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3 Star and Planet Formation 3 Star and planet formation Part I: Star formation Abstract: All galaxies with a significant mass fraction of molecular gas show continuous formation of new stars. To form stars out of molecular clouds the physical properties of the gas have to change dramatically. Star formation is therefore all about: Initiating the collapse (Jeans criterion, demagnetization by ambipolar diffusion, external triggering) Compression of the gas by self-gravity Losing angular momentum (magnetic braking and fragmentation) 3.1 Criteria for gravitational collapse The basic idea to cause a molecular cloud to collapse due to its own gravity is to just make it massive enough, but the details are quite tricky. We look first at the Jeans criterion that gives the order of magnitude mass necessary for gravitational collapse. Then we consider the influence of a magnetic field before we discuss mechanisms for triggering a collapse by external forces. Jeans criterion (Sir James Jeans, 1877–1946): Let us consider the Virial theorem 20EEkin pot It describes the (time-averaged) state of a stable, gravitationally bound (and ergodic) system. Collins (1978) wrote a wonderful book on the Virial theorem including its derivation and applications in astrophysics, which has also been made available online (http://ads.harvard.edu/books/1978vtsa.book/). The Virial theorem applies to a variety of astrophysical objects including self-gravitating gas clouds, stars, planetary systems, stars in galaxies, and clusters of galaxies. Basically it describes the equilibrium situation of a gas for which pressure and gravitational forces are in balance. Depending on the values of kinetic and potential energies the following behavior results: Astrobiology: 3 Star and planet formation S.V. Berdyugina, University of Freiburg 3-1 2EEkin pot 0 collapse of cloud 2EEkin pot 0 stable 2EEkin pot 0 expansion of cloud In equilibrium the kinetic energy of the gas cloud is equal to the thermal energy 33M EEkin therm NkT kT, 22mH where is the mean molecular weight and mH is the mass of the hydrogen atom. If we assume a homogenous, isothermal gas sphere with radius R, total mass M and temperature T the potential energy is given by 3 GM 2 E . pot 5 R Inserting into the Virial theorem (stable configuration) yields the so called Jeans mass or, alternatively, the Jeans radius 32 12 53kT T 32 M J 12 , GmH 4 12 15kT T 12 RJ 12 . 4GmH with the mass density. Therefore, the cloud starts to collapse spontaneously when the Jeans criterion M MRRJJ or , is fulfilled. The higher the temperature the more massive the cloud has to be to overcome the internal pressure and collapse. On the other hand, a larger mass density increases self-gravity and thus decreases the Jeans mass. An illuminating version of the Jeans criterion (Dyson & Williams 1997) is obtained when considering the free-fall time-scale for the collapse 12 3 tff . 32G From the sound speed in the cloud 2 kT cs mH Astrobiology: 3 Star and planet formation S.V. Berdyugina, University of Freiburg 3-2 we can estimate the sound travel time across the cloud: tRcss . Then the Jean criterion can be rewritten as 12 15 2 10 tttsffff 2 . 4G This means that the cloud becomes unstable for gravitational collapse when the free-fall time for the collapse drops below the sound travel time across the cloud. Then the cloud can start to collapse but the information about the collapse reaches the other side of the cloud too late for any reaction. If the free-fall time is smaller than the sound travel time the pressure gradients inside the cloud can adjust in time to prevent further collapse. Let us consider two examples of Jeans masses: Diffuse hydrogen cloud (H I): TM50 K, 1021 g cm 3 , 1 100 M MM1500 M J stable Dense cores of giant molecular cloud (GMC): TM150 K, 1016 g cm 3 , 10 1000 M M 17 M J unstable to gravitational collapse Molecular clouds, more precisely dense cores of GMC’s and Bok globules (Bart J. Bok, 1906–1983), represent ideal candidates for star forming regions because they can become unstable to gravitational collapse (Fig. 1) due to the following reasons: Cold ( small Jeans mass, small ionization fraction) Large mass with “large” density and often a clumpy structure Figure 1: Ideal candidates for gravitational collapse. Left image: Orion cloud complex, a GMC, in the optical and infrared (IRAS, the Infrared Astronomical Satellite, right panel). Right image: Barnard 68, a Bok globule of about 2 solar masses and a diameter of half a light-year. Astrobiology: 3 Star and planet formation S.V. Berdyugina, University of Freiburg 3-3 The influence of the small ionization fraction becomes clear in the following section on ambipolar diffusion. Note that typically MJ > M, i.e. the Jeans mass of our candidates are often much larger than the average mass of stars. Therefore, stars often form in groups or clusters. The Jeans criterion is a strong simplification but gives the correct order of magnitude of the critical mass. In reality the critical mass