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Planet Formation

Sean N. Raymond and Willy Benz

Introduction

Statistically speaking, one new star is born in our Milky Way galaxy each year. This

star will typically form in the densest parts of the galaxy, either close to the central bulge or in

the spiral arms. This is where giant clouds of cold molecular gas are concentrated, and these

are the birthplaces of stars. Within such a cloud, the star forms when a small parcel of gas

begins to “feel” its own gravity and begin a slow but accelerating inward collapse. It is not

known whether an external trigger—such as shockwaves from a nearby supernova—is needed

to start this collapse, but once the collapse begins it follows a well-charted path. The angular

momentum of the initial parcel of gas causes a disk to spin out as the gas contracts, and it is

through this disk that gas is funneled onto the growing proto-star at the center. On a timescale

of 105 years, the central object reaches a large enough mass to increase its internal pressure

and temperature above the critical value for nuclear fusion of hydrogen into helium and a star

is truly born. An evolving disk of gas and dust orbits the star. This is where planets form.

The Hubble Space Telescope has taken exquisite images of nearby star-forming

regions, some of which are, in cosmic terms, right next door. The Orion Nebula—found by

Orion’s sword in the constellation—is one of the most famous. Although it is more than a

thousand light years away, it is large and bright enough to be visible by eye. Within the Orion

Nebula and in other star-forming regions, Hubble has imaged young stars and their dusty

protoplanetary disks (O’Dell and Wen 1994). The disks themselves are far too small to be

resolved in detail, but they confirm our basic picture: stars form in molecular clouds, and

planets form in disks that are ubiquitous around young stars.

Like most of the Universe, protoplanetary disks are made up almost entirely of

hydrogen (H) and helium (He). Only about 1% of the mass in these disks (or anywhere in the

nearby universe for that matter) is made up of heavier elements. However, it is from those

heavy elements—and not even all of them but just a subset—that planets like Earth, Venus

and Mars must form, because the Earth is made up almost entirely of so-called condensable

material, meaning elements that are able to exist as solids. By contrast, H and He are almost

always found in gaseous form (except in high-pressure situations such as the interiors of stars

or giant planets, where they can exist in more exotic states such as a liquid, plasma, or even

“metallic” forms). The situation is somewhat different for gaseous planets like Jupiter and

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Saturn that are much closer to the mean galactic composition, although we think that they

probably needed to grow from solid “cores” that were themselves made from condensable

material.

The question addressed in this chapter is the following: within protoplanetary disks,

how do planets form? We summarize our current, albeit incomplete, understanding that has

been built up by hundreds of astronomers—both theorists and observers—over the past few

hundred years (for recent theory, see Armitage 2007). Theories are constrained by a plethora

of new observations: information on the masses, sizes and distributions of proto-planetary

disks, and how they change depending on the type of star, measurements of the dust content

and evolution of disks, and of course the masses and orbital distribution of planets around

other stars, which now number more than 700 (see http://www.exoplanets.org).

Figure 4.1 An illustration of the main phases

of planet formation. First, a parcel of gas

within a molecular cloud starts to collapse

under its own gravity (panel a). As the parcel

collapses, it inevitably creates a disk (panel b),

and a star begins to form at the center (panel c).

The inner disk is of course hotter than the outer

disk, so rocky and metallic bodies condense in

the inner disk while the outer disk becomes

dominated by volatile, icy bodies (panel d). On

timescales of millions of year, these solid

bodies accumulate and grow into both the cores

of gas giant planets, the smaller and less gas-

dominated ice giants (like Uranus and

Neptune) and rocky, terrestrial planets (panel

e). Within 100 million years the system’s

formation is complete (panel f); the system in

this figure represents of course our own Solar

System. Image credit: Chaisson and

McMillan, Astronomy Today, Pearson, 2011.

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From Disks to Embryos The naïve answer to the question framed by this chapter is that planets form by

successive collisions between smaller bodies. In other words, starting with tiny grains, they

simply bash together to form larger grains, which bash together to form even larger grains,

and so on until full-sized planets are formed. However, it has been shown that this simple

picture of collisional growth fails at remarkably small sizes. Micron-sized grains do indeed

grow in low-speed collisions, and the resulting dust aggregates continue to grow until they

reach a few millimeters in size. At this point, collisions simply do not result in further growth,

as any pebble-throwing youngster playing on a sandy beach already knows. How then, are

larger objects created?

