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Context. The extent of the gas in protoplanetary discs is observed to be universally larger than the extent of the dust. This is often attributed to radial drift and grain growth of the millimetre grains, but line optical depth produces a similar observational signature. Aims. We investigate in which parts of the disc structure parameter space dust evolution and line optical depth are the dominant drivers of the observed gas and dust size difference. Methods. Using the thermochemical model DALI with dust evolution included we ran a grid of models aimed at reproducing the observed gas and dust size dichotomy. Results. The relation between Rdust and dust evolution is non-monotonic and depends on the disc structure. The quantity Rgas is directly related to the radius where the CO column density drops below 1015 cm−2 and CO becomes photodissociated; Rgas is not affected by dust evolution but scales with the total CO content of the disc. While these cases are rare in current observations, Rgas/Rdust > 4 is a clear sign of dust evolution and radial drift in discs. For discs with a smaller Rgas/Rdust, identifying dust evolution from Rgas/Rdust requires modelling the disc structure including the total CO content. To minimize the uncertainties due to observational factors requires FWHMbeam < 1× the characteristic radius and a peak S/N > 10 on the 12CO emission moment zero map. For the dust outer radius to enclose most of the disc mass, it should be defined using a high fraction (90–95%) of the total flux. For the gas, any radius enclosing >60% of the 12CO flux contains most of the disc mass. Conclusions. To distinguish radial drift and grain growth from line optical depth effects based on size ratios requires discs to be observed at high enough angular resolution and the disc structure should to be modelled to account for the total CO content of the disc. [ABSTRACT FROM AUTHOR]

Context. How protoplanetary disks evolve is still an unsolved problem where different processes may be involved. Depending on the process, the disk gas surface density distribution Σgas may be very different and this could have diverse implications for planet formation. Together with the total disk mass, it is key to constrain Σgas as function of disk radius R from observational measurements. Aims. In this work we investigate whether spatially resolved observations of rarer CO isotopologues, such as 13CO, may be good tracers of the gas surface density distribution in disks. Methods. Physical-chemical disk models with different input Σgas(R) were run, taking into account CO freeze-out and isotope-selective photodissociation. The input disk surface density profiles were compared with the simulated 13CO intensity radial profiles to check whether and where the two follow each other. Results. For each combination of disk parameters, there is always an intermediate region in the disk where the slope of the 13CO radial emission profile and Σgas(R) coincide. In the inner part of the disk, the line radial profile underestimates Σgas, as 13CO emission becomes optically thick. The same happens at large radii where the column densities become too low and 13CO is not able to efficiently self-shield. Moreover, the disk becomes too cold and a considerable fraction of 13CO is frozen out, thus it does not contribute to the line emission. If the gas surface density profile is a simple power-law of the radius, the input power-law index can be retrieved within a ~20% uncertainty if one choses the proper radial range. If instead Σgas(R) follows the self-similar solution for a viscously evolving disk, retrieving the input power-law index becomes challenging, in particular for small disks. Nevertheless, we find that the power-law index γ can be in any case reliably fitted at a given line intensity contour around 6 K km s−1, and this produces a practical method to constrain the slope of Σgas(R). Application of such a method is shown in the case study of the TW Hya disk. Conclusions. Spatially resolved 13CO line radial profiles are promising to probe the disk surface density distribution, as they directly trace Σgas(R) profile at radii well resolvable by ALMA. There, chemical processes like freeze-out and isotope-selective photodissociation do not affect the emission, and, assuming that the volatile carbon does not change with radius, no chemical model is needed when interpreting the observations. [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. One of the methods for deriving disk masses relies on direct observations of the gas, whose bulk mass is in the outer cold regions (T ≲ 30 K). This zone can be well traced by rotational lines of less abundant CO isotopologues such as 13CO, C18O, and C17O, which probe the gas down to the midplane. The total CO gas mass is then obtained with the isotopologue ratios taken to be constant at the elemental isotope values found in the local interstellar medium. This approach is imprecise, however, because isotope-selective processes are ignored. Aims. The aim of this work is an isotopologue-selective treatment of CO isotopologues, to obtain a more accurate determination of disk masses. Methods. The isotope-selective photodissociation, the main process controlling the abundances of CO isotopologues in the CO-emissive layer, is properly treated for the first time in a full-disk model. The chemistry, thermal balance, line, and continuum radiative transfer are all considered together with a chemical network that treats 13CO, C18O and C17O, isotopes of all included atoms and molecules as independent species. Results. Isotope selective processes lead to regions in the disk where the isotopologue abundance ratios of C18O/12CO, for example, are considerably di erent from the elemental 18O/16O ratio. The results of this work show that considering CO isotopologue ratios as constants can lead to underestimating disk masses by up to an order of magnitude or more if grains have grown to larger sizes. This may explain observed discrepancies in mass determinations from di erent tracers. The dependence of the various isotopologue emission on stellar and disk parameters is investigated to set the framework for the analysis of ALMA data. Conclusions. Including CO isotope selective processes is crucial for determining the gas mass of the disk accurately (through ALMA observations) and thus for providing the amount of gas that may eventually form planets or change the dynamics of forming planetary systems. [ABSTRACT FROM AUTHOR]

