Aims. In this paper, we explore the diagnostic power of the far-IR fine-structure lines of [Oi] 63.2 μm, 145.5 μm, [Cii] 157.7 μm, 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 to 2.2 × 10 −2 M (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 μm line to originate in LTE from the surface layers of the disk, where T g 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 μm line, which has a larger critical density, decreases more rapidly with disk mass than the 63.2 μm line. Therefore, the [Oi] 63.2 μm/145.5 μm 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 > ∼ 0.05. For too low disk masses (M disk < ∼ 10 −4 M ) 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 μm/[C ii]157.7 μm 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.

We present detailed model fits to observations of the disc around the Herbig Ae star HD 163296. This well-studied object has an age of ∼4 Myr, with evidence of a circumstellar disc extending out to ∼540 AU. We use the radiation thermo-chemical disc code ProDiMo to model the gas and dust in the circumstellar disc of HD 163296, and attempt to determine the disc properties by fitting to observational line and continuum data. These include new Herschel/PACS observations obtained as part of the open-time key program GASPS (GAS in Protoplanetary Systems), consisting of a detection of the [Oi] 63 μm line and upper limits for several other far infrared lines. We complement this with continuum data and ground-based observations of the 12 CO 3-2, 2-1 and 13 CO J = 1-0 line transitions, as well as an upper limit for the H 2 0-0 S(1) transition. We explore the effects of stellar ultraviolet variability and dust settling on the line emission, and on the derived disc properties. Our fitting efforts lead to derived gas/dust ratios in the range 9-100, depending on the assumptions made. We note that the line fluxes are sensitive in general to the degree of dust settling in the disc, with an increase in line flux for settled models. This is most pronounced in lines which are formed in the warm gas in the inner disc, but the low excitation molecular lines are also affected. This has serious implications for attempts to derive the disc gas mass from line observations. We derive fractional PAH abundances between 0.007 and 0.04 relative to ISM levels. Using a stellar and UV excess input spectrum based on a detailed analysis of observations, we find that the all observations are consistent with the previously assumed disc geometry.

We have combined the thermo-chemical disc code ProDiMo with the Monte Carlo radiative transfer code MCFOST to calculate a grid of ∼300 000 circumstellar disc models, systematically varying 11 stellar, disc and dust parameters including the total disc mass, several disc shape parameters and the dust-to-gas ratio. For each model, dust continuum and line radiative transfer calculations are carried out for 29 far-infrared, sub-mm and mm lines of [O I], [C II], 12 CO and o/p-H 2 O under five inclinations. The grid allows us to study the influence of the input parameters on the observables, to make statistical predictions for different types of circumstellar discs and to find systematic trends and correlations between the parameters, the continuum fluxes and the line fluxes. The model grid, comprising the calculated disc temperature and chemical structures, the computed spectral energy distributions, line fluxes and profiles, will be used in particular for the data interpretation of the HERSCHEL open time-key program GASPS. The calculated line fluxes show a strong dependence on the assumed ultraviolet excess of the central star and on the disc flaring. The fraction of models predicting [O I] and [C II] fine-structure lines fluxes above HERSCHEL/PACS and SPICA/SAFARI detection limits is calculated as a function of disc mass. The possibility of deriving the disc gas mass from line observations is discussed.

Aims. We want to understand the chemistry and physics of discs on the basis of a large unbiased and statistically relevant grid of disc models. One of the main goals is to explore the diagnostic power of various gas emission lines and line ratios for deriving main disc parameters such as the gas mass. Methods. We explored the results of the DENT grid (Disk Evolution with Neat Theory) that consists of 300 000 disc models with 11 free parameters. Through a statistical analysis, we searched for correlations and trends in an effort to find tools for disc diagnostic. Results. All calculated quantities like species masses, temperatures, continuum, and line fluxes differ by several orders of magnitude across the entire parameter space. The broad distribution of these quantities as a function of input parameters shows the limitation of using a prototype T Tauri or Herbig Ae/Be disc model. The statistical analysis of the DENT grid shows that CO gas is rarely the dominant carbon reservoir in discs. Models with large inner radii (10 times the dust condensation radius) and/or shallow surface density gradients lack massive gas-phase water reservoirs. Also, 60% of the discs have gas temperatures averaged over the oxygen mass in the range between 15 and 70 K; the average gas temperatures for CO and O differ by less than a factor two. Our study of the observational diagnostics shows that the [C ii] 158 μm fine structure line flux is very sensitive to the stellar UV flux and presence of a UV excess, and that it traces the outer disc radius (R out ). In the submm, the CO low J rotational lines also trace R out . Low [O i] 63/145 line ratios (