Structure of Circumstellar Disks

Some basic constraints on the structure of circumstellar disks can be derived by modeling their spectral energy distribution (SED). As a first approximation, the SED of a circumstellar disk can be modeled as the sum of the contribution of annuli, each emitting as black body at a local temperature Td(r), where r is the distance from the central star. Under these assumptions the SED of a circumstellar disk can be written as

COS n C

where Bv is the Planck function, and tv is proportional to the dust opacity at the frequency v and the dust surface density distribution. The local temperature at each radius is determined by the balance between cooling due to the emitted radiation and the heating. The two main heating sources are the direct radiation from the central star and the viscous dissipation. Both these processes predict temperature distributions Td ~ r-q with q = 0.75 (see [22] for a detailed discussion).

These simple parametric models have been widely used to infer global properties of disks around young stars. The general result (e.g. [3]) has been that such models account well for overall shape of the observed SEDs in T Tauri and HAeBe systems, but the temperature profile Td(r) has to fall off much more slowly than predicted by the simplistic models described above. To fit the observed data, the derived value of q is close to 0.5.

The most successful solution to this inconsistency is the class of disk models that include a flaring outer disk [18] and an optically thin disk atmosphere [8]. These models predict that the disk-opening angle or the ratio between the scale height and the radius increases toward the outer disk. The grazing angle at which the stellar radiation impinges on the disk changes with radius, allowing for an increase of the heating of the outer regions of the disk. The optically thin (to the disk radiation) atmosphere absorbs the stellar radiation and is warmer than the disk (optically thick) interior at the same radius.

These disk models have been extremely successful in explaining a number of observational properties of disks that range from the overall shape of the SED to the scattered light images of disks. These are, thus, the reference models that are used as benchmark for the observations. The disk structure predicted by these models has important implications on which regions of the disk are probed by different observational techniques.

Scattered light emission in the visible and near-infrared are a sensitive probe of the small dust grains population in the upper layers of the disk atmosphere, while emission in the mid-infrared features of the silicates probe the emission of dust grains in the atmosphere. The disk midplane, which contains the bulk of the disk mass, can only be probed directly at millimeter and longer wavelengths, where the emission becomes optically thin. In the following section, I will discuss how the use of different high angular resolution observations allow to constrain the structure and physical properties in different regions of the disk.

2.1 The Disk Atmosphere

The properties of dust grains and macro-molecules in the disk atmosphere can be probed indirectly by observing the scattered light emission from the central star or directly observing the emission features in the mid-infrared.

By comparison with disk models, both observables also allow to constrain the geometrical structure of the disk atmosphere, such as the disk flaring.

In this lecture, I will concentrate on the dust emission diagnostics and refer to [33] for a recent review on the properties of disks derived from scattered light images at various wavelengths.

2.2 Diamonds and PAH

Very small dust particles and macro-molecules emit a rich spectrum of features in the mid-infrared, most of which have not been univocally identified so far. It is generally believed that the unidentified features at 3.3, 7.7-7.9, 8.6, 11.3, and 12.7 |m are associated with transiently heated large Policyclic Aromatic Hydrocarbons (PAH). These have been widely detected in HAeBe systems [1]. The exact region of the system in which these are located has been debated for some time, until diffraction-limited 10-12 |m observations with large telescopes [6] and adaptive optics-assisted L-band spectroscopy have resolved the emission as predicted by flared disk models [14, 15]. In one system, HD97048 (see Fig. 1), an additional feature was detected and resolved at

Fig. 1. NAOS/CONICA VLT observations of the 3.6 |m "diamonds" and 3.3 |m PAH features and the adjacent continuum in the HD97048 intermediate mass system (adapted from [14, 15]). The upper panel shows the intensity profile of the continuum subtracted diamond feature as a thick line histogram, the adjacent continuum profile as a thin histogram, and the profile of an unresolved star as dashed line; the diamond emission is clearly resolved. In the bottom panel the PAH and continuum profiles are compared with disk model computations for the PAH line (dot-dashed) and the continuum (dotted)

Fig. 1. NAOS/CONICA VLT observations of the 3.6 |m "diamonds" and 3.3 |m PAH features and the adjacent continuum in the HD97048 intermediate mass system (adapted from [14, 15]). The upper panel shows the intensity profile of the continuum subtracted diamond feature as a thick line histogram, the adjacent continuum profile as a thin histogram, and the profile of an unresolved star as dashed line; the diamond emission is clearly resolved. In the bottom panel the PAH and continuum profiles are compared with disk model computations for the PAH line (dot-dashed) and the continuum (dotted)

Fig. 2. Compilation of observations of silicates profiles in HAebe, TTS, and BD systems and in the laboratory (adapted from [25] and references therein)

3.6 |m, which is suggested to be associated with C-C stretch in diamond-like carbon grains.

The presence and abundance of these macro-molecules in the disk atmospheres has a strong impact on the gas heating and chemistry in the disk as they contribute to a significant fraction of the gas heating via the photoelectric effect. They may also affect the formation rate of molecular hydrogen on the grain surfaces. These grains need to be taken into account in most accurate disk models; however, one of the most serious limitations, in doing this is that observations of these grains cannot probe the population in the disk interiors, and models have to rely on assumptions on the abundance throughout the disk.

2.3 Silicates

Astronomical silicates have one of the most prominent emission features at 10 |m; one of the successes of the flared disks models with atmosphere is the natural explanation for the emission observed in this feature in a large variety of circumstellar disks [8]. In recent years with high quality mid-infrared spectra becoming available first with ISO and more recently with Spitzer, it has been possible to attempt to understand the diversity of the profiles observed in various regions.

As reviewed in [25], the modeling of silicate profiles in disks, as well as comparison to laboratory measurements, can give indications on the degree of "crystallinity" and on the size of the emitting particles. The observed systems show a range of properties with grains similar to those present in the diffuse

Fig. 3. VLTI/MIDI observations of the silicate profile in the three HAeBe systems HD163296, HD144432, and HD142527. In the top panel a flared disk is sketched, in the bottom panels the MIDI observations of the inner disks are compared to the emission from the outer disk derived by subtracting the interferometric spectrum from single telescope spectra (adapted from [5])

Fig. 3. VLTI/MIDI observations of the silicate profile in the three HAeBe systems HD163296, HD144432, and HD142527. In the top panel a flared disk is sketched, in the bottom panels the MIDI observations of the inner disks are compared to the emission from the outer disk derived by subtracting the interferometric spectrum from single telescope spectra (adapted from [5])

interstellar medium to grains that have undergone a significant processing, both in terms of crystallization and growth. It is still difficult to properly understand the zoo of properties observed, and in particular the expectation that dust processing evolves with time, i.e., with the age of the system, is still not evident from the current observations.

High angular resolution observations with the VLTI (see contribution from Malbet, this volume) allows one to investigate the properties of the silicate profile as a function of the distance from the central star. In Fig. 3, we show the results of [5] who demonstrated that the dust in the inner regions of disks is more processed than in the outer region. This is consistent with the expectations that the evolution of dust is faster closer to the star [12].

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