Our current answer to this quandary is an interesting offshoot of what just a few years

ago was called the “meter-sized barrier.” Any object that does grow to 1 centimeter up to 1

meter in size in a proto-planetary disk should fall into the central star in just a century or two,

thousands of times faster than the planetary formation timescale. In the collisional growth

scenario this is a disaster, because if objects need to pass through this stage to reach the

planetary scale, then everything should just grow to one meter then fall into the star. The

results is no planets, case closed. But clearly, a huge body of evidence (including the

existence of our own planet Earth) tells us that this thinking is flawed.

Let’s look in more detail at what happens in a proto-planetary disk. The gas orbits the

star slightly slower than the rocks (which have orbital speed given by Kepler’s law) because

the gas pressure offsets a fraction of the gravitational force. Dust grains are simply blown

along with the gas, but larger rocky bodies feel the gas as a headwind (because the gas is

moving more slowly) that slows down the objects and makes them spiral inward. Massive

objects have enough inertia (in this case, what matters is the ratio of their volume to surface

area) that they spiral in slowly. Smaller objects—those that are just big enough not to be

blown around with the gas—are the unlucky ones that feel the gas most strongly and spiral in

very quickly. These are the centimeter to meter-sized objects.

The concept of the meter-sized barrier makes a key assumption that is its undoing. It

assumes that protoplanetary disks are well behaved and that the properties of the gas disk are

well-regulated and smooth throughout. This is important because the meter-sized bodies that

are thought to spiral inward actually just seek out maxima in the gas pressure (they follow the

local pressure gradient). Real protoplanetary disks are decidedly lumpy and un-smooth. They

are very turbulent. In fact, small-scale turbulence due to magnetic effects is thought to be the

driving force behind their evolution. Even the simple settling of dust grains to the mid-plane

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of the disk creates turbulence. Turbulent disks create uneven structures at a variety of size

scales, and it is into these structures that centimeter to meter-sized objects are drawn, not into

the center of the star. And by the same arguments as before, objects should converge to these

regions very quickly.

Once particles begin to accumulate in turbulent zones, there are feedback mechanisms

that keep the process going. Even though they make up such a small fraction of the total mass,

when sufficiently concentrated, solid bodies can have an effect on the gas and in fact increase

the local pressure to attract ever more boulders. Once particles become so concentrated that

they dominate the local mass distribution, they begin to feel their collective gravity and

become gravitationally bound, much larger bodies. This is a far gentler type of gravitational

collapse than the parcel of gas that ended up as the star, but the general physical mechanism is

the same: when the conditions are right, gravity trumps all. In this case, the outcome is objects

with a spectrum of sizes—current simulations suggest that many of these objects are 100-

1000 kilometers in size, although the details of this process are an active area of study. The

most important point for our story is that these objects are on the right side of the meter-sized

barrier. They are called planetesimals and are the building blocks of planets.

From Embryos to Planets Once a sufficient number of planetesimals exist in the protoplanetary disk, they start to

collide and grow (Johansen et al. 2007). Once a planetesimal grows larger than its neighbors,

its rate of growth also grows (Blum and Wurm 2008). The big planetesimal’s increased

gravity acts to focus the orbits of smaller planetesimals and, like the Death Star’s tractor beam

in Star Wars, it draws them in. The more massive the planetesimal gets, the stronger the

focusing, leading to rapid phase of runaway growth. Runaway growth slows down when the

big planetesimal’s gravity is so large that it stirs up nearby smaller planetesimals to the point

that their relative speeds are high enough to shut down the gravitational focusing. At this

point, the large bodies are called “planetary embryos.”

Let’s rewind the clock a little to consider the composition of the disk. The material

that is available to form solid planets is not the same everywhere in the disk. The inner disk is

hot, so only compounds that remain solid at high temperatures—namely, rock and iron—can

be incorporated into planetesimals and planetary embryos. These are called “refractory”

elements. Moving away from the star the disk cools off such that compounds that condense at

lower temperatures, i.e. more “volatile” species, can exist as solids. For any given compound

there is a condensation temperature that, in the context of a proto-planetary disk, corresponds

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to a radial transition (Lodders 2003). Interior to this transition, the compound will be in gas

phase simply because it is too hot to condense, but exterior to the transition it will be a solid

(note that liquids are virtually non-existent in proto-planetary disks because the pressure is too

low). For particularly abundant compounds like water, these transitions are thought to be of

vital importance for planet formation because exterior to the transition the abundance of

solids increases substantially. In fact, the water transition front even has a special name: the

snow line. Interior to the snow line, small planets should form from rock and iron but exterior

they should contain a large fraction of ice and be much larger.

