Effects of scattering and dust grain size on the temperature structure of protoplanetary discs: A three-layer approach

The temperature in the optically thick interior of protoplanetary discs is essential for the interpretation of millimeter observations of the discs, for the vertical structure of the discs, for models of the disc evolution and the planet formation, and for the chemistry in the discs. Since large icy grains have a large albedo even in the infrared, the effect of scattering of the diffuse radiation in the discs on the interior temperature should be examined. We have performed a series of numerical radiation transfer simulations including isotropic scattering by grains with various typical sizes for the diffuse radiation as well as for the incident stellar radiation. We also have developed an analytic model including isotropic scattering to understand the physics concealed in the numerical results. With the analytic model, we have shown that the standard two-layer approach is valid only for grey opacity (i.e. grain size \ga10 \micron) even without scattering. A three-layer interpretation is required for grain size \la10 \micron. When the grain size is 0.1--10 \micron, the numerical simulations show that isotropic scattering reduces the temperature of the disc interior. This reduction is nicely explained by the analytic three-layer model as a result of the energy loss by scatterings of the incident stellar radiation and of the warm diffuse radiation in the disc atmosphere. For grain size \ga10 \micron (i.e. grey scattering), the numerical simulations show that isotropic scattering does not affect the interior temperature. This is nicely explained by the analytic two-layer model; the energy loss by scattering in the disc atmosphere is exactly offset by the "green-house effect" due to scattering of the cold diffuse radiation in the interior.Comment: MNRAS accepte

A semi-analytical model of disk evaporation by thermal conduction

The conditions for disk evaporation by electron thermal conduction are examined, using a simplified semi--analytical 1-D model. The model is based on the mechanism proposed by Meyer & Meyer-Hofmeister (1994) in which an advection dominated accretion flow evaporates the top layers from the underlying disk by thermal conduction. The evaporation rate is calculated as a function of the density of the advective flow, and an analysis is made of the time scales and length scales of the dynamics of the advective flow. It is shown that evaporation can only completely destroy the disk if the conductive length scale is of the order of the radius. This implies that radial conduction is an essential factor in the evaporation process. The heat required for evaporation is in fact produced at small radii and transported radially towards the evaporation region.Comment: 9 pages, 4 postscript figures, accepted for publication in A&

Radiative transfer in very optically thick circumstellar disks

In this paper we present two efficient implementations of the diffusion approximation to be employed in Monte Carlo computations of radiative transfer in dusty media of massive circumstellar disks. The aim is to improve the accuracy of the computed temperature structure and to decrease the computation time. The accuracy, efficiency and applicability of the methods in various corners of parameter space are investigated. The effects of using these methods on the vertical structure of the circumstellar disk as obtained from hydrostatic equilibrium computations are also addressed. Two methods are presented. First, an energy diffusion approximation is used to improve the accuracy of the temperature structure in highly obscured regions of the disk, where photon counts are low. Second, a modified random walk approximation is employed to decrease the computation time. This modified random walk ensures that the photons that end up in the high-density regions can quickly escape to the lower density regions, while the energy deposited by these photons in the disk is still computed accurately. A new radiative transfer code, MCMax, is presented in which both these diffusion approximations are implemented. These can be used simultaneously to increase both computational speed and decrease statistical noise. We conclude that the diffusion approximations allow for fast and accurate computations of the temperature structure, vertical disk structure and observables of very optically thick circumstellar disks.Comment: Accepted for publication in A&

Planetesimal formation during protoplanetary disk buildup

Models of dust coagulation and subsequent planetesimal formation are usually computed on the backdrop of an already fully formed protoplanetary disk model. At the same time, observational studies suggest that planetesimal formation should start early, possibly even before the protoplanetary disk is fully formed. In this paper, we investigate under which conditions planetesimals already form during the disk buildup stage, in which gas and dust fall onto the disk from its parent molecular cloud. We couple our earlier planetesimal formation model at the water snow line to a simple model of disk formation and evolution. We find that under most conditions planetesimals only form after the buildup stage when the disk becomes less massive and less hot. However, there are parameters for which planetesimals already form during the disk buildup. This occurs when the viscosity driving the disk evolution is intermediate ($\alpha_v \sim 10^{-3}-10^{-2}$) while the turbulent mixing of the dust is reduced compared to that ($\alpha_t \lesssim 10^{-4}$), and with the assumption that water vapor is vertically well-mixed with the gas. Such $\alpha_t \ll \alpha_v$ scenario could be expected for layered accretion, where the gas flow is mostly driven by the active surface layers, while the midplane layers, where most of the dust resides, are quiescent.Comment: 6 pages, 5 figures, accepted for publication in A&A, minor changes due to language editio

Can dust coagulation trigger streaming instability?

