Star Formation and Protoplanetary Disks

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Observation of stars at different stages of their life has enabled us to retrace the processes of their formation and of the different stages in their evolution. Stars are born within interstellar condensations that are inhomogeneous and turbulent, as a result of the gravitational collapse of a rotating cloud. After a contraction phase, they reach a long period of equilibrium during which they move along the Main Sequence in the Hertzsprung-Russell diagram, which defines the evolution of their luminosity as a function of the temperature (see Appendix A.4 and Fig. 11.2). The collapse process of the initial cloud leads to the formation of a disk, perpendicular to the cloud's axis of rotation, within which planets may form by the accretion of solid particles.

In this chapter, we summarize the first stages of star formation, from the collapse of the interstellar cloud until the star arrives at the Main Sequence, and we describe the evolution of protoplanetary disks as well as their spectral signature. Finally, we describe the physical mechanisms governing the formation of planetesimals and planetary embryos inside the disk. The dynamical evolution of planetary systems and the dynamical interaction between planets and disks are studied in Chap. 6.

5.1 The First Stages in Star Formation 5.1.1 Properties of the Interstellar Medium

The existence of an interstellar medium that was 'not empty' was suspected at the end of the 18th century, when the British astronomer William Herschel observed dark areas among the stars, and which might correspond with material that absorbed visible radiation (Fig. 5.1). At the beginning of the 20th century, this theory was confirmed by spectroscopic detection of narrow absorption lines, which could be attributed to the presence of gas along the line of sight to the star being observed. Following predictions made by C. Van de Hulst and J. Oort, the neutral hydrogen transition at 21 cm was observed in the 1950s. This transition, although intrinsically very faint, is observable only because of the long optical path-lengths available

M. Ollivier et al., Planetary Systems. Astronomy and Astrophysics Library, DOI 978-3-540-75748-1.5, © Springer-Verlag Berlin Heidelberg 2009

Fig. 5.1 The Horsehead Nebula (B33) in the Orion Nebula. The dark silhouette is caused by the absorption by the dust in a dark molecular cloud of the light from the nebulosity lying behind the cloud (IC 434) (image credit: courtesy NOAO, AURA, NFS)

for observation in the Galaxy. Detection of the transition proved the existence of significant quantities of gas in the form of atomic hydrogen. In the 1940s, the CH and CN radicals and the CH+ ion were detected in the centimetric region, followed, in the 1960s, by OH H2O, and NH3, and finally, beginning in the 1970s, CO and numerous molecules, detected in the millimetric region. The interstellar medium does not contain just atomic hydrogen, but also radicals, ions, and molecules. Beginning in the 1970s, observations from space in the UV region (from the Copernicus and IUE - International Ultraviolet Explorer) satellites allowed intense UV sources to be detected, together with absorption lines in their spectra. Infrared observations (with IRAS - InfraRed Astronomical Satellite - then ISO - Infrared Space Observatory, and most recently, Spitzer) have opened access to the study of interstellar dust and circumstellar envelopes. Infrared spectroscopy is a valuable tool for the study of cool regions, such as dense molecular clouds, because the thermal flux from dust peaks in that region, where the spectral signatures from molecules are also the most intense.

What have we learned from observations? The interstellar medium consists, by mass, of 99 per cent gas (of which about 76 per cent is hydrogen, and 22 per cent helium), and about 1 per cent dust. It is characterized by various phases under very different physical conditions (see, for example, Acker, 2005 and Lequeux, 2005): (1) a cold phase (about 80 K) that is neutral and relatively dense (approximately 40 H cm-3); (2) a hot phase (8000 K) that is neutral and very tenuous (0.4 H cm-3);

(3) an ionized phase, with similar physical parameters; and (4) an extremely hot, ionized phase (where T is around 106 K, and the density 0.003H+ cm-3). The extreme diversity of these physical conditions is explained by the variety of sources of radiation in which they are bathed (stellar radiation, cosmic rays, etc.). In addition to these four phases, there are dense molecular clouds, with average temperatures of 10 K and with densities H > 300 cm-3. Even though they occupy only a small volume, they contain a significant fraction (about 50 per cent) of the overall mass of interstellar material.