Context. For stars to form, material must fall inwards from core scales through the envelope towards the central protostar. While theories of how this takes place have been around for some time, the velocity profile around protostars is poorly constrained. The combination of observations in multiple transitions of a tracer which is sensitive to kinematics and radiative transfer modelling of those lines has the potential to break this deadlock. Aims. Seven protostars observed with the Heterodyne Instrument for the Far-Infrared (HIFI) on board the Herschel Space Observatory as part of the "Water in star-forming regions with Herschel" (WISH) survey show infall signatures in water line observations. We aim to constrain the infall velocity and the radii over which infall is taking place within the protostellar envelopes of these sources. We will also use these data to constrain the chemistry of cold water. Methods. We use 1-D non-LTE ratran radiative transfer models of the observed water lines to constrain the infall velocity and chemistry in the protostellar envelopes of six Class 0 protostars and one Class I source. We assume a free-fall velocity profile and, having found the best fit, vary the radii over which infall takes place. Results. In the well-studied Class 0 protostar NGC1333-IRAS4A we find that our observations probe infall over the whole envelope to which our observations are sensitive (r ≳ 1000 AU). For L1527, L1157, BHR71 and IRAS 15398 infall takes place on core to envelope scales (i.e. ~10 000-3000 AU). In Serpens-SMM4 and GSS30 the inverse P-Cygni profiles seen in the ground-state lines are more likely due to larger-scale motions or foreground clouds. Models including a simple consideration of the chemistry are consistent with the observations, while using step abundance profiles are not. The non-detection of excited water in the inner envelope in six out of seven protostars is further evidence that water must be heavily depleted from the gas-phase at these radii. Conclusions. Infall in four of the sources is supersonic and in all sources must take place at the outer edge of the envelope, which may be evidence that collapse is global or outside-in rather than inside-out. The mass infall rate in NGC1333-IRAS4A is large (≳10-4 M☉ yr-1), higher than the mass outflow rate and expected mass accretion rates onto the star. This suggests that any flattened disk-like structure on small scales will be gravitationally unstable, potentially leading to rotational fragmentation and/or episodic accretion. [ABSTRACT FROM AUTHOR]

Context. With the Herschel Space Observatory, lines of simple molecules (C+, O, and high-J lines of CO, Jup ≳ 14) have been observed in the atmosphere of protoplanetary disks. When combined with ground-based data on [C i], all principle forms of carbon can be studied. These data allow us to test model predictions for the main carbon-bearing species and verify the presence of a warm surface layer. The absence of neutral carbon [Ci], which is predicted by models to be strong, can then be interpreted together with ionized carbon [C ii] and carbon monoxide. Aims. We study the gas temperature, excitation, and chemical abundance of the simple carbon-bearing species C, C+, and CO, as well as O by the method of chemical-physical modeling. Using the models, we explore the sensitivity of the lines to the entering parameters and constrain the region from which the line radiation emerges. Methods. Numerical models of the radiative transfer in the lines and dust are used together with a chemical network simulation and a calculation of the gas energetics to obtain the gas temperature. We present our new model, which is based on our previous models but includes several improvements that we report in detail, together with the results of benchmark tests. Results. A model of the disk around the Herbig Be star HD 100546 is able to reproduce the CO ladder together with the atomic finestructure lines of [O i] and either [C i] or [Cii].We find that the high-J lines of CO can only be reproduced by a warm atmosphere with Tgas ⪢ Tdust. The low-J lines of CO, observable from the ground, are dominated by the outer disk with a radius of several 100 AU, while the high-J CO observable with Herschel-PACS are dominated from regions within some tens of AU. The spectral profiles of high-J lines of CO are predicted to be broader than those of the low-J lines. We study the effect of several parameters including the size of the disk, the gas mass of the disk, the PAH abundance and distribution, and the amount of carbon in the gas phase. Conclusions. The main conclusions of our work are (i) only a warm atmosphere with Tgas ⪢ Tdust can reproduce the CO ladder. (ii) The CO ladder together with [O i] and the upper limit to [Ci] can be reproduced by models with a high gas/dust ratio and a low abundance of volatile carbon. These models however produce too small amounts of [Cii]. Models with a low gas/dust ratio and more volatile carbon also reproduce CO and [O i], are in closer agreement with observations of [Cii], but overproduce [C i]. Owing to the uncertain origin of the [Cii] emission, we prefer the high gas/dust ratio models, indicating a low abundance of volatile carbon. [ABSTRACT FROM AUTHOR]

Aims. Young stars interact vigorously with their surroundings, as evident from the highly rotationally excited CO (up to Eu/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. [ABSTRACT FROM AUTHOR]