Gas modelling in the disc of HD 163296

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 ~ 540AU. 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]63mic line and upper limits for several other far infrared lines. We complement this with continuum data and ground-based observations of the 12CO 3-2, 2-1 and 13CO J=1-0 line transitions, as well as the H2 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.

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

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_Sun to 2.2 10^-2 M_Sun (between 0.5 and 700 AU) to discuss the dependency of the line fluxes and ratios on disk mass for otherwise fixed disk parameters. Results. We find the [CII] 157.7 mum line to originate in LTE from the surface layers of the disk, where Tg > Td . 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. The high-excitation [OI] 145.5 mum line, which has a larger critical density, decreases more rapidly with disk mass than the 63.2 mum line. Therefore, the [OI] 63.2 mum/145.5 mum ratio is a promising disk mass indicator, especially as it is independent of disk outer radius for Rout > 200 AU. CO is abundant only in deeper layers A_V >~ 0.05. For too low disk masses (M_disk <~10^-4 M_Sun) 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 mum/[CII]157.7 mum 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.

Disc evolution and the relationship between $L_{rm acc}$ and $L_ast$ in T Tauri stars

We investigate the evolution of accretion luminosity $L_{rm acc}$ and stellar luminosity ${L_ast}$ in pre-mainsequence stars. We make the assumption that when the star appears as a Class II object, the major phase of accretion is long past, and the accretion disc has entered its asymptotic phase. We use an approximate stellar evolution scheme for accreting pre-mainsequence stars based on Hartmann, Cassen & Kenyon, 1997. We show that the observed range of values $k = L_{rm acc}/L_ast$ between 0.01 and 1 can be reproduced if the values of the disc mass fraction $M_{rm disc}/M_*$ at the start of the T Tauri phase lie in the range 0.01 -- 0.2, independent of stellar mass. We also show that the observed upper bound of $L_{rm acc} sim L_ast$ is a generic feature of such disc accretion. We conclude that as long as the data uniformly fills the region between this upper bound and observational detection thresholds, then the degeneracies between age, mass and accretion history severely limit the use of this data for constraining possible scalings between disc properties and stellar mass.