Probes of the molecular gas within galaxies have shown that the gas is often concentrated in the spiral arms, within vast molecular complexes that are about one kiloparsec across, and whose mass may reach 107 solar masses. These complexes contain giant molecular clouds, some hundred parsecs in diameter, with masses of one million solar masses. They may, in turn, contain massive concentrations, several parsecs across and containing several thousand solar masses, and also small dense clouds, about 0.1 parsec across and of a few solar masses (Larson, 2003). The interstellar medium appears to exhibit a hierarchical structure, that is probably fractal in nature (see, in particular, Pfenniger and Combes, 1994; Pfenniger et al., 1994; Larson, 1995; and Elmegreen et al., 2000). A summary of the different stages of stellar evolution and the evolution of planetary disks may be found in Najita (2001) and Cassen (2006).

5.1.2 The Formation of Molecular Clouds

Molecular clouds form within the interstellar medium through gravitational collapse. Let us discuss the mechanism of this collapse in broad outline. We assume, to make things simpler, a spherical, uniform cloud (in reality, it may, of course, have a far more complex form and structure). This sphere of gas is subject to gravitational forces which tend to make it collapse, but also to a thermal (or kinetic) pressure that acts against the former. The kinetic energy Ek of the sphere may be expressed as:

where k is the Boltzmann constant, T the temperature of the cloud, M its mass and m the mass of an atom of hydrogen. The potential (gravitational) energy of the cloud, where we assume the density is constant as a function of distance from the centre, is

GM2 R

G being the gravitational constant and R the radius of the cloud. According to the virial theorem, collapse occurs if Ep > Ek, that is if

By expressing M as a function of R and of density p (number of atoms H cm~3) we obtain:

p being the number density of particles per cubic metre. MJ, expressed in solar masses, is the Jeans mass, as defined by the British astronomer James Jeans, in 1926. When the medium is hot and low in density, the material is almost completely in the form of hydrogen atoms. From values typical of the interstellar medium, the Jeans mass is about 5 x 107 solar masses for the inter-cloud medium, a few tens of solar masses for the densest clouds, which is comparable with observations.

It should be emphasized again that the above treatment assumes a cloud with constant density and temperature, which is far from being realistic. In reality, stability/instability is determined not by a general virial theorem applied to a constant-density configuration, but by the details of the true equilibrium. There is also a great deal of evidence that the formation and structure of molecular clouds are controlled by magnetic fields. The effect of magnetic fields on the stability and collapse of a cloud are complex. Discussions on these processes may be found in Spitzer (1978) and, more recently, Lequeux (2005).

5.1.3 Collapse of a Molecular Cloud

Within a molecular cloud, the same gravitational-collapse mechanism leads to the formation of stars. The mass of the initial cloud may vary between a few tens and a few tens of thousands of solar masses. The rotation of this cloud, which is linked, for example, to the large-scale galactic rotation, may brake the compression, as may the action of the interstellar magnetic field, the energy of which, Em, defined by

opposes the cloud's potential energy. The collapse may continue if Ep > Em, which defines a critical mass proportional to the product BR2. The magnetic field of the protostar will have the effect of ejecting material in bipolar jets, such as those that may be observed in young objects of the Herbig-Haro type (see Sect. 5.2). In certain cases, the magnetic field helps the collapse, most notably by causing the loss of angular momentum. Lequeux (2005) gives a thorough discussion of collapse mechanisms and star formation.

5.1.4 Observation of Young Stars

Our knowledge of the processes of star formation rest primarily on observation of T-Tauri type stars - stars of spectral types G, K or M at an evolutionary stage prior to the Main Sequence. They were first noted because of strong emission lines (Balmer lines) of atomic hydrogen, but also have strong emission in the UV and IR regions. These features are now understood and explained by an accretion disk surrounding the protostar (Lynden-Bell and Pringle, 1974). The ultraviolet emission and certain millimetre and sub-millimetre signatures may be attributed to material falling onto the protostar along the magnetic-field lines. The material falling onto the centre exhibits a specific spectral signature with a double emission peak (which is, however, very difficult to observe), but which may be explained by a spherically symmetrical model of dynamical collapse (Choi et al., 1995; Fig. 5.2).

Since the 1970s, astronomers have detected the ejection of material around young stars (Fig. 5.3) by observing molecular jets delineated by mapping the millimetric transitions of CO. Such images might show a characteristic bipolar structure, with opposing lobes, one shifted towards the blue and the other towards the red, indicating massive ejection of material, the emission from which is focussed along a particular axis, and with terminal velocities of several hundred kilometres per second. These jets have been identified by line profiles in the visible and near infrared (Acker, 2005).

