Early planetary formation processes during the assembling of the protoplanetary disk (DISKBUILD)

Abstract:

Planets form in a protoplanetary disks (PPD) around a protostar. Both the star and the disk result from the collapse of a dense molecular cloud. However, the vast majority of planet formation studies still assume, for historical reasons, that planetary formation processes take place after the cloud infall, when the circumstellar disk is isolated, which is at odds with many observational evidences. In the Solar System (S.S), the condensation of the oldest and most refractory solids, the Calcium Aluminium rich Inclusions (CAIs) define the “T=0” of the S.S. They are increasingly thought to be contemporary to the disk assembling age due to the necessity of extremely high initial temperatures and of their distribution throughout the disk. Measured formation ages of iron meteorites span about one million years but the oldest may have formed as early as 100 Kyrs after CAIs, which would be contemporary to the cloud infall.  Millimetric observations of Class 0 to Class II disks in star forming regions reveal that their dust content decreases sharply with time, suggesting that most of the planet forming process happens simultaneously with the infall of the protostellar cloud, within 500 Kyrs. 

Whereas abundant literature exists on planet formation inside isolated disks, these above data suggest the need to revisit deeply planet formation scenarios by considering non-isolated disks where growth of dust and planetary objects happens during the infall of the proto-stellar cloud. This is the aim of the DISKBUILD project.

This is an exploratory project aiming at changing the paradigm of planet formation to put it in a more realistic context. However we will focus on 3 outstanding and important conundrums that are keys to understand the formation of planetary objects, and are thought to reveal the importance of the molecular cloud infall during the formation of the Solar System: 

1-The distribution of CAIs in the Solar System is heterogeneous; they are much more abundant in the Carbonaceous Chondrites (CC) family  (which should have formed far from the Sun), than in the non-carbonaceous family (NC) (which should have formed closer to the Sun).  Whereas some studies propose that CAIs have been transported outward, differences in isotopic anomalies carried by CAIs between NC and CC iron meteorites, argue that CAIs have never resided in the inner Solar System, even at early times. How to solve this conundrum, considering that we think that all CAIs must form at high temperature close to the Sun ? For the moment we have no answer.

2-Planetesimals, the parent bodies of chondrites and iron meteorites, are found to assemble rapidly in numerical models assuming an isolated nebula (< 200 Kyrs, see e.g. Drążkowska et al., 2016; Charnoz et al., 2019). Once formed, planetesimals could differentiate rapidly due to radiogenic heating. However measurement of metal-silicate segregation ages of iron meteorites spans more than 1 Myr (see review in Kruijer et al., 2017)  suggesting either a protracted phase of planetesimal formation, or a multi-stages process. 

3-To explain the observation of different reservoirs of material characterized by distinct nucleosynthetic anomalies, it is argued that Jupiter formed early (within 1 Myr) and separated the Solar System in two non-communicating parts by creating a dynamical barrier. But in our current understanding, if Jupiter had formed early it should have substantially migrated towards the Sun; thus it is difficult to understand its current orbital location.

We do believe that considering the effect of molecular cloud infall, using a 3D MHD approach, coupled to the protoplanetary disk evolution may solve simultaneously these important issues and may open a new framework to understand planet formation: we hypothesize that, as the molecular cloud gas shocks the disk, Reynold stresses are enhanced and gas adiabatically heats-up; this raises the temperