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.
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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. 2006 (A&A)
Figure 5: Collect and collapse process at work. Astrobiology: 3 Star and planet formation S.V. Berdyugina, University of Freiburg 3-6
3.2 Gravitational collapse
The gravitational collapse occurs in two stages:
1. Free-fall: o Initial phase o Fast, free-fall time-scale 2. Quasi-hydrostatic collapse: o Starts as soon as cloud becomes optically thick to own radiation o Slow, Kelvin-Helmholtz time-scale o Cloud is already called protostar
Free-fall:
As soon as gravity overcomes the pressure support the molecular cloud enters into a nearly free-fall collapse. Pressure cannot react quickly enough to stop the collapse. This stage is very short since the collapse happens on the dynamical time-scale of the free- fall
12 3 3 tff 10 y, 32G for dense cores of GMC’s. The density is higher towards the center of the cloud. This was usually already the case before the collapse. Even if it was not the case at the beginning, the cloud establishes such a density distribution quickly. This reduces the free-fall time at the center relative to the outer layers of the cloud, resulting in faster collapse of the center and the formation of a central cusp.
The free-fall happens almost isothermally. The potential energy of the gravitational field released by the collapse is transformed into radiation and lost as long as the cloud remains optically thin for its own (submm–infrared) radiation.
However, the density increases. Combined with the constant temperature we find that the Jeans mass decreases because
T 32 M . J 12
Therefore, sub-structures of the molecular cloud can become unstable themselves and can start to collapse individually leading to fragmentation (Fig. 6). This is the reason why we often observe binary or multiple star systems or even clusters of stars that have formed at the same time. The typically large total mass of the collapsing cloud (original Jeans mass) is subdivided into smaller parts. The fragmentation into ever smaller clumps stops only in the second stage of the collapse, the quasi-hydrostatic phase (see below).
Astrobiology: 3 Star and planet formation S.V. Berdyugina, University of Freiburg 3-7
Figure 6: Fragmentation of the collapsing cloud due to decreasing Jeans mass.
Quasi-hydrostatic collapse:
As soon as the density increased sufficiently enough (which happens first in the denser central part) the cloud becomes optically thick for its own radiation, i.e. the mean free path of the emitted submm–infrared photons drops to below the size of the cloud. The potential energy released by the collapse cannot escape anymore, at least not quickly enough, and it is transferred into thermal energy of the particles, thus heating the gas. The collapse becomes therefore quasi-adiabatic. The temperature of an adiabatic hydrogen gas is given by
TP25 23 .
Therefore, the Jeans mass
T 32 M 12 , J 12 starts to increase again so that the fragmentation stops. Furthermore, the collapse is slowed down and the free-fall phase ends. Further collapse requires radiative losses. To understand this let us consider again the Virial theorem for a gravitationally bound system in equilibrium
20EEkin pot .
If the potential energy is reduced due to contraction then we can reach a new equilibrium state (i.e. Virial theorem satisfied again for smaller potential energy) if half of the released potential energy is put into kinetic or rather thermal energy. The other half of the released potential energy must be lost. i.e. radiated away. Note that this does not contradict energy conservation because the total energy (including radiation) remains unchanged.
The collapse (or contraction) proceeds therefore much slower, namely on the Kelvin- Helmholtz time-scale, which is the time it takes for an optically thick star to contract and lose its gravitational (potential) energy by radiation:
Astrobiology: 3 Star and planet formation S.V. Berdyugina, University of Freiburg 3-8
GM 2 t KH RL
For the Sun the Kelvin-Helmholtz time is about 30 million years, and shorter for more massive stars (remember the mass-luminosity relation for main sequence stars, L M4 2.8 for M > 0.4M, and L M for M < 0.4M).
The moment when the second stage of the collapse, the quasi-hydrostatic contraction, starts is usually defined as “zero time”. From now on the cloud is called protostar.
Because the cloud becomes first optically thick at the center material continues to fall onto the slowly contracting protostar. In fact the remaining dust and gas forms a disk around the protostar (in-falling matter plus centrifugal force). The protostar therefore continues to contract and accretes material from the disc. However, accretion from the disk requires loss of angular momentum of the disk particles, which leads us to one of the biggest difficulties of star formation, the angular momentum problem.
Angular momentum problem:
An important issue in star formation is angular momentum conservation. In general, the cloud has some possibly random rotational velocity prior to the collapse. Conservation of angular momentum increases the rotational velocity during the collapse with a corresponding increase of centrifugal forces.
Gravitational force Centrifugal force Mm L2 FG Fmr 2 G r 2 Z mr3
In fact, the collapse is stopped for sufficiently small radius of the cloud due to the centrifugal barrier.
Conservation of angular momentum,r 2 const , implies
223 starr cloud star 16 3 24 3 10 with star 1 g cm , and cloud 10 g cm . cloudr star cloud
Observed ratios of rotational velocities of final star and original clouds are however of the order
16 starP cloud 10 s 10 6 10 . cloudP star 10 s
Therefore, we have to lose about 6 orders of magnitude in angular momentum! Otherwise the Sun would rotate a million times faster, which would immediately cause disruption. Without loss of angular momentum the collapse of the cloud would be stopped well before stars have formed. The question is only how we can achieve this.
Astrobiology: 3 Star and planet formation S.V. Berdyugina, University of Freiburg 3-9
We distinguish four possibilities to lose angular momentum:
Magnetic braking Fragmentation Viscosity in the accretion disk Jets
The first process, magnetic braking (Fig. 7), is due to the fact that the magnetic field is frozen to the movement of the gas. Rotation spirals up the magnetic field lines. The tension in the magnetic field lines tends however to prevent this rotation, thus exerting a torque through which angular momentum is lost. Due to ambipolar diffusion this process works only to a certain degree in the early stage of the collapse. But it remains relevant also during the phase of disk accretion and later (slowing down the rotation of young stars) due to surface magnetic fields produced in the star itself.
Figure 7: Magnetic braking, a method to lose angular momentum.
The next very important process for “losing” angular momentum is fragmentation. The fragmentation taking place during the fee-fall phase (Fig. 6) can form fragments with “small” internal angular momentum, although the total angular momentum remains conserved. Within individual cloud cores, which will later lead to different stars, this acts like losing angular momentum. During the protostellar phase the disk can further fragment if the angular momentum is still to large. Such a disk would be unstable and “disrupt”. This leads naturally to the formation of binary or multiple systems, in particular also to close binaries (Fig. 8).
In later stages viscosity in the accretion disk is often inferred for losing angular momentum, which would lead to further accretion. This is however an open problem because the viscosity of the gas and dust appears to be too small.
Astrobiology: 3 Star and planet formation S.V. Berdyugina, University of Freiburg 3-10
12 Figure 8: Simulation of the collapse and fragmentation of a molecular cloud (Bate et al. 1995). 1. Spherical cloud of H2 gas with temperature T = 10 K, rotating clockwise, assuming two density perturbations as initial condition. 2. As the cloud collapses under its own gravity these over-dense regions collapse faster than the cloud as a whole, with the result that a binary protostellar system is 34 formed. 3. The rest of the cloud continues to fall in and, due to the angular momentum of the gas, it forms disks of gas around each of the two protostars. Spiral density waves grow in the discs. These transfer angular momentum outwards and mass inwards in the discs, stabilizing them. 4./5. In one of the discs, the two spiral arms collide resulting in collapse to form a third 5 6 protostar. 6. The system finally settles down to form a system of three stars, with a wide binary system whose two components are a close binary system and a lone star surrounded by a large circumstellar disc. The remaining gas falls in around the system to form a circumbinary disc.
Another possibility for the protostar to lose angular momentum is by “throwing” material out, as it is often observed in protostars in terms of jets (Fig. 11). These jets might carry away angular momentum especially if magnetic fields are also involved.
Cooling efficiency:
The gravitational collapse requires efficient cooling mechanisms in order to quickly radiate the released potential energy. Since the cooling rate depends strongly on opacity, the metallicity (fraction of chemical elements heavier then H and He) of the collapsing cloud is an important parameter in star formation (see e.g. Spaans 2004).