Streaming instability can be a very efficient way of overcoming growth and drift barriers to planetesimal formation. However, it was shown that strong clumping, which leads to planetesimal formation, requires a considerable number of large grains. State-of-the-art streaming instability models do not take into account realistic size distributions resulting from the collisional evolution of dust. We investigate whether a sufficient quantity of large aggregates can be produced by sticking and what the interplay of dust coagulation and planetesimal formation is. We develop a semi-analytical prescription of planetesimal formation by streaming instability and implement it in our dust coagulation code based on the Monte Carlo algorithm with the representative particles approach. We find that planetesimal formation by streaming instability may preferentially work outside the snow line, where sticky icy aggregates are present. The efficiency of the process depends strongly on local dust abundance and radial pressure gradient, and requires a super-solar metallicity. If planetesimal formation is possible, the dust coagulation and settling typically need ~100 orbits to produce sufficiently large and settled grains and planetesimal formation lasts another ~1000 orbits. We present a simple analytical model that computes the amount of dust that can be turned into planetesimals given the parameters of the disk model.Comment: 12 pages, 6 figures, 1 table, accepted for publication in A&A (minor corrections with respect to v1

An efficient algorithm for two-dimensional radiative transfer in axisymmetric circumstellar envelopes and disks

We present an algorithm for two-dimensional radiative transfer in axisymmetric, circumstellar media. The formal integration of the transfer equation is performed by a generalization of the short characteristics (SC) method to spherical coordinates. Accelerated Lambda Iteration (ALI) and Ng's algorithm are used to converge towards a solution. By taking a logarithmically spaced radial coordinate grid, the method has the natural capability of treating problems that span several decades in radius, in the most extreme case from the stellar radius up to parsec scale. Flux conservation is guaranteed in spherical coordinates by a particular choice of discrete photon directions and a special treatment of nearly-radially outward propagating radiation. The algorithm works well from zero up to very high optical depth, and can be used for a wide variety of transfer problems, including non-LTE line formation, dust continuum transfer and high temperature processes such as compton scattering. In this paper we focus on multiple scattering off dust grains and on non-LTE transfer in molecular and atomic lines. Line transfer is treated according to an ALI scheme for multi-level atoms/molecules, and includes both random and systematic velocity fields. The algorithms are implemented in a multi-purpose user-friendly radiative transfer program named RADICAL. We present two example computations: one of dust scattering in the Egg Nebula, and one of non-LTE line formation in rotational transitions of HCO$^{+}$ in a flattened protostellar collapsing cloud.Comment: 18 pages, 32 figure

Size-sorting dust grains in the surface layers of protoplanetary disks

Aims: We wish to investigate what the effect of dust sedimentation is on the observed 10 mum feature of protoplanetary disks and how this may affect the interpretation of the observations. Methods: Using a combination of modeling tools, we simulated the sedimentation of a dust grain size distribution in an axisymmetric 2-D model of a turbulent protoplanetary disk, and we used a radiative transfer program to compute the resulting spectra. Results: We find that the sedimentation can turn a flat feature into a pointy one, but only to a limited degree and for a very limited set of particle size distributions. Only if we have a bimodal size distribution, i.e. a very small grain population and a bigger grain population, do we find that the transformation from a flat to a pointy feature upon dust sedimentation is strong. However, our model shows that, if sedimentation is the sole reason for the variety of silicate feature strengths observed in protoplanetary disks, then we would expect to find a correlation such that disks with weak mid- to far-infrared excess have a stronger 10 mum silicate feature than disks with a strong mid- to far-infrared excess. If this is contrary to what is observed, then this would indicate that sedimentation cannot be the main reason for the variety of 10 mum silicate features observed in protoplanetary disks.Comment: Astronomy and Astrophysics, in pres

Interferometer predictions with triangulated images: solving the multi-scale problem

Interferometers play an increasingly important role for spatially resolved observations. If employed at full potential, interferometry can probe an enormous dynamic range in spatial scale. Interpretation of the observed visibilities requires the numerical compu- tation of Fourier integrals over the synthetic model images. To get the correct values of these integrals, the model images must have the right size and resolution. Insufficient care in these choices can lead to wrong results. We present a new general-purpose scheme for the computation of visibilities of radiative transfer images. Our method requires a model image that is a list of intensities at arbitrarily placed positions on the image-plane. It creates a triangulated grid from these vertices, and assumes that the intensity inside each triangle of the grid is a linear function. The Fourier integral over each triangle is then evaluated with an analytic expression and the complex visibility of the entire image is then the sum of all triangles. The result is a robust Fourier trans- form that does not suffer from aliasing effects due to grid regularities. The method automatically ensures that all structure contained in the model gets reflected in the Fourier transform.Comment: 9 pages, 7 figures, accepted for publication in MNRA