Protoplanetary Disks Disk Behaviour

A typical cloud core has a velocity gradient across its (nominally ~ 0.1 pc) diameter of about 1 km s-1 pc-1, although accurate determinations are difficult because of turbulence. If this gradient is attributed to rotation, the angular momentum exceeds that of the Sun by more than a factor of 100,000 (Armitage, 2007). To allow collapse, the angular momentum is predicted to be deposited into a massive circumstellar disk (e.g., Terebey et al. (1984); Hogerheijde (2001)).

Stars emerge from this phase surrounded by disks with sizes of 70 to 1000 AU (e.g., Kitamura et al. (2002); Qi et al. (2003); Semenov et al. (2005); Andrews & Williams (2007)). Hillenbrand (2002) reviews the evolution of these disks. Initially, their inner regions (< 1AU) are heated by continuing accretion, while the heating in the outer zones is dominated by absorption of stellar radiation. The energy deposited by accretion can be estimated from the release of potential energy, showing that it is dominant at accretion rates larger than about 3 x 10~8 M©/yr. Measured rates range from well above this value to two orders of magnitude below (Gullbring et al., 1998). Thus, as the star ages and accretion dies out, the entire disk begins to emit passively, powered by radiative energy absorbed from the star. During this later phase, the disks absorb and reradiate in the infrared about 1-10% of the stellar output2. This ratio of infrared excess to total luminosity is termed the fractional luminosity of the disk.

Initially, the inner zones of these disks out to a few stellar radii are cleared by the effects of the magnetic field. Another fixed boundary is set by the radius within which the dust is destroyed by the radiation field of the star. Because the inner rim of the region where the dust can survive is directly exposed to the stellar radiation, it is much hotter than the rest of the disk and may puff up. This effect is proposed to be dramatic for luminous Herbig Ae stars (where the rim is near 0.5 AU) (Dullemond et al. (2001), but see also Muzerolle et al. (2004)). It is more subdued for lower mass T Tauri stars (where the rim is within 0.1 AU: Muzerolle et al. (2003)). Terrestrial planets cannot form in these inner cleared regions, and the temperatures are too high for gaseous planets.

Outside this inner rim, the stellar energy is absorbed in the outer layers of the optically thick disk; half is promptly radiated away into space and the other half is radiated inward to heat the interior of the disk. Models combining both radiative transfer and hydrostatic equilibrium in the disk interior show that the disk flares at increasing distances from the star, such that it absorbs more energy than would be the case for a flat disk (Kenyon & Hartmann, 1987; Chiang & Goldreich, 1997). Scattered light images of young disks confirm that they have significant depth and, in favourable cases, show the flaring (e.g., Burrows et al. (1996); Stapelfeldt et al. (1998); Padgett et al. (1999)), see Fig. 4.1. Analysis of the scattered light images

2 Although the role of protoplanetary disks in young stellar infrared excesses now seems obvious, it took more than a decade after the first infrared detections for this explanation to be proposed (Grasdalen et al., 1984; Beall, 1987)

Fig. 4.1. Image of protoplanetary disk HH30 (Burrows et al., 1996). The edge-on disk occults the star to act as a natural coronagraph and allow detailed structures to be seen in both the disk and the jets.

can provide constraints on the disk inclination, the wavelength-dependent opacity (and hence can search for evidence of grain growth), and the scale height of the disk. Flaring can be measured directly by analysis of the dark, obscured lane. Further discussion can be found in the reviews by Dullemond et al. (2007) and Armitage (2007).

From this state, protoplanetary disks clear progressively to larger radii as the system evolves. There are a variety of dispersal mechanisms, such as photoevapo-ration, grain growth, accretion onto planetesimals, and ejection from the system. Clearing times for the inner disks (order of 1 AU) in these systems are typically 3 Myr (Haisch et al., 2001). Spitzer observations provide good statistics to track this behaviour out to its final stages. Lada et al. (2006) find 30 ± 4% optically thick disks (indicated by excesses at 5.8 and 8 pm) in the 2-3 Myr old IC 348 cluster. Hernandez et al. (2007) report that about 35% of the roughly solar-mass members of the 3 Myr old a Ori cluster have excesses at 5.8 and 8 pm (see also Oliveira et al. (2006)). Dahm & Hillenbrand (2007) find 7 ± 2% optically thick disks left in NGC 2362 at 5 Myr. Currie et al. (2007a) find in h and x Per at 13 Myr that no more than half this many stars still have excesses at both 5.8 and 8 pme. Gorlova et al. (2007) find an upper limit of about 1% for disks emitting at 5.8 and 8 pm in NGC 2547 at 25 Myr. For additional examples, see Sicilia-Aguilar et al. (2006) and Bonatto et al. (2006), but note Megeath et al. (2005) and Haisch et al. (2005); Hillenbrand (2005) reviews observations of disk dispersal.

Snapshots of the evolution of young disks are provided by images in scattered light, both with HST and from the ground. Because such observations are limited

Fig. 4.2. Scattered light image of the disk around the 5 Myr old star HD 141569A (Clampin et al., 2003). The left panel is the HST/ACS image; the star has been occulted by the instrument coronagraph. In the right image, the disk is viewed as if face-on to show the structure in more detail (the image has also been filtered to remove diffraction artifacts). The structures in the disk may arise from planets, or from interactions with passing stars, or a combination.