Molecular clouds forming population I stars, i.e. stars with a high metallicity contain more heavy atoms and thus more dust. Dust can cool very efficiently. In addition, dust serves as catalyst for the formation of molecules, which themselves help cooling as long as temperatures are small enough for molecules to exist. It turns out that even clouds forming population II stars (with a low metallicity) cool efficiently enough to yield similar results.
However, the first generations of stars that formed in the Universe after the Big Bang (population III stars) had to form through the collapse of clouds with zero metallicity (see e.g. Larson & Bromm 2004). Dust grains did not exist, reducing both the cooling Astrobiology: 3 Star and planet formation S.V. Berdyugina, University of Freiburg 3-11
efficiency as well as the formation rate of molecules. Due to the lack of atoms heavier than He, the H2 molecule was almost the only existing type of molecule. The H2 molecule, being homonuclear, cannot cool very well, only down to about 200 K. This larger temperature of the first molecular clouds (as compared to today’s molecular clouds) led to very high Jeans masses. As a result, first-generation stars are believed to have been extremely massive (several hundred solar masses), which were stable despite the enormous radiation pressure thanks to the low metallicity and opacity (cf. first lecture of this course).
3.3 Protostars: pre-main-sequence evolution
Having discussed the basic physical principles of the collapse we now turn our attention to the more detailed evolution of the protostars on their approach towards the main sequence.
First we look at the theoretical evolution in the Hertzsprung-Russell (H-R) diagram (Fig. 9). Then we discuss the more observational point of view, namely the classification of young stellar objects (YSO), as protostars are often called (Fig. 10). As the collapse of a protostar is shrouded in obscuring dust and gas clouds observations need to take place in the infrared and submm regions.
Pre-main-sequence evolution in the H-R diagram (Fig. 9):
Theoretical evolutionary tracks of the protostellar stage, called Hayashi tracks or Pre- main sequence (PMS) tracks, can be shown in a H-R diagram. Four of these are shown Fig. 9 below, with that for a one solar mass star explained in more detail in the following.
Stages in the formation of a 1 solar mass star (cf. Fig. 9):
1. Initial collapse of a cloud causes it to heat up and become a protostar. Although cool it is very large, perhaps 20 × the diameter of the Sun, thus its surface area is so great that its overall luminosity is very high, maybe 100 × its main sequence luminosity. 2. As it radiates away energy, gravitational collapse pulls the protostar inwards rapidly. Its temperature rises but this is offset by the decrease in size so that overall luminosity decreases significantly as shown by the vertical drop on the H- R diagram. In this phase the temperature becomes high enough to start fusion of deuterium. But the influence on the star remains small due to the small amount of deuterium. 3. Once the core temperature reaches 10 million K, Coulomb repulsion between the now ionized hydrogen atoms (protons) is overcome and nuclear fusion commences. Hydrogen fuses to form helium nuclei, releasing energy in the process. Initially the increased outward radiation pressure is still insufficient to halt gravitational collapse but it does slow it down. The star's surface temperature increases significantly, compensating for the drop in size so that its luminosity
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increases slightly. The star's track moves up slightly and to the left on the H-R diagram over 10 million years. 4. As the rate of core fusion increases due to higher core temperature, the outward gas and radiation pressures eventually match the inward gravitational force. The star attains a state of hydrostatic equilibrium and settles down onto the main sequence. This stage may take a few tens of million years.
As you can see from the Hayashi tracks for stars of other masses, their evolutionary paths are different. Again the key factor is the mass of the protostar. In general more massive stars collapse and thus heat up more quickly so core fusion starts much sooner. Their luminosity remains essentially constant so they evolve almost horizontally across the H-R diagram. Low mass stars such as the 0.5 solar mass protostar can only transport energy from the core by convection. The decrease in the radius of such protostars as they collapse is more important than the increase in surface temperature so their luminosities drop as they move down onto the main sequence.
Figure 9: The four Hayashi tracks show the predicted evolutionary paths on the H-R diagram for 9, 5, 1 and 0.5 solar mass stars during their protostar stages. The four stages labeled for a star such as our Sun are explained in the text above. The dashed line (just before reaching stage 1) indicates the path that the cloud takes in the transition period from free-fall to the quasi-hydrostatic collapse.
