Protoplanetary disks and the formation of planet systems

Stars and planets form within dense, cold clouds of gas and dust, known as molecular clouds. Surveys of many molecular clouds show that most stars form as members of entire star clusters. These stellar nurseries arise from dense regions within molecular clouds known as clumps which extend over about 1 pc in physical scale (or about 3 light years, or 205 000 astronomical units - AU - where 1 AU =1.5 x 1013 cm is the distance between the Earth and the Sun) and typical initial temperatures around 20 K. The gas in clouds and clumps is stirred vigorously by supersonic turbulence which also generates its filamentary structure. A single star, or a binary stellar system, forms within a small, dense subregion of a clump (known as a core) that, for stars like the Sun, extends over a scale of 0.04 pc and has a (particle) number density ranging from 104 to 108 cm-3.

Numerical simulations of supersonic turbulent gas under the observed conditions show how stars and their protoplanetary disks form. Supersonic turbulence first sweeps up the gas into systems of shocked sheets and filaments. Dense core-like regions are produced as such flows develop. Also, the shock waves that produce the cores are oblique and hence impart spin to the cores (see MacLow and Klessen (2004) for a review). The eventual gravitational collapse of such slowly spinning cores under their own weight preserves most of their angular momentum, resulting in the formation of protoplanetary disks (e.g., Tilley and Pudritz (2004)).

Surveys of star-forming regions have established that disks are universal around solar mass stars. Stars range over more than three decades in mass, and for all of them, one has evidence for disks. The least massive of these is the disk around an object that has only 15 MJ (Jovian masses)! (Note, the mass of Jupiter is one thousandth the mass of the sun; MJ = 0.001 MQ.) Disks are commonly observed around solar-like stars as they form. At the most massive end, rotating disks have been found around B stars that are up to 10 MQ (e.g., Schreyer et al. (2005)).

Most studies generally do not resolve a disk around a star but infer its presence from the excess of infrared emission that is seen in the spectrum of the star. Disks around forming solar-type stars typically extend out to more than 100 AU, with the temperature varying as a function of the radius r. In our Solar System, the orbital radius of the Earth around the Sun is 1 AU, while that of the most massive outer planet, Neptune, is 30 AU. The total emission from this collection of rings of gas and dust, each of which emits radiation like a blackbody, adds up to the observed excess infrared emission (known as the spectral energy distribution or SED).

For solar-type stars, the disk temperature that can be inferred from such observations scales with disk radius as T a r-0 6, with a temperature at 100 AU of about 30 K. Similarly, one can deduce that the column density of the disk (which is the volume density integrated over the disk thickness at a given radius) varies as X a r-15 and has a value at 100 AU of 0.8 g cm-2. Disks seen at these later stages of their evolution are far less massive than are their central stars, having typically 10-2Mq of gas and dust (e.g., Dutrey et al. (2006)). Hence, their dynamics are governed by the gravitational field of the central star, and the material is expected to be in nearly Keplerian orbit about the star (i.e., vKep(r) = ^f(GM^/r)).

Occasionally, one can also spatially resolve the disk around a young star. The rotation curves of the disks can be measured under such conditions, as has been done in molecular observations (Simon et al., 2000), and these have been found to be nearly Keplerian. At a slightly later stage (a few hundred thousand years), after the surrounding cloud is blown away by the young massive star, stars and their disks still in formation can be seen in optical images. This is seen in the Hubble Space Telescope (HST) image in Figure 4.1, where we see several images of young stars that are forming in the Orion Nebula Cluster. A massive star has created a strongly illuminated background of glowing nebular gas. The HST image shows a disk around each young star which is seen as a silhouette against this bright background (McCaughrean and Stauffer, 1994). Disks are heated primarily by the young star that they surround as well as by a massive nearby star in the case of

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