Radiation thermo-chemical models of protoplanetary disks II. Line diagnostics

Aims. In this paper, we explore the diagnostic power of the far-IR fine-structure lines of [Oi] 63.2 mu m, 145.5 mu m, [Cii] 157.7 mu m, as well as the radio and sub-mm lines of CO J = 1-0, 2-1 and 3-2 in application to disks around Herbig Ae stars. We aim at understanding where the lines originate from, how the line formation process is affected by density, temperature and chemical abundance in the disk, and to what extent non-LTE effects are important. The ultimate aim is to provide a robust way to determine the gas mass of protoplanetary disks from line observations. Methods. We use the recently developed disk code ProDiMo to calculate the physico-chemical structure of protoplanetary disks and apply the Monte-Carlo line radiative transfer code Ratran to predict observable line profiles and fluxes. We consider a series of Herbig Ae type disk models ranging from 10(-6) M(circle dot) to 2.2 x 10(-2) M(circle dot) (between 0.5 and 700 AU) to discuss the dependency of the line fluxes and ratios on disk mass for otherwise fixed disk parameters. This paper prepares for a more thorough multi-parameter analysis related to the Herschel open time key program Gasps. Results. We find the [Cii] 157.7 mu m line to originate in LTE from the surface layers of the disk, where T(g) not equal T(d). The total emission is dominated by surface area and hence depends strongly on disk outer radius. The [Oi] lines can be very bright (> 10(-16) W/m(2)) and form in slightly deeper and closer regions under non-LTE conditions. For low-mass models, the [Oi] lines come preferentially from the central regions of the disk, and the peak separation widens. The high-excitation [Oi] 145.5 mu m line, which has a larger critical density, decreases more rapidly with disk mass than the 63.2 mu m line. Therefore, the [Oi] 63.2 mu m/145.5 mu m ratio is a promising disk mass indicator, especially as it is independent of disk outer radius for R(out) > 200 AU. CO is abundant only in deeper layers A(V) greater than or similar to 0.05. For too low disk masses (M(disk) less than or similar to 10(-4) M(circle dot)) the dust starts to become transparent, and CO is almost completely photo-dissociated. For masses larger than that the lines are an excellent independent tracer of disk outer radius and can break the outer radius degeneracy in the [Oi] 63.2 mu m/[C ii] 157.7 mu m line ratio. Conclusions. The far-IR fine-structure lines of [Cii] and [Oi] observable with Herschel provide a promising tool to measure the disk gas mass, although they are mainly generated in the atomic surface layers. In spatially unresolved observations, none of these lines carry much information about the inner, possibly hot regions < 30 AU.