Astrobiology: 3 Star and planet formation S.V. Berdyugina, University of Freiburg 3-13
Figure 10: Classification of young stellar objects (cf. explanation below). From Lada (1987) and André et al. (1993). Astrobiology: 3 Star and planet formation S.V. Berdyugina, University of Freiburg 3-14
Classification of young stellar objects (cf. Fig. 10):
Pre-stellar dense core is cold (~10 K) and emits as a blackbody peaking in the submillimeter.
Class 0 is an object where the bulk of the accretion occurs. The YSO and infalling gas are still cold enough to emit as a blackbody. Outflows are already occurring at this point.
Class I (about stage 1 of Fig. 9): A star with an accretion disk. As it collapses, the rate of rotation increases to conserve angular momentum. The density of the inner part increases more than the outer parts and a protostar begins to form at the center with a flat, slowly-rotating accretion disk in the plane perpendicular to the rotational axis. The star and the disk warm up so that the spectrum of the object is no longer a simple blackbody, but has an infrared excess due to the disk. By this point the accretion rate is slowing down. The infall of the gas and dust from the accretion disk is channeled to bipolar jets that eject material out the rotational poles of the protostar.
Class II (about stage 2 of Fig. 9, classical T Tauri stars): A stage with no accretion, and a diminishing accretion disk. The central star brightens and the accretion disk is either accreted onto the star or dispersed. Planetesimal bodies are accreted through out the former accretion disk.
Class III (about stage 3 of Fig. 9): A star with possible remnants of circumstellar disk which shows up as a slight infrared excess or as reddening that steepens the short-wavelength end of the stellar blackbody spectrum. The density and temperature of the star increases to the point that thermonuclear fusion takes place in the core of the star. Radiation pressure and stellar winds disperse remaining gas to the outer limits of the system and planets form from the planetesimals.
Figure 11: Observations of young stellar objects with jets. The upper left panel shows also the proto- planetary disk on the left. Dust obscures the central disk, which is seen edge-on from the side. The scale in the bottom left corner of each picture corresponds to 1000 AU. Astrobiology: 3 Star and planet formation S.V. Berdyugina, University of Freiburg 3-15
Giant molecular cloud
Supergiant, nearing end of life Bok globules: Molecular clouds prior to collapse Hot blue stars: UV radiation cleared nearby material Nurseries of newborn stars Circumstellar disks
Figure 12: Observation of the molecular cloud NGC 3603 with several generations of stars and different stages of star formation.
Astrobiology: 3 Star and planet formation S.V. Berdyugina, University of Freiburg 3-16
Part II: Planet formation
Abstract:
Planets form as a by-product of star formation out of the protoplanetary disks. According to the standard model, planets form completely by accretion, starting from dust grains. Inside the snow line growth is slow ( 108 y), which leaves no time for gas accretion and thus gives terrestrial planets. Outside the snowline in the Jupiter/Saturn region the density of solid particles is larger (due to the additional presence of ices). Therefore, the growth rate of the rocky/icy core is large enough to reach the critical mass of about 10 M (where M stands for the total mass of Earth) while gas in the protoplanetary disk is still available. Above this critical mass gas is accreted, thus forming the giant planets.
3.4 Properties of planets in the solar system
First, we have a look at some important properties of solar system planets that are relevant for the formation of planets.
Their orbits are prograde, i.e. in the same direction, and lie in almost the same plane. The rotation directions are also prograde (with few exceptions: Venus, Uranus, also Pluto although not counted as planet anymore). These are strong indications that all planets formed at the same time as the Sun out of the protoplanetary disk. This is supported by comparing the ages of the oldest Moon rocks and the Sun.
Figure 13: HST images of dusty circumstellar disks around two young stars. The observed radiation from the disks is caused by dust particles which scatter the light of the central star. The disk around HD 141569 (left panel) shows a wide dark gap that might have been swept out by a planet.
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Figure 14: Trapezium cluster in the Orion Nebula (M42) observed with HST. Left image: these four bright stars are at the center of the Orion Nebula, and provide most of the ionizing radiation that illuminates the nebula. Located around these four massive stars are young stars with protoplanetary disks or "proplyds" that appear cometary in nature, with the tails pointing away from Theta 1C, the brightest of the four Trapezium stars. Right panels: A gallery of proplyds in Orion's Trapezium. The first four objects are being evaporated by the central massive stars, while the last two disks are visible in silhouette against the background nebula.
We distinguish between the terrestrial planets and the giant planets (Fig. 15). The giant planets can be further subdivided into two classes with Jupiter and Saturn on one hand and the “ice giants” Uranus and Neptune with only little H and He content on the other hand.
Terrestrial planets: rocky, close to Sun ( < 3 AU), maximum 1 M
Giant planets: large H and He content, far from Sun ( > 3AU) much more massive than Earth.
Jupiter (at 5 AU) and Saturn (10 AU): o Predominantly H and He (but not solar composition) o Rocky/icy cores with a mass of 5–10 M
Uranus (19 AU) and Neptune (30 AU): o Only about 15% H and He (by mass) o Rocky/icy cores and mantles with a mass of about 15 M o Sometimes called “ice giants”
Figure 15: All planets of the solar system. Top panel: the terrestrial planets Mercury, Venus, Earth, Mars (from left to right). Bottom panel: the giant planets Jupiter, Saturn, Uranus, Neptune (from left to right). Astrobiology: 3 Star and planet formation S.V. Berdyugina, University of Freiburg 3-18
Figure 16: Excess infrared (JHKL) radiation (corresponding to the disk fraction) as a function of mean cluster age. The decline in the disk fraction as a function of age suggests an average disk lifetime of 6 My. From Haisch et al. (2001).
The lifetime of the protoplanetary disk sets the time scale during which material is available for planet formation. Observations indicate typical lifetimes of protoplanetary disks of several million years, e.g. by the dust measurements shown in Fig. 16. At least in one case observations of H2 indicate the presence of gas in the disk for up to 20 My (Thi et al. 2001). However, the typical consent among scientists is that typical disk lifetimes are not more than 10 My. The mass of the disk is lost by photoevaporation from the central or nearby hot stars and by the bipolar outflows (jets).
3.5 Standard model of planet formation
From the observed properties we conclude that planets are likely nothing else than a by- product of star formation that form in the protoplanetary disk. In the case of the solar system, the disk is generally taken to have a mass of a few percent of a solar mass and to be less than 100 AU in size.
According to the standard model planets form through collisions at first between dust grains and as time goes by between larger and larger bodies. The flow diagram in Fig. 17 illustrates these concepts.
The basic challenge of planet formation consists therefore of assembling in a disk orbiting a central star micron-sized or smaller dust grains in bodies with over 104 km in diameter (Fig. 18), a growth by nearly a factor 1013 in size or 1040 in mass! Since giant planets are mainly gaseous planets, their formation must take place while gas supply lasts, i.e. within a few million years (Fig. 16). Hence, as paradoxical as it sounds, giant planets must be formed in less than ten million years while forming terrestrial planets may take much longer.
On their path to becoming a planet, dust grains reach the size of comets and asteroids which, if they can avoid being incorporated in a larger object, are left behind like crumbs on a table after a good meal. Astrobiology: 3 Star and planet formation S.V. Berdyugina, University of Freiburg 3-19
Figure 17: Planetary formation as a by- product of star formation. In the standard model, the planets form entirely through collisions (solid line) while in other models gravitational collapse is invoked. From Benz (2000).
Gas supply disappears in a few My!
Figure 18: The challenge of planetary formation: assembling micro-meter dust grains in planets through collisions in an amazingly short time-scale. From Benz (2000).
The early phases: the first million year:
At first, dust grains collide at relatively gentle velocities which are determined by gas drag. The dust grains stick to each other by means such as the Van der Waals force. As bodies grow larger, the importance of gas drag diminishes and vanishes completely by the time bodies reach several tens of meters in size. Once km-sized bodies have been formed (so called planetesimals) the collisional cross-section of these planetesimals increases due to gravitational focusing, i.e. they start to attract other planetary bodies gravitationally. This results in the so-called runaway growth phase, during which the larger bodies sweep up all the smaller ones within their gravitational reach.
