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Context. ALMA observations of protoplanetary disks confirm earlier indications that there is a clear difference between the dust and gas radial extents. The origin of this difference is still debated, with both radial drift of the dust and optical depth effects suggested in the literature. Aims. In thermo-chemical models, the dust properties are usually prescribed by simple parametrisations. In this work, the feedback of more realistic dust particle distributions onto the gas chemistry and molecular emissivity is investigated, with a particular focus on CO isotopologues. Methods. The radial dust grain size distribution is determined using dust evolution models that include growth, fragmentation, and radial drift for a given static gas density structure. The vertical settling of dust particles is computed in steady-state. A new version of the code DALI is used to take into account how dust surface area and density influence the disk thermal structure, molecular abundances, and excitation. Synthetic images of both continuum thermal emission and low J CO isotopologues lines are produced. Results. The difference of dust and gas radial sizes is largely due to differences in the optical depth of CO lines and millimeter continuum, without the need to invoke radial drift. The effect of radial drift is primarily visible in the sharp outer edge of the continuum intensity profile. The gas outer radius probed by 12CO emission can easily differ by a factor of ~two between the models for a turbulent α ranging between 10-4 and 10-2, with the ratio of the CO and mm radius Rout CO=Rout mm increasing with turbulence. Grain growth and settling concur in thermally decoupling the gas and dust components, due to the low collision rate with large grains. As a result, the gas can be much colder than the dust at intermediate heights, reducing the CO excitation and emission, especially for low turbulence values. Also, due to disk mid-plane shadowing, a second CO thermal desorption (rather than photodesorption) front can occur in the warmer outer mid-plane disk. The models are compared to ALMA observations of HD 163296 as a test case. In order to reproduce the observed CO snowline of the system, a binding energy for CO typical of ice mixtures, with Eb ≥ 1100 K, needs to be used rather than the lower pure CO value. Conclusions. The difference between observed gas and dust extent is largely due to optical depth effects, but radial drift and grain size evolution also affect the gas and dust emission in subtle ways. In order to properly infer fundamental quantities of the gaseous component of disks, such as disk outer radii and gas surface density profiles, simultaneous modelling of both dust and gas observations including dust evolution is needed. [ABSTRACT FROM AUTHOR]

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 (Menv > Mdisk) 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 Ju = 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 ~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 ~ 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. [ABSTRACT FROM AUTHOR]

Context. Disks are observed around pre-main sequence stars, but how and when they form is still heavily debated. While disks around young stellar objects have been identified through thermal dust emission, spatially and spectrally resolved molecular line observations are needed to determine their nature. Only a handful of embedded rotationally supported disks have been identified to date. Aims. We identify and characterize rotationally supported disks near the end of the main accretion phase of low-mass protostars by comparing their gas and dust structures. Methods. Subarcsecond observations of dust and gas toward four Class I low-mass young stellar objects in Taurus are presented at significantly higher sensitivity than previous studies. The 13CO and C18O J = 2-1 transitions at 220 GHz were observed with the Plateau de Bure Interferometer at a spatial resolution of ⩽0.8" (56 AU radius at 140 pc) and analyzed using uv-space position velocity diagrams to determine the nature of their observed velocity gradient. Results. Rotationally supported disks (RSDs) are detected around 3 of the 4 Class I sources studied. The derived masses identify them as Stage I objects; i.e., their stellar mass is higher than their envelope and disk masses. The outer radii of the Keplerian disks toward our sample of Class I sources are ⩽100 AU. The lack of on-source C18O emission for TMR1 puts an upper limit of 50 AU on its size. Flattened structures at radii >100 AU around these sources are dominated by infalling motion (υ ∝ r-1). A large-scale envelope model is required to estimate the basic parameters of the flattened structure from spatially resolved continuum data. Similarities and differences between the gas and dust disk are discussed. Combined with literature data, the sizes of the RSDs around Class I objects are best described with evolutionary models with an initial rotation of Ω = 10-14 Hz and slow sound speeds. Based on the comparison of gas and dust disk masses, little CO is frozen out within 100 AU in these disks. Conclusions. Rotationally supported disks with radii up to 100 AU are present around Class I embedded objects. Larger surveys of both Class 0 and I objects are needed to determine whether most disks form late or early in the embedded phase. [ABSTRACT FROM AUTHOR]