Protoplanetary disks:
Solar systems under construction

Introduction

One of my main topics is circumstellar dust+gas disks surrounding pre-main-sequence stars. These are the disks from which planetary systems are formed. By studying these disks it is hoped that it can be figured out how our own solar system was formed billions of years ago, and if our own solar system is unique, or one of many. It is an intriguing topic, not in the least part because there is an increasing volume of observations available, and much more will come in the near future when large interferometer telescopes will come on-line (VLTI, ALMA). Moreover, it seems that the latest models for these disks actually work and agree with observations (see below). It is therefore a fruitful area of research. My main collaborators are Carsten Dominik, Antonella Natta, Rens Waters, Roy van Boekel, Mario van den Ancker, Bram Acke and Gerd-Jan van Zadelhoff. But many others contributed as well in many ways.

My main efforts in this context are currently on the construction of fully self-consistent 2-D models of protoplanetary disks. This involves 2-D radiative transfer calculations coupled to the equations of vertical hydrostatic equilibrium. It is a "2-D radiation-hydrostatics" calculation in that sense. This has never been done before, and it turns out that the resulting disk models are quite different from the models described in the literature so far. Moreover, it seems that these new models can explain many observations much more naturally than earlier models. On this page I will describe a bit how the models are made and the conclusions drawn from them. All of this is described in much more detail in my papers, to which links are provided.

Some sub-pages relating to my work in this field

My radiative transfer home page (many more links here)

Download FITCGPLUS version 2.1 [new version, Sept 2005!] (Dullemond Dominik & Natta 2001)

1+1D Disk models

1+1D Disk models: a comparison to CG models

1+1D Disk models: the effects of scattering

1+1D Disk models: some benchmark tests

2-D Disk models (grey opacity; old models)

2-D Disk models (NEW ONES WITH REALISTIC OPACITIES)

Movies and images

Pictograms of various disk geometries

Postscript versions of Openoffice Presentations

A description of my main line of research: "The structure of protoplanetary disks"

Protoplanetary disks are the remnants of the accretion disks from which the stars were formed. It is believed that planets are formed in these disks by growing dust grains (through sticking) to ever larger clumps of matter until planetesimals are formed leading finally to the formation of planets. Conventional wisdom says that disks have a `flaring geometry' so that the stellar radiation is able to reach the surface of the disk and keep the disk warm. The thermal emission from such a flaring disk is then held responsible for the infrared emission seen from most of the protoplanetary systems known. Much work has been done by various authors on detailed models of this kind (e.g. by Paola D'Alessio at al., Eugene Chiang et al., Fabien Malbet et al. and many more).

One of the first indications I found that this flaring geometry might not always be true in reality was the existence of an instability in the disk due to self-shadowing effects. Tiny ripples in the disk's surface might be amplified, and it is unknown to which level this instability saturates. It could be that the disk will develop cold and hot rings, created at a certain radius and slowly moving towards smaller radii. This might be seen by ALMA as if these were planetary gaps! But it is unknown what is really happening with such unstable modes, since the computational capabilities were not there yet when I wrote this article.

Dullemond, Astron. Astrophys. 361, L17-L20 (2000): Are passive protostellar disks stable to self-shadowing?

At a workshop in Amsterdam in November 2000 Antonella Natta presented her ideas concerning the `near infrared bump' seen in the SEDs of all Herbig Ae/Be stars (intermediate mass pre-main-sequence stars). Inward of a certain radius (for HAeBe stars typically 0.5 AU or so) the dust in the disk evaporates. Since the dust is the main source of opacity and the gas in the disk is usually optically thin, this effectively burns a hole in the disk. The inner rim of the remaining dusty part of the disk is irradiated by the star `frontally' (i.e. at a 90 degrees angle), while the flaring disk behind it is irradiated under a small flaring angle of about alpha = 0.05 or thereabout. This means that the inner rim is very hot and bright compared to the rest of the disk, and it forms a good explanation for the observed near infrared thermal emission. Also, due to the heat of the rim it will have a `puffed-up' shape compared to the rest of the disk.

Carsten Dominik and I had just finished some first 2-D models of such an inner rim, although for an entirely different application (as a model for the circumstellar disk around the old star HR4049). In combination with my previous work on disks, and Carsten's earlier discussions with Antonella, this presentation by Antonella motivated us to make self-consistent models along these lines. We outfitted the Chiang & Goldreich model with a consistent treatment of the `puffed-up inner rim' and were able to reproduce many of the characteristic features of the SEDs of Herbig Ae/Be stars.

