The formation of the solar system

Studying meteorites from our solar system is the only way to directly constrain timescales of its protoplanetary disc evolution. Most meteorites are older than 4.5 billion years and originate from the asteroid belt. The asteroid belt between Mars and Jupiter provides the only vestige of 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 represent unprocessed, brecciated early solar system matter, whereas differentiated meteorites such as achondrites and iron meteorites originate from asteroids that have undergone melting 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 system evolution.

The oldest dated solar system matter are Ca, Al-rich inclusions (CAIs) in chondritic meteorites that have been dated by the U–Pb method to 4.567–4.568 billion years (Amelin et al 2002, Bouvier et al 2007). CAIs are an important anchor point to constrain the abundance of 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 than 100 million years enable dating of meteorites and their components at an age resolution as low as several tens of thousands of years. Based on combined U–Pb and Al–Mg chronometry, 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 between the formation of the first CAIs and the formation of the first chondrules (see Villneuve 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, Kleine et al 2008). Because of their younger accretion ages, chondrites escape internal heating triggered by ²⁶Al (Trieloff et al 2003, Henke et al 2013), and thus they preserved their pristine structure.

Recent high precision dating using Hf–W and Al–Mg chronometry has shown that some differentiated meteorite groups do in fact predate formation of chondrites. Beside CAIs, 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 accreted earlier than 0.5 million years after solar system formation (Kruijer et al 2013, 2014, Wittig et al 2013). Some older groups of achondrites that sample the outer silicate portion of differentiated asteroids differentiated only slightly later than iron meteorites. The particularly pristine group of angrites (achondrites consisting mostly of the mineral augite) is inferred to have differentiated by around 3–5 million years after the CAIs (Larsen et al 2011, Brennecka and 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 and 5 million years after solar system formations, with inferred accretion ages between 1 and 2 million years after solar system formation (Schulz et al 2009, 2010).

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, because the heat supply from short-lived nuclides such as ²⁶Al was insufficient, or, alternatively, their parent body size was too small. Alternatively, undifferentiated chondrites may sample the outer layers of planetesimals that differentiated in their interiors.

The larger rocky planets in the inner solar system formed much later than the small asteroids, 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, König et al 2011) and probably as late as 120 million years after solar system formation (Allègre et al 2008, Rudge et al 2010). There are fewer indicators to constrain the age of Mars, but estimates reach from 2 to 10 million years after solar system formation (Nimmo and Kleine 2007, Dauphas and 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 been explained by radial migration of Jupiter, suggesting that Mars represents a 'starved' planet 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 changed over the past years (e.g. Canup and Asphaug 2001, Cuk and Stewart 2012, Canup 2012). 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. Allègre et al 2008, Rudge et al 2010, Wood and Halliday 2005). A combination of experimental and geochemical studies now rather argue that volatile elements such as Pb were delivered late to the growing Earth, implying that the U–Pb systematics of the Earth's silicate mantle bear no chronological significance (Albarède 2009, Ballhaus et al 2013, Marty 2012, Schönbächler et al 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 larger terrestrial planets in the inner solar system occurred via collision of smaller asteroidal bodies. 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 planetary growth.

Since 1962 and the discovery of ¹²⁹I (T_1/2 = 15.7 Myr), a long list of SLRs has been identified in meteorites (see the table of Dauphas and Chaussidon (2011)). SLRs are important because they can potentially help to build an early solar system chronology and are the most likely heat source of the building blocks of planets, planetesimals (Wadhwa et al 2007). In addition, 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' origin is the only tool to trace back what was the relationship of the Sun with other stars born in the same molecular cloud.

The presence in the early solar system of SLRs having the longest half-lives is not surprising. Similarly to stable isotopes they have been produced in the interior of stars, which have preceded our Sun in the Galactic history and were delivered to the interstellar medium (ISM) by supernova (SN) explosions and massive star winds. Their abundance is roughly in line with Galactic evolution models (Meyer and Clayton 2000). The presence of SLRs with shorter half-lives (T_1/2 ≲ 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 clearly known.