Astrobiology: 3 Star and planet formation S.V. Berdyugina, University of Freiburg 3-20
This phase is not without problems. Laboratory experiments have shown that at the very small scale dust aggregates readily. Similarly, various impact simulations have shown that self-gravity will ensure growth once km-sized planetesimals have been formed. However, the situation is much less clear for objects ranging in size from centimeters to kilometers since in this size range no real “sticking" mechanism has yet been found. Indeed, at this size, the forces operating at the micron size level are no longer effective and gravity is still much too weak. The escape velocity of a 1 meter sized rock is of order 1 mm/s while the typical collisional velocity between these objects is of order 100 m/s. Therefore, for sticking the involved bodies have to be able to dissipate all but 10–10 of the incoming kinetic energy. Whether this can be achieved by purely mechanical structures or requires the presence of a “glue” with special visco-elastic properties remains to be seen. Figure 19 summarizes the main three stages of growth, the relevant physical mechanisms operating, and the main study tools.
Fast: 104 y
Escape velocity of 1 m object: 1 mm/s Typical collision velocities: 100 m/s Must be quite fast: 105 y
Giants: 107 y Terr. planets: 108 y
Slow: 107 –108 y
Figure 19: Planetary growth stages (referring only to the rocky/icy part). In green the main physical mechanism ensuring growth and in blue the main tool (lab or computer) used to study these phases. Note that the growth mechanism in the meter size range is still unknown, but we know that it has to work quite fast, in about 105 years. From Benz (2000).
The late phases: 100 million years: giant impacts
The early planetary accretion phase was, over a few million years, replaced by an even more violent period of giant impacts when growing bodies encountered one another at increasingly high velocities boosted by mutual gravitational interactions. This phase lasts for another 100 to 200 million years until all remaining bodies have been swept up by the planets. Collisions occur in a random fashion involving objects of different masses, structures, composition, and moving at different speeds. Thus, this phase of planet formation must not be viewed as a monotonic process by which material is incrementally added to a growing planet. Instead, accretion must be viewed as a long chain of stochastic events in which non-disruptive infall exceeds, over time, violent dispersal. The so-called giant impacts in which proto-planets of comparable size collide
Astrobiology: 3 Star and planet formation S.V. Berdyugina, University of Freiburg 3-21
represent the ultimate in violence during planetary accretion. While they can lead to the total destruction of the planets involved they can also leave scares arguably the best evidences remaining today of such a violent past.
Figure 20: Paintings illustrating the impact theory for the formation of Earth’s Moon. According to this theory the Moon has formed about 50 My after Earth out of the debris left over from a collision of a giant object (maybe Mars sized) with Earth. Paintings and copyright William K. Hartmann.
The Earth's Moon, for example, is believed to originate from the debris ejected after such a giant impact which was subsequently reaccreted in Earth's orbit (Fig. 20). Simulations of both impact and re-accumulation have not only shown that such a scenario is possible but have made it today's favorite theory of lunar origin. Studies of lead and tungsten isotopic composition of the silicate Earth have even allowed us to date the giant impact to about 50 million years after the start of the solar system!
Mercury's anomalous composition (very large density, almost as large as Earth’s density, despite Mercury being much smaller) can also be explained in terms of a giant impact which ejected most of the mantle of the planet leaving behind essentially the iron core. A similar event could have caused the large obliquity of Uranus. Furthermore, such impacts could also add heat that could be used in the process of differentiation of the planets (process whereby a planetary body evolves into compositionally distinct layers).
Giant impacts, by explaining many individual planetary characteristics as outcome of a general process rather than the result of unique and ad hoc local conditions, have undoubtedly become a central characteristic of the modern paradigm of planetary formation.
Giant planets:
If a body grows beyond a critical mass of about 10 times the Earth’s mass while still being embedded in a gaseous disk, it will be able to accrete dynamically a considerable amount of surrounding gas eventually becoming a giant gaseous planet such as Jupiter or Saturn (Fig. 22).
