Characterizing the velocity field in hydrodynamical simulations of low-mass star formation using spectral line profiles

Context. When low-mass stars form, the collapsing cloud of gas and dust goes through several stages which are usually characterized by the shape of their spectral energy distributions. Such classification is based on the cloud morphology only and does not address the dynamical state of the object. Aims. In this paper we investigate the initial cloud collapse and subsequent disk formation through the dynamical behavior as reflected in the sub-millimeter spectral emission line profiles. If a young stellar object is to be characterized by its dynamical structure it is important to know how accurately information about the velocity field can be extracted and which observables provide the best description of the kinematics. Of particular interest is the transition from infalling envelope to rotating disk, because this provides the initial conditions for the protoplanetary disk, such as mass and size. Methods. We use a hydrodynamical model, describing the collapse of a core and formation of a disk, to produce synthetic observables which we compare to calculated line profiles of a simple parameterized model. Because we know the velocity field from the hydrodynamical simulation we can determine in a quantitative way how well our best-fit parameterized velocity field reproduces the original. We use a molecular line excitation and radiation transfer code to produce spectra of both our hydrodynamical simulation as well as our parameterized model. Results. We find that information about the velocity field can reasonably well be derived by fitting a simple model to either single-dish (15′′ resolution) lines or interferometric data (1′′ resolution), but preferentially by using a combination of the two. The method does not rely on a specific set of tracers, but we show that some tracers work better than others. Our result shows that it is possible to establish relative ages of a sample of young stellar objects using this method, independently of the details of the hydrodynamical model.