Solar system formation

Introduction

For decades the solar system was assumed to be the prototype for planetary system form. With the detection of over a thousand confirm planets and many more candidates,it has become apparent that many planetary system wet that differ substantially in their strut properties from our solar system. Nevertheless the formation of the solar system is still of special interest for several reasons. First, it is only for the solar system that we can directly examine material that is left over from the formation process in the form of meteorites. Second, only for the solar system do we have detailed structural information about the entire system including its smaller bodies. Last but not least, it is only for the solar system that we know for sure that life exists.

The three major sources about the formation of the solar system are meteorites, the present solar system structure and contemporary young planets forming systems. We  start  by reviewing the current status of meteorite chain ending the chronology of Earl system formation including the formation oft trial planets in sections2.In this context the question of the origin of shorts lived radioactive nuclei in these meteorites is of special interest. Some of these can only be produced in supernovae events of high amass stars - different possibilities are discussed in sections3.

Other sources of information are young stars surrounded by accretion discs from which planetary systems might form. In section 4 the properties of these discs - masses, gas content and chemical composition - are discussed. Estimates of the life times of these discs are given and the consequences for planet formations I credits cussed. Sections 5 provides a closer look at the different stages of planet formation. Starting from dust grains, then considering pebbles sized objects to planet is master hereby state off his presented. This is followed by the final step in which planets form.

Many of these young systems are part of a cluster of stars. There are several indications that our own solar system also formed as part of a star cluster. Section 6 gives the arguments for such a nearly cluster environment and fiefs the possibilities of finding today's ta formed in the same cluster as our Sun did. Not only the location and masses of the planets but also those of the asteroid and Kohler rotate teristics of our solar system that might potentially give clues to it's formation. Insection7 the early dynamical evolution of the Kipper belt is illustrated. Possible scenarios for the late heavy bomb aten4.0and3.7Gyr ago are discussed. It is still an open question to what degree the solar system characteristics changed since its formation and how stable the solar system is in the long-run. The likelylong-term evolution of the solar and other planetary systems is discussed in section 8. Thisis followed by a summary in section9.

First, we look at the information that meteorites give about the formation of the solar system. In order to do so a relative age dating of these meteorites is necessary.

Themeteorite record of early solar systemevolution

Thesignificance ofmeteorites

Studying meteorites from our solar system is the only way to directly constrain timescalesof itsprotoplanetarydiscevolution.Mostmeteoritesareolderthan4.5billionyearsandoriginate fromtheasteroidbelt.TheasteroidbeltbetweenMarsandJupiterprovidestheonlyvestigeof

 

the planetesimals which were the first larger objects in the protoplanetary disc that provided the building materials for the larger planets. Simulations indicate that it is most likely that the larger planets formed via collisions of such first generation planetesimals (e.g. Wetherill 1990, Chambers 2003). The different groups of meteorites sample these first generation planetesimals and cover the different evolutionary steps of early solar system evolution in great detail. In general, three major groups of meteorites can be distinguished. Chondrites representunprocessed,brecciatedearlysolarsystemmatter,whereasdifferentiatedmeteorites such as achondrites and iron meteorites originate from asteroids that have undergonemelting and internal differentiation. These asteroidal melting events were triggered by either decay of short-lived 26Al or by impact events. Due to the short half life of 26Al (0.7 Myr), the first heating mechanism is confined to the first 5 million years of solar systemevolution.

Chondritesand theircomponents

TheoldestdatedsolarsystemmatterareCa,Al-richinclusions(CAIs)inchondriticmeteorites that have been dated by the U-Pb method to 4.567-4.568 billion years (Amelin et al. 2002, 2011;Bouvieretal.2007).CAIsareanimportantanchorpointtoconstraintheabundanceof significant short-lived nuclides such as 26Al or 182Hf at the beginning of the solar system. In addition to the long lived U-Pb chronometer, short-lived nuclides with their half-lifes of less than100millionyearsenabledatingofmeteoritesandtheircomponentsatanageresolutionas lowasseveraltensofthousandsofyears.BasedoncombinedU-PbandAl-Mgchronometry, the ages of chondrules, a major component of chondrites, has been constrained to as late as up to 4 million years after solar system formation (e.g. Bizzarro et al. 2004; Villeneuve et  al. 2009). It is currently contentious, as to whether there is a circa 1.5 million years age gap betweentheformationofthefirstCAIsandtheformationofthefirstchondrules(seeVillneuve et al. 2009; Amelin et al. 2011; Larsen et al 2011; Connelly et al. 2012). There is, however,now consensus that the undifferentiated asteroidal parent bodies of chondrites themselves accreted ca. 2-4 million years after the beginning of the solar system (e.g. Bizzarro et al. 2005;Kleineetal.2008).Becauseoftheiryoungeraccretionages,chondritesescapeinternal heating triggered by 26Al (Trieloff et al. 2003, Henke et al. 2013), and thus they preserved their pristinestructure.

Differentiatedasteroids

Recent high precision dating using Hf-W and Al-Mg chronometry has shown that some differentiatedmeteoritegroupsdoinfactpredateformationofchondrites.BesideCAIs,some groups of magmatic iron meteorites that represent the cores of differentiated asteroids have been shown to constitute the oldest solar system objects (Kleine et al. 2005). If corrected for cosmic ray exposure, magmatic iron meteorites can be shown to have differentiated within the first 2 million years of solar system history, and their asteroidal parent bodies must have accretedearlierthan0.5millionyearsaftersolarsystemformation(Kruijeretal.2013,2014; Wittigetal.2013).Someoldergroupsofachondritesthatsampletheoutersilicateportionof differentiatedasteroidsdifferentiatedonlyslightlylaterthanironmeteorites.Theparticularly

 

pristine group of angrites (achondrites consisting mostly of the mineral augite) is inferred to havedifferentiatedbyaround3-5millionyearsaftertheCAIs(Larsenetal.2011,Brennecka & Wadhwa 2012; Kleine et al. 2012). Likewise, achondrite groups such as acapulcuites, eucrites, and winonaites as well as non-magmatic iron meteorites differentiated in the time interval between 3-5 million years after solar system formations, with inferred accretionages between 1 and 2 million years after solar system formation (Schulz et al. 2009,2010).

Thenew early solar systemchronology

In summary, there is now clear evidence from short-lived nuclide and long-lived U-Pb chronometry that CAIs are the oldest solar system objects, followed by magmatic iron meteorites (differentiation of 1-2 million years after solar system formation) and most achondrite groups and non-magmatic iron meteorites (differentiation 3-5 million years after solar system formation). Differentiation of these asteroidal bodies was likely driven by internal heat sources, with decay of 26Al being the most important one.  The  parent asteroids of chondrites accreted much later (2-4 million years after solar system formation) than those of the differentiated asteroids (less than 2 million years after solar system formation). It is therefore likely that the chondritic parent bodies did not undergo internal differentiation,becausetheheatsupplyfromshort-livednuclidessuchas26Alwasinsufficient, or,alternatively, their parent body size was too small. Alternatively, undifferentiated chondritesmaysampletheouterlayersofplanetesimalsthatdifferentiatedintheirinteriors.

Age of the inner terrestrialplanets

Thelargerrockyplanetsintheinnersolarsystemformedmuchlaterthanthesmallasteroids, at timescales of tens of millions of years. Hf-W systematics in terrestrial samples and chondrites constrain the age for the Earth’s growth to at least 38 million years (Kleine et    al. 2002, Yin et al. 2002; Knig et al. 2011) and probably as late as 120 million years after solar system formation (Allegre et al. 2008; Rudge et al. 2010). There are fewer indicators toconstraintheageofMars,butestimatesreachfrom2to10millionyearsaftersolarsystem formation (Nimmo & Kleine 2007; Dauphas & Pourmand 2011). The uncertainties of these estimates originate from the parameters that are used to model planetary growth and internal differentiation into metal cores and silicate mantles. The small size of Mars, for instance,has beenexplainedbyradialmigrationofJupiter,suggestingthatMarsrepresentsastarvedplanet that could not accrete further because of interaction with Jupiter (Walsh et al.2011).

For constraining the age of the Earth, the Moon-forming giant impact event is of great importance, and physical models explaining the formation of the Moon have dramatically changedoverthepastyears(e.g.Canup&Asphaug2001;Cuk&Stewart2012;Canup2012). Likewise, the Hf-W and U-Pb chronometry of Earth’s formation has undergone significant reinterpretation. Most earlier studies agreed that both the Hf-W and U-Pb chronometers date segregation of the Earth’s core during the final stages of Earth’s accretion (e.g. Allegre et  al. 2008;  Rudge et al.  2010,  Wood  & Halliday 2005).  A combination of experimental  andgeochemicalstudiesnowratherarguethatvolatileelementssuchasPbweredelivered

 

late to the growing Earth, implying that the U-Pb systematics of the Earth’s silicate mantle bear no chronological significance (Albarede 2009; Ballhaus et al. 2013; Marty et al. 2012; Scho¨nba¨chleretal.2010).

The geochemical and isotopic inventory of meteorites provides a unique chronological record of early solar system evolution. It took only less than one million years after condensation of the first solid matter to form the first generation of planetesimals. These planetesimals underwent internal heating between 1 and 4 million years after solar system formation, largely caused by 26Al decay, triggering their differentiation into metal cores and silicate mantles. The parent asteroids of undifferentiated chondritic meteorites formed 1-2 million years later, and therefore these bodies did not differentiate. Formation of the largerterrestrialplanetsintheinnersolarsystemoccurredviacollisionofsmallerasteroidalbodies. The timescales involved in planetary growth are in the order of tens of million years, with Mars being a possible exception due to gravitational interaction with nearby Jupiter. There is growing evidence, that the volatile element inventory of the inner solar system was added late, i.e. during the last stages of planetarygrowth.

Theorigin of short-livedradionuclides

Chondriteshavenotenduredanygeologicalactivitysincetheyformedduringthefirstmillion years of our solar system. As such, they record physical processes in the solarprotoplanetary disc (SPD) but also of the molecular cloud stage, which preceded the formation of the proto- Sun (Wadhwa et al.,2007).

Chondrites are made of CAIs, chondrules and iron-nickel metal. All these components are cemented by a fine-grained matrix (Fig. 1). A key property of chondrites is the past presence within their components of short-lived radionculides (SLRs). SLRs are radioactive elements, which have half-lives, T1/2, smaller than 200 Myr and were present in the early solar system (Russell et al., 2001).Though they have now decayed, their past presence in chondrites and other meteorites is demonstrated by excess of their daughter isotopes.

Astrophysicalcontext

Since1962andthediscoveryof129I(T1/2=15.7Myr),alonglistofSLRshasbeenidentified in meteorites (see the Table of Dauphas & Chaussidon (2011)).SLRs are important because theycanpotentiallyhelptobuildanearlysolarsystemchronologyandarethemostlikelyheat sourceofthebuildingblocksofplanets,planetesimals(Wadhwaetal.,2007).Inaddition,they can help decipher the astrophysical context of our solar system formation. In other words, assuming the Sun was born as most stars in a (Giant) Molecular Cloud, elucidating SLRs’ originistheonlytooltotracebackwhatwastherelationshipoftheSunwithotherstarsborn in the same molecularcloud.

The presence in the early solar system of SLRs having the longest half-lives is not surprising.Similarlytostableisotopestheyhavebeenproducedintheinteriorofstars,which have preceded our Sun in the Galactic history and were delivered to the InterstellarMedium

 

Figure 1. Composite false colour chemical map of the interior of the Renazzo chondrite: aluminum (white), magnesium (green), silicion (blue), calcium (yellow), iron (red). ChondrulesaretheabundantMg-andSi-richobjects,CAIsaretherareyellowwhiteinclusions and iron-nickel metal are the red grains. Credit: Anton Kearsley (NHMLondon).

(ISM) by supernova (SN) explosions and massive star winds.  Their abundance is roughly  in line with Galactic evolution models (Meyer & Clayton,2000).The presence of SLRs with shorter half-lives (T1/2Ç 10 Myr) is more difficult to understand because their half-life is comparable or smaller than the typical timescales of star formation processes (Williams,2010).Obviously, constraining the origin of SLRs depends also on their initial abundance, which is not always clearlyknown.

Some SLRs have been synthesised via the irradiation of the SPD gas/dust by proto-solar cosmic-rays (Chaussidon et al., 2006).As we saw in section 2 this is especially thecase of 10Be (T1/2= 1.4 Myr) whose abundance in CAIs is variable (Gounelle et al., 2013).Independent evidence for early solar system irradiation is given by the variable and intense X-ray emission of protostars (Feigelson, 2010).Other SLRs such as 36Cl (T1/2= 0.3 Myr)  or 41Ca (T1/2= 0.1 Myr) could also have been produced by irradiation according to some models (Gounelle et al., 2001; Duprat & Tatischeff, 2007; Leya et al., 2003).We note that thesituationfortheseSLRsiscomplicatedbythefactthattheirinitialabundanceinthesolar system is not well constrained (Liu et al.,2012b).

Specialrole of 26Al and60Fe

Aluminium-26 (T1/2= 0.72 Myr) and iron-60 (T1/2= 2.6 Myr) are probably the SLRs, which have  attracted the most attention during the last decade.  Iron-60 is too rich in neutrons to  be produced by irradiation processes (Lee et al.,1998).As 60Fe is absent from massive star winds, its only possible source in the early solar system is - at least one - supernova, which is known to produce large abundances of that SLR (Wang  et al.,2007).Because   the initial abundance of 60Fe has long been considered to be elevated (60Fe/56Fe ∼ 10−6 (Tachibana&Huss,2003)),thepresenceof60Fehasbeeninterpretedasevidenceforanearby supernova (Hester et al., 2004). According to supernova nucleosynthetic models, the SNhad

 

Figure 2. Incorporation of 26Al in a dense shell created by a massive star wind. Phases 1 and 2 correspond to the collection of interstellar gas and injection of 26Al by the wind (arrows). Phase3correspondstothegravitationalcollapseoftheshellandtheformationofanew, 26Al- rich star and other stars including the Sun (yellow). The whole process lasts a few Myr (see text).

to be located within a few pc from the nascent solar system (Looney et al., 2006).In N- body simulations of the birth environment of the Sun it is often assumed that the progenitor of this supernova was a star with a mass of ≈ 25 M(see section 6). However, from the cosmochemical side there are some difficulties with thisscenario.

Cosmochemical constraints on the birthenvironment

It is very unlikely to find a protoplanetary disc or a dense core that close to a SN. Before theyexplodeasSNe,massivestarscarvelargeionizedregionsintheISM(calledHIIregions) where the gas density is too low and temperature too high for star formation to take place. Observations show that even around a massive star that still needs to evolve for 2 Myrbefore it becomes a SN, discs and cores are found only several parsecs away (Hartmann, 2005), too far to incorporate 60Fe at the solar abundance. In addition, because SNe ejecta are vastly enriched in 60Fe relative to 26Al and their respective solar abundances (Woosley & Weaver 2007), all models relying on SN injection lead to a 26Al/60Fe ratio far lower than the initial solar ratio,  unless specific and ad hoc conditions are adopted (Pan et al.,2012).Finally,  the initial abundance of 60Fe has been recently revised downwards by almost two orders of magnitude (Moynier et al., 2011; Tang & Dauphas, 2012).The revised 60Fe abundance is compatible with a somewhat enhanced galactic background due to stars born and died inthe same molecular cloud as the Sun but in a prior generation (Gounelle et al.,2009).

Because supernovae vastly overproduce 60Fe relative to 26Al, 26Al cannot originate from

 

asinglesupernovaasfirstproposedbyCameron&Truran(1977).Italsoimplies26Alcannot have a background origin because at the molecular cloud scale, SLRs are mainly due to supernovae. In addition, the 26Al distribution in the early solar system seems to have been heterogeneous (Liu et al., 2012a; Larsen et al., 2011), which is incompatible with a global (molecular cloud) scale origin (Young,2014).

The most likely origin for 26Al is therefore local, i.e. the wind of a single massive star (Arnould et al., 2006).Tatischeff et al. (2010) proposed that a single runaway Wolf-Rayet (WR) star injected 26Al in a shock-induced dense shell. Given the required velocity of the star (20 pc/Myr) and gas ambient density (n ∼ 100 cm−3) it is however likely the star will have escaped the molecular cloud well before the star collects enough gas and enters theWR phase during which 26Al is injected. This model suffers from the brevity and therefore the rarity of the WR phase. Gounelle & Meynet (2012) have proposed that 26Al originated in a wind-collectedshellaroundamassivestar(Figure2).Inthismodel,thedenseshellcollected bythemassivestarwindiscontinuouslyenrichedby26Albroughttothesurfaceofthestarby convection promoted by rotation (Meynet et al., 2008). After several Myr, the collected shell reaches densities large enough to make it gravitationally unstable and a new star generation forms in the shell. In this model, the Sun is a second generation star and the massive star having provided 26Al can be seen as its parent star. This mechanism is generic in the sense thatthismodeofstarformation,thoughnottherule,isrelativelycommon(Hennebelleetal.,2009). This model constraints the astrophysical context of our Sun’s formation as it requires thattheparentclustertowhichbelongstheparentstar(baptisedCoatlicue)containedroughly 1200 stars (Gounelle & Meynet,2012).

In conclusion, though the origin of SLRs is still a complex and debated issue (seeDavis et al. 2014 for a more detailed review) it seems that three star formation spatial scales are relevant. SLRs with the longest half-lives originate at the scale of star complexes, while 60Fe (T1/2= 2.6 Myr) originates at the scale of the molecular cloud and 26Al (T1/2= 0.72 Myr) at the local massive star wind scale. The distribution of SLRs in the solar system is the record of hierarchical (in termes of spatial and temporal scales) star formation in theISM.

Protoplanetarydiscs

Another source of potential information about the formation of the solar system are young stars that are currently forming planets from the disc material surrounding them (Safronov,1969).Thesediscsformasaconsequenceofangularmomentumconservationduringthestar formation process (e.g. Shu et al., 1987). In the early stages of the star formation process the discmediatesaccretionfromtheparentalcoretotheformingprotostar,whileatlaterstagesit providesthenaturallocationandmaterialfortheplanetformationprocess.Theobservational studyofthepropertiesandevolutionofprotoplanetarydiscsisthusadirectprobeoftheinitial conditions for planetformation.

The presence of protoplanetary discs around young stars was originally inferred from the emission in excess to the stellar photosphere at infrared- and submillimetre-wavelengths (eg. Beckwith et al., 1986, 1990).It was very rapidly understood that the excess emission

 

was likely due to a disc-like distribution of dust located around and heated by the young  star at the centre, this interpretation was also consistent with the dynamics of the molecular gas, which could be interpreted as orbiting the star in Keplerian fashion. The inferred sizes (up to few times 100 AU  in radius) and masses (up to 10-20% of the central star mass)were also consistent with the expected values for a pre-solar nebula. These ideas were then spectacularly confirmed by the HST silhouette optical absorption images a few years later (O’dell et al., 1993). Following these initial observations, protoplanetary discs around young solar analogues have been extensively studied in nearby star forming regions. The recent reviewbyWilliams&Cieza(2011)summarizesmostofourcurrentknowledgeofthegeneral properties of protoplanetary disc populations in nearby star formingregions.

Protoplanetary disclifetimes

The current best estimate of the lifetime of the disc, or the timescale for planetesimal andgas giant formation, is derived from the variation of the fraction of stars, which show infrared excessasafunctionoftheageofthestarformingregions(e.g.Herna´ndezetal.,2007),which is also found to be consistent with the variation of the fraction of young stars that showsigns of interactions with the inner disc (e.g. Fedele et al., 2010). The fraction of young stars with inner disc is found to drop exponentially with an e-folding time of ∼3 Myr. This estimate  is uncertain because of a number of possible systematic and environmental effects, e.g. the uncertaintiesintheagedeterminationofyoungstars(Belletal.,2013),orenvironmentaldisc dispersal mechanisms in clusters, which may not be applicable to the progenitors of the bulk of the field stellar population (Pfalzner et al., 2014).Nevertheless, it is obvious that if the majorityofstarshostplanetarysystems,theformationprocesshastooccurwithinafewMyr, at least for planet types, which contain significant gaseous envelopes (gas giants, ice giants andlow-densitysuper-Earths).InlargestarformingcomplexesintheMagellanicCloudsand ourownGalaxy,thereiscontroversialevidenceforstarswithcircumstellardiscsatrelatively old ages (up to and even beyond 30 Myr Beccari et al., 2010; De Marchi et al., 2011). While in nearby regions the few existing candidates have not been confirmed so far (Manara et al.,2013), it is possible that a small but non-negligible fraction of the stellar population born in large complexes reaccrete a disc and possibly have multiple chances of forming planetary systems (Scicluna et al.,2014).

Protoplanetary disc gas content andchemistry

Young protoplanetary discs are gas rich and most of the raw material available for planet formation is in the form of molecular gas, just like in clouds and cores.  Most of this mass  is in the observationally elusive form of H2and can only be traced, indirectly, through the emission of less abundant species. The molecular gas content, chemistry and emission from protoplanetary discs has been recently reviewed by Dutrey et al.(2014),and we refer tothat work for a detailed account. The key feature for constraining the conditions for planet formationisthataroundyoungsolaranaloguesmostofthediscmidplaneisatlowtemperature andthemostabundantmolecularspecies(withtheobviousexceptionofH2)arefrozeninside

 

the ice mantles of grains. In these conditions, the chemistry is likely to be dominated by reactions on ices and may lead to significant production of complex organic and pre-biotic molecules,asobservedinlaboratoryexperiments(e.g.Mun˜ozCaroetal.,2002;Holtometal.,2005; Islam et al., 2014).While complex organic compounds have been revealed in solar system objects (Glavin et al., 2006; Elsila et al., 2009), the direct detection and abundance measurements in protoplanetary discs is challenging. Nevertheless, in the cold discmidplane cosmic-rayinduceddesorptionoficesmayreleaseasmallfractionofthecomplexmolecules inthegasphase,aprocesssimilartotheonethatisthoughttooccurincoldprotostellarcores (Casellietal.,2012;Jime´nez-Serraetal.,2014).

Alternative promising locations to search for these complex compounds are the snowlines‡of the major molecular species, which could carry in the gas phase complexorganic molecules as impurities as part of the sublimation process. The major snowlines that may produce such an effect are the CO snowline at ∼20K and the H2O one at ∼150K. The CO snowline is now within grasp of the ALMA observatory in nearby star forming regions (Mathews et al.,2013;Qi et al.,2013),and much work dedicated to the characterisation    of this important transition in protoplanetary discs is expected in the coming years. Future instruments may help quantifying gas to dust ratio by combining high spatial and spectral resolution.

Protoplanetary disc masses and massdistribution

Asaconsequenceofthecomplexityofthemoleculargaschemistryindiscsandthedifficulty inobservingH2,themostreliablemassestimatesforprotoplanetarydiscsstillcomefromthe measurements of the thermal dust emission.  Most of the disc is optically thin at submm and longer wavelengths. Therefore,  the thermal dust emission is directly proportional to  the mass, which can be readily estimated from the observed fluxes assuming a dust opacity coefficient and a temperature structure for the disc. The latter is normally computed using a selfconsistentthermalbalancemodel,fortypicalaccretionratesmeasuredinyoungpre-main sequence objects the heating from the central star dominates the disc heating and thethermal structure of the dust is usually well constrained by models (see e.g. Dullemond et al., 2007;Bitsch et al., 2014a)§ The disc masses derived with this method are typically between 0.2% and20%ofthemassofthecentralstar,implyingthatalargefractionofyoungsolaranalogues are hosting a disc with a mass well above the minimum mass solar nebula and in principle capableofformingaplanetarysystemsimilartoourown(e.g.Andrewsetal.,2013;Williams& Cieza,2011).

Highangularresolutionobservationsallowtoresolvethediscemissionandestimatethe distribution of matter in the disc. The surface density of solids, traced by the thermal dust emission, are typically found to fall off as r−1 with radial distance r until a critical radius and thendropsharply,consistentlywithanexponentialfalloff(e.g.Isellaetal.,2007;Hughes

‡The snow, or ice, line is the distance from a central protostar beyond which ice grains can form.

§ The next challenge in modelling discs will be to include simulataneously an advanced radiation transporttreatment and the three-dimenisonla dynamics.

 

et al., 2008; Andrews et al., 2009; Trotta et al., 2013).The observed surface densities of  the most massive discs are broadly consistent with the average surface density of our own solar system (Andrews et al. 2009). However, most systems that have  a total mass above  the minimum mass solar nebula threshold are larger than our own solar system, resulting in a lower surface density. These estimates are not without uncertainties: firstly, the solids are assumed to trace approximately 1% of the total mass (following the estimates of the dust to gas ratio in the interstellar medium), however this number is highly uncertain in discs and also expected to evolve with time and location, as gas and dust evolve following different pathways; secondly, the dust opacity coefficient depend on the composition, size, shape,and porosity of the dust grains (Natta & Testi, 2004; Testi et al., 2014).Measurements of proto planetary disc masses are relatively rare as of today: up-coming ALMA observations maybe abletoprovideastatisticalviewofthedistributionofdustsurfacedensitiesandpossiblyalso gas surfacedensities.

Dustevolution and the first steps of solidsgrowth

As the dust emission is optically thin, multi-wavelength observations at submillimetre wavelength allow us to probe the dust opacity coefficient, which in turn can be a powerful probeofthegrainpopulationproperties.Inaprotoplanetarydisc,grainsareexpectedtogrow and settle onto the midplane (for a recent review,  see Testi  et al., 2014).As grains grow   to sizes of the same order or larger than observing wavelengths, the dust opacity coefficient dependencewithwavelengthchangesfromthetypicalvalueofthesub-micronsizeinterstellar grains (κν∼ ν−1.7) to a much shallower dependence, approaching κν∼ const. in the limit of a population of grains all much larger than the observing wavelength (Beckwith et al., 1986;Draine, 2006; Natta et al., 2007). This argument has been used to constrain the level of grain growth in protoplanetary discs, finding that in most discs around young stars the dust has grown to pebble-size aggregates (Testi et al., 2001, 2003; Wilner et al., 2005; Ricci et al.,2010).

The observational results can be understood in the framework of global dust evolution models in discs (e.g. Birnstiel et al., 2010), which describe the evolution of dust in the disc environment based on constraints from laboratory measurements of the grain-grain collision outcomes (see e.g. Blum & Wurm,2008).More specifically, the emerging observational constraints on the dust grain size distribution as a function of disc radius (Guilloteau et al.,2011;Pe´rezetal.,2012;Trottaetal.,2013)matchestheexpectationsfromtheevolutionary models (Birnstiel et al., 2012; Laibe, 2014).

Thisapparentsuccesshidesanumberofdifficultiesthatstillneedtobesolved,in

particular,smoothdiscmodelsstillpredictaradialdriftandfragmentationofthelargegrains thatisinconsistentwiththeobservationsandrequiretoartificiallyslowdowntheradialdrift. The planet formation process then requires that additional growth barriers are overcome, a variety of possibility exist,  from pressure traps generated by disc instabilities (e.g. Pinillaet al.,2012),localised growth across snowlines (Ros & Johansen,2013),or the efficient accretion of pebbles onto existing planetary cores (Lambrechts & Johansen, 2014).Someof

 

these models predict observational signatures that are within reach of the current generation of observing facilities. Indeed the effect of pressure traps induced by planet-disc interaction has been observed in some systems with ALMA (e.g. van der Marel et al., 2013).

An intriguing development in recent years has been the observation by several groups of the possibility of significant dust evolution before the disc stage in prestellar cores and protostars (Chiang et al., 2012; Miotello et al., 2014).If confirmed, these findings would imply a significant revision of our assumptions on the initial conditions for planet formation in protoplanetarydiscs.

Planetgrowth

From dust topebbles

Planets from the gas and dust present in protoplanetary discs. In the first stage of planet formationdustandiceparticlescollideandsticktogethertoformlargeraggregates(Dominik& Tielens, 1997). The aggregates maintain a high porosity during the growth, since collision speeds are initially too low to cause restructuring. Particles obtain increasingly higher collision speeds as they grow in size and their frictional coupling with the gas diminishes (Voelk et al., 1980; Ormel & Cuzzi, 2007), so that particle pairs decouple from the smallest eddies and thus will have different velocity vectors even when at the same location. An additionalcontributiontothecollisionspeedistherelativeradialandazimuthaldriftbetween different-sized particles (Weidenschilling,1977).

Silicate dust aggregates in the inner protoplanetary disc are compactified by collisions when they reach approximately mm sizes (Zsom et al.,2010).The combination of high collision speeds and low porosity halts growth by direct sticking, since compact particles cannotdissipateenoughenergyduringacollisiontoallowsticking(Gu¨ttleretal.,2010).This is referred to as the bouncing barrier. Ice monomers are generally stickier than silicate monomers and this increases their resistance against compactification (Wada et al., 2009).Thesizeoftheconstituentmonomersalsoplaysanimportantroleindeterminingthecollision outcome. Ice aggregates, which consist of very small monomers of 0.1 µm sizes, can stick  at up to 50 m/s collision speeds (Wada et al., 2009).It is nevertheless not known whether such small ice monomers are prevalent in protoplanetary discs or whether sublimation and condensation cycles drive ice particles to much larger sizes (Ros & Johansen,2013).

From pebbles toplanetesimals

The continued growth from mm-sizes faces the formidable radial drift barrier. The gas in the protoplanetary disc is slightly pressure supported in the radial direction, since viscous heatingandstellarirradiationheattheinnerregionsmorestrongly(Bitschetal.,2014a).This outwards-directed push on the gas causes the gas to orbit slower than the Keplerian speed, by approximately 50 m/s (Weidenschilling, 1977).Solid particles do not sense the pressure differencefromfronttoback(sincetheirmaterialdensityismuchhigherthanthegasdensity), soparticleswouldorbitattheKeplerianspeedinabsenceofgasdrag.However,thedragfrom

 

the slower moving gas drains particles of their angular momentum and causes them to spiral inwards towards the star. In the asteroid belt the radial drift peaks for m-sized particles, which fall towards the star in a few hundred years, to be destroyed at the silicatesublimation line close to the star. The peak of the radial drift occurs for cm-sized particles in the outer protoplanetary disc where the giant planetsform.

There are three main ways by which particles can cross the radial drift barrier:

Mass transfer. At collision speeds from 1 to 25 m/s particles can grow by masstransfer. The projectile is destroyed in the collision but leaves up to 50% of its mass attached to      the target (Wurm  et al.,2005).Particles stuck at the bouncing barrier do not collide at   such high speeds. However, artificially injected cm-sized seeds can grow from the sea of bouncing barrier particles through mass transfer (Windmark et al., 2012). The growth rate is nevertheless too low to compete with the radial drift, so formation of planetesimals by direct stickingrequiresareductionintheradialdriftspeedoftheparticles,e.g.throughthepresence of a long-lived pressure bump. Such a pressure bump may arise at the inner edge of the dead zone(Lyraetal.,2008;Kretkeetal.,2009;Dra¸z˙kowskaetal.,2013)oraroundthewater ice line where the jump in dust density has been proposed to cause a jump in the turbulent viscosity (Kretke & Lin, 2007), although this requires a very steep viscosity transition at the ice line (Bitsch et al.,2014b).

Fluffyparticles.Iceaggregatesconsistingofsmallmonomersacquireverylowdensitiesduring their growth, down to 10−5 g cm−3 (Okuzumi et al., 2012). Particle growth isonlyabletooutcompetetheradialdriftiftheparticlegrowslargerthanthemeanfreepathofthegasmolecules and enters the Stokes drag force regime.Here the friction time is proportionaltothe particle radius squared; hence decoupling is much more rapid than in the Epsteinregimevalidforsmallparticles(Johansenetal.,2014).Very fluffyparticlesarelargeenoughtobeintheStokesregimeandcancrosstheradialdriftbarrierwithin10AUbygrowinginsizewhiledriftingradially(Okuzumietal.,2012).Hencethisisawaytocrosstheradialdriftbarrier,ifparticlescanremainfluffyandavoidcompactificationanderosionbythegaseousheadwind.Particle concentration. Particles can become strongly concentrated in theturbulentgas,triggeringtheformationofplanetesimalsbyagravitationalcollapseoftheoverdenseregions.Particles  concentrate  either  passivelyoractively. For passive concentrationthegeneralmechanismisthatparticlespileupwherethegaspressureishigh,sinceanyrotatingstructureintheturbulentgasflowmustbeinsemi-equilibriumbetweenthedominantforces,namelythepressuregradientforceandthecentrifugal/Coriolisforce(Barge&Sommeria1995).Particlesdonotsensegaspressureandmustthereforemovetowardsthedirectionofincreasinggaspressure.Onthesmallestscalesoftheturbulentflow,approximatelykmunderprevalentconditionsintheasteroidbelt,mm-sizedparticlespileupbetweenrapidlyover-turningeddies(Cuzzi et al., 2001, 2008). The largest scales of the protoplanetary disc are dominatedby theCoriolis force, and the turbulence organises into axisymmetric pressurebumps,surroundedbyzonalflows(Fromang&Nelson,2005;Johansenetal.,2009a;Simonetal.,2012),orelongatedvortices(Klahr&Bodenheimer,2003;Lesur&Papaloizou,2010;Lyra&Klahr,2011).Inthestreaminginstabilityscenariotheparticlesactivelydriveconcentration,bypilingupinfilaments,whichlocallyacceleratethegastowardstheKeplerianspeedandhencedo

 

notdriftradially(Youdin&Goodman,2005;Johansen&Youdin,2007;Bai&Stone,2010b).Strong particle concentration by the streaming instability is triggered at a metallicity slightly higher than solar (Johansen et al., 2009b; Bai & Stone, 2010a).The gravitational collapse  of overdense regions leads to the formation of planetesimals of sizes from 100 to 1000 km (Johansen et al., 2007, 2011, 2012; Kato et al.,2012).

The solar system contains remnant planetesimals from the epoch of planet formation,in the asteroid belt and in the Kuiper belt. These populations of planetesimals can be studied  to infer constraints on the actual processes that led to planetesimal formation in the solar system. The relative lack of asteroids smaller than 100 km in diameter,  compared to a  direct extrapolation from the largest sizes, does not agree with the formation of asteroids by hierarchical coagulation in a population of km-sized planetesimals (Morbidelli et al., 2009,butseeWeidenschilling(2011)foranalternativeview).Asteroidsmayinsteadhavehadbirth sizes larger than 100 km, in agreement with gravitational collapse models, while the smaller asteroids that are found in the asteroid belt today are mainly collisional fragments (Bottkeet al., 2005).Large birth sizes have also proposed to explain a similar lack of small Kuiper belt objects (Sheppard & Trujillo,2010).

From planetesimals toplanets

Planetesimals are the building blocks of both terrestrial planets and the cores of the giantplanets. In the core accretion scenario giant planets form as gas from the protoplanetary disc collapses onto a core that has grown to approximately 10 Earth masses by accumulation of planetesimals (Mizuno, 1980; Pollack et al., 1996). In this picture, the ice giants Uranus and Neptune only manage to attract a few Earth masses of gas before the gaseous protoplanetary disc dissipates after a few million years. Core accretion by planetesimals is neverthelessvery slowbecausethenumberdensityofplanetesimalsislowintheregionwherethegiantplanets form.Anenhancementof4-6overtheMinimumMassSolarNebulaisneededtoformJupiter and Saturn within 10 million years in the classical core accretion scenario (Pollack et al.,1996).

Core accretion timescales can be decreased when accreting planetesimal fragments. Smallfragmentshavetheirscaleheightsdampedbygasdragandhencethegrowingcorecan accrete a much larger fraction of the solid material (Goldreich et al., 2004; Rafikov, 2004).However, global disc simulations show that a large fraction of the slowly drifting fragments are trapped in resonances with the cores (Levison et al., 2010).The formation of a system  of giant planets is further complicated by the excitation of planetesimal eccentricities and inclinationswhenscatteredbythegrowingcores.Thisleadstoaslowoligarchicgrowthphase withgrowthratesthataretoolowtoformcoreswithinthelife-timeoftheprotoplanetarydisc (Levison et al.,2010).