Fig. 5.2 Spectra of rotational transitions of H2CO and CS observed in the young star B335, compared with the spherically symmetrical model of dynamical collapse (After Choi et al., 1995)

Fig. 5.2 Spectra of rotational transitions of H2CO and CS observed in the young star B335, compared with the spherically symmetrical model of dynamical collapse (After Choi et al., 1995)

Fig. 5.3 A diagram illustrating star formation. The star forms following the collapse of a rotating cloud of interstellar material, which flattens into a disk, perpendicular to its rotation axis. The stellar wind, which is confined by the magnetic field, escapes in two lobes that are aligned with the rotation axis (After Acker, 2005)

disk disk

Fig. 5.3 A diagram illustrating star formation. The star forms following the collapse of a rotating cloud of interstellar material, which flattens into a disk, perpendicular to its rotation axis. The stellar wind, which is confined by the magnetic field, escapes in two lobes that are aligned with the rotation axis (After Acker, 2005)

expanding lobes

Snell 1980

Several mechanisms may be responsible for the mass loss of a single young star: stellar winds; magnetic fields; or turbulent viscosity within the protoplanetary disk. In the presence of a magnetic field, ionized particles spiralling along field lines will co-rotate with the rotating star, contributing to angular-momentum transfer outwards. As a result, the spin rate of the star will slow down (a more complete discussion may be found in Cole and Woolfson, 2002). Their analysis shows that for a rotating system of constant angular momentum, the inner material will move inwards and thus will be accreted by the star, while the outer material will orbit at greater and greater distances. This mechanism also leads to a transfer of the angular momentum from the inner part to the outer. Finally, as discussed below (Sect. 5.2.4), the formation of multiple systems is another efficient way of dissipating the angular momentum of a protostellar object.

Figure 5.4 illustrates the different components of a typical protostar, the young object HH 211 (a Herbig-Haro object, named after the two astronomers who first discovered the associated nebulae). The two elongated lobes correspond to a molecular flow, defined by contours of the emission from CO. The dark patches at the end of the lobes correspond to emission from molecular hydrogen. The length of each lobe is approximately 10 000 AU. The lobes are aligned along the protostar's rotation axis. The latter is surrounded by an accretion disk, lying in a plane perpendicular to the rotation axis, which extends out for a few hundred AU. At this stage, the object does not emit any visible radiation.

Fig. 5.4 A diagrammatic representation of the object HH 211, showing the bipolar jet identified by CO emission in the millimetre band. A shock wave forms at the boundary between the jet and the interstellar medium. It is identified by the infrared emission from molecular hydrogen. The central disk, perpendicular to the axis of the bipolar flow, has been identified by its thermal emission, detectable in the millimetric continuum (After Bertout, 2003)

Fig. 5.4 A diagrammatic representation of the object HH 211, showing the bipolar jet identified by CO emission in the millimetre band. A shock wave forms at the boundary between the jet and the interstellar medium. It is identified by the infrared emission from molecular hydrogen. The central disk, perpendicular to the axis of the bipolar flow, has been identified by its thermal emission, detectable in the millimetric continuum (After Bertout, 2003)

5.2 Structure and Evolution of Protoplanetary Disks 5.2.1 Observation of Protoplanetary Disks

Until the end of the 1970s, the existence of circumstellar disks around young stars was not commonly accepted (Meyer et al., 2006), with most astronomers preferring the idea of a spherical envelope surrounding the young object. Circumstellar disks were first revealed by their infrared emission. The infrared excess measured in the spectra of certain stars, including Vega, by the IRAS satellite (Aumann et al., 1984), proved the existence of a disk around the star, and where subsequent estimates were made of its average temperature and dimensions. Another of the discoveries by IRAS, the disk surrounding the evolved star Beta Pictoris, was subsequently mapped in the visible region, using coronagraphy, first by a ground-based instrument (Smith and Terrile, 1984), and then, highly accurately, by the HST. It should be noted that in this last case, the circumstellar disk that was observed was not a protoplanetary disk, but the evolved disk around a Main-Sequence star. Such disks have been called debris disks (see Sect. 5.3). Other protoplanetary disks have also been observed by the HST (Fig. 5.5).

A circumstellar disk becomes detectable (first in infrared and then at optical wavelengths) at the stage at which the initial collapse of the molecular cloud takes place. Observation of protoplanetary disks that are about 100 AU across requires a high angular resolution. To take an example, a disk lying at a distance of 50 pc has an angular size of 2 s of arc if its diameter is 100 AU. To resolve structure within the disk, an angular resolution of less than one arcsec is required, which is possible in the visible with the HST, or in the radio region by interferometry (for example via millimetric interferometry with the IRAM array on the Plateau de Bure, or with the VLA in the centimetric region, Fig. 5.6).

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