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&

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

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

Radiation hydrodynamics including irradiation and adaptive mesh refinement with AZEuS. I. Methods

Aims. The importance of radiation to the physical structure of protoplanetary disks cannot be understated. However, protoplanetary disks evolve with time, and so to understand disk evolution and by association, disk structure, one should solve the combined and time-dependent equations of radiation hydrodynamics. Methods. We implement a new implicit radiation solver in the AZEuS adaptive mesh refinement magnetohydrodynamics fluid code. Based on a hybrid approach that combines frequency-dependent ray-tracing for stellar irradiation with non-equilibrium flux limited diffusion, we solve the equations of radiation hydrodynamics while preserving the directionality of the stellar irradiation. The implementation permits simulations in Cartesian, cylindrical, and spherical coordinates, on both uniform and adaptive grids. Results. We present several hydrostatic and hydrodynamic radiation tests which validate our implementation on uniform and adaptive grids as appropriate, including benchmarks specifically designed for protoplanetary disks. Our results demonstrate that the combination of a hybrid radiation algorithm with AZEuS is an effective tool for radiation hydrodynamics studies, and produces results which are competitive with other astrophysical radiation hydrodynamics codes.Comment: 15 pages, 10 figures, accepted for publication in A&

Lopsided dust rings in transition disks

Context. Particle trapping in local or global pressure maxima in protoplanetary disks is one of the new paradigms in the theory of the first stages of planet formation. However, finding observational evidence for this effect is not easy. Recent work suggests that the large ring-shaped outer disks observed in transition disk sources may in fact be lopsided and constitute large banana-shaped vortices. Aims. We wish to investigate how effective dust can accumulate along the azimuthal direction. We also want to find out if the size- sorting resulting from this can produce a detectable signatures at millimeter wavelengths. Methods. To keep the numerical cost under control we develop a 1+1D method in which the azimuthal variations are treated sepa- rately from the radial ones. The azimuthal structure is calculated analytically for a steady-state between mixing and azimuthal drift. We derive equilibration time scales and compare the analytical solutions to time-dependent numerical simulations. Results. We find that weak, but long-lived azimuthal density gradients in the gas can induce very strong azimuthal accumulations of dust. The strength of the accumulations depends on the P\'eclet number, which is the relative importance of advection and diffusion. We apply our model to transition disks and our simulated observations show that this effect would be easily observable with ALMA and in principle allows to put constraints on the strength of turbulence and the local gas density.Comment: 4 pages, 4 figures, accepted for publication in A&A Letter

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&

Flaring and self-shadowed disks around Herbig Ae stars: simulations for 10 micron interferometers

We present simulations of the interferometric visibilities of Herbig Ae star disks. We investigate whether interferometric measurements in the 10 micrometer atmospheric window are sensitive to the presence of an increased scale height at the inner disk edge, predicted by recent models. Furthermore, we investigate whether such measurements can discriminate between disks with a ``flaring'' geometry and disks with a ``flat'' geometry. We show that both these questions can be addressed, using measurements at a small number of appropriately chosen baselines. The classification of Herbig Ae stars in two groups, based on the appearance of the spectral energy distribution (SED), has been attributed to a difference in disk geometry. Sources with a group I SED would have a flaring outer disk geometry, whereas the disk of group II sources is proposed to be flat (or ``self-shadowed''). We show that this hypothesis can be tested using long-baseline interferometric measurements in the micrometer atmospheric window.Comment: 10 pages, 7 figures, accepted for publiction in Astronomy and Astrophysic

Gas- and dust evolution in protoplanetary disks

Context. Current models of the size- and radial evolution of dust in protoplanetary disks generally oversimplify either the radial evolution of the disk (by focussing at one single radius or by using steady state disk models) or they assume particle growth to proceed monodispersely or without fragmentation. Further studies of protoplanetary disks - such as observations, disk chemistry and structure calculations or planet population synthesis models - depend on the distribution of dust as a function of grain size and radial position in the disk. Aims. We attempt to improve upon current models to be able to investigate how the initial conditions, the build-up phase, and the evolution of the protoplanetary disk influence growth and transport of dust. Methods. We introduce a new version of the model of Brauer et al. (2008) in which we now include the time-dependent viscous evolution of the gas disk, and in which more advanced input physics and numerical integration methods are implemented. Results. We show that grain properties, the gas pressure gradient, and the amount of turbulence are much more influencing the evolution of dust than the initial conditions or the build-up phase of the protoplanetary disk. We quantify which conditions or environments are favorable for growth beyond the meter size barrier. High gas surface densities or zonal flows may help to overcome the problem of radial drift, however already a small amount of turbulence poses a much stronger obstacle for grain growth.Comment: accepted to A&

Dust-driven viscous ring-instability in protoplanetary disks

Protoplanetary disks often appear as multiple concentric rings in dust continuum emission maps and scattered light images. These features are often associated with possible young planets in these disks. Many non-planetary explanations have also been suggested, including snow lines, dead zones and secular gravitational instabilities in the dust. In this paper we suggest another potential origin. The presence of copious amounts of dust tends to strongly reduce the conductivity of the gas, thereby inhibiting the magneto-rotational instability, and thus reducing the turbulence in the disk. From viscous disk theory it is known that a disk tends to increase its surface density in regions where the viscosity (i.e. turbulence) is low. Local maxima in the gas pressure tend to attract dust through radial drift, increasing the dust content even more. We investigate mathematically if this could potentially lead to a feedback loop in which a perturbation in the dust surface density could perturb the gas surface density, leading to increased dust drift and thus amplification of the dust perturbation and, as a consequence, the gas perturbation. We find that this is indeed possible, even for moderately small dust grain sizes, which drift less efficiently, but which are more likely to affect the gas ionization degree. We speculate that this instability could be triggered by the small dust population initially, and when the local pressure maxima are strong enough, the larger dust grains get trapped and lead to the familiar ring-like shapes. We also discuss the many uncertainties and limitations of this model.Comment: Accepted for publication in A&