Pebblesleftoverfromtheplanetesimalformationprocesscanbeaccretedveryefficiently

by the growing cores (Johansen & Lacerda,2010;Ormel & Klahr,2010;Lambrechts &Johansen,2012;Morbidelli&Nesvorny,2012).TheHillsphereofthecoredenotestheradial distanceoverwhichanincomingparticleonafaster(interior)orslower(exterior)orbitis

 

0.02

0.01

0.00

0.01

0.02

0.02

0.01

0.00

0.01

0.02

0.00 0.01 0.02

x/H

Figure 3.Accretion of pebbles onto a 1000-km-scale protoplanet. The simulation box corotates with the protoplanetary disc at an arbitrary distance from the star. The top plot shows the column density of cm-sized pebbles in the radial-vertical plane, while the bottom plot shows the column density in the radial-azimuthal plane. Two streamers of material enter the Hill sphere, which is approximately 0.007 times the gas scale-height H for the considered protoplanet mass, and feed a particle accretion disc orbiting the protoplanet. Figure adapted from Johansen & Lacerda (2010).

scattered gravitationally by the core. The core only extends a small fraction of its Hill radius (0.1%at5AU,0.01%at50AU).Gravitationalfocussingoftheincomingplanetesimalsmakes the accretion radius much larger than the physical radius, but planetesimals are still onlyaccretedfromabout3%oftheHillradiusat5AU.Pebblesofmm-cmsizesexperiencestrong dragduringthegravitationalscatteringandloseenoughenergytobegravitationallyboundto the core, for any impact parameter up to approximately the Hill radius (see Figure 3).This leadstoveryhighaccretionrates,about1,000timesfasterthanclassicalcoreaccretionat5AU and10,000timesfasterat50AU. Suchhighgrowthratesareneededtoexplaintheformation ofgasgiantsobservedinwideorbitsaroundsomeyoungstars(e.g.HR8799,Maroisetal.,

 

2008, 2010) assuming they are not formed from other means (like gravitational instability). As detailed in section 4.4, protoplanetary discs observed at mm- and cm-wavelengths show signs of large populations of mm-cm-sized pebbles, which can boost planet formation (Testiet al., 2003, 2014).

Manyoftheyoungstarssurroundedbydiscsarepartofaclusterofstars,indeeditseems that most stars are born in a clustered environment (Lada & Lada 2003). In the next section we will discuss the possible birth environment of the Sun. In particular we consider whether we can constrain the properties of the birth cluster, indeed its possible identity, and whether we can identify solar siblings, i.e. the stars that were born from the same molecular cloud as the Sun (see for example, Portegies Zwart, 2009; Adams, 2010; Pfalzner,2013).

Formation within stellarclusters

Evidencesuggesting the Sun formed in a stellarcluster

Analysisoftheisotopicabundancesofmeteoritesrevealthattheycontainthedecayproducts of the radioactive isotopes 26Al and 60Fe, which have half lives of 0.7 Myr and 2.6 Myr  (Lee et al., 1976).As mentioned in section 3 the most likely source of these isotopes aresupernovaeexplosions(e.g.Chevalier,2000).Howmanyisstillamatterofdebate.Giventhe observed distribution of stellar masses of newly-formed stars follows a power law favouring less-mass stars (dN/dm ∝ m−2.35 - Salpeter, 1955) one would need a fairly large group of stars reasonably close to the forming Sun to explain the observedabundancies.

There are other indications that the Sun once was part of a fairly dense and therefore large stellar cluster. First, the fairly abrupt cut-off in the mass distribution at 30-50AU, which is usually not observed in protoplanetary discs, but could be caused by a fly-byduring the protoplanetary disc phase. Second, the trans-Neptunian objects Sedna and 2012VP113(Morbidelli & Levison 2004, Kenyon & Bromley 2004, Brasser et al. 2006, Trujillo & Sheppard 2014) with their high excentricities are another property that could be explained by an encounter during the planet forming phase. Calculations of encounter probabilities in clusters suggest that the Sun was formed in a stellar cluster containing 2000 to 10000 stars (Portegies Zwart 2009). Further evidence for the sun having been in a cluster, comes from the measured tilt of the sun’s rotation, one suggestion being that the protoplanetary disc was titled by a star-disc interaction (Heller 1993; Thies et al. 2005).

Encounters and other processes within stellarclusters

Stellar clusters are potentially dangerous environments for planetary systems. Close encounters between stars are relatively frequent in such crowded places.  The timescale for  a particular star to have another star pass within some distance Rmincan be approximated by (Binney & Tremaine,2008)

7 .100pc−3Σ.v∞ Σ.103AUΣ.MΣ

 

One can distinguish between different phases during which such an encounter couldhappen: (i) the early phase when the star is surrounded by an accretion disc (first few Myr),

(ii) the planet growth phase, and (up to 100 Myr), and (iii) after the solar system was fully formed(uptonow).Closeencountersoccurringwhilststarsstillpossessprotoplanetarydiscs could lead to their truncation (Kobayashi & Ida, 2001; Forgan & Rice, 2009; Breslau et al.,2014; Rosotti et al., 2014).In addition, illumination by massive stars may lead to the early evaporation of protoplanetary discs around young stars (Armitage, 2000). Thus, clustersmay inhibit the planet formationprocess.

Planetary systems, once formed, are also affected by other stars within clusters. Fly-by

encounters with other stars may perturb otherwise stable planetary systems (e.g. Malmberget al., 2007b, 2011) Changes in planetary orbits within a system can lead to the growth in eccentricities until orbits cross. Scattering can then lead to the ejection of planets leaving those remaining on more bound and eccentric orbits. For lower-mass planets on tighter orbits, orbit crossing tends to lead to collisions between planets (e.g. Davies et al., 2013).Alternatively, stars hosting planetary systems may exchange into (wide) binaries. The stellar companion may then perturb planets’ orbits via the Kozai-Lidov mechanism, where planets’ orbits periodically pass through phases of high eccentricity. Planetary orbits may then cross leading to scattering or collisions (e.g. Malmberg et al., 2007a; Davies et al., 2013).In the early phases the probability of encounters are highest, as afterwards clusters expand and therefore the encounter likelihooddecreases.

Placingthe solar system inside a stellarcluster

We have seen above how the measured isotopic abundances in meteorites are well explained by the enrichment of the protosolar-system material from a nearby supernova formed from  a relatively massive star or from a combination of supernovae and a massive 26 Al-producing star. The rarity of such objects in turn led us to argue that the solar system likely formed within a stellar cluster containing at least 2000 stars. As just discussed, stellar clusters are hazardousenvironments.Therateofdestructiveclosestellarencounterstendstoincreasewith increasing cluster mass (see Eq. 1).Therefore, there is an optimum stellar cluster containing around a few thousand stars where pollution from supernovae is at least possible whilst at the same time a reasonable fraction of planetary systems may survive unperturbed (Adams& Laughlin, 2001).One can perform N-body simulations of stellar clusters containing one25 Mstar to determine the number of solar-like stars,  which are 0.1 - 0.3 pc from the 25   M  star when it explodes as a supernova.  One can then follow the subsequent trajectories   of these polluted stars within the cluster to determine the fraction of them, which avoid both perturbing fly-by encounters and exchange encounters into binaries. Such numerical studies of clusters containing 2100 stars (including one 25 M star) reveal that some 25 percent of clusters contain enriched, unperturbed solar-like stars (i.e. G-dwarfs), and usually only one or two per cluster out of a total of 96 G-dwarfs (Parker et al., 2014).Therefore, roughly one percent of G-dwarfs from such clusters are enriched whilst beingunperturbed.

 

Figure 4.The current orbits of the Sun (red line) and the open cluster M 67 (blue line) in cylindrical coordinates where R is the cylindrical radius from the Galactic centre and z is the distancefromtheGalacticplane(Figure7ofPichardoetal.,2012,reproducedwithpermission of theAAS).

M67 as a possible hostcluster

If the Sun was indeed born in an open cluster, it is rather natural to ask whether this cluster is still around today, and if so, whether we can identify it. There have been a number of observations of star clusters of different ages dedicated to find planets in them (Meibom et al. 2013, and references therein). However, planet detection in clusters provides some added difficulties, for example, even nearby clusters are often more distant than the field stars one findsusuallyplanetsaround),thusthefrequencyofplanetsinclusterenvironmentscompared to that in the field is still an open question. However, probably most clusters in the solar neighbourhood loose a considerable fraction (> 70%) of their stars (Pfalzner & Kaczmarek 2013). Measuring detailed abundance patterns in stellar atmospheres throughhigh-resolution spectroscopy offers us the hope of identifying other stars, which originate from the same gas cloudastheSun(e.g.PortegiesZwart,2009;PortegiesZwartetal.,2010).Evenifthecluster haslongsincedissolved,starsfromitwillstillsharesimilarorbitswhosepropertiescouldbe measured astrometrically (e.g. Brown et al.,2010).

The open cluster M 67 is one candidate which we will consider here, though there  musthavebeenanumberofclusterproducedintheMilkywayhavingsimilaragesand

galactocentric radii. M 67 has an age. of about 3.5–4.8 Gyr (Yadav et al., 2008) and the starswithinitalsohaveacompositionsimilartotheSun.O¨nehagetal.(2011)haveidentified onestarinthecluster,whichisabettermatchtoourSunthanmostsolar-likestarsinthesolar

neighbourhood. The analysis of 13 additional stars in M 67 confirm that the abundances of theSunandM67aresimilar(O¨nehagetal.,2014).

 

However, as pointed out by Pichardo et al. (2012) the current orbits of M 67 and the Sun are very different, as shown in Fig. 4, where we plot their current orbits in cylindrical coordinates(figure7fromPichardoetal.,2012).Theradialdistancefromthegalacticcentre, R, for the Sun and M67 are similar. Earlier mention of abundance enhancements in the Sun compared to its distance from the Galactic centre (Holmberg et al., 2009) would indicatethat the Sun experienced a radial migration of 0.8–4.1 kpc (Minchev et al., 2013).In that case M 67shouldalsohavemigratedoverthesamedistance.Possibly,themigrationhappenedwhile the Sun was still a member of its birth cluster. Extensive numerical analysis of the orbit of the Sun in the Galactic potential however indicates that this radial migration in the current Galactic potential would be negligible (Mart´ınez-Barbosa et al.,2014).

One can see from Fig. 4 that the orbit of M 67 takes the cluster significantly further out ofthegalacticplanetomuchlargervaluesofzthanisexperiencedbytheSun.Ifoneassumes thatM67hasalwayshaditscurrentorbitandthattheSunwasejectedfromM67,thiswould imply that the Sun received a significant kick in order to leave it on its current orbit,residing in the plane of the galaxy (Pichardo et al., 2012).The point here is that it is not possible to impart such a large kick whilst keeping the solar systemintact.

A possible solution to this problem has been suggested in Gustafsson et al. (2014). The keyideaisthattheorbitofM67haschangedovertime.Theorbitcouldoriginallyhavebeen more in the galactic plane (i.e. with lower maximum values of z) allowing the Sun to escape from it with a relatively low velocity. Scattering off giant molecular clouds (GMCs) could then leave the cluster on the orbit we see today. Simulations of scattering due to GMCs show that it is possible to put M 67 on its current orbit beginning with an orbit similar to the Sun’s (Gustafsson et al., 2014). In that case the Sun must have left M 67 before the scatteringevent with a GMC tookplace.

TheKuiper Belt and the Late HeavyBombardment

TheKuiperBelt

Beyond Neptune lies a reservoir of remnant icy planetesimals from the formation of the solar system analogous to the main asteroid belt between Mars and Jupiter. Known as the Kuiper belt, this distant population displays an intricate orbital structure that has inspired and constrained a number of ideas on the early evolution of our planetary system. The high abundance of Kuiper belt objects (KBOs) in mean-motion resonances with planet Neptune led to the idea that the ice giant has migrated through the original disc of planetesimals, sweepingasignificantfractionintostableresonantorbits(Malhotra,1995).Thesuperposition of dynamically hot (high inclination and eccentricity) and cold (low inclination and nearly circular) orbits suggests that while some KBOs have been scattered  onto  theircurrent orbits (Gomes, 2003), likely by the outer planets, others have formed in-situ and remained unperturbed(Batyginetal.,2011).Analternativeexplanantionisprovidedbyanencountering star that scattered the Kuiper belt (Ida et al. 2000). The current morphology of the scattered Kuiper belt could only be reproduced if the mass of the encountering star M had animpact

 

parameter of b = 170 + 45(M/M− 0.5) AU (Punzo et al. 2014). However, such an encounter would like scatter the entire Kuiperbelt. In addition, cooling off part of the hot population to re-populate the cold population would require some 1000 Pluto-mass objects, which are not observed.

EarlyDynamicalEvolution

The need to explain the dynamical structure of the Kuiper belt and to reconcile the orbits  of the giant planets with the discovery of hot-Jupiters were main drivers in the evolution of planet migration theories. In the solar system, the current paradigm considers that the giant planetsemergedfromtheprotoplanetarydiscinamorecompact,near-resonantconfiguration, allwithin15AUfromtheSun(Batygin&Brown,2010).Angularmomentumexchangeswith the surrounding disc of planetesimals led to the outward migration of Neptune, Uranus, and Saturn, as they scattered small bodies inwards, while Jupiter, sufficiently massive to eject planetesimals from the solar system, migrated predominantly towards the Sun (Fernandez &Ip,1984;Hahn&Malhotra,1999).ThedivergingmigrationsofJupiterandSaturneventually resulted in a mutual resonance crossing and triggered a dynamical instability throughout the solar system, which impulsively expanded the orbits of Uranus and Neptune to near their currentlocationsandviolentlyscatteredtheplanetesimaldisc(Tsiganisetal.,2005).TheLate HeavyBombardmentwasalsolikelycausedbythisinstabilityevent(Gomesetal.,2005).

TheLate HeavyBombardment

Geochronological studies of the lunar rocks returned by the Apollo missions yielded the surprising result that all large multi-ring basins on the Earth’s moon – they are also called Mare: Orientale, Crisium, Imbrium, Nectaris, Humorum, Serenitatis – originated by giant impacts in an extremely confined time interval between 4.0 and 3.7 Gyr ago (Tera et al.,1974;Turner,1977;Jessbergeretal.,1974).ThisprocessiscalledtheLunar(orLate)Heavy Bombardment (LHB), as it was completed only 800 Myr after solar system formation. It requires that long after final formation of the terrestrial planets, there was an increased fluxof small bodies (up to about 100 km in size) in the inner solar system 3.8 Gyr ago. Possible evidence of the LHB is also inferred from HED meteorites (Bogard, 1995; Kunz et al.,1995;Bogard&Garrison,2003),whichareinferredtocomefromVesta,andMartianmeteoriteslike ALHA84001 (Ash et al., 1996; Turner et al., 1997), although this is not undisputed (Bogard& Garrison,1999).

Two general scenarios appear plausible for the early solar system impact history:

The LHB was the final phase of terrestrial planet accretion – this requires that the small body flux must have been considerably higher before (implying somewhat unrealistic totalmassestimationsofinitialsmallbodypopulations),andthattherecordofearlierimpacts must have been erased by the late impact phase 3.8 Gyrago.

The LHB was an episodic spike of the influx of asteroidal or cometary bodies, caused by dynamical excitation of small body populations in the asteroid or Kuiper belts. As generalexplanationforthedynamicalexcitation,planetarymigrationprocessesarepromising

 

candidates,inparticulartheaforementionedresonancecrossingofJupiterandSaturn(Gomeset al., 2005; Tsiganis et al., 2005),i.e. in more general terms, the giant planet instability (Morbidelli et al., 2007, Levison et al., 2011). Advanced models consider a more prolonged bombardment history induced by planet migration processes (Morbidelli et al.2012).

However,thereisincreasingevidencethatbeforethetimeoftheLHB3.8Gyrago,there were other episodic times of increased impact rates on the Earth-moon system, registered  by, e.g. Ar-Ar and zircon chronology (Fernandes et al.,2013;Nemchin et al.,2008),and also by other meteorite parent bodies, e.g. 4.2 Gyr impact events affecting the LL chondrite parentbody(Trieloffetal.,1989,1994;Dixonetal.,2004).Itwassuggested(Trieloff,2014)to consider close stellar encounters as a possible reason for repeated episodic dynamical excitation. However, there is increasing evidence that before the time of the LHB 3.8 Gyr ago, there were other episodic times of increased impact rates on the Earth-moon system, with concomitant impact episodes on other inner solar system bodies. For example, both Ar- Arandzirconchronology(Fernandesetal.2013,Nemchinetal.2008)evidenceanincreased impact cratering rate 4.2 Ga ago, which was also experienced by the LL chondrite parent body (Trieloff et al. 1989, 1994, Dixon et al. 2004). Although the chronological data base has still to be improved, age clustering can only hardly be reconciled with stochastical bias effects, as multiple celestial bodies were affected. As giant planet instabilities can only once trigger bombardments, it was suggested (Trieloff 2014) to consider close stellar encounters as a possible reason for repeated episodic dynamical excitation. However, the corresponding dynamical scenarios are only poorlyexplored.

DecodingKBODiversity

KBOs possess the most diverse surfaces of any small body population in the solar system (Luu&Jewitt,1996;Jewitt&Luu,1998).Thisispuzzling,giventhelowandslowlyvarying temperatures in the Kuiper belt region. The migration-driven instability event described aboveoffersaplausiblesolutiontothisproblembyallowingplanetesimalsformedinthe

∼10 to 30 AU region to be scattered to the current Kuiper belt. However, the stochastic character of this process complicates the mapping of current KBO surface properties to their formationlocation.ArecentsurveyofKBOsandCentaursusingHerschel(Mu¨lleretal.,2009) has built on an earlier Spitzer survey (Stansberry et al., 2008) to produce the largest sampleofalbedosandsizesforthistypeofobject(Table 1).ThesedatarevealthatKBOsare alsoextremelydiverseinreflectivity,withalbedosspanningmorethananorderofmagnitude from about 0.03 to 0.40. An interesting trend emerges when combining the KBO colour and albedodata(Lacerdaetal.,2014):analbedo-colourplot(Figure5)showsthatKBOsfallinto two main groups: a broad bright-red (BR) cluster, centred around albedo ∼0.15 and colour spectral slope ∼30% and a more compact dark-neutral (DN) clump near albedo ∼0.05 and colour slope ∼10%. Importantly, KBOs in dynamical classes believed to originate beyond Neptune occupy only the bright-red group,  while KBOs that may have  been scattered outto the Kuiper belt from nearer the Sun are found in both the bright-red and the dark-neutral groups. This result hints at a compositional gradient that was present in the planetesimaldisc

 

0.02 0.05 0.10 0.20 0.50

Albedo

Figure5.Albedoandcolourdistributionofintermediate-sizedKBOsintheHerschelsample. Selected dynamical classes are plotted: Cen=Centaurs, Plu=Plutinos, ScD=Scattered Disc, hCl=Hot Classicals, Det=Detached, cCl=Cold Classicals, oRe=Outer Resonants (beyond the classical belt). For a description of these dynamical classes see Gladman et al.(2008).

Table 1.Summary of the KBO/Centaur Herschel Sample Properties. Columns are 1) Dynamical class (Gladman et al.,2008),2) median albedo and central 68% interval, 3)  mean spectral slope in %/(1000 Å) and standard deviation. Statistics includes measurement uncertaintiesbybootstrapresamplingandexcludesdwarfplanetsandHaumea-typeKBOs.4) Dominant surface types (BR=bright-red, DN=dark-neutral) present in class (see caption for Figure5)

Dynamical class   Albedo     Colour SurfaceTypes

 ScatteredDisc 0.05+0.04

Centaurs 0.06+0.07

HotClassicals 0.08+0.05

Plutinos 0.09+0.07

OuterResonants 0.13+0.09

ColdClassicals 0.15+0.08

DetachedKBOs 0.17+0.20

−0.09

16.3± 12.6 DN,BR

21.5± 16.5 DN,BR

22.8± 15.6 DN,BR

20.1± 15.4 DN,BR

31.6± 12.8 BR

33.2± 10.3 BR

33.2± 14.6 BR

 

prior to the planetary instability event.

Long-TermEvolution

Planetary system development is often considered in the context of dynamical stability, or the ability of a planet, moon, or asteroid to adhere to its regular motion – i.e. approximately retain its original orbit – over time. Past or future instability can help constrain and explain observations and place our solar system today into context (Davies et al.,2013).In this section,weask,areplanetarysystems-andinparticularthesolarsystem-stableastheirhost

 

Figure6.FromFigure9ofLaskar(2008):Normaliseddensityfunctionsfortheeccentricities of Earth and Mercury. On each plot the 19 curves represent intervals of 250 Myr. Each  curve is based on 1001 solutions with very close initial conditions. The variation of these curves reflects the chaotic diffusion of the solutions. Mercury’s eccentricity is clearly shown onaveragetoincreasewithtime,whereastheEarth’seccentricityremainsrelativelyconstant.

stars evolve?

Long-Term Evolution of the SolarSystem

The future orbital evolution of the solar system, like all other planetary systems, cannot be determined to infinite precision. Instead, we obtain likelihoods for particular futures through suitesofnumericalsimulations.Qualitatively,theevolutionarybehaviourcanbesplitintotwo parts depending on the state of the Sun: (i) the main sequence and (ii) post-main-sequence phases of Solarevolution.

The Sun will exist in its present state for about a further 6 Gyr before turning off the main

sequence. During these 6 Gyr, the eight planets will technically evolve chaotically (Sussman&Wisdom,1988;Laskar,1989)butrealisticallyareverylikelytoavoiddynamicalinstability. In fact, through a suite of simulations, Laskar (2008) determined that the inner four planets have a 98%-99% chance of surviving and not having planetary orbits cross; 100% of all his simulations yielded survival of the outer four planets. Figure 6 shows how the eccentricity of the Earth and Mercury evolve over this timescale. Earth’s eccentricity remains nearly constant. Mercury’s eccentricity gradually increases, but rarely becomes large enough for its orbit to cross that ofVenus.

AftertheSunleavesthemainsequence,itwillsimultaneouslyshedabouthalfofitsmass whilebecomingaredgiantstarthatisnearly1AUinradius.Theincreaseinradiuscanmore easily allow the Sun to tidally capture objects encountered by the Solar envelope (Villaver etal., 2014), whereas the mass loss will push out and potentially warp the orbits of surviving bodies (Hadjidemetriou,1963).

The result on the inner three planets will be dramatic, and on the outer five less so. Mercury and Venus will be swallowed and Earth will suffer an uncertain fate. Our home

 

planetwilllieonthecuspofbeingtidallydrawnintotheSun(Schro¨der&ConnonSmith,2008).Mars’s orbit will simply expand. All 4 outer planets will also survive and expand their orbits such that the ratios of their mutual separations will remain unchanged (Duncan& Lissauer, 1998).Beyond Neptune and the Kuiper belt, the Sun’s mass loss will trigger instability in the Oort cloud, allowing for objects beyond 103 − 104 AU to escape the solar system (Veras & Wyatt,2012).

Long-Term Evolution of Other PlanetarySystems

Observationaldataforextrasolarplanetsaresignificantlylessaccurateandprecisethanthose for the solar system planets (Perryman,2011).Consequently, the future of exoplanetary systems is not as well constrained. However, every exoplanetary system so far discovered contains fewer planets than the solar system, simplifying theanalysis.

The majority of known planetary systems contain either two or three planets (www.exoplanets.org), motivating study of these two cases in detail. During the main sequence evolution of the host star two planets will never cross orbits if they are sufficiently far away from each other to be Hill stable ǁ(Gladman, 1993).A Hill stable system could potentially become Lagrange unstable if the inner planet collides with the star or the outer planetescapesthesystem(Barnes&Greenberg,2006).Empiricalandanalyticalestimatesfor thesestabilityboundaries,evenwhenscaleddowninmasstothetestparticlelimit,showgood agreement with numerical simulations of the long-term evolution (Wisdom, 1980; Mustill &Wyatt, 2012; Deck et al., 2013; Giuppone et al., 2013; Veras & Mustill,2013).

Three-planetsystemsdonotappeartoadmitanalyticalstabilityboundaries,andtherefore investigations of these systems require a numerical approach. These studies have yielded portraits of instability times as a function of initial separation, as well as empirical estimates for these times (Chambers et al.,1996;Marzari & Weidenschilling,2002;Chatterjee etal.,2008).These instabilities can occur any time during the main sequence evolution,    and  fundamentally  change  the  resulting  dynamical  architecture,  perhaps  leading  to the

establishmentofapopulationofhotJupitersandeccentricplanets(Beauge´&Nesvorny´,

2012).The study of systems with a higher number of exoplanets produce a similarly-wide variety of outcomes to the three-planet case (Smith & Lissauer, 2009).

