The unusual protoplanetary disk around the T Tauri star ET Chamaeleontis

We present new continuum and line observations, along with modelling, of the faint (6-8) Myr old T Tauri star ET Cha belonging to the eta Chamaeleontis cluster. We have acquired Herschel/PACS photometric fluxes at 70 mu m and 160 mu m, as well as a detection of the [OI] 63 mu m fine-structure line in emission, and derived upper limits for some other far-IR OI, CII, CO and o-H2O lines. These observations were carried out in the frame of the open time key programme GASPS, where ETCha was selected as one of the science demonstration phase targets. The Herschel data is complemented by new simultaneous ANDICAM B-K photometry, new HST/COS and HST/STIS UV-observations, a non-detection of CO J = 3 -> 2 with APEX, re-analysis of a UCLES high-resolution optical spectrum showing forbidden emission lines like [OI] 6300 angstrom, [SII] 6731 angstrom and 6716 angstrom, and [NII] 6583 angstrom, and a compilation of existing broad-band photometric data. We used the thermo-chemical disk code ProDiMo and the Monte-Carlo radiative transfer code MCFOST to model the protoplanetary disk around ETCha. The paper also introduces a number of physical improvements to the ProDiMo disk modelling code concerning the treatment of PAH ionisation balance and heating, the heating by exothermic chemical reactions, and several non-thermal pumping mechanisms for selected gas emission lines. By applying an evolutionary strategy to minimise the deviations between model predictions and observations, we find a variety of united gas and dust models that simultaneously fit all observed line and continuum fluxes about equally well. Based on these models we can determine the disk dust mass with confidence, M-dust approximate to (2-5) x 10(-8) M-circle dot whereas the total disk gas mass is found to be only little constrained, M-gas approximate to (5 x 10(-5)-3 x 10(-3)) M-circle dot. Both mass estimates are substantially lower than previously reported. In the models, the disk extends from 0.022 AU (just outside of the co-rotation radius) to only about 10 AU, remarkably small for single stars, whereas larger disks are found to be inconsistent with the CO J = 3 -> 2 non-detection. The low velocity component of the [OI] 6300 angstrom emission line is centred on the stellar systematic velocity, and is consistent with being emitted from the inner disk. The model is also consistent with the line flux of H-2 v = 1 -> 0 S(1) at 2.122 mu m and with the [OI] 63 mu m line as seen with Herschel/PACS. An additional high-velocity component of the [OI] 6300 angstrom emission line, however, points to the existence of an additional jet/outflow of low velocity 40-65 km s(-1) with mass loss rate approximate to 10(-9) M-circle dot/yr. In relation to our low estimations of the disk mass, such a mass loss rate suggests a disk lifetime of only similar to 0.05-3 Myr, substantially shorter than the cluster age. If a generic gas/dust ratio of 100 was assumed, the disk lifetime would be even shorter, only similar to 3000 yrs. The evolutionary state of this unusual protoplanetary disk is discussed.