Modelling Herschel observations of hot molecular gas emission from embedded low-mass protostars^⋆,⋆⋆

¹ Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands
² Department of Astronomy, University of Michigan, 500 Church Street, Ann Arbor, MI 48109-1042, USA
e-mail: visserr@umich.edu
³ Max-Planck-Institut für extraterrestrische Physik, Giessenbachstrasse 1, 85748 Garching, Germany
⁴ Institute of Astronomy, ETH Zurich, Wolfgang-Pauli-Strasse 27, 8093 Zurich, Switzerland
⁵ Department of Physics and Astronomy, Denison University, Granville, OH 43023, USA
⁶ Department of Astronomy, University of Maryland, College Park, MD 20742-2421, USA

Received: 19 April 2011
Accepted: 20 October 2011

Abstract

Aims. Young stars interact vigorously with their surroundings, as evident from the highly rotationally excited CO (up to E_u/k = 4000 K) and H₂O emission (up to 600 K) detected by the Herschel Space Observatory in embedded low-mass protostars. Our aim is to construct a model that reproduces the observations quantitatively, to investigate the origin of the emission, and to use the lines as probes of the various heating mechanisms.

Methods. The model consists of a spherical envelope with a power-law density structure and a bipolar outflow cavity. Three heating mechanisms are considered: passive heating by the protostellar luminosity, ultraviolet irradiation of the outflow cavity walls, and small-scale C-type shocks along the cavity walls. Most of the model parameters are constrained from independent observations; the two remaining free parameters considered here are the protostellar UV luminosity and the shock velocity. Line fluxes are calculated for CO and H₂O and compared to Herschel data and complementary ground-based data for the protostars NGC 1333 IRAS2A, HH 46 and DK Cha. The three sources are selected to span a range of evolutionary phases (early Stage 0 to late Stage I) and physical characteristics such as luminosity and envelope mass.

Results. The bulk of the gas in the envelope, heated by the protostellar luminosity, accounts for 3–10% of the CO luminosity summed over all rotational lines up to J = 40–39; it is best probed by low-J CO isotopologue lines such as C¹⁸O 2–1 and 3–2. The UV-heated gas and the C-type shocks, probed by ¹²CO 10–9 and higher-J lines, contribute 20–80% each. The model fits show a tentative evolutionary trend: the CO emission is dominated by shocks in the youngest source and by UV-heated gas in the oldest one. This trend is mainly driven by the lower envelope density in more evolved sources. The total H₂O line luminosity in all cases is dominated by shocks (>99%). The exact percentages for both species are uncertain by at least a factor of 2 due to uncertainties in the gas temperature as function of the incident UV flux. However, on a qualitative level and within the context of our model, both UV-heated gas and C-type shocks are needed to reproduce the emission in far-infrared rotational lines of CO and H₂O.