| Abstract
| - Context. Star and planet formation theories predict an evolution in the density, temperature, and velocity structure as the envelope collapses and forms an accretion disk. While continuum emission can trace the dust evolution, spectrally resolved molecular lines are needed to determine the physical structure and collapse dynamics. Aims. The aim of this work is to model the evolution of the molecular excitation, line profiles, and related observables during low-mass star formation. Specifically, the signatures of disks during the deeply embedded stage ( Menv > M⋆) are investigated. Methods. The semi-analytic 2D axisymmetric model of Visser and collaborators has been used to describe the evolution of the density, stellar mass, and luminosity from the pre-stellar to the T-Tauri phase. A full radiative transfer calculation is carried out to accurately determine the time-dependent dust temperatures. The time-dependent CO abundance is obtained from the adsorption and thermal desorption chemistry. Non-LTE near-IR (NIR), far-IR (FIR), and submm lines of CO have been simulated at a number of time steps. Results. In single dish (10−20′′ beams), the dynamics during the collapse are best probed through highly excited 13CO and C 18O lines, which are significantly broadened by the infall process. In contrast to the dust temperature, the CO excitation temperature derived from submm/FIR data does not vary during the protostellar evolution, consistent with C 18O observations obtained with Herschel and from ground-based telescopes. The NIR spectra provide complementary information to the submm lines by probing not only the cold outer envelope but also the warm inner region. The NIR high- J (≥8) absorption lines are particularly sensitive to the physical structure of the inner few AU, which does show evolution. The models indicate that observations of 13CO and C 18O low- J submm lines within a ≤1″ (at 140 pc) beam are well suited to probe embedded disks in Stage I ( Menv < M⋆) sources, consistent with recent interferometric observations. High signal-to-noise ratio subarcsec resolution data with ALMA are needed to detect the presence of small rotationally supported disks during the Stage 0 phase and various diagnostics are discussed. The combination of spatially and spectrally resolved lines with ALMA and at NIR is a powerful method to probe the inner envelope and disk formation process during the embedded phase.
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