Published by the Association Pro ISSI No. 41, May 2018

SPATIUMINTERNATIONALSPACESCIENCEINSTITUTE

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Editorial

Impressum

ISSN 2297–5888 (Print)ISSN 2297–590X (Online)

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Extrasolar planets – why should we care? Simple answer … first of all, a planet in general is an interesting place, we should best know, we in-habit one. The Universe is filled with planetary systems, and for over two decades now increasingly more of them are being discovered. This is neither a surprise nor any-thing to start being bored of, in fact every new planet helps to im-prove our knowledge and also to push the limits of what we want to learn. This exactly is the implica-tion given by the title of the talk: “A Laboratory to Confront the Theory of Planet Formation with Observations”.

However, almost with each new discovery, there is at least one new question that is opened up as well. The more we observe, the more we realise that there is still much more to learn, in fact, there are a huge number of open questions in planet formation.

Still, the search for extrasolar plan-ets is a demanding undertaking and needs extremely precise instru-mentation. It is understandably hard to detect a light signal of a small object next to a million or billion times brighter one, its host star. Similarly, it is not easy to iden-tify a tiny dark spot on a bright ob-ject or a minuscule shift in a star’s spectrum due to the presence of one or more companions.

As instrumentation techniques are progressing, this fosters new mod-els to be developed to explain what has been observed. Of course, the ultimate test for all new theories are then the observations again,

and a fruitful combination of mod-els and data can lead to better un-derstanding of our environment. The sheer number of planets now has made statistics an appropriate tool to do exactly that.

The successive extension of our laboratory space from the home lab Earth to the neighbour lab Solar System to remote parts is still on-going, and we are in for surprises. Discovering new worlds far out-side our own and noting their vast diversity does not only help in un-derstanding basic physical pro-cesses but also in realising that the very system we have the chance to inhabit is special among all the planetary systems discovered so far.

The present text is based on a lec-ture by Prof. Christoph Mordasini in the Pro ISSI seminar series. It has been edited and arranged with valuable input from Prof. M.C.E. Huber and Dr. H. Schlaepfer.

Anuschka PauluhnMönthal, February 2018

Title CaptionArtist’s view on how common planets are around the stars in the Milky Way – the rule rather than the exception. (Credit: ESA, C. Carreau). The inset shows the plot of a com-puted and a measured planetary mass distribution, from Benz et al. (2014).

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Introduction

Naturally, our understanding of planets has so far been swayed by the Solar System planets that have been observed for ages. These have shaped theories that can now be tested against increasing numbers of examples from systems that are very different from ours. New sys-tems, some with new and unex-pected properties are forcing us to adapt and re-think our theories, as already anticipated some years ago, just shortly after the first extraso-

lar planetary systems had been dis-covered2. Every new discovery is checked – does it fit into our mod-els? If so, fine, one more for the current theories; if not, what is wrong – faulty observation, f laws in the measurement, or a com-pletely new feature that needs more explanation and study. The goal is not “to detect for the detection’s sake”, but to improve our know l-edge, our theory, our understand-ing of the world we live in.

The exoplanet detection count jumped up after 1995: Michel Mayor and Didier Queloz had de-

tected the gas giant planet 51 Pegasi b3, which orbits a rather ordinary G-type main-sequence star, not too much different from our Sun and thus had found a rather big planet of half the mass of Jupiter with an orbital period of only 4.23 days. Following this discovery of a gas giant in a short-period orbit close to its host star, astronomers now looked as a matter of course for more unexpected types of companions!

Several branches can be followed in planetary research – from the exoplanets’ orbital dynamics to

Extrasolar PlanetsConfronting the Theory of Planet Formation with Observations1

by Prof. Christoph Mordasini, University of Bern

Figure 1: The Solar System planets, together with some dwarf planets located beyond Neptune’s orbit in the Kuiper belt. Sizes to scale, not distances. Credit: The International Astronomical Union/Martin Kornmesser.

1 The current text is a summary of Prof. Mordasini’s talk for the Pro ISSI audience on 15 March 2017. It was drafted by Dr. Anuschka Pauluhn and revised by Prof. Mordasini.

2 See Spatium 6 by W. Benz (2000). 3 The official name of an exoplanet is a combination of the parent star’s name and a lower-case letter, in the order of

detection. The first planet of the system is denoted “b”, the second “c”, etc.

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their structure and composition, and in particular also that of their atmospheres4. Of course, all these studies are closely related, and of central interest is the way planets are evolving – following their en-tire life cycle from formation to later stages in their career in a plan-etary system like in ours, for example.

However, observing them is not simple in most cases. Stars, on the

other hand, are much easier to observe; they outshine any planet around them. Indeed, a large part of their evolution has been recon-structed a long time ago. Ordering them according to their tempera-ture and luminosity, stars can be classified into certain groups in the famous Hertzsprung-Russell dia-gram5. Such a helpful diagram would be nice to have for planets, so that one could find suitable sys-tematics of classes and evolution.

With more and more exoplanets found, this has now become possi-ble. An example of such a classifi-cation of planets is the mass-dis-tance diagram, relating the planets’ masses (in multiples of Earth masses M ) to their distances to the host star (defined by the semi-major axis of their orbits, and given in multiples of the Earth’s distance from the Sun, the so-called Astro-nomical Unit, AU).

4 See Spatium 36 by H. Lammer (2015). 5 H-R diagram: A scatter plot of absolute magnitude of stars and their effective temperature. It turns out that luminosity

and temperature are not random but related to physical and chemical properties of the stars and to their age. In this dia-gram, most stars are found along a region, which is called the main sequence. A star remains on the main sequence while it is fusing hydrogen in its core. Other regions in the H-R diagram define classes of stars with specific properties such as giant or white dwarf stars.

Figure 2: Two planetary disks observed with the SPHERE instrument mounted on ESO’s Very Large Telescope (VLT). The central part of the image at the location of the bright host star has been blocked in order to reveal the fainter surrounding. Credit: ESO.

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The structure of the Solar System

Planetary studies are as old a disci-pline as humans have been observ-ing the sky, and even the possibil-ity of habitable planets somewhere in the Universe had already been suggested by scholars like Imma-nuel Kant6. Until the last decades, however, the observation of planets had been restricted to the Solar Sys-tem, and all of the early theories on planet formation had been derived from the conditions found there.

Moreover, what had been the source of knowledge on the forma-tion of planets a few years ago was given by only two states in their life cycle, namely their very begin-ning – in nebular disks during star formation processes, and the end product – in a developed planetary system.

The protoplanetary nebular disks (various examples are shown in Fig-ure 2 and Figure 3) are formed dur-ing and almost immediately after the collapse of a molecular cloud into a protostar. As material fur-ther from the protostar begins to fall inward, the conservation of an-gular momentum prevents it from falling directly onto the protostar and the material will f latten into a

disk that surrounds the protostar. These disks can stretch directly from the protostar to distances of hundreds of astronomical units (i. e., well over a hundred times the distance between Sun and Earth). Because the dust and gas of the disk are heated by light from the new-born star, the parts of the disk clos-est to the star will be the hottest and the parts farthest from the star will be the coldest. This dust and gas will emit as a black body, with the hotter material emitting mainly in the infrared, and the colder in the (sub-) millimetre wavelength bands. Consequently, these wave-lengths are a good target for obser-vations, and a combination of space- and ground-based infrared

and (sub-) millimetre interfero-metric observations have been pro-viding valuable data for decades.

At least one of the outcomes of such a process of planet formation is very well known – the Solar Sys-tem – and, of course, any model for planet formation has to be con-sistent with the constraints given by the Solar System planets. The basic structure and the conditions in the Solar System are character-ised by a few remarkable proper-ties (cf., Figure 4 overleaf ).

“Orderly Orbits”: Our Solar System features prograde, nearly coplanar and nearly circular orbits. The or-bital motions and rotations of the

Figure 3: Protoplanetary disks, observed in the infrared by the Hubble Space Tele-scope. Most of the nebulae represent the small dust particles around the stars, which are seen because they are scattering the starlight. Credit: D. Padgett (IPAC/Caltech), W. Brandner (IPAC), K. Stapelfeldt ( JPL) and NASA/ESA.

6 Already in 1755 Immanuel Kant, based on work by Thomas Wright (1750) and probably also by Emanuel Swedenborg (1734), developed a theory on the formation and evolution of the Solar System (Allgemeine Naturgeschichte und Theo-rie des Himmels, 1755). Independently, Pierre-Simon Laplace later (1796) developed a similar theory on the formation of the Solar System, cf., Kant-Laplace theory. The assumption that the Solar System formed from nebular material, i. e., the “nebular hypothesis” is still the basis of modern cosmogony. In fact, Kant was also convinced of the existence of ex-traterrestrial life forms.

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Sun, the planets and their moons are predominantly in one sense7, and the planets circle the Sun on orbits with small inclinations. Mer-cury’s inclination is rather large with 7 °, and Pluto, also formerly known as a planet, has an orbital inclination of 17.1 ° from the eclip-tic; but note that Pluto is now clas-sified as a “dwarf planet” and not considered to be a planet any more.