Some SLRs have been synthezised 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 the case of ¹⁰Be (T_1/2 = 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 (T_1/2 = 0.3 Myr) or ⁴¹Ca (T_1/2 = 0.1 Myr) could also have been produced by irradiation according to some models (Gounelle et al 2001, Leya et al 2003, Duprat and Tatischeff 2007). We note that the situation for these SLRs is complicated by the fact that their initial abundance in the solar system is not well constrained (Liu et al 2012b).

Aluminium-26 (T_1/2 = 0.72 Myr) and iron-60 (T_1/2 = 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—SN, 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 and Huss 2003)), the presence of ⁶⁰Fe has been interpreted as evidence for a nearby SN (Hester et al 2004). According to SN nucleosynthetic models, the SN had 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 SN was a star with a mass of ≈25 M$_{\odot }$(see section 6). However, from the cosmochemical side there are some difficulties with this scenario.

It is very unlikely to find a protoplanetary disc or a dense core that close to a SN. Before they explode as SNe, massive stars carve large ionized regions in the ISM (called HII regions) 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 Myr before 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, 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 and Dauphas 2012). The revised ⁶⁰Fe abundance is compatible with a somewhat enhanced galactic background due to stars born and died in the 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 a single SN as first proposed by Cameron and Truran (1977). It also implies ²⁶Al cannot 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 (Larsen et al 2011, Liu et al 2012a), 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 the WR phase during which ²⁶Al is injected. This model suffers from the brevity and therefore the rarity of the WR phase. Gounelle and Meynet (2012) have proposed that ²⁶Al originated in a wind-collected shell around a massive star (figure 1). In this model, the dense shell collected by the massive star wind is continuously enriched by ²⁶Al brought to the surface of the star by 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 that this mode of star formation, though not the rule, is relatively common (Hennebelle et al 2009). This model constraints the astrophysical context of our Sun's formation as it requires that the parent cluster to which belongs the parent star (baptised Coatlicue) contained roughly 1200 stars (Gounelle and Meynet 2012).

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In conclusion, though the origin of SLRs is still a complex and debated issue (see Davies 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 (T_1/2 = 2.6 Myr) originates at the scale of the molecular cloud and ²⁶Al (T_1/2 = 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 the ISM.

The current best estimate of the lifetime of the disc, or the timescale for planetesimal and gas giant formation, is derived from the variation of the fraction of stars, which show infrared excess as a function of the age of the star forming regions (e.g. Hernández et al 2007), which is also found to be consistent with the variation of the fraction of young stars that show signs 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 uncertainties in the age determination of young stars (Bell et al 2013), or environmental disc 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 majority of stars host planetary systems, the formation process has to occur within a few Myr, at least for planet types, which contain significant gaseous envelopes (gas giants, ice giants and low-density super-Earths). In large star forming complexes in the Magellanic Clouds and our own Galaxy, there is controversial evidence for stars with circumstellar discs at relatively 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).

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 H₂ and 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 to that work for a detailed account. The key feature for constraining the conditions for planet formation is that around young solar analogues most of the disc midplane is at low temperature and the most abundant molecular species (with the obvious exception of H₂) are frozen inside 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, as observed in laboratory experiments (e.g. Muñoz Caro et al 2002, Holtom et al 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 disc midplane cosmic-ray induced desorption of ices may release a small fraction of the complex molecules in the gas phase, a process similar to the one that is thought to occur in cold protostellar cores (Caselli et al 2012, Jiménez-Serra et al 2014).

Alternative promising locations to search for these complex compounds are the snowlines¹² of the major molecular species, which could carry in the gas phase complex organic molecules as impurities as part of the sublimation process. The major snowlines that may produce such an effect are the CO snowline at ∼20 K and the H₂O one at ∼150 K. 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 characterization 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.

As a consequence of the complexity of the molecular gas chemistry in discs and the difficulty in observing H₂, the most reliable mass estimates for protoplanetary discs still come from the 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 self consistent thermal balance model, for typical accretion rates measured in young pre-main sequence objects the heating from the central star dominates the disc heating and the thermal structure of the dust is usually well constrained by models (see e.g. Dullemond et al 2007, Bitsch et al 2014a)¹³ The disc masses derived with this method are typically between 0.2% and 20% of the mass of the central star, implying that a large fraction of young solar analogues are hosting a disc with a mass well above the minimum mass solar nebula and in principle capable of forming a planetary system similar to our own (e.g. Williams and Cieza 2011, Andrews et al 2013).

