Models of Chemistry, Thermal Balance, and Infrared Spectra from Intermediate‐Aged Disks around G and K Stars

Abstract

We model gas and dust emission from regions 0.3-20 AU from a central low-mass star in intermediate-aged (~107 yr) disks whose dust is fairly optically thin to stellar radiation. The models treat thermal balance and chemistry self-consistently and calculate the vertical density and temperature structure of the gas in a disk. The gas and dust temperatures are calculated separately. The models cover gas masses 10-3 to 1 MJ and dust masses 10-7 to 10-4 MJ and treat solar-type (G and K) stars. We focus on mid-infrared and far-infrared emission lines from various gas species such as the rotational lines of H2, OH, H2O, and CO molecules and the fine-structure lines of carbon, oxygen, sulfur, iron, and silicon atoms and ions. These lines and the dust continuum are observable by the Spitzer Space Telescope and future missions including SOFIA and the Herschel Space Observatory. We find that the [S I] 25.23 μm line is the strongest emission line for a wide range of disk and stellar parameters, followed by emission from [Si II] 34.8 μm, [Fe II] 26 μm, and [O I] 63 μm. [Fe I] 24 μm and rotational lines of OH and H2O are strong when gas masses are high (0.1 MJ). Emission from the rotational lines of H2 is more difficult to detect unless disk gas masses are substantial (0.1 MJ). For emission from H2 lines to be observable and yet for the dust to be optically thin in stellar light, the ratio of gas to small submillimeter-sized dust particle mass in the disk needs to be 1000, or at least an order of magnitude higher than that in the interstellar medium. This may be possible at intermediate stages in disk evolution, such as in the gas-gathering stage of the core accretion scenario for giant planet formation, in which most of the dust has coagulated into larger objects (1 mm) but the gas has not yet fully dispersed. Whereas the absolute fluxes observed in some lines such as [Fe I] 24 μm and H2 S(0) 28 μm primarily measure the gas mass in the disks, various line ratios diagnose the inner radius of the gas and the radial temperature and surface density distribution of the gas. Many lines become optically thick and/or suffer chemical or thermal effects such that the line luminosities do not increase appreciably with increasing gas mass. We predict that it may be difficult for the Spitzer Space Telescope to detect 1 MJ of gas in optically thin (in dust) disks at distances 150 pc. The models presented here will be useful in future infrared studies of the timescale for the dispersion of gas in a planet-forming disk and tests of core accretion models of giant planet formation.