Dullemond, Dominik & Natta, ApJ 560, 957-969 (2001): Passive Irradiated Circumstellar Disks with an Inner Hole
Dominik, Dullemond, Waters & Walch, A&A 398, 607-619 (2003): Understanding the spectra of isolated Herbig stars in the frame of a passive disk model

However, we found out that there are many things that we cannot model in enough detail using this simplified approach: the puffed-up inner rim casts a shadow over the disk behind it, and sometimes the simple CG+rim model breaks down since it cannot find a flaring disk solution. Moreover, we also found indications that some of the sources we had in our sample may not be very consistent with flaring disks anyway. It became clear that more detailed models were needed: models with 2-D radiative transfer.

Although our work on the puffed up inner rim (see above) taught us that the 1+1D approach to disk modeling is not always adequate, I still continued to develop 1+1D models for the detailed vertical structure of protoplanetary disks, mainly because I felt that there were still a number of questions that remained unanswered in the literature on such models. Moreover, it was as an intermediate step between the simple Chiang & Goldreich + inner rim models and the planned fully 2-D (R,Theta) models. This work also enabled us to make detailed comparisons between CG97-type models versus 1+1D models, as a preliminary stage to comparing things to the fully 2-D models.

Dullemond, van Zadelhoff & Natta, A& A 389, 464-474 (2002), Vertical structure models of T Tauri and Herbig Ae/Be disks (see also it's web page)
Dullemond & Natta, accepted A& A An analysis of two-layer models for circumstellar disks (see also it's web page)
Dullemond & Natta, accepted A& A The effect of scattering on the structure and SED of protoplanetary disks (see also it's web page)

After a long period of code development I finally came in the position to make self-consistent models in 2-D (R, Theta spherical coordinates). This enabled me to make the first-ever self-consistent 2-D axisymmetric models for Herbig Ae/Be disks with radiative transfer coupled to vertical hydrostatic equilibrium. And this means we came in fully unexplored territory.

What I found is that in addition to the usual `flaring disks' there exists a whole new class of disks that are entirely `self-shadowed'. These disks are only irradiated at their inner rim, but the entire outer disk lies in the shadow of the inner rim. The fact that our simple old CG+rim model broke down in certain circumstances was simply an indication that the disk was fully self-shadowed, which the CG+rim model was not able to handle. These first fully self-consistent 2-D models show that flaring- and self-shadowed disks are two main classes of disks around Herbig Ae/Be stars that are natural solution to the equations of radiative transfer coupled to hydrostatic equilibrium.

I found that the SEDs predicted by these two types of disk solutions can very well explain the two types of SEDs found among the sample of Herbig Ae/Be stars of Meeus et al. (2001). They found two classes of SEDs: the group I sources with strong far-IR emission and the group II sources with weak far-IR emission. The results from my models seem to indicate that group I sources are flared disks while group II sources are self-shadowed disks. This confirms a suspicion already noted in the paper by Meeus: that some disks do not flare.

Dullemond, A&A 395, 853-862 (2002) The 2-D structure of dusty disks around Herbig Ae/Be stars (see also it's web page)

This first work on 2-D models had one great shortcoming: it used simple grey opacities. In the last year or so I worked together with Carsten Dominik to refine these models, and include more realistic dust opacities, and investigate the effects of dust coagulations (albeit in a crude way), to see if dust coagulation could transform a flaring disk into a self-shadowed disk. Also we made parameter cubes of models to explore the parameter space in more detail. Our basic results are that we can indeed explain the SEDs of Herbig Ae/Be stars in terms of flaring and self-shadowed disks, and that the models seem to be consistent with a number of other observations as well:

• The presence or absense of PAH features in the ISO spectra. We predict that flaring disks (group I sources) may have PAH features while self-shadowed disks (group II sources) cannot have PAH features. Preliminary results by Acke & van den Ancker (in prep) seem to confirm this result.
• The predictions for near-IR interferometry. Our models make strong predictions for the visibility functions that should be observed. Initial results by some authors seem to hint that our model may be correct indeed (e.g. Eisner et al. Astrophys.J. 588 (2003) 360-372).

A nice side-effect of the 2-D modeling effort is that the resulting new solutions (the self-shadowed solutions) form a natural explanation for UX Orionis variable stars. Previous authors have already noted that nearly-edge-on disks may be held responsible for the sporadic absorption events in the V band. But with the usual flaring disk model this is difficult to understand, as the absobing hydrodynamic filaments of the disk should be located in the outer parts of the disk where the time scales are much too long to be consistent with the observed time scales of weeks to months. The self-shadowed disks allow disk inclinations at which hydrodynamic turbulent eddies at the inner rim can be held responsible for the UXOR absorption events. The time scales are right, and so are the densities in the disk. This makes the prediction that UXORs are self-shadowed disks, i.e. group II sources. We find in our sample of over 80 Herbig Ae/Be stars that this is indeed mostly the case, and the few exceptions to this rule lie close to the border with the group II classification. This seems to be yet another confirmation of the flaring/self-shadowed group I/II identification.

Dullemond, van den Ancker, Acke & van Boekel, submitted to ApJL, Explaining UXOR variability with self-shadowed disks