Fig. 4.2. Scattered light image of the disk around the 5 Myr old star HD 141569A (Clampin et al., 2003). The left panel is the HST/ACS image; the star has been occulted by the instrument coronagraph. In the right image, the disk is viewed as if face-on to show the structure in more detail (the image has also been filtered to remove diffraction artifacts). The structures in the disk may arise from planets, or from interactions with passing stars, or a combination.

in surface brightness sensitivity, they have been successful primarily on the relatively dense disks that are emerging from the protoplanetary stage. Among other examples, images have been obtained for T Tauri stars such as GG Tau and UY Aur (Krist et al., 2005; Close et al., 1998), pre-main-sequence stars such as TW Hya (Roberge et al. (2005) and references therein), and very young more massive stars such as HD 141569A (see Fig. 4.2) and AB Aur (Ardila et al. (2005); Marinas et al. (2006)). The number of imaged systems is now adequate to support a vigorous field of comparative anatomy and physical analysis of the dynamics of young disks. It is often found that they have marked asymmetries and complex structures possibly associated with gravitational instabilities, either within the disk or due to perturbations by passing stars. This subject is reviewed by Watson et al. (2007).

Despite the trend of clearing from the inner to the outer regions, the dense outer disk zones also disperse rapidly: Andrews & Williams (2005) report that only 10% of young stars have evidence for a cold and dense outer disk in submm emission yet do not have near-infrared excesses indicative of material in the ~ 1 AU zone. They also tentatively conclude that the dense outer disks dissipate on a ~ 6 Myr time scale, as predicted by some models of disk photoevaporation (Alexander et al., 2006a,b).These trends also depend on stellar mass, with disks disappearing more rapidly around stars significantly more massive than the Sun (Carpenter et al., 2006; Hernandez et al., 2007; Dahm & Hillenbrand, 2007; Currie et al., 2007a).

The amount of raw material in protoplanetary disks can be determined by measurements in the submillimetre. There, the disks are generally optically thin and the emission is in the Rayleigh-Jeans regime, so the flux density and disk mass

Fig. 4.3. Cumulative distribution of disk masses, from Andrews & Williams (2005). The best fitting log-normal distributions are shown as dashed lines. The best estimate of the intrinsic distribution is the fit for the full sample, including upper limits in the fit.

OB O

Fig. 4.3. Cumulative distribution of disk masses, from Andrews & Williams (2005). The best fitting log-normal distributions are shown as dashed lines. The best estimate of the intrinsic distribution is the fit for the full sample, including upper limits in the fit.

are directly proportional (Hildebrand, 1983). Andrews & Williams (2005) report submillimetre measurements of 153 young stellar objects. The data are fitted by a lognormal distribution with a mean value of 3 x 10~3 M© and a variance of 1.31 dex, i.e. there is a very broad range of masses (see Fig. 4.3). This result is reinforced by a study of 336 stars in the Orion Trapezium region (Eisner & Carpenter, 2006). Although less than 10% of the systems were detected directly, stacking the data yielded an estimate of 5 x 10~3 M© for the average disk mass. The wide range of disk mass for a narrow range of stellar mass indicates that there must be important variables in disk formation such as the residual angular momentum of the collapsing cold cloud core. As a result, there is little reason to expect planetary system formation to have a strong dependence on stellar type.

The conditions that might lead to a planetary system similar to ours make an interesting benchmark. The minimum mass of the solar protoplanetary disk can be derived by taking each planet and adding to its mass sufficient material to represent the solar composition (Weidenschilling, 1977; Hayashi, 1981). Thus, a substantial mass must be added for each terrestrial planet to account for the missing hydrogen and helium, while for Jupiter and Saturn the correction is small. The resulting mass surface density is roughly from about 0.7 to 30 AU. From integrating this profile, the minimum mass required to form the planets is about 0.01 M©. Based on the submm emission, Andrews & Williams (2005) found that only 37% of the disks exceed the minimum mass required for the planets in the Solar System; in agreement, Eisner & Carpenter (2006) found

an average disk mass slightly below this minimum mass. These estimates are subject to significant systematic errors (largely because of uncertainties in the grain optical constants due to grain growth in the disk environment (Andrews & Williams, 2007)). However, due to the inefficiencies in planet formation, it is also likely that the Solar System started with a substantially more massive disk than the minimum possible. It appears likely that a substantial fraction of stars do not have disks massive enough to replicate our Solar System.

The evolution of the innermost parts of disks is generally correlated with the accretion rates onto their stars. About 80% of binary pairs are either both CTTS or both WTTS (e.g., Hartigan et al. (1994); Prato & Simon (1997); Duchene et al. (1999); Hartigan & Kenyon (2003)), showing that the inner disks of both stars have evolved at similar rates. However, disk structures are seen to vary at a given age due to variations in the clearing time of the ~ 1 AU disk zones prominent in the mid-infrared (Hernandez et al. (2007) and references therein). Variations in the infrared characteristics of very young binary pairs are also common (Haisch et al., 2006). Much of the variety may result from the range of initial disk properties, as is apparent from the range of masses. Another contributor may be that the transition in disk properties occurs rapidly and therefore may not synchronise precisely with emission line properties. In addition, a small number of systems appear to retain warm, primordial dust for perhaps 10 Myr, significantly longer than is typical (Silverstone et al., 2006).

In conclusion, there is a well-defined overall pattern of protoplanetary disk characteristics. However, equally striking is the wide range of starting conditions, e.g. disk masses, along with some variation in evolutionary time scales. These differences presumably translate into a wide range of properties for the planetary systems that develop within these disks.

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