Back to our story. Planetary embryos take about a million years to form (Figure 4.1).

In the terrestrial planet-forming part of the disk, embryos are Moon-sized to Mars-sized, but

in the giant planet-forming region embryos can grow much larger, to several Earth masses,

because they are beyond the snow line. Wherever they are, embryos will interact

gravitationally with the gaseous disk in which they are embedded (Armitage 2011). While

discovered much earlier, the importance of these interactions was really only realized once the

first extrasolar planets were discovered in 1995.

Planet Migration The gravitational interactions of a growing embryo with the gas disk will result in the

launching of density waves in the disk. From resonant locations between these waves and the

embryo, torques are exerted on the embryo’s orbit. The first order of these so-called Lindblad

resonances is located roughly a disk scale height inside and outside the orbit of the planet

while the higher orders are located further away. Gas located near outside resonances orbits

the star slower than the embryo while gas located near inner resonances orbit the star faster.

The zeroth order resonance, or co-rotation, lies exactly at the orbit of the planet and gas

located near this co-rotation region follows so-called horseshoe orbits. The differences

between all these different torques results in a net change of the angular momentum of the

embryo and therefore to a net inward our outward motion depending upon if angular

momentum has been gained or lost. This motion of a body embedded in a gaseous proto-

planetary gaseous disk has been called type-I migration.

In a highly simplified proto-planetary disk, the net torque is such that the embryo loses

angular momentum thus giving rise to inward type-I migration. The rate at which it spirals

inwards has been found to be directly proportional to the mass of the embryo (e.g., a ten Earth

mass planet spirals inward ten times faster than an Earth-mass planet). When the embryo

reaches a few tenths of an Earth-mass, type-I migration becomes so rapid that the body

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literally “falls” onto the star within ten to a hundred thousand years, a blink of an eye in this

context. In other words, this simple analysis tells us that the more an embryo grows, the faster

its will fall into its star and therefore no planet more massive than this should be able to

survive very long (Lyra et al. 2010). As before, we know that this cannot be true since we

observe countless planets (both inside and outside the Solar System) that are larger than a few

tenths of an Earth-mass!

This problem with the short inward type-I migration timescale is still not fully

resolved, although new studies are encouraging. The solution appears to lie once again in the

reality that disks are not as simple and smooth as initially thought. The calculations

suggesting very rapid migration made simplifying assumptions about the temperature

structure of the disk, which is important because it controls the behavior of the density waves

launched by the embryo. Complex new simulations that account for how the disk actually

cools itself off by radiating away energy show that in reality, type-I migration probably does

not behave in the predicted, simple fashion. In fact, for some conditions the co-rotation

torques can largely dominate the dynamics and can be such that the embryo gains angular

momentum and migrates outwards. As the disk evolves or the embryo gains in mass, the co-

rotation torques eventually saturate and the embryo migrates inwards again. To make matters

even more complicated, in a given disks there can be several regions where the conditions

necessary for outward migration are met. So we can imagine a disk in which embryos are

moving inwards in some regions and outwards in others. Of particular interest are the

locations where the two types of motion meet, since these define regions in which embryos

migrate in a convergent manner and may efficiently accumulate into larger bodies.

Although the implications of these new findings have not been fully fleshed out, this

result is good news. Embryos are probably not overly susceptible to falling into their stars,

although, like a toddler on a sugar rush, they have trouble staying in one place.

