Testing protostellar disk formation models with ALMA observations

Context. Recent simulations have explored different ways to form accretion disks around low-mass stars. However, it has been difficult to differentiate between the proposed mechanisms because of a lack of observable predictions from these numerical studies. Aims. We aim to present observables that can differentiate a rotationally supported disk from an infalling rotating envelope toward deeply embedded young stellar objects (M-env > M-disk) and infer their masses and sizes. Methods. Two 3D magnetohydrodynamics (MHD) formation simulations are studied with a rotationally supported disk (RSD) forming in one but not the other (where a pseudo-disk is formed instead), together with the 2D semi-analytical model. We determine the dust temperature structure through continuum radiative transfer RADMC3D modeling. A simple temperature-dependent CO abundance structure is adopted and synthetic spectrally resolved submm rotational molecular lines up to J(u) = 10 are compared with existing data to provide predictions for future ALMA observations. Results. The 3D MHD simulations and 2D semi-analytical model predict similar compact components in continuum if observed at the spatial resolutions of 0.5-1" (70-140 AU) typical of the observations to date. A spatial resolution of similar to 14 AU and high dynamic range (>1000) are required in order to differentiate between RSD and pseudo-disk formation scenarios in the continuum. The first moment maps of the molecular lines show a blue- to red-shifted velocity gradient along the major axis of the flattened structure in the case of RSD formation, as expected, whereas it is along the minor axis in the case of a pseudo-disk. The peak position-velocity diagrams indicate that the pseudo-disk shows a flatter velocity profile with radius than does an RSD. On larger scales, the CO isotopolog line profiles within large (>9") beams are similar and are narrower than the observed line widths of low-J (2-1 and 3-2) lines, indicating significant turbulence in the large-scale envelopes. However a forming RSD can provide the observed line widths of high-J (6-5, 9-8, and 10-9) lines. Thus, either RSDs are common or a higher level of turbulence (b similar to 0.8 km s(-1)) is required in the inner envelope compared with the outer part (0.4 km s(-1)). Conclusions. Multiple spatially and spectrally resolved molecular line observations can differentiate between the pseudo-disk and the RSD much better than continuum data. The continuum data give a better estimate of disk masses, whereas the disk sizes can be estimated from the spatially resolved molecular lines observations. The general observable trends are similar between the 2D semi-analytical models and 3D MHD RSD simulations.