We know that planetary systems do survive the giant branch phases of stellar evolution based on abundant evidence of atmospheric metal pollution in white dwarfs (WDs) (Zuckerman et al.,2010;Koester et al.,2014);WDs, which are the size of the Earth but  with the mass of the Sun, represent the end-product of stellar evolution. In over 35 systems, WD atmospheric metal pollution is accompanied by compact accretion discs of gas and/or dust(Ga¨nsickeetal.,2006;Farihietal.,2009).Althoughthepreciseoriginofthepollutionanddiscshaveyettobeidentified,theymustarisefromcurrentlydynamicallyactiveplanetary systemremnants.

ǁThe concepts of Hill and Lagrange stability are applicable to 3-body systems (2-planet systems) only. In a Hill stable system, the orbits of both planets can never cross. A Lagrange stable system is Hill stable and also does not allow the outer planet to escape the system nor the inner planet to crash into the star.

 

Figure 7. Fig. 1 of Mustill, Veras & Villaver (2014): Approximate stability behaviour of three-planet systems as a function of stellar mass and separation on the main sequence (MS). ThequantityrHonthey-axisrepresentsthesingle-planetHillradius.Theplanetmassandthe innermostsemi-majoraxisarefixedat1MJand10AU,respectively.Systemsbelowtheblack solid line will be unstable on the MS. Systems in the tiny strip between the black solid and the black dotted lines will become unstable at some point between the end of the MS and the end of the asymptotic giant branch (AGB). Systems below the red solid line will be unstable during the WD phase, assuming that the star formed at the big bang; systems above this line must be stable for the age of the Universe. The red dotted and dashed lines show the stability boundaries for WD cooling ages of 1 and 5 Gyr. This plot demonstrates that after the star has become a white dwarf, many more systems can becomeunstable.

During giant branch mass loss, the dynamical stability limits of a multi-body systemare changed (Debes & Sigurdsson, 2002).Consequently, two-planet systems, which remained stable throughout the entire main sequence may become unstable either during the giant branch phase, or the WD phase (Veras et al., 2013).For three-planet systems, the situation becomes more complex, allowing for multiple instabilities to occur during different phases of stellar evolution (Mustill et al., 2014).See Figure 7 for a phase portrait of stability limits through all phases of stellar evolution for three-planet systems. Planets residing close to the giant star will tidally interact in a complex way depending on the pulsations of the giant (Mustill & Villaver,2012).

A likely progenitor of the WD discs are exo-asteroids. Although unobservable during main sequence and giant branch phases, their evolution through these epochs will crucially determine their placement in WD systems. The effect of mass loss on a single planet and single exo-asteroid belt has been considered in the context of an exo-Kuiper belt at about 30 AU (Bonsor et al., 2011) and an exo-asteroid belt at about 5 AU (Debes et al., 2012; Frewen& Hansen, 2014).

 

Summary

Combining the evidence from these different sources for the early history of the solarsystem the following pictureemerges:

The geochemical and isotopic inventory of meteorites provides a unique chronological record of early solar system evolution. It took less than one million years after condensation of the first solid matter to form the first generation of planetesimals. These planetesimals underwent internal heating between 1 and 4 million years after the solar system formation, largely caused by 26Al decay, triggering their differentiation into metal core and silicate mantle. The parent asteroids of undifferentiated chondritic meteorites formed 1-2 million years later, and therefore these bodies did not differentiate. Formation of the largerterrestrial planets in the inner solar system likely occurred via collisions of smaller asteroidal bodies. The timescales involved in planetary growth are of the order tens of millions of years, with Mars being a possible exception due to gravitational interaction with nearby Jupiter. There is growing evidence that the volatile element inventory of the inner solar system was added later, i.e. during the last stages of planetarygrowth.

The presence of the remnants of short-lived radioactive nuclei in meteorites was for a long time interpreted as evidence for the formation of the Sun in a large star cluster. It was usually assumed that the different radioactive nuclei were formed in one single event in a supernovaexplosion.However,therenowexistargumentstosupportthatasequenceofevents took place. Here the SLRs with the longest half-lives originate from star complexes, while 60Fe (T1/2= 2.6 Myr) originates from a molecular cloud and 26Al (T1/2= 0.72 Myr) from the wind of a local massive star. In this picture the distribution of SLRs in the solar system isthe result of sequential star formation in theISM.

Theobservationofyoungdisc-surroundedstarsalsoimposesconstraintsonthetimescale of planet formation. The disc fractions in star clusters strongly indicate that most stars dissipate their discs within 2-3 Myr which would favour  rapid planet formation - at least  for the gas giants. However, recent works argue in favour of longer disc dissipation times,  of the order of 5-10 Myr. Here a comparison with the meteorite record could possibly bring clarification in the future.

Comparingthetypicalmassesofthediscsaroundyoungstarsitisfoundalargefraction of young solar analogues are hosting a disc with a mass well above the minimum mass solar nebula and in principle are capable of forming a planetary system similar to our own. For the most massive of these discs the observed surface densities distribution of the disc mass is roughly consistent with the average surface density of our own solar system. However, most systems are larger than our own solar system, resulting in a lower surface density.  It  is currently unclear whether this difference is real or due to the large uncertainties in the observations.

The formation of planets from dust and ice particles likely proceeds in the initial stages by sticking collision, the so-formed porose aggregates eventually compactify. The continued growth from mm-sized particles faces the the formidable bouncing and radial drift barrier. Planetesimals form despite these difficult circumstances, likely by a combination ofparticle

 

stickingandgravitationalcollapseofregionsoverdenseinpebble-sizedparticles.Thevarious mechanisms which allow particles to avoid this process have been suggested. Future studies of the properties of the remnant planetesimals in the asteroid belt and in the Kuiper belt will becrucialtoshedlightonthisopenissue.Inaddition,studyingprotoplanetarydiscswillhelp to understand this phase of planet formation better, as populations of mm-cm sized pebbles have been detected in discs around youngstars.

It is presently unclear to what degree nearby others stars influence the formation of planetary systems. From the SLR abundances and the size of the solar system it can be concluded that the birth cluster of the Sun contained at least 2000 stars. Measuring detailed abundancepatternsseveralgroupshaverecentlystartedthesearchforotherstarsthatoriginate from the same gas cloud as the Sun. There are currently some candidate siblings, however further studies are required to confirm thoseresults.

The orbital structure of the Kuiper belt and the cratering record on the Moon are evidence for a dynamically active early solar system. Planetary migration and resonance- driveninstabilitieshave actedontheplanetesimaldisctoenhanceimpactratesontotheinner solar system, to boost the mixing of populations formed at different distances from the Sun, and to sculpt the dynamics of the main planetesimal reservoirs. On the other hand, external forcesfromclosestellarencounterswithintheSunsparentalclustercouldhavebeenthecause of episodic dynamical excitations of minor body populations and impact rates. The current challenge for understanding the origin of the solar system (and other planetary systems) is  to seek clues that allow us to see past these dynamical events, to the time when the first planetesimals began toform.

What will happen to the solar system in the future? After the Sun leaves the main sequence Mercury and Venus  will be swallowed and Earth will suffer an uncertain fate as   it will lie on the cusp of being tidally drawn into the Sun. Mars and the 4 outer planets will also survive and expand theirorbits.

In summary, in recent years we have seen many new insights into the formation of the solarsystem.However,therearestillaconsiderablenumberofopenquestionswheredifferent competing theories exist. So far the different fields contributing in the investigations to theorigin of the solar system have generally worked fairly orthogonally. However, it would be timelytostartcombiningtheseseperateefforts,usingthemtobuildamorecompletepictures. Progress can be expected in determining the actual chronology ofevents.

Acknowledgements

We  want to thank both referees for their very constructive comments.   SP is supported     by the Minvera program of the Max-Planck society. MBD is supported by the Swedish Research Council (grant 2011-3991). AJ was supported by the Knut and Alice Wallenberg Foundation, the Swedish Research Council (grant 2010-3710) and the European Research Council (ERC Starting Grant 278675). LT is partly supported by the Italian Ministero dellIstruzione, Universita‘ e Ricerca through the grant iALMA - Progetti Premiali 2012 (CUP C52I13000140001). MT acknowledges support by DeutscheForschungsgemeinschaft

 

(DFG), and Klaus Tschira Stiftung gGmbH. DV is supported from the European Research Council under the European Unions Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement n. 320964 (WD Tracer).

References References

Adams, F. C. & Laughlin, G. 2001, Icarus, 150, 151 Adams, F. C. 2010, ARA&A, 48, 47

Albare`de,F.2009,Nature,461,1227

Alle`gre,C.J.,Manhe`s,G.,Go¨pel,C.2008,EarthandPlanetaryScienceLetters,267,386 Amelin, Y., Kaltenbach, A., Iizuka, T., et al. 2010, Earth and Planetary Science Letters, 300,

343

Amelin, Y., Krot, A. N., Hutcheon, I. D., & Ulyanov, A. A. 2002, Science, 297, 1678Andrews, S. M., Rosenfeld, K. A., Kraus, A. L., & Wilner, D. J. 2013, ApJ, 771, 129 Andrews, S. M., Wilner, D. J., Hughes, A. M., Qi, C., & Dullemond, C. P. 2009, ApJ, 700,

1502

Armitage, P. J. 2000, A&A, 362, 968

Arnould, M., Goriely, S., & Meynet, G. 2006, A&A, 453,653Ash, R. D., Knott, S. F., & Turner, G. 1996, Nature, 380, 57Bai, X.-N. & Stone, J. M. 2010a, ApJ, 722,1437

Bai, X.-N. & Stone, J. M. 2010b, ApJS, 190,297

Ballhaus,C.,Laurenz,V.,Mu¨nker,C.,etal.2013,EarthandPlanetaryScienceLetters,362, 237

Barge, P., & Sommeria, J. 1995, A&A, 295, L1Barnes, R., & Greenberg, R. 2006, ApJL, 647, L163Batygin, K., & Brown, M. E. 2010, ApJ, 716, 1323

Batygin, K., Brown, M. E., & Fraser, W. C. 2011, ApJ, 738, 13Beauge´,C.,&Nesvorny´,D.2012,ApJ,751,119

Beccari, G., Spezzi, L., De Marchi, G., et al. 2010, ApJ, 720, 1108Beckwith, S., Sargent, A. I., Scoville, N. Z., et al. 1986, ApJ, 309, 755

Beckwith, S. V. W., Sargent, A. I., Chini, R. S., & Guesten, R. 1990, AJ, 99, 924

Bell,C.P.M.,Naylor,T.,Mayne,N.J.,Jeffries,R.D.,&Littlefair,S.P.2013,MNRAS,434,806

Binney, J. & Tremaine, S. 2008, Galactic Dynamics: Second Edition (Princeton UniversityPress)

Birnstiel, T., Klahr, H., & Ercolano, B. 2012, A&A, 539, A148

 

Birnstiel, T., Ricci, L., Trotta, F., et al. 2010, A&A, 516, L14

Bitsch, B., Morbidelli, A., Lega, E., & Crida, A. 2014a, A&A, 564, A135

Bitsch, B., Morbidelli, A., Lega, E., Kretke, K., & Crida, A. 2014b, ArXiv e-prints Bizzarro, M., Baker, J. A., & Haack, H. 2004, Nature, 431, 275

Bizzarro, M., Baker, J. A., Haack, H., & Lundgaard, K. L. 2005, ApJ, 632, L41Blum, J. & Wurm, G. 2008, ARA&A, 46, 21

Bogard, D. 1995, Meteoritics, 30, 244

Bogard, D. D., & Garrison, D. H. 1999, Meteoritics and Planetary Science, 34, 451

—. 2003, Meteoritics and Planetary Science, 38, 669

Bonsor, A., Mustill, A. J., & Wyatt, M. C. 2011, MNRAS, 414, 930 Bottke,W.F.,Durda,D.D.,Nesvorny´,D.,etal.2005,Icarus,175,111

Bouvier,A.,Blichert-Toft,J.,Moynier,F.,Vervoort,J.D.,&Albare`de,F.2007, Geochim. Cosmochim. Acta, 71, 1583

Brennecka, G. A., & Wadhwa, M. 2011, Meteoritics and Planetary Science Supplement, 74,5030

Breslau, A., Steinhausen, M., Vincke, K., & Pfalzner, S. 2014, A&A, 565, A130Brasser, R., Duncan, M. J., & Levison, H. F. 2006, Icarus, 184, 59