High angular resolution observations allow to resolve the disc emission and estimate the 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 then drop sharply, consistently with an exponential fall off (e.g. Isella et al 2007, Hughes 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 ISM), 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 and Testi 2004, Testi et al 2014). Measurements of proto planetary disc masses are relatively rare as of today: up-coming ALMA observations may be able to provide a statistical view of the distribution of dust surface densities and possibly also gas surface densities.

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 probe of the grain population properties. In a protoplanetary disc, grains are expected to grow 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 dependence with wavelength changes from the typical value of the sub-micron size interstellar grains (${{\kappa }_{\nu }}\sim {{\nu }^{-1.7}}$) to a much shallower dependence, approaching ${{\kappa }_{\nu }}\sim {\rm const}.$ 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 and Wurm 2008). More specifically, the emerging observational constraints on the dust grain size distribution as a function of disc radius (Guilloteau et al 2011, Pérez et al 2012, Trotta et al 2013) matches the expectations from the evolutionary models (Birnstiel et al 2012, Laibe 2014).

This apparent success hides a number of difficulties that still need to be solved, in particular, smooth disc models still predict a radial drift and fragmentation of the large grains that is inconsistent with the observations and require to artificially slow down the radial drift. 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. Pinilla et al 2012), localized growth across snowlines (Ros and Johansen 2013), or the efficient accretion of pebbles onto existing planetary cores (Lambrechts and Johansen 2014). Some of 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 protoplanetary discs.

Planets form the gas and dust present in protoplanetary discs. In the first stage of planet formation dust and ice particles collide and stick together to form larger aggregates (Dominik and 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 and 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 additional contribution to the collision speed is the relative radial and azimuthal drift between 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 cannot dissipate enough energy during a collision to allow sticking (Güttler et al 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). The size of the constituent monomers also plays an important role in determining the collision outcome. Ice aggregates, which consist of very small monomers of 0.1 μm sizes, can stick at up to 50 m s⁻¹ 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 and Johansen 2013).

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 heating and stellar irradiation heat the inner regions more strongly (Bitsch et al 2014a). This outwards-directed push on the gas causes the gas to orbit slower than the Keplerian speed, by approximately 50 m s⁻¹ (Weidenschilling 1977). Solid particles do not sense the pressure difference from front to back (since their material density is much higher than the gas density), so particles would orbit at the Keplerian speed in absence of gas drag. However, the drag from 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 silicate sublimation line close to the star. The peak of the radial drift occurs for cm-sized particles in the outer protoplanetary disc where the giant planets form.

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⁻¹ particles can grow by mass transfer. 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 sticking requires a reduction in the radial drift speed of the particles, e.g. through the presence of a long-lived pressure bump. Such a pressure bump may arise at the inner edge of the dead zone (Lyra et al 2008, Kretke et al 2009, Dra̧żkowska et al 2013) or around the water ice line where the jump in dust density has been proposed to cause a jump in the turbulent viscosity (Kretke and Lin 2007), although this requires a very steep viscosity transition at the ice line (Bitsch et al 2014b).

Fluffy particles. Ice aggregates consisting of small monomers acquire very low densities during their growth, down to 10⁻⁵ g cm⁻³ (Okuzumi et al 2012). Particle growth is only able to outcompete the radial drift if the particle grows larger than the mean free path of the gas molecules and enters the Stokes drag force regime. Here the friction time is proportional to the particle radius squared; hence decoupling is much more rapid than in the Epstein regime valid for small particles (Johansen et al 2014). Very fluffy particles are large enough to be in the Stokes regime and can cross the radial drift barrier within 10 AU by growing in size while drifting radially (Okuzumi et al 2012). Hence this is a way to cross the radial drift barrier, if particles can remain fluffy and avoid compactification and erosion by the gaseous headwind.