In comparison to terrestrial planets, giant planets formation must proceed very rapidly due to the lifetimes of circumstellar disks ranging from one to ten million years (Fig. 16). The time available is therefore relatively short especially since the envelope accretion begins rather slowly at first (Fig. 22). It is therefore important that the seed body reaches critical mass rapidly. Hence relatively high densities of solids are required.
Astrobiology: 3 Star and planet formation S.V. Berdyugina, University of Freiburg 3-22
Figure 21: Illustration of the snow line at about 3 AU. Outside the snow line temperatures were low enough for ice to be present. Therefore, planetesimals consist of rocky and icy material outside the snow line, but only of rocky material closer to the Sun.
The density of available solid material in the disk is a function of both distance from the Sun and temperature. On large scales, the density decreases with increasing distance from the Sun. But the so called snow line (or ice line) plays a decisive role (Fig. 21). Beyond the snow line, which is generally assumed to lie in the region of 3 AU from the Sun, the temperature is low enough for ice to be present. This increases the density of available solids drastically (despite the smaller total mass density). Closer to the Sun ice melts, so that planetesimals have to form entirely from rocky material such as silicates.
The term surface density of solids is often used in the literature (with the dimension g/cm2). It refers actually to the density of solids in the disk. These heavier particles accumulate naturally in the central plane of the disk hence forming basically a 2- dimensional plane.
Stage 3
Stage 2
Stage 1 Figure 22: Accretion history of Jupiter in three stages. Stage 1: formation of the rocky and icy core. Stage 2: After reaching the critical mass of about 10 M the gravity of the core was large enough that gas could be accreted slowly until Mcore Mgas. Stage 3: runaway accretion of gas. With the assumptions made for this model, Jupiter reaches its final mass in about 8 My. Adapted from Pollack et al. (1996). Astrobiology: 3 Star and planet formation S.V. Berdyugina, University of Freiburg 3-23
It is now clear why giant planets were believed to form only outside the snow line, sufficiently far away from the star where ices and not just silicates are present. They can reach quickly critical mass to start accreting gas, before the disk disappears.
Figure 22 shows the simulated accretion history of Jupiter (the model starts from planetesimals). The Jupiter formation proceeds in three stages (cf. Fig. 22):
Stage 1: “fast” formation of the rocky and icy core in a runaway process, reaching critical mass for gas accretion within less than a million years. Stage 2: slow accretion of gas until Mgas Mcore. Stage 3: Runaway gas accretion, which is truncated by the formation of a gap in the disk, when the gas in the vicinity of Jupiter is used up. It results in Mgas > Mcore.
The total formation time of a giant planet depends strongly on the initial surface density and on the distance from the Sun. Far away from the Sun the surface density reduces, thus increasing the length of stages 1 and 2. Therefore, it appears natural that Uranus and Neptune contain much less H and He than Jupiter and Saturn: they did not even complete stage 2 before the gas of the disk disappeared.
However, closer inspection of Uranus and Neptune formation reveals a problem. Typically assumed surface densities at 20–30 AU are so low that default models result in a core accretion time for Uranus of many 107 years and of 108–109 years for Neptune, way too slow for any gas accretion.
Two possible solutions have been proposed for the Uranus/Neptune problem:
1. Planetesimals are smaller than typically assumed, maybe even less than 1 km in size, possibly because they were ground down by collisions with bigger bodies. Such small planetesimals can be very quickly accreted (Goldreich et al 2004). 2. The Jupiter/Saturn region (4–10 AU) produces excess cores. The winners (Jupiter and Saturn) get most of the gas, while the losers (Uranus and Neptune) are scattered away (Thommes et al 1999, 2002).
Within the snow line formation of planet-sized bodies is much slower, too slow for having a chance to accrete gas, which naturally results in terrestrial planets. The terrestrial planets in the solar system did not even accumulate enough mass to reach the critical value for gas accretion.
Astrobiology: 3 Star and planet formation S.V. Berdyugina, University of Freiburg 3-24
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