“Rocks, Gas and Ice”: There is a kind of order or sequence of the planets in our Solar System: with increas-ing distance from the Sun, there are the rocky planets (Mercury, Venus, Earth, Mars), the gas giants ( Jupiter, Saturn), and finally the ice planets (Uranus and Neptune).

“A distinguished inner circle”: In our Solar System no planets are found inside 0.4 AU and no planets reside outside Neptune’s orbit, i. e., be-yond 30 AU.

Planet formation as suggested from the Solar System

Surely, a satisfactory theory has to explain all these conditions. The central ingredient and fundamen-tal quantity to start with is the mass present in the protoplanetary disk:

how much raw material is availa-ble? Early models for planet forma-tion used a kind of reverse engi-neering: the idea was to assume that the planets had been formed where they are now in the disk, take the distribution of hydrogen and helium gas and other elements present in the Solar System and

Figure 5: The planets of the Solar System, from left to right, Mercury, Venus, Earth and Mars, Jupiter and Saturn, Uranus and Neptune. Sizes are shown ap-proximately to scale, distances not. Image credit: NASA.

Giant planets, gas and ice: Giant planets, also referred to as Jovian planets, are usually mainly composed of low-boiling-point materials (gases or ices), rather than rock or other solid mat-ter, but massive planets containing large amounts of solids also exist. The giant planets consist primarily of high-pressure f luids above their critical points, where distinct gas and liquid phases do not exist. The principal components are hydro-gen and helium in the case of Jupiter and Saturn (gas giants) and water, ammo-nia and methane in the case of Uranus and Neptune (ice giants). A planet is called “Hot Jupiter” when its mass is similar to Jupiter but its orbit lies much closer to its host, with the orbital period being rather short, on the order of 10 days or less, and with the surface temperature of its atmosphere being accordingly high. At masses greater than roughly 13 Jupiter masses, the planets would start burn-ing deuterium and thus qualify as so-called brown dwarfs.

Rocky planets:Rocky planets, also called terrestrial or telluric planets, are composed primar-ily of silicate rocks or metals. Within the Solar System, the terrestrial planets are the inner planets closest to the Sun, i. e., Mercury, Venus, Earth, and Mars. Ter-restrial planets have a solid planetary surface, making them substantially differ-ent from the larger giant planets, which are composed mostly of some combi-nation of hydrogen, helium, and water existing in various physical states.

7 However, the rotations of Venus and Uranus are retrograde.

Figure 4: Mass-distance diagram with the positions of the Solar System plan-ets Venus, Earth, Jupiter, Saturn, Ura-nus, Neptune, showing the areas 1 and 2 where until the mid-nineties no plan-ets were thought to reside and the pre-ferred location 3, the “comfort zone” for planets in the Solar System.

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spread it out to their nearest neigh-bours. The distribution of gas and dust and the temperature are the initial conditions – and then a baby planet is set to grow from a grain to a planetesimal and further. An important parameter in the disk is thus the radial density and its var-iation. By neglecting the vertical variation one defines the so-called surface density, i. e., the disk den-sity integrated over the vertical di-rection of the disk; in principle this describes how much mass per sur-face shell is available. The surface density provides a snapshot of the mass distribution, governed by the

viscous and gravitational torques of the gas and solids that determine the accretion f lows and the angu-lar momentum transport. The ba-sic assumptions for the simplistic solar nebula (also called the “min-imum mass solar nebula”, MMSN) modelled the gas surface density by a so-called power law, decreasing with distance as r –3/2. This funda-mental quantity is shown in Figure 6a in a doubly logarithmic plot (that bridges several orders of mag-nitude and presents the strongly decreasing function as a straight line).

The abrupt rise in the plot of Figure 6a marks the so-called snow line (also called frost line or ice line): This is the location in a protoplanet-ary disk, in the case of the Solar System between Mars and Jupiter, where the surface density increases due to the condensation of water. The inner parts of the disk are hotter due to the irradiation from the host star. Of course, this snow line can also be defined for other volatile compounds like ammonia, methane, carbon monoxide, carbon dioxide, and its particular distance depends on the substance and the ambient pressure and temperature.

Figure 6a: Left: The surface density of the protoplanetary disk for the Solar System planets versus distance from the host star in a doubly logarithmic plot, from Ruden (2000). The sudden increase of the density marks the position of the snow line. Right: A schematic of the temperature structure of the MMSN, the minimum mass solar nebula model for our system.

Figure 6b: An artist’s impression of the water snow line around the young star V883 Orionis, as detected with the Atacama Large Millimeter/Submillimeter Array ALMA. Credit: A. Angelich (NRAO/AUI/NSF)/ALMA (ESO/NAOJ/NRAO). A nice terrestrial snow line is shown on the right.

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The temperature and mass distri-butions provide the relevant build-ing blocks for planets: The lack of close-in planets in the Solar System can be explained by the fact that there is simply not enough mate-rial found close to the star in order to form planetesimals. There are less solids close to the star, and gi-ant planets can form only outside the snow line in annuli of sufficient volume for them to grow.

Core-accretion

The standard model of planet for-mation, the core-accretion theory, is a “bottom-up” process: first the planetesimals form solid cores, some of which later accrete massive gaseous envelopes and become giant planets. The remaining cores collide to form both ice giants and terrestrial, rocky planets. The planet grows by accretion. If the planet does not change its distance from the host star, the stellar grav-ity limits the area from where it can accrete mass to an annulus around the planet’s orbit, whose width is a few times the Hill sphere radius8, the so-called feeding zone. Conse-quently, the mass of a planet can grow locally only to a limiting mass Miso, the isolation mass. Following the standard accretion theory, five to ten Earth masses are required for Jovian-mass planet growth, but at

close distances to the star, the mass availability is smaller. Thus, the classical models predict giant plan-ets only at larger distances.

Similarly, the “pure” core-accre-tion model explained why the po-sitions of the planets in the Solar System do not exceed about 30 AU. The accretion by collisional growth is governed by the so-called Sa-fronov relation9, which states that the planetesimal’s change of mass is proportional to the surrounding density, the effective cross-section of its interaction with its environ-ment and its velocity – and both, density as well as velocity decrease with distance from the host. The further away from the star, the longer it thus takes to grow to a

certain mass, and the planets have to form within the lifetime of the protoplanetary disk! So, the model implies that the gas giants form earlier, typically on time scales of the lifetime of the protoplanetary disk, which have been observed to be not longer than 10 million years10, and the rocky planets take more time, around hundred mil-lion years. That would nicely ex-plain the lack of far-out planets in the Solar System: the time scales just do not fit, there is not enough material left at the boundary of the disk by then. The possibility that the giant planets could form fast and directly from a gravitational instability in the protoplanetary gas disk was not much supported in most classical theories.

Figure 7: Mass-distance diagram, showing the areas 1 and 2 where no planets were thought to form, this time with positions of the exoplanets (counted until 2017) included. It clearly shows that planets in general are by far less discriminating in choosing their preferred locations than our Solar System ones. Not only all kinds of close-in planets are found but also far-out ones.

8 The Hill sphere approximates the gravitational sphere of inf luence of a smaller body in the presence of perturbations from a more massive body.

9 In 1969 Viktor Safronov quantitatively described the states of accretion and terrestrial planet formation.10 The lifetimes of protoplanetary disks have been determined by observations in the infrared (from the warmer core

region of 100 K to 1500 K) and millimetre (from the outer regions of colder dust of around 10 K) wavelength bands to be widely in the range from 106 years to 1.5 × 107 years, and not longer. While the protostar accretes, the mass of its envelope/disk decreases significantly and the formation of planetary systems cannot exceed the lifetime of a sufficiently massive disk. Thus, the time available for planet formation is limited.

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The exoplanet revolution

Fine! That’s it – all done and un-derstood. However, now enter the 1990ies and the successive “exo-planet revolution”, starting with the first Hot Jupiter in 1995. But not enough – the more planetary systems had (and have) been dis-covered, the more was (and is be-ing) understood that things are re-ally different out there – and that our Solar System is in fact a very special instance of a planetary system. Ordering the new findings in a mass-distance diagram like in Fig-ure 4, gives a slightly different im-pression of planets’ favored loca-tions, see Figure 7.

Of course, it is difficult to under-stand the structure of an iceberg seeing only its tip. That this guide-line applies to the theory of planet formation as well became obvious

with the increasing number of ex-oplanet detections: most of the planets found did not fit into the well-ordered scheme known from the Solar System. Soon it became clear that a lot of different and pos-sibly new physical processes had to be included in the models in order to represent the findings. Figure 8 shows the count of detections as of March 2018. The current count can be followed on the webpages www.exoplanet.eu and www.exo-planets.org.

New theories and before-neglected approaches had to be invoked to explain the observations of Hot Jupiters and far-out planets. The model of core accretion alone did not seem to be enough and needed to be extended; for example, the theory of gravitational instability was revived, and also the idea of “static” planetary orbits was par-tially abandoned in favour of more “dynamic” ones and the possibil-ity of orbital migration.