Brown, A. G. A., Portegies Zwart, S. F., & Bean, J. 2010, MNRAS, 407, 458 Cameron, A. G. W. & Truran, J. W. 1977, Icarus, 30, 447

Canup, R. M. 2012, Science, 338, 1052

Canup, R. M., & Asphaug, E. 2001, Nature, 412, 708 Caselli, P., Keto, E., Bergin, E. A., et al. 2012, ApJ, 759,L37Chambers, J. E. 2003, Treatise on Geochemistry, 1,461

Chambers, J. E., Wetherill, G. W., & Boss, A. P. 1996, Icarus, 119, 261

Chaussidon, M., Robert, F., & McKeegan, K. D. 2006, Geochim. Cosmochim. Acta, 70, 224Chatterjee, S., Ford, E. B., Matsumura, S., & Rasio, F. A. 2008, ApJ, 686, 580

Chevalier, R. A. 2000, ApJ, 538, L151

Chiang, H.-F., Looney, L. W., & Tobin, J. J. 2012, ApJ, 756, 168 Connelly, J. N., Bizzarro, M., Krot, A. N., et al. 2012, Science, 338, 651C´uk,M.,&Stewart,S.T.2012,Science,338,1047

Cuzzi, J. N., Hogan, R. C., Paque, J. M., & Dobrovolskis, A. R. 2001, ApJ, 546, 496Cuzzi, J. N., Hogan, R. C., & Shariff, K. 2008, ApJ, 687, 1432

Dauphas, N. & Chaussidon, M. 2011, Annual Review of Earth and Planetary Sciences, 39, 351

Dauphas, N., & Pourmand, A. 2011, Nature, 473, 489

Davies, M. B., Adams, F. C., Armitage, P., et al. 2013, arXiv:1311.6816

 

Debes, J. H., & Sigurdsson, S. 2002, ApJ, 572, 556

Debes, J. H., Walsh, K. J., & Stark, C. 2012, ApJ, 747, 148Deck, K. M., Payne, M., & Holman, M. J. 2013, ApJ, 774, 129

De Marchi, G., Paresce, F., Panagia, N., et al. 2011, ApJ, 739, 27

Dixon, E. T., Bogard, D. D., Garrison, D. H., & Rubin, A. E. 2004, Geochim.  Cos-mochim. Acta, 68,3779

Dominik, C. & Tielens, A. G. G. M. 1997, ApJ, 480, 647Draine, B. T. 2006, ApJ, 636, 1114

Dra¸z˙kowska,J.,Windmark,F.,&Dullemond,C.P.2013,A&A,556,A37 Dukes, D., & Krumholz, M. R. 2012, ApJ, 754, 56

Dullemond, C. P., Hollenbach, D., Kamp, I., & D’Alessio, P. 2007, Protostars and Planets V,555

Duncan, M. J., & Lissauer, J. J. 1998, Icarus, 134, 303Duprat, J. & Tatischeff, V. 2007, ApJ, 671, L69

Dutrey, A., Semenov, D., Chapillon, E., et al. 2014, ArXiv e-prints

Elsila,J.E.,Glavin,D.P.,&Dworkin,J.P.2009,MeteoriticsandPlanetaryScience,44,1323Farihi, J., Jura, M., & Zuckerman, B. 2009, ApJ, 694,805

Fedele, D., van den Ancker, M. E., Henning, T., Jayawardhana, R., & Oliveira, J. M. 2010,A&A, 510, A72

Feigelson, E. D. 2010, Proceedings of the National Academy of Science, 107, 7153 Fernandes,V.A.,Fritz,J.,Weiss,B.P.,Garrick-Bethell,I.,&Shuster,D.L.2013,Meteoritics

and Planetary Science, 48, 241

Fernandez, J. A., & Ip, W.-H. 1984, Icarus, 58, 109Forgan, D. & Rice, K. 2009, MNRAS, 400, 2022

Frewen, S. F. N., & Hansen, B. M. S. 2014, MNRAS, 439, 2442Fromang, S. & Nelson, R. P. 2005, MNRAS, 364, L81

Ga¨nsicke,B.T.,Marsh,T.R.,Southworth,J.,&Rebassa-Mansergas,A.2006,Science,314, 1908

Giuppone, C. A., Morais, M. H. M., & Correia, A. C. M. 2013, MNRAS, 436, 3547Gladman, B. 1993, Icarus, 106, 247

Gladman, B., Marsden, B. G., & Vanlaerhoven, C. 2008, Nomenclature in the Outer solar system, ed. M. A. Barucci, H. Boehnhardt, D. P. Cruikshank, A. Morbidelli, & R. Dotson,43–57

Glavin, D. P., Dworkin, J. P., Aubrey, A., et al. 2006, Meteoritics and Planetary Science, 41,889

Goldreich, P., Lithwick, Y., & Sari, R. 2004, ARA&A, 42, 549 Gomes, R. S. 2003, Icarus, 161, 404

 

Gomes, R., Levison, H. F., Tsiganis, K., & Morbidelli, A. 2005, Nature, 435, 466Guilloteau,S.,Dutrey,A.,Pie´tu,V.,&Boehler,Y.2011,A&A,529,A105 Gounelle, M., Chaussidon, M., & Rollion-Bard, C. 2013, ApJ, 763, L33Gounelle, M., Meibom, A., Hennebelle, P., & Inutsuka, S.-i. 2009, ApJ, 694, L1Gounelle, M. & Meynet, G. 2012, A&A, 545, A4

Gounelle, M., Shu, F. H., Shang, H., et al. 2001, ApJ, 548, 1051

Gu¨ttler,C.,Blum,J.,Zsom,A.,Ormel,C.W.,&Dullemond,C.P.2010,A&A,513,A56 Gustafsson, B., Church, R. P., Davies, M. B., & Rickman, H. 2014, A&A, submittedHadjidemetriou, J. D. 1963, Icarus, 2, 440

Hahn, J. M., & Malhotra, R. 1999, AJ, 117, 3041

Hartmann, L. 2005, in Astronomical Society of the Pacific Conference Series, Vol. 341, Chondrites and the Protoplanetary Disk, ed. A. N. Krot, E. R. D. Scott, & B. Reipurth, 131

Heller, C. H. 1993, ApJ, 408, 337

Henke, S., Gail, H.-P., Trieloff, M., & Schwarz, W. H. 2013, Icarus, 226, 212

Hennebelle, P., Mac Low, M.-M., & Vazquez-Semadeni, E. 2009, in Structure Formation inAstrophysics, ed. G. Chabrier (Cambridge University Press), 205

Herna´ndez,J.,Hartmann,L.,Megeath,T.,etal.2007,ApJ,662,1067

Hester, J. J., Desch, S. J., Healy, K. R., & Leshin, L. A. 2004, Science, 304, 1116Holmberg,J.,Nordstro¨m,B.,&Andersen,J.2009,A&A,501,941

Holtom, P. D., Bennett, C. J., Osamura, Y., Mason, N. J., & Kaiser, R. I. 2005, ApJ, 626, 940 Hughes, A. M., Wilner, D. J., Qi, C., & Hogerheijde, M. R. 2008, ApJ, 678, 1119

Ida, S., Larwood, J., & Burkert, A. 2000, ApJ, 528, 351Isella, A., Testi, L., Natta, A., et al. 2007, A&A, 469, 213

Islam, F., Baratta, G. A., & Palumbo, M. E. 2014, A&A, 561, A73

Jessberger, E. K., Huneke,  J. C.,  Podosek,  F.  A.,  & Wasserburg,  G. J. 1974,  in Lunar  and Planetary Science Conference Proceedings, Vol. 5, Lunar and Planetary ScienceConference Proceedings,1419–1449

Jewitt, D., & Luu, J. 1998, AJ, 115, 1667

Jime´nez-Serra,I.,testi,L.,Caselli,P.,&Viti,S.2014,ApJ,787,L33 Johansen, A., Blum, J., Tanaka, H., et al. 2014, Protostars and PlanetsVJohansen, A., Klahr, H., & Henning, T. 2011, A&A, 529, A62Johansen, A. & Lacerda, P. 2010, MNRAS, 404,475

Johansen, A., Oishi, J. S., Mac Low, M.-M., et al. 2007, Nature, 448, 1022Johansen, A. & Youdin, A. 2007, ApJ, 662, 627

Johansen, A., Youdin, A., & Klahr, H. 2009a, ApJ, 697, 1269

 

Johansen, A., Youdin, A., & Mac Low, M.-M. 2009b, ApJ, 704,L75Johansen, A., Youdin, A. N., & Lithwick, Y. 2012, A&A, 537, A125 Kato, M. T., Fujimoto, M., & Ida, S. 2012, ApJ, 747,11

Kenyon, S. J., & Bromley, B. C. 2004, Nature, 432, 598 Klahr, H. H. & Bodenheimer, P. 2003, ApJ, 582, 869

Kleine,T.,Hans,U.,Irving,A.J.,&Bourdon,B.2012,Geochim.Cosmochim.Acta,84,186 Kleine,T.,Mezger,K.,Palme,H.,Scherer,E.,Mu¨nker,C.2005,Geochim.Cosmochim.Acta,

69, 5805

Kleine,T.,Mu¨nker,C.,Mezger,K.,&Palme,H.2002,Nature,418,952

Kleine, T., Touboul, M., Van Orman, J. A., et al. 2008, Earth and Planetary Science Letters,270, 106

Kobayashi, H. & Ida, S. 2001, Icarus, 153, 416

Ko¨nig,S.,Mu¨nker,C.,Hohl,S.,etal.2011,Geochim.Cosmochim.Acta,75,2119 Koester,D.,Ga¨nsicke,B.T.,&Farihi,J.2014,A&A,566,A34

Kretke, K. A. & Lin, D. N. C. 2007, ApJ, 664, L55

Kretke, K. A., Lin, D. N. C., Garaud, P., & Turner, N. J. 2009, ApJ, 690, 407

Kruijer,T.S.,Fischer-Go¨dde,M.,Kleine,T.,etal.2013,EarthandPlanetaryScienceLetters, 361, 162

Kruijer,T.S.,Touboul,M.,Fischer-Go¨dde,M.,etal.2014,LunarandPlanetaryScience Conference, 45, 1814

Kunz,J.,Trieloff,M.,DieterBobe,K.,Metzler,K.,Sto¨ffler,D.,&Jessberger,E.K.1995, Planet. Space Sci., 43, 527

Lacerda, P., et al. 2014, The Astrophysical Journal Letters, 793, L2Laibe, G. 2014, MNRAS, 437, 3037

Lambrechts, M. & Johansen, A. 2012, A&A, 544, A32Lambrechts, M. & Johansen, A. 2014, ArXiv e-prints

Larsen, K. K., Trinquier, A., Paton, C., et al. 2011, ApJ, 735, L37Laskar, J. 1989, Nature, 338, 237

Laskar, J. 2008, Icarus, 196, 1

Lee, T., Papanastassiou, D. A., & Wasserburg, G. J. 1976, Geophys. Res. Lett., 3, 109Lee, T., Shu, F. H., Shang, H., Glassgold, A. E., & Rehm, K. E. 1998, ApJ, 506, 898Lesur, G. & Papaloizou, J. C. B. 2010, A&A, 513, A60

Levison, H. F., Thommes, E., & Duncan, M. J. 2010, AJ, 139, 1297Leya, I., Halliday, A. N., & Wieler, R. 2003, ApJ, 594, 605

Liu,M.-C.,Chaussidon,M.,Go¨pel,C.,&Lee,T.2012a,EarthandPlanetaryScienceLetters, 327, 75

Liu, M.-C., Chaussidon, M., Srinivasan, G., & McKeegan, K. D. 2012b, ApJ, 761, 137

 

Looney, L. W., Tobin, J. J., & Fields, B. D. 2006, ApJ, 652, 1755Luu, J., & Jewitt, D. 1996, AJ, 112, 2310

Lyra, W., Johansen, A., Klahr, H., & Piskunov, N. 2008, A&A, 491, L41Lyra, W. & Klahr, H. 2011, A&A, 527, A138

Malhotra, R. 1995, AJ, 110, 420

Malmberg, D., Davies, M. B., & Chambers, J. E. 2007a, MNRAS, 377, L1Malmberg, D., Davies, M. B., & Heggie, D. C. 2011, MNRAS, 411, 859Malmberg, D., de Angeli, F., Davies, M. B., et al. 2007b, MNRAS, 378, 1207 Manara, C. F., Beccari, G., Da Rio, N., et al. 2013, A&A, 558, A114