Particle concentration. Particles can become strongly concentrated in the turbulent gas, triggering the formation of planetesimals by a gravitational collapse of the overdense regions. Particles concentrate either passively or actively. For passive concentration the general mechanism is that particles pile up where the gas pressure is high, since any rotating structure in the turbulent gas flow must be in semi-equilibrium between the dominant forces, namely the pressure gradient force and the centrifugal/Coriolis force (Barge and Sommeria 1995). Particles do not sense gas pressure and must therefore move towards the direction of increasing gas pressure. On the smallest scales of the turbulent flow, approximately km under prevalent conditions in the asteroid belt, mm-sized particles pile up between rapidly over-turning eddies (Cuzzi et al 2001, 2008). The largest scales of the protoplanetary disc are dominated by the Coriolis force, and the turbulence organizes into axisymmetric pressure bumps, surrounded by zonal flows (Fromang and Nelson 2005, Johansen et al 2009a, Simon et al 2012), or elongated vortices (Klahr and Bodenheimer 2003, Lesur and Papaloizou 2010, Lyra and Klahr 2011). In the streaming instability scenario the particles actively drive concentration, by piling up in filaments, which locally accelerate the gas towards the Keplerian speed and hence do not drift radially (Youdin and Goodman 2005, Johansen and Youdin 2007, Bai and Stone 2010b). Strong particle concentration by the streaming instability is triggered at a metallicity slightly higher than solar (Johansen et al 2009b, Bai and 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 but see Weidenschilling (2011) for an alternative view). Asteroids may instead have had birth 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 (Bottke et al 2005). Large birth sizes have also proposed to explain a similar lack of small Kuiper belt objects (KBOs) (Sheppard and Trujillo 2010).

Planetesimals are the building blocks of both terrestrial planets and the cores of the giant planets. 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 nevertheless very slow because the number density of planetesimals is low in the region where the giant planets form. An enhancement of 4–6 over the minimum mass solar nebula is needed to form Jupiter 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. Small fragments have their scale heights damped by gas drag and hence the growing core can 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 inclinations when scattered by the growing cores. This leads to a slow oligarchic growth phase with growth rates that are too low to form cores within the life-time of the protoplanetary disc (Levison et al 2010).

Pebbles left over from the planetesimal formation process can be accreted very efficiently by the growing cores (Johansen and Lacerda 2010, Ormel and Klahr 2010, Lambrechts and Johansen 2012, Morbidelli and Nesvorny 2012). The Hill sphere of the core denotes the radial distance over which an incoming particle on a faster (interior) or slower (exterior) orbit is scattered gravitationally by the core. The core only extends to a small fraction of its Hill radius (0.1% at 5 AU, 0.01% at 50 AU). Gravitational focussing of the incoming planetesimals makes the accretion radius much larger than the physical radius, but planetesimals are still only accreted from about 3% of the Hill radius at 5 AU. Pebbles of mm-cm sizes experience strong drag during the gravitational scattering and lose enough energy to be gravitationally bound to the core, for any impact parameter up to approximately the Hill radius (see figure 2). This leads to very high accretion rates, about 1000 times faster than classical core accretion at 5 AU and 10 000 times faster at 50 AU. Such high growth rates are needed to explain the formation of gas giants observed in wide orbits around some young stars (e.g. HR8799, Marois et al 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 (Testi et al 2003, 2014).

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Many of the young stars surrounded by discs are part of a cluster of stars, indeed it seems that most stars are born in a clustered environment (Lada and 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).

Analysis of the isotopic abundances of meteorites reveal that they contain the decay products 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 are supernovae explosions (e.g. Chevalier 2000). How many is still a matter of debate. Given the observed distribution of stellar masses of newly-formed stars follows a power law favouring less-mass stars (${\rm d}N/{\rm d}m\propto {{m}^{-2.35}}$—Salpeter 1955) one would need a fairly large group of stars reasonably close to the forming Sun to explain the observed abundancies.

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 30–50 AU, which is usually not observed in protoplanetary discs, but could be caused by a fly-by during the protoplanetary disc phase. Second, the trans-Neptunian objects Sedna and 2012VP₁₁₃ (Kenyon and Bromley 2004, Morbidelli and Levison 2004, Brasser et al 2006, Trujillo and 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 2000–10000 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).