Planetary embryos can serve as the seeds of gas giant planets if they form fast enough

and are massive enough. Once its gravity becomes substantial, an embryo gravitationally traps

gas from the disk into an extended envelope that is much larger than any present-day

atmospheres of Solar System bodies. This gas is gravitationally bound to the embryo but only

loosely, and the amount of gas that is initially trapped is small simply because the gas is not

very dense. The gaseous envelope extends all the way to the edge of the embryo’s

gravitational reach (called the “Hill sphere”), so in order to increase the mass in this gaseous

envelope, the envelope itself must contract to make room for the new gas. For this to happen,

the envelope needs to cool down by radiating its thermal energy away, which it does mainly

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at infrared wavelengths. However, this is easier said than done since it is also is heated up by

the simple act of falling deeper into the embryo’s gravitational potential well and also by the

dissipation of the kinetic energy of planetesimals falling into it. If one does the calculations,

one finds that the net cooling rate remains quite small until the envelope becomes relatively

massive. This slow cooling rate, in turn, implies a small mass accretion rate and since the

overall lifetime of the gaseous disk is rather limited (less than 10 million years), this slow

contraction represents a real bottleneck on the path of becoming a gas giant planet.

If the gas in the disk dissipates during this protracted stage then the embryo will end

up as something like Uranus and Neptune, both of which contain some gas but are still

dominated by solids (ices, mainly). However, if the contraction of the embryo’s gaseous

envelope continues for long enough the mass in the envelope can become substantial. When

the envelope mass is roughly equal to the mass of the solid core, the process becomes

runaway. When this happens, the planet’s mass increases very quickly as it accretes a large

fraction of the gas in its local neighborhood. As more gas falls onto the growing planet, its

Hill sphere grows and more distant gas falls within its reach. While technically gas accretion

proceeds at a rate increasing with increasing mass, there comes a time when the gas supply is

limited by the disk itself. This is essentially due to two factors. The first is that the disk cannot

transport gas radially faster than the transport mechanism (usually assumed to be a form of

turbulent viscosity) actually allows. The second is that as the planet grows it eventually clears

an annular gap thereby quenching its own further growth.

As the planet clears this gap, type-I migration becomes irrelevant. In fact, the planet

now migrates at a rate that is given by the transport of the gas itself. This can be understood

by considering that the planet simply receives angular momentum from the inner edge region

and transfers it to the outer edge region of the gap. If the inner edge of the gap moves inwards

and therefore further away from the planet, the planet will receive less angular momentum

while still transferring as much to the outer edge. This will lead to an inward migration of the

planet. However, the outer now receiving less angular momentum from the planet will move

inwards as well and the process repeats itself effectively capturing the planet in the gap. This

new type of migration is called type-II migration and its rate is equivalent to the rate at which

the gas is transported radially in the disk thereby linking the migration of the planet to the

evolution of the disk itself (Figure 4.2).

The fact that planets migrate was a surprise. Even though theorists had an inkling of

the processes just described, simulations were quite primitive in the 1980’s and nobody was

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willing to predict that planets change their orbits substantially, especially when the current

orbits in our Solar System seem stable.

Figure 4.2 Snapshots from hydro-dynamical simulations of low-mass (left) and high-mass

(right) planets embedded in gaseous protoplanetary disks. Here, the colors represent the

magnitude of the perturbations to the gas density caused by the planet’s gravity: yellow

represents an increase in density while purple or black represents a decrease. Note that the

high-mass planet has completely cleared out an annular gap in the disk, while the low-mass

planet does not have enough gravity to create a gap. Image credit: Philip J. Armitage.

Growing Gas Giants How does the disk evolve? Disks around other stars are observed to be slowly

trickling onto their host stars at a rate that depends on their age. The simplest model that can

explain the observations is that the disk has some internal viscosity and as such is simply

spreading out over time. But, since it is in orbit around a star, the gas that spreads inward ends

up falling onto the star. Over its lifetime, it is thought that three quarters or more of the total

gas disk falls onto the star. The rest of the disk is evaporated by absorbing high-energy

(ultraviolet) photons from both the central star and from nearby massive stars. So, a given

piece of disk gas is most likely to stream inward to either fall on the star or evaporate, but has

about a one in four chance of streaming outward and eventually evaporating. Thus, as they are

“bullied” by the disk most giant planets should type-II migrate inward, but a fraction should

go outward. Migration stops when the disk’s dwindling mass drops to a fraction of the giant

planet’s mass.