Marchi, S., Bottke, W. F., Kring, D. A., & Morbidelli, A. 2012, Earth and Planetary ScienceLetters, 325, 27

Marois, C., Macintosh, B., Barman, T., et al. 2008, Science, 322, 1348

Marois, C., Zuckerman, B., Konopacky, Q. M., Macintosh, B., & Barman, T. 2010, Nature,468, 1080

Mart´ınez-Barbosa, C., Brown, A. G. A., & Portegies Zwart, S. F. 2014, MNRAS, submittedMarty, B. 2012, Earth and Planetary Science Letters, 313, 56

Marzari, F., & Weidenschilling, S. J. 2002, Icarus, 156, 570

Mathews,G.S.,Klaassen,P.D.,Juha´sz,A.,etal.2013,A&A,557,A132 Meibom, S., Torres, G., Fressin, F., et al. 2013, Nature, 499, 55

Meyer, B. S. & Clayton, D. D. 2000, Space Sci. Rev., 92, 133

Meynet,G.,Ekstro¨m,S.,Maeder,A.,etal.2008,inIAUSymposium,Vol.250,IAU Symposium, ed. F. Bresolin, P. A. Crowther, & J. Puls, 147–160

Minchev, I., Chiappini, C., & Martig, M. 2013, A&A, 558, A9Miotello, A., Testi, L., Lodato, G., et al. 2014, A&A, 567, A32 Mizuno, H. 1980, Progress of Theoretical Physics, 64, 544Morbidelli, A., & Levison, H. F. 2004, AJ, 128, 2564

Morbidelli,A.,Bottke,W.F.,Nesvorny´,D.,&Levison,H.F.2009,Icarus,204,558 Morbidelli, A. & Nesvorny, D. 2012, A&A, 546, A18

Morbidelli, A., Tsiganis, K., Crida, A., Levison, H. F., Gomes, R. 2007, AJ 134, 1790Moynier, F., Blichert-Toft, J., Wang, K., Herzog, G. F., & Albarede, F. 2011, ApJ, 741, 71Mu¨ller,T.G.,etal.2009,EarthMoonandPlanets,105,209

Mun˜ozCaro,G.M.,Meierhenrich,U.J.,Schutte,W.A.,etal.2002,Nature,416,403 Mustill, A. J., & Wyatt, M. C. 2012, MNRAS, 419, 3074

Mustill, A. J., & Villaver, E. 2012, ApJ, 761, 121

Mustill, A. J., Veras, D., & Villaver, E. 2014, MNRAS, 437, 1404

 

Natta, A. & Testi, L. 2004, in Astronomical Society of the Pacific Conference Series, Vol. 323, Star Formation in the Interstellar Medium: In Honor of David Hollenbach, ed.

D. Johnstone, F. C. Adams, D. N. C. Lin, D. A. Neufeeld, & E. C. Ostriker, 279Natta, A., Testi, L., Calvet, N., et al. 2007, Protostars and Planets V, 767

Nemchin, A. A., Pidgeon, R. T., Whitehouse, M. J., Vaughan, J. P., & Meyer, C. 2008, Geochim. Cosmochim. Acta, 72, 668

Nimmo, F., & Kleine, T. 2007, Icarus, 191, 497O’dell, C. R., Wen, Z., & Hu, X. 1993, ApJ, 410, 696

O¨nehag,A.,Gustafsson,B.,&Korn,A.2014,A&A,562,A102

O¨nehag,A.,Korn,A.,Gustafsson,B.,Stempels,E.,&Vandenberg,D.A.2011,A&A,528, A85

Okuzumi, S., Tanaka, H., Kobayashi, H., & Wada, K. 2012, ApJ, 752, 106Ormel, C. W. & Cuzzi, J. N. 2007, A&A, 466, 413

Ormel, C. W. & Klahr, H. H. 2010, A&A, 520, A43

Pan, L., Desch, S. J., Scannapieco, E., & Timmes, F. X. 2012, ApJ, 756, 102

Parker, R. J., Church, R. P., Davies, M. B., & Meyer, M. R. 2014, MNRAS, 437, 946Pe´rez,L.M.,Carpenter,J.M.,Chandler,C.J.,etal.2012,ApJ,760,L17

Perryman, M. 2011, The Exoplanet Handbook by Michael Perryman, Cambridge UniversityPress; 1 edition, 424 p., ISBN: 0521765595,

Pfalzner, S. 2013, A&A, 549, A82

Pfalzner, S., & Kaczmarek, T. 2013, A&A, 559, AA38

Pfalzner, S., Steinhausen, M., & Menten, K. 2014, ApJ, 793, LL34Pichardo, B., Moreno, E., Allen, C., et al. 2012, AJ, 143, 73Pinilla, P., Birnstiel, T., Ricci, L., et al. 2012, A&A, 538, A114

Pollack, J. B., Hubickyj, O., Bodenheimer, P., et al. 1996, Icarus, 124, 62Portegies Zwart, S. F. 2009, ApJ, 696, L13

Portegies Zwart, S. F., McMillan, S. L. W., & Gieles, M. 2010, ARA&A, 48, 431Punzo, D., Capuzzo-Dolcetta, R., & Portegies Zwart, S. 2014, MNRAS, 444, 2808Qi,C.,O¨berg,K.I.,Wilner,D.J.,etal.2013,Science,341,630

Rafikov, R. R. 2004, AJ, 128, 1348

Ricci, L., Testi, L., Natta, A., et al. 2010, A&A, 512,A15 Ros, K. & Johansen, A. 2013, A&A, 552,A137

Ros, K. & Johansen, A. 2013, A&A, 552,A137

Rosotti, G. P., Dale, J. E., de Juan Ovelar, M., et al. 2014, MNRAS, 441, 2094Rudge, J. F., Kleine, T., & Bourdon, B. 2010, Nature Geoscience, 3, 439

Russell, S. S., Gounelle, M., & Hutchison, R. 2001, Royal Society of London Philosophical Transactions Series A, 359, 1991

 

Safronov, V. S. 1969, Evoliutsiia doplanetnogo oblaka. Salpeter, E. E. 1955, ApJ, 121, 161

Scho¨nba¨chler,M.,Carlson,R.W.,Horan,M.F.,Mock,T.D.,&Hauri,E.H.2010,Science, 328, 884

Schro¨der,K.-P.,&ConnonSmith,R.2008,MNRAS,386,155

Schulz,T.,Mu¨nker,C.,Mezger,K.,&Palme,H.2010,Geochim.Cosmochim.Acta,74,1706 Schulz,T.,Mu¨nker,C.,Palme,H.,&Mezger,K.2009,EarthandPlanetaryScienceLetters,

280, 185

Scicluna, P., Rosotti, G., Dale, J. E., & Testi, L. 2014, A&A, 566, L3Sheppard, S. S. & Trujillo, C. A. 2010, ApJ, 723, L233

Shu, F. H., Adams, F. C., & Lizano, S. 1987, ARA&A, 25, 23

Simon, J. B., Beckwith, K., & Armitage, P. J. 2012, MNRAS, 422, 2685Smith, A. W., & Lissauer, J. J. 2009, Icarus, 201, 381

Stansberry, J., Grundy, W., Brown, M., Cruikshank, D., Spencer, J., Trilling, D., & Margot, J.-L. 2008, in The solar system beyond Neptune, ed. M. A. Barucci, H. Boehnhardt, D. P.Cruikshank, & A. Morbidelli (The Univ. of Arizona Press, 2008), 161–179

Sussman, G. J., & Wisdom, J. 1988, Science, 241, 433Tachibana, S. & Huss, G. R. 2003, ApJ, 588, L41

Tang, H. & Dauphas, N. 2012, Earth and Planetary Science Letters, 359, 248Tatischeff,V.,Duprat,J.,&deSe´re´ville,N.2010,ApJ,714,L26

Tera, F., Papanastassiou, D. A., & Wasserburg, G. J. 1974, Earth and Planetary ScienceLetters, 22, 1

Testi, L., Birnstiel, T., Ricci, L., et al. 2014, ArXive-prints

Testi, L., Natta, A., Shepherd, D. S., & Wilner, D. J. 2001, ApJ, 554,1087 Testi, L., Natta, A., Shepherd, D. S., & Wilner, D. J. 2003, A&A, 403,323Thies, I., Kroupa, P., & Theis, C. 2005, MNRAS, 364,961

Trieloff, M. 2014

Trieloff, M., Deutsch, A., Kunz, J., & Jessberger, E. K. 1994, Meteoritics, 29, 541 Trieloff, M., Jessberger, E. K., & Oehm, J. 1989, Meteoritics, 24, 332

Trieloff, M., Jessberger, E. K., Herrwerth, I., et al. 2003, Nature, 422, 502 Trotta, F., Testi, L., Natta, A., Isella, A., & Ricci, L. 2013, A&A, 558, A64Trujillo, C. A., & Sheppard, S. S. 2014, Nature, 507, 471

Tsiganis, K., Gomes, R., Morbidelli, A., & Levison, H. F. 2005, Nature, 435, 459Turner, G. 1977, Physics and Chemistry of Earth, 10, 145

Turner, G., Knott, S. F., Ash, R. D., & Gilmour, J. D. 1997, Geochim. Cosmochim. Acta, 61,3835

van der Marel, N., van Dishoeck, E. F., Bruderer, S., et al. 2013, Science, 340, 1199

 

Veras, D., & Wyatt, M. C. 2012, MNRAS, 421, 2969Veras, D., & Mustill, A. J. 2013, MNRAS, 434, L11

Veras, D., Mustill, A. J., Bonsor, A., & Wyatt, M. C. 2013, MNRAS, 431, 1686 Villaver, E., Livio, M., Mustill, A. J., & Siess, L. 2014, arXiv:1407.7879Villeneuve, J., Chaussidon, M., & Libourel, G. 2009, Science, 325, 985

Voelk, H. J., Jones, F. C., Morfill, G. E., & Roeser, S. 1980, A&A, 85, 316

Wada, K., Tanaka, H., Suyama, T., Kimura, H., & Yamamoto, T. 2009, ApJ, 702, 1490Wadhwa, M., Amelin, Y., Davis, A. M., et al. 2007, Protostars and Planets V, 835 Wang, W., Harris, M. J., Diehl, R., et al. 2007, A&A, 469, 1005

Walsh,K.J.,Morbidelli,A.,Raymond,S.N.,O’Brien,D.P.,&Mandell,A.M.2011,Nature, 475,206

Wasserburg, G. J., Busso, M., Gallino, R., & Nollett, K. M. 2006, Nuclear Physics A, 777, 5Weidenschilling, S. J. 1977, MNRAS, 180, 57

Weidenschilling, S. J. 2011, Icarus, 214, 671

Wetherill, G. W. 1990, Annual Review of Earth and Planetary Sciences, 18, 205Williams, J. 2010, Contemporary Physics, 51, 381

Williams, J. P. & Cieza, L. A. 2011, ARA&A, 49, 67

Wilner, D. J., D’Alessio, P., Calvet, N., Claussen, M. J., & Hartmann, L. 2005, ApJL, 626,L109

Windmark,F.,Birnstiel,T.,Gu¨ttler,C.,etal.2012,A&A,540,A73 Wisdom, J. 1980, AJ, 85, 1122

Wittig, N., Humayun, M., Brandon, A. D., Huang, S., & Leya, I. 2013, Earth and Planetary Science Letters, 361, 152

Wood, B. J., & Halliday, A. N. 2005, Nature, 437, 1345Wood, B. J., & Halliday, A. N. 2010, Nature, 465, 767Wurm, G., Paraskov, G., & Krauss, O. 2005, Icarus, 178,253

Yadav, R. K. S., Bedin, L. R., Piotto, G., et al. 2008, A&A, 484, 609Yin, Q., Jacobsen, S. B., Yamashita, K., et al. 2002, Nature, 418,949Youdin, A. N. & Goodman, J. 2005, ApJ, 620,459

Young, E. D. 2014, Earth and Planetary Science Letters, 392, 16

Zsom,A.,Ormel,C.W.,Gu¨ttler,C.,Blum,J.,&Dullemond,C.P.2010,A&A,513,A57 Zuckerman, B., Melis, C., Klein, B., Koester, D., & Jura, M. 2010, ApJ, 722, 725