Detection techniques for exoplanets

All signals from exoplanets are ex-tremely faint, and most methods so far are indirect – the planet is de-tected, for example, via its inf lu-ence on the motion of its host star or via its inf luence on the path of light emitted by another, distant star.

The most important methods for finding exoplanets are

1. The radial velocity method (RV)This is a spectroscopic method that

measures the net Doppler shift in as many as possible lines of a star’s spectrum. The result is a velocity at which the star is moving in di-rection of the observer’s line of sight. Removing all other known motions, like, e.g., that of the tele-scope relative to the barycentre of the Solar System, the resulting mo-tion is due to the inf luence of the planetary orbits. The signals are tiny – of the order of metres per second. Due to the viewing geom-etry, the measurements yield the product of the mass of the planet and the sine of the unknown incli-nation angle i between the orbital plane and the plane of the sky, MP sin i, which is a lower limit to the mass only. The method is most sensitive to massive planets and to those in short-period orbits. Addi-tionally, the number of spectral lines emitted by a star is crucial for the precision. One of the most pre-cise instruments for this technique is the HARPS (High Accuracy Radial velocity Planet Searcher) spectrograph, attached to the ESO 3.6 m telescope in La Silla, Chile. It has been developed and built mainly by the universities of Ge-neva and Bern and can detect ve-locity shifts down to 0.6 m/s.

2. Transit techniquesThe theory is simple, the measure-ments are hard. As the previous method, it is an indirect detection via the light curve of the host star. Transit photometry identifies planet candidates by the periodic drops in observed stellar brightness that are caused by the planet ob-scuring a portion of the stellar disk once per orbit. Transit photometry can only detect planets whose or-

Figure 8: Cumulative number of de-tections grouped by the detection method, generated by the NASA Exo-planet Archive operated by the Califor-nia Institute of Technology. The plan-ets are grouped by detection method. See also on https://exoplanetarchive.ipac.caltech.edu/exoplanetplots/.

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bits are viewed nearly edge-on, and it measures size, not mass. To get good signals, it is necessary to go to space. After the first interesting transit detections with the CoRoT spacecraft, the NASA Kepler mis-sion has provided thousands of can-didates that need to be further in-vestigated via the RV method. In order to precisely measure plane-tary radii and even test for the pres-ence of atmospheres, the CHEOPS (CHaracterizing ExOPlanet Satel-lite) mission of the University of Bern will provide high-precision photometry of transiting planets. Its launch is planned for 2018, like that of NASA’s Transiting Exo-planet Survey Satellite TESS. Both missions can also help to prepare a target catalogue for the Hubble Space Telescope (HST) follow-on mission, the James Webb Space Telescope ( JWST).

3. Direct imaging Relative to their host stars, planets are very faint light sources. Corona-

graphs, i. e., telescopes with an oc-culting central disk, are thus used to block the light of the star, and most observations have been made in the infrared where the planets are brighter than in the visible part of the spectrum. (The ratio of the spectral radiances of Jupiter to the Sun is 10–9 in the visible range, however 10–6 and larger in the infrared and longer wavelengths.) The demand on angular resolution is high as well: to resolve an angu-lar diameter of 1 AU at a distance of 1 pc (which spans 1 arcsec, by definition of the parsec11) corre-sponds to resolving the diameter of a human hair at 20 m distance. To overcome disturbances by the at-mospheric seeing (that are caused by the irregular variation of the local index of refraction), use of adaptive optics is mandatory. The great advantage of direct signals from the planet is the possibility for spectroscopic analysis and thus to learn about the atmospheres. This method favours planets orbiting

less luminous stars. A spectacular directly-imaged planet around the host star Beta Pictoris located 63 light years from Earth is shown in Figure 9: Although the first images had been taken in 2003, only with improved data reduction methods in 2008 the faint source could be identified as a planet. Follow-up observations then showed the planet re-appear on the other side of the star.

4. Gravitational microlensing Gravitational microlensing occurs when the gravitational field of a star acts like a lens, magnifying the light of a distant background star. This happens only when the two stars are almost exactly aligned. Lensing events are brief, lasting for weeks or days, as the two stars and Earth are all moving relative to each other. If the foreground lens-ing star has a planet, then that plan-et’s own gravitational field can make a detectable contribution to the lensing effect. As the alignment

Figure 9: Directly imaged planet in the disk of Beta Pictoris. This “Super-Jupiter” with a mass of roughly 7 Jupiter masses was first measured with the VLT in November 2003 and identified as a planet many years later. Credit: Lagrange/ESO.