is about a factor of 2 larger than the Jeans mass derived above. In particular we have neglected: 2 Magnetic fields: PPgas P magn B8 Angular momentum ( centrifugal force) Pressure waves (ionization front, expanding SN remnants, density waves in galactic spiral arms, colliding galaxies) Heating (turbulence or radiation from nearby stars) Cooling through radiative losses Obviously the effects of magnetic fields, angular momentum and heating have to be overcome before a gravitational collapse can start. Effect of magnetic fields and ambipolar diffusion: The support of clouds due to the magnetic fields (magnetic pressure) is reduced by a process known as ambipolar diffusion (Fig. 2). The magnetic fields are frozen to the movement of the plasma, more precisely to the ions in the gas. When the cloud contracts the magnetic field lines are therefore dragged along, thus increasing the magnetic pressure and counteracting further collapse. However, the magnetic field is only coupled to the gas via the ions. The ionization fraction is very small in the cold environment of molecular clouds, resulting in a very small collision rate between ions and neutral particles. Therefore, the magnetic field effectively decouples from the neutral particles. The ions can leave the cloud on the diffusion time-scale and drag the magnetic field along, thus reducing the magnetic pressure inside the cloud. Figure 2: Schematic representation of ambipolar diffusion. Astrobiology: 3 Star and planet formation S.V. Berdyugina, University of Freiburg 3-4 Effect of turbulence: Turbulence can also support a gas cloud (Larson 2003, by the way a very nice, current review of star formation). It can create a clumpy, fractal structure of the gas even without the need of self-gravity, which gives the clouds a hierarchical nature. This can be interesting because we require dense cores in GMC’s for instability to occur. However, if the clumpy structure is not self-gravitating it becomes questionable how a collapse can be triggered. This might be achieved by collisions of turbulent clumps or, probably, only after the dissipation of turbulence, which however heats the cloud. Triggering the collapse: The gravitational collapse of a molecular cloud can be initiated by the following means: Wait long enough (mass accumulation, ambipolar diffusion, dissipation of turbulence). But it is a race against time before the cloud disappears (photoevaporation, internal pressure…). External triggering of collapse: o Globule squeezing o Collect and collapse process ( massive stars!) Globule squeezing works as follows: Hot stars can photoevaporate the gas of a nearby molecular cloud (possibly part of the same GMC these hot stars were formed from). Pre- existing dense cores in the molecular cloud can resist longer and can even be squeezed by the intense UV radiation, thus possibly triggering gravitational collapse. The age of these second-generation stars varies in principle depending on the distance to the original hot stars and depending on the structure of the GMC. Figure 3: Triggered collapse by globule squeezing. Hot stars photoevaporate the gas of a nearby molecular cloud. Pre-existing dense cores are squeezed by the intense UV radiation. Left image: “pillars of creation” in the Eagle nebula (M16), see Hester et al. (1996). The squeezed globules are found in the “tiny” fingers (called EGGs, evaporating gaseous globules) protruding from the three giant columns, particularly well visible on the leftmost column. Right image from Elmegreen (1998). Astrobiology: 3 Star and planet formation S.V. Berdyugina, University of Freiburg 3-5 Figure 4: Collect and collapse mechanism for triggering star formation. The collect and collapse process is schematically explained in Fig. 4. The intense UV radiation of a cluster of young, hot stars ionizes and heats the hydrogen in the neighborhood. The hot H II region expands creating a more or less spherical shock front where gas is “collected” and compressed until it becomes unstable to gravitational collapse. This creates a second generation of stars (with second-generation H II regions around them), spherically distributed around the original open cluster. All second generation stars have about the same age. Recently a beautiful example of the collect and collapse process was identified in the RCW79 H II region (Zavagno et al. 2006) which proves that the mechanism works (Fig. 5). This process is particularly interesting because it is able to form very massive stars (which was confirmed by the RCW79 observations). Note that the default star formation theory favors very strongly the formation of small stars because of fragmentation. Observations of the H II region RCW79 Orange (infrared, Spitzer): dust shell surrounding HII region Blue (SuperCOSMOS): ionized hydrogen filling the HII region Yellow contours (millimeter wavelengths): cold dust condensations Near-infrared image of one condensation (NTT-ESO, La Silla): Region includes second-generation H II Zavagno et al.
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