opacity is either numerical or given theoreticalfitting, and the fitting formula is different in different papers. The values of the opacities are functions of temperature. To obtain the effecton the evolution of the disks, we adopt four different fitting formulaeand compare the evolution of the disk.For the formation of the disks, we adopt the disk evolution model ofJin&Sui (2010). The disks form from the collapse the molecular cloudcores. To obtain the effects of the opacity, in all situations, we usethe same molecular cloud core parameters, i.e. the median of the observedvalues. The mass, temperature, viscosity, and metallicity of themolecular cloud cores are1M⊙,15K,1104, and the stellar value,respectively. The angular velocity is0.31014s-1, which is the minimumvalue from the observation.We research on the dependence of the surface density, temperature,and the instability on the opacity. We use fitting formulae of opacityin Bell&Lin (1994), Bell et al.(1997), Nakamoto&Nakagawa (1994), andRuden&Lin (1986). The results show that when the difference of theopacities is small, the change of the physical quantities is small. Hencethe dependence of these quantities on the opacity is not very sensitive.When very simple opacities are adopted, the mentioned quantities haveimportant changes at small radii. The simple opacity leads to low surfacedensity, high temperature, and strong stability.In all four situations, the protoplanetary disks are stable throughthe evolution of the disks. The main reason is we adopt small angular velocity of molecular cloud cores. When the angular velocity increases,the different formula of the opacity may change the stability of the disks.Although the opacity has effects on the structure and evolution ofthe disk, there are also invariable characters. In the isolation stage,i.e., after the molecular cloud core collapse, the surface densitydecreases with time at small radii while increases at large radii, andthe temperature decreases with time at all the radii, and the minimum ofthe Q parameter increases with time. The dependence on the radius is thatthe surface density and the temperature decrease with radius while theQ parameter decreases with radius first and then increases.