11 One parsec (pc) is the distance at which the Sun-Earth distance 1 AU subtends one second of arc, 1 arcsec. 1 pc = 3.26 light years.

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of the bodies in space does not oc-cur twice, the measurement can-not be repeated.

5. Timing methods, e.g., Pulsar timing

Pulsars are rapidly rotating, strongly magnetised, radio-wave emitting neutron stars, which are the remnants of supernova explo-sions. From variations of their ex-tremely regular signal, the presence of companions can relatively easily be deduced. However, pulsars are not too frequently found, and their planetary systems have to over-come extreme conditions. Timing methods can also be applied to some other classes of pulsating var-iable stars. Their signals have to be regular enough that radial veloci-ties of companions can be detected by the Doppler shift in the pulsat-ing frequency.

6. Astrometry Astrometric detection is based on precise measurements of the posi-tion of objects and the change of position over time. If a star has a planet, then the gravitational in-f luence of the planet will cause the star itself to move in a tiny circu-lar or elliptical orbit. Effectively, star and planet each orbit around their mutual centre of mass. One potential advantage of the astro-metric method is that it is most sen-sitive to planets with large orbits. This makes it complementary to other methods that are most sensi-tive to planets with small orbits. However, very long observation times will be required – years, and possibly decades, as planets far enough from their star to allow de-tection via astrometry also take a

long time to complete an orbit. No detections have been confirmed yet, however, the ESA mission Gaia (Global Astrometric Interfer-ometer for Astrophysics, launched 2013) is expected to detect thou-sands of planets via this method.

The two first methods have been the most productive as of March 2018. Depending on the method, certain systems are more probable to be found than others – this is the observational bias. In general, given the faint signals and large distances, all techniques require utmost pre-cision of the measurements.

With all these methods a multitude and enormous diversity of planets has been discovered – and their fea-

tures and properties cannot any more be explained by the models that have been successful in de-scribing the conditions found in the Solar System. In particular, we find Hot Jupiters, as well as far-out planets! Can we now find theories and models to explain and repro-duce our findings?

The sheer number of exoplanets suggests the employment of statis-tical methods. It now is feasible to use sample sets of exoplanets and extract statistical constraints that can be applied to theoretical mod-els. Furthermore, the population-wide approach can be used to in-vestigate distributions of properties, like their masses, semi major axes, radii, and eccentricities.

Figure 10: There is an enormous diversity in protoplanetary disks. Such disks vary in their lifetimes, gas masses, dust masses, and thus in the initial conditions for plan-etary evolution. The image shows a collection of 30 protoplanetary disks in the Orion nebula, observed by the Hubble Space Telescope in the visual wavelength range. Credit: NASA, ESA, and L. Ricci (ESO).

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Simulating the diversity

Through observations, we know already a lot about protoplanetary disks, i. e., the beginning of plan-etary systems and also about their fully developed state. Already these disks show an enormous diversity (see Figure 10). However, the knowl-edge about the intermediate states, i. e., how a planetary system be-comes one, is still rather limited to-day. What is desired is a theory that can bridge the gap of (so far) miss-ing information between the states of the early disks and the observed planetary systems. The task is clear: given a distribution of initial con-ditions – can the distribution of ex-oplanets be generated by a physi-cal model?

Modelling – Population synthesis

The method of population synthe-sis uses a statistical approach in or-der to model and understand the planet formation process; it gener-ates an output of planetary systems from a sample distribution of ini-tial conditions. The result is subse-quently filtered with the appropri-ate restrictions applying for a specific observation method, i. e., considering the observation bias, in order to compare with the re-spective measurements. For exam-ple, gas and dust masses as given by a number of observations are used as input for a simulation scheme as is displayed in Figure 11.

The important physics is hidden in the term “formation model”. As usual with modelling, one has to break down the intrinsically com-plex and interacting processes into smaller bits and lower-dimensional parts, in order to be able to handle them mathematically and compu-tationally. If, given all the neces-sary simplifications, a result is in reasonable agreement with obser-vation, this could mean that our understanding of what happens is not too far off. Another important application of course is to make predictions – from the output of a simulation, tell the observers what to search for. This latter is in fact a valid application of the method – it helps space agencies designing missions by defining goals for fu-ture instruments.

A global formation model builds on many detailed theories and models that each addresses one spe-cific physical mechanism. Most models are based on the core-ac-cretion paradigm; recent studies

employ also the gravitational insta-bility model. In general, the start is a protoplanetary disk and at the end of a simulation a fully devel-oped planetary system at an age of several billion years should be the result. The modular outline of such a model (here the one from the University of Bern) is shown in the box.