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 R_min can be approximated by (Binney and Tremaine 2008)

$$\begin{eqnarray}&&\begin{array}{l} {{\tau }_{{\rm enc}}}\simeq 3.3\times {{10}^{7}}{\rm yr}\left( \frac{100\ {\rm p}{{{\rm c}}^{-3}}}{n} \right)\left( \frac{{{v}_{\infty }}}{1\ {\rm km}\;{{{\rm s}}^{-1}}} \right) \\ \quad \times \left( \frac{{{10}^{3}}\;{\rm AU}}{{{r}_{{\rm min} }}} \right)\left( \frac{{{{\rm M}}_{\odot }}}{M} \right). \\ \end{array}\end{eqnarray} \tag{ 1 }$$

One can distinguish between different phases during which such an encounter could happen: (i) the early phase when the star is surrounded by an accretion disc (first few Myr), (ii) the planet growth phase (up to 100 Myr), and (iii) after the solar system was fully formed (up to now). Close encounters occurring whilst stars still possess protoplanetary discs could lead to their truncation (Kobayashi and Ida 2001, Forgan and 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, clusters may inhibit the planet formation process.

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. Malmberg et 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 2014). 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 2014). In the early phases the probability of encounters are highest, as afterwards clusters expand and therefore the encounter likelihood decreases.

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 SN formed from a relatively massive star or from a combination of supernovae and a massive $^{26}{\rm Al}$-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 hazardous environments. The rate of destructive close stellar encounters tends to increase with increasing cluster mass (see equation (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 and Laughlin 2001). One can perform N-body simulations of stellar clusters containing one 25 M$_{\odot }$ star to determine the number of solar-like stars, which are 0.1–0.3 pc from the 25 M$_{\odot }$ star when it explodes as a SN. 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$_{\odot }$ 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 being unperturbed.

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 finds usually planets around, thus the frequency of planets in cluster environments compared to that in the field is still an open question. However, probably most clusters in the solar neighbourhood loose a considerable fraction ($\gt$70%) of their stars (Pfalzner 2013). Measuring detailed abundance patterns in stellar atmospheres through high-resolution spectroscopy offers us the hope of identifying other stars, which originate from the same gas cloud as the Sun (e.g. Portegies Zwart 2009, Portegies Zwart et al 2010). Even if the cluster has long since dissolved, stars from it will still share similar orbits whose properties could be measured astrometrically (e.g. Brown et al 2010).

The open cluster M 67 is one candidate which we will consider here, though there must have been a number of clusters produced in the Milky way having similar ages and galactocentric radii. M 67 has an age of about 3.5–4.8 Gyr (Yadav et al 2008) and the stars within it also have a composition similar to the Sun. Önehag et al (2011) have identified one star in the cluster, which is a better match to our Sun than most solar-like stars in the solar neighbourhood. The analysis of 13 additional stars in M 67 confirms that the abundances of the Sun and M 67 are similar (Önehag et al 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 figure 3, where we plot their current orbits in cylindrical coordinates (figure 7 from Pichardo et al 2012). The radial distance from the galactic centre, 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 indicate that the Sun experienced a radial migration of 0.8–4.1 kpc (Minchev et al 2013). In that case M 67 should also have migrated over the same distance. Possibly, the migration happened while 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 (Martínez-Barbosa et al 2014).

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One can see from figure 3 that the orbit of M 67 takes the cluster significantly further out of the galactic plane to much larger values of z than is experienced by the Sun. If one assumes that M 67 has always had its current orbit and that the Sun was ejected from M 67, this would 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 system intact.

A possible solution to this problem has been suggested in Gustafsson et al (2014). The key idea is that the orbit of M 67 has changed over time. The orbit could originally have been 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 scattering event with a GMC took place.

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 KBOs in mean-motion resonances with planet Neptune led to the idea that the ice giant has migrated through the original disc of planetesimals, sweeping a significant fraction into stable resonant orbits (Malhotra 1995). The superposition of dynamically hot (high inclination and eccentricity) and cold (low inclination and nearly circular) orbits suggests that while some KBOs have been scattered onto their current orbits (Gomes 2003), likely by the outer planets, others have formed in situ and remained unperturbed (Batygin et al 2011). An alternative explanantion is provided by an encountering 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 an impact parameter of $b=170+45(M/{{M}_{\odot }}-0.5)$ 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.