Gas giants’ bulk—for example, Jupiter is 318 times Earth’s mass and has a radius 11

times larger than Earth’s—means they are the easiest planets to detect around other stars. The

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planets that have been found were not at all expected. What was expected were planetary

systems more or less like our own, with small rocky planets close to their stars and gas giants

farther out, with maybe with an ice giant or two sprinkled amongst them. The very first planet

confirmed around a Sun-like star was completely un-Solar System-like. It was a “hot Jupiter”,

a gas giant planet orbiting its star every 4.2 days (as opposed to Jupiter’s own 12 year orbital

period). The discovery was quickly followed by the realization that it could not have formed

at the distance from its star where it was observed (Mayor and Queloz 1995, Lin et al. 2006).

Another notable surprise in the giant extrasolar planet population is the abundance of very

stretched-out, or elliptical (rather than circular) orbits. The typical extrasolar planet has an

eccentricity of 25%, five times larger than the eccentricity of Jupiter and Saturn. Extrasolar

planets systems are extremely diverse (Kobuko and Ida 2002). Based on the current sample,

the architecture of our Solar System seems to be unusual. However, given the 10-15 years

needed to detect true Jupiter analogs and the fact that many are now being found, only time

will tell if we live in a typical or an unusual planetary system.

Where do hot Jupiters come from? Until very recently the answer was thought to lie

with type-II migration. Giant planets would form at Jupiter-like distances, then migrate in and

stall at the inner edge of the disk, around 0.05 AU, right where hot Jupiters are seen to pile up.

However, new observations have succeeded in measuring the orbital inclination of hot

Jupiters with respect to the equatorial plane of their host stars. If we assume that

protoplanetary disks are lined with the stellar equator, then hot Jupiters should have very

small inclinations. However, what has been measured is an astounding range of inclinations,

from co-planar to highly inclined to co-planar but retrograde! In retrograde systems, the

planet orbits the star in the opposite direction than it started, like a minute hand of a clock

going counter-clockwise. Neither retrograde nor highly-inclined planets are easily explained

with type-II migration (Winn et al. 2010).

It turns out that both hot Jupiters and the eccentric orbits of more distant planets are

telling us that the typical planet-forming environment is extremely violent (Nagasawa et al.

2008). The story goes as follows. Giant planets form in groups of at least two, probably of

three or more. After a time, their orbits become unstable; the instability probably starts as the

gas disk evaporates because, like a TV for a pack of kids, the disk has a calming effect on the

orbits of adjacent planets. The orbits of the giant planets cross, leading to close encounters

and planet-planet scattering events (Chatterjee et al. 2008). During an encounter between two

giant planets, each planet can be accelerated by up to the escape speed of the other (the escape

speed is a measure of how fast something must be thrown from a planet’s surface for it never

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to come back). Jupiter’s escape speed is sixty kilometers per second but its orbital speed is

only thirteen, so a single encounter with Jupiter can toss a planet onto any possible orbit

including ejection from the star on a hyperbolic trajectory. The outcome of planet-planet

scattering in a system of multiple giant planets is that one or more planets are removed from

the system via either ejection or a collision with either the central star or another planet. The

planets that survive this dynamical instability bear its mark with their eccentric and inclined

orbits (Papaloizou and Turquem 2006).

The surviving planets explain the exoplanet eccentricities, but what about the hot

Jupiters? During the instability, some scattered planets have extremely high eccentricities and

therefore perihelion distances so small that tidal forces between the star and planet become

important. Tidal dissipation within both the star and planet act to re-circularize and shrink the

planet’s orbit and on the time span of a billion years or more the planet can become a hot

Jupiter. The orbital inclination of the hot Jupiter will depend on both its starting value, which

can take a very wide range of initial values after scattering including retrograde

configurations, and the tidal dissipation. Around stars less massive than roughly 1.2 solar

masses, hot Jupiters are measured to have very low inclinations, but around higher-mass stars

they have a huge range in inclination including retrograde values (Mordasini et al. 2009).

This is explained by a fundamental change in the internal structure of stars of different

masses: stars less massive than 1.2 solar masses have substantial outer convective zones

(comprising a few percent of their total mass) but stars more massive than 1.2 solar masses

have virtually no convective zone. Since the convective zone is the outermost layer of the

star, it makes sense that this layer is of vital importance in the dissipation of internal energy

(tides). So, the observed inclinations of hot Jupiters are explained if tides are controlled by the

width of the stellar convective zone. If this model is correct, hot Jupiters are really thrown

into place rather than gently migrating.