A test bed for the theories

All models are complex compos-ites of several sub-models; every single part is critically dependent on the output of the step before, and interrelated to the other parts. There are lots of parameters to tune, lots of assumptions and sim-plifications have to be made and new approaches have to be tested. A lot of progress has been made in the last years, but modelling always has room for more improvements, be it through new theoretical ideas, better algorithms or sheer comput-ing power. Using such a modular

Figure 11: Flow diagram that shows the outline of population synthesis (Morda-sini et al 2009).

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model, the suitable statistics and the corresponding observations the extended theories can now be tested, with emphasis on the afore-mentioned open questions.

Hot Jupiters/close massive planets:

The finding of massive planets close to their host star (cf., Figure 12) revived some older theory to be included in the models – the pos-

sibility that planets are mobile: or-bital migration. In a protoplane-tary gas disk, embedded planets and gas interact gravitationally which can lead to an exchange of angular momentum. The planet reacts by adjusting its semi major axis. Both in- and outward migra-tion are possible, depending on planet mass and the properties of the disk. Including the orbital mi-gration part in the models, close

massive planets can be successfully reproduced. However, choosing the parameters is not simple – in a number of simulations, the planets just end up falling into the star too fast instead of orbiting peacefully around it for a while. Quantitative predictions are hard: it is to date one of the most debated subjects in formation theory, other mecha-nisms are also possible and under study.

Figure 13: HR 8799 in Columba where at least four massive planets are far out ones. Credit: J. Wang, C. Marois.

Figure 12: An illustration of the Hot Jupiter K2-33b, which (at an age estimated to be between five and ten million years) is one of the youngest exoplanets detected to date. Its orbital period is about five days. Credits: NASA/JPL-Caltech.

The sub-models of the Bern model

0)  Observed distributions of initial conditions, i. e., properties of protoplanetary disks, such as metallicity, lifetimes, mass

1)  Structure and evolution of the gaseous protoplanetary disk

2)  Gas surface density evolution: viscosity/mass loss by photo-evaporation/accretion

3)  Structure and evolution of the disk of small bodies (planetesimals)

4)  Core growth of protoplanet by accretion of planetesimals and collision

5)  Radial structure model of the gaseous envelope of the protoplanet

6)  Atmosphere of the protoplanet 7)  Interaction of planetesimals and

the gaseous envelope of the protoplanet

8)  Radius of the solid core as a function of its mass, bulk com-position and external pressure due to the surrounding gas envelope

9)  Mass loss due to atmospheric escape of the primordial H/He envelope

10)  Orbital migration due to tidal interaction

11)  Gravitational interaction of young planets

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Far-out planets/timescales for planet growth:

Direct imaging of the system HR 8799 in the Columba moving group showed some surprisingly large companions farther out than 30 AU (Figure 13 on page 13). Still, a mechanism is needed to repro-duce these planets. The alternative, or rather additional model to pure core accretion that can be tested in population synthesis is gravita-

tional instability. It proposes a self-gravitative formation: gas in the protoplanetary disks collapses un-der its own gravity and directly forms a large, gravitationally bound clump with a mass of several Jovian masses. Other possible explana-tions for far-out planets that can be tested in the models include vari-ous accretion mechanisms to sim-ulate the still not well-understood growth stages of particles in the metre-size range.

Different planet types (rocky, icy, gaseous):

In extrasolar planetary systems, a large variety of both planets and planetary structure has been ob-served with no simple partition into gas giants, icy or rocky plan-ets. Instead, many planets with masses between the Earth and the ice giants have been detected; there is no large gap and no clear type difference as in the Solar System. Are these planets Super-Earths or Mini-Neptunes? The key to this question is in the composition when it comes to modelling the at-mospheres, starting from the mi-crophysics of the grains suspended there and defining the opacity

Figure 15: Simulated planetary tracks, the relation of planets’ masses to their distance from the host star, and how they have arrived there – formation pro-cesses as generated with the Bern model (Mordasini et al 2009). The colours mark different types of orbital migra-tion, which are determined by the planet and disk mass, and the viscosity of the disk gas.

Figure 14: Comparison of observed and synthetic planetary masses as found with high-precision radial velocity observa-tions. The black line shows the raw count, while the red line is corrected for the observational bias (that misses the detection of low-mass planets). The panel on the right shows the planetary mass function (i. e., the number distri-butions of planets as a function of their mass) as found in a population-synthe-sis calculation. The black line gives the full underlying population, while the blue, red, and green lines are the detect-able synthetic planetary mass distribu-tions using, respectively, low (10 m/s), high (1 m/s), and very high (0.1 m/s) ra-dial velocity precision. Figure from Mordasini et al. (2015).

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(i. e., the attenuation coefficient, describing how radiation is trans-ported in a medium). Here, as in many other parts of the planet-for-mation processes, various theories are under debate, and a better un-derstanding of the grain dynamics and how the growth from tiny particles to planetesimals really happens is desired. Within exist-ing models, various potential mechanisms and scenarios can be simulated. Figure 14 places side by side an important result of the Bern model and observations made by using the radial velocity method.

Planetary life cycles:

The ultimate goal is to illustrate the life cycle of planets, from their birth to late stages, as is possible for stars in the HR diagram. For ex-ample, the formation process is best visualised in planetary formation tracks in the mass-semi-major axis diagram, where different phases of concurrent growth and migration can be identified (Figure 15). These tracks can be generated from the models in population synthesis cal-culations. The different phases in the formation process lead to the emergence of distinguishable sub-populations of planets; there is a vast group of low-mass planets, a “horizontal branch”, a sub-popu-lation of Neptune-mass planets ex-tending out to 6 AU, and the “main clump”, a concentration of giant gaseous planets at around 0.3 AU to 2 AU.

Outlook

The Universe is filled with plane-tary systems, and the study of these systems is a good example of a vastly developing theory, not in-significantly being driven by pro-gress in observations. In fact, the field of planetary studies has be-come a sound example of a very successful mutual exchange be-tween theory and measurement. The combination of modelling and statistics is an adequate and practi-cal tool for dealing with the in-creasingly large number of samples and advanced observations.

Models could possibly be used to make predictions about the habit-ability of a planet based on its for-mation and evolution. This will be supported by future high-precision observational data, as not only photometric but also spectroscopic missions are foreseen to provide more information about the geo-physical properties of planets. Maybe in the not too far-away fu-ture we can obtain more insight into possibilities how life has been evolving in the Universe.

All this is contributing to a better understanding of our closer envi-ronment and also a bit further out. Surely, it has added to the compre-hension that the Solar System is in-deed special among the planetary systems.

Further reading/Literature:

Spatium No 6, Benz, W., From Dust to Planets, Oct. 2000.

Spatium No 36, Lammer, H., Origin and Evolution of Planetary Atmospheres, Nov. 2015.

Benz, W., Ida, S., Alibert, Y., Lin, D., Mordasini, C., Planet Population Synthe-sis, in: Protostars and Planets IV. Eds: H. Beuther, R.S. Klessen, C.P. Dullemons, T. Henning, Univ. Arizona Press, Tucson, 2014, p. 691.

Laughlin, G., Lissauer, J.J, Exoplanetary Geophysics – An Emerging Discipline, 2016, eprint arXiv:1501.05685.

Mordasini, C., Alibert, Y., Benz, W., Extrasolar planet population synthesis. I. Method, formation tracks, and mass-distance distribution. Astronomy and Astrophysics, 2009, vol. 501, p. 1139.

Mordasini, C., Mollière, P., Dittkrist, K.-M., Jin, S., Alibert, Y., Global models of planet formation and evolution. International Journal of Astrobiology, 2015, vol. 14, p. 201, eprint arXiv:1406.5604.

Ruden, S.P., The Formation of Planets, in: The Origin of Stars and Planetary Systems. Eds: C.J. Lada and N.D. Kylafis, Kluwer Academic Press, 1999, p. 643, eprint arXiv:astro-ph/9910331.

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The Author

SPATIUM

After his study of Physics and Mathematics at the University of Bern Christoph Mordasini very soon specialized in Astronomy, not only theoretically oriented but also dedicated to observations.

In particular the topic of extra-solar planets found his interest, and after his master thesis on “Plane-tesimal impacts into forming giant planets” under the supervision of Prof. Willy Benz had been awarded the best thesis of the year in 2004 at the physics department of the University of Bern, he continued his research with a PhD thesis on “Extrasolar planet population syn-thesis” and a summa cum laude graduation in 2008.

He spent several years at the Max-Planck Institut for Astronomy in Heidelberg as a post-doctoral fel-low. During this time he was awarded an Alexander von Hum-boldt fellowship, as well as a Rei-mar Lüst fellowship.

In 2013 he finished his Habilita-tion and became Privatdozent at the University of Heidelberg, and since 2015 has held a professorship at the University of Bern where he leads the research group “Planets-InTime”. He is a member of the HARPS and SPHERE consortia that search for extrasolar planets using the radial velocity and direct imaging technique, respectively.

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