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 planets emerged from the protoplanetary disc in a more compact, near-resonant configuration, all within 15 AU from the Sun (Batygin and Brown 2010). Angular momentum exchanges with 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 and Ip 1984, Hahn and Malhotra 1999). The diverging migrations of Jupiter and Saturn eventually 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 current locations and violently scattered the planetesimal disc (Tsiganis et al 2005). The Late Heavy Bombardment was also likely caused by this instability event (Gomes et al 2005).

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, Jessberger et al 1974). This process is called the Lunar (or Late) 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 flux of 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 and Garrison 2003), which are inferred to come from Vesta, and Martian meteorites like ALHA84001 (Ash et al 1996, Turner et al 1997) although this is not undisputed (Bogard and Garrison 1999).

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

• (i)  
  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 total mass estimations of initial small body populations), and that the record of earlier impacts must have been erased by the late impact phase 3.8 Gyr ago.
• (ii)  
  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 general explanation for the dynamical excitation, planetary migration processes are promising candidates, in particular the aforementioned resonance crossing of Jupiter and Saturn (Gomes et 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, 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–Ar and zircon chronology (Nemchin et al 2008, Fernandes et al 2013) evidence an increased 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 poorly explored.

KBOs possess the most diverse surfaces of any small body population in the solar system (Luu and Jewitt 1996, Jewitt and Luu 1998). This is puzzling, given the low and slowly varying temperatures in the Kuiper belt region. The migration-driven instability event described above offers a plausible solution to this problem by allowing planetesimals formed in the ∼10–30 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 formation location. A recent survey of KBOs and Centaurs using Herschel (Müller et al 2009) has built on an earlier Spitzer survey (Stansberry et al 2008) to produce the largest sample of albedos and sizes for this type of object (table 1). These data reveal that KBOs are also extremely diverse in reflectivity, with albedos spanning more than an order of magnitude from about 0.03–0.40. An interesting trend emerges when combining the KBO colour and albedo data (Lacerda et al 2014): an albedo-colour plot (figure 4) shows that KBOs fall into 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 BR group, while KBOs that may have been scattered out to the Kuiper belt from nearer the Sun are found in both the BR and the DN groups. This result hints at a compositional gradient that was present in the planetesimal disc prior to the planetary instability event.

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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 suites of numerical simulations. Qualitatively, the evolutionary behaviour can be split into two parts depending on the state of the Sun: (i) the main sequence and (ii) post-main-sequence phases of solar evolution.

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 and Wisdom 1988, Laskar 1989) but realistically are very likely to avoid dynamical instability. 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 5 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 of Venus.

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After the Sun leaves the main sequence, it will simultaneously shed about half of its mass while becoming a red giant star that is nearly 1 AU in radius. The increase in radius can more easily allow the Sun to tidally capture objects encountered by the Solar envelope (Villaver et al 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 planet will lie on the cusp of being tidally drawn into the Sun (Schröder and Connon Smith 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 and 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 and Wyatt 2012).

Observational data for extrasolar planets are significantly less accurate and precise than those 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 the analysis.

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 ¹⁴ (Gladman 1993). A Hill stable system could potentially become Lagrange unstable if the inner planet collides with the star or the outer planet escapes the system (Barnes and Greenberg 2006). Empirical and analytical estimates for these stability boundaries, even when scaled down in mass to the test particle limit, show good agreement with numerical simulations of the long-term evolution (Wisdom 1980, Mustill and Wyatt 2012, Deck et al 2013, Giuppone et al 2013, Veras and Mustill 2013).

Three-planet systems do not appear to admit analytical stability boundaries, and therefore 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 and Weidenschilling 2002, Chatterjee et al 2008). These instabilities can occur any time during the main sequence evolution, and fundamentally change the resulting dynamical architecture, perhaps leading to the establishment of a population of hot Jupiters and eccentric planets (Beaugé and Nesvorný 2012). The study of systems with a higher number of exoplanets produce a similarly-wide variety of outcomes to the three-planet case (Smith and 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 (Gänsicke et al 2006, Farihi et al 2009). Although the precise origin of the pollution and discs have yet to be identified, they must arise from currently dynamically active planetary system remnants.

During giant branch mass loss, the dynamical stability limits of a multi-body system are changed (Debes and 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 6 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 and Villaver 2012).

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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 and Hansen 2014).