Forming Rocky Planets We have explored the formation and evolution of gas giants, but what about the rocky,

terrestrial planets? Those are the most interesting planets of all in terms of the search for

potentially habitable (or inhabited) worlds. So, once more, we will travel back to our

protoplanetary disk. It is late in the gas disk lifetime, perhaps five million years after the

parcel of gas began its collapse into a star-planet system. The gas is evaporating away and the

gas giants are already formed. The terrestrial planet region contains perhaps 100 planetary

embryos and a swarm of billions of planetesimals. The planetesimals continue to collide with

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the embryos and, once the mass in planetesimals and embryos is comparable, embryos being

to collide with other embryos. During this last stage of growth, terrestrial planets grow and

settle onto stable orbits. Collisions between embryos can sometimes have dramatic

consequences. High-speed, “hit and run” embryo-embryo impacts may bounce off one

another and lead to net erosion rather than growth (Asphaug et al. 2006). Low-speed off-

center impacts can spin a disk of material off of the larger body and lead to the formation of a

large satellite like the Earth’s moon (Canup and Asphaug 2001). Within 50-100 million years

terrestrial planet growth is finished.

For potentially habitable planets, water is a major concern. Embryos at 1 A.U. are

thought to have been dry—the snow line (at least for the Sun) is thought to have been located

somewhere between 2-4 AU. How, then, do Earth-like planets acquire water? The simplest

answer (although this is a matter of debate) is that water must be delivered to these planets in

the form of hydrated planetesimals that formed beyond the snow line. The isotopic signature

of Earth’s water is virtually identical to that of carbonaceous meteorites thought to have

originated in the outer asteroid belt, and that is our best guess for the source of our water.

This water-rich material from asteroids was probably “delivered” to the growing Earth in the

form of millions of planetesimals and a few large embryos (Morbidelli et al. 2000). The

implication is that terrestrial planets form from material that comes from a range of orbital

distances. In other words, the “feeding zones” of terrestrial planets are wide. This shouldn’t

be too surprising at this point, given that planets can migrate inward and/or outward at various

times (Raymond et al. 2006); in fact, the inner Solar System may have been sculpted by the

inward-then-outward migration of Jupiter (Walsh et al 2011). Nonetheless, it is an important

realization: the water we drink came from asteroids.

As we’ve seen before, giant planets form much faster than terrestrial planets and are

therefore fully formed during the late stages of terrestrial planet growth. The giant planets’

gravitational influence is a major influence during these stages by affecting the orbits of

embryos and also by ejecting any bodies that stray too close. For example, a giant planet on a

Jupiter-like orbit but with significant eccentricity clears out a large portion of the inner disk

and excites embryos’ eccentricities. The terrestrial planets that form in such a system are

closer to the star (farther from the giant planet) and drier than for the case of a giant planet on

a circular orbit, because water-rich material lies closer to the giant planet and is therefore

preferentially ejected. In contrast, lower-mass giant planets and giant planets on circular orbits

help rich systems of terrestrial planet to form with substantial water contents.

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Given our understanding of the influence of giant planets on terrestrial planet growth,

what can we learn from the hundreds of known extra-solar giant planets? The majority are not

good candidates for having formed a terrestrial planet, at least not in its star’s habitable zone

(Udry amd Santos 2007). These systems either contain eccentric giant planets or hot Jupiters:

bodies whose violent past probably destroyed all terrestrial building blocks. This still leaves

over 90% of stars around which no close-in giant planet could be detected and which make

potentially ideal hosts for terrestrial planets (Raymond et al. 2004). As time goes on and with

improving detection techniques, a growing population of truly Jupiter-like planets is slowly

emerging as well as the recognition that planetary systems are probably extremely common.

Our detection techniques are not quite yet capable of detecting truly terrestrial analogs, but

serious efforts are underway and NASA’s Kepler mission has the requisite sensitivity. It

should not be too long before the first detection will be announced of a near-clone of the

Earth.

To summarize, stars form in giant molecular clouds. Planets form in disks around

those stars, from dust, then planetesimals and planetary embryos. This process is extremely

dynamic and may involve large-scale orbital migration at several different phases. Giant

planets form faster than terrestrial planets, and influence their growth. Given our evolving

understanding of planet formation, there are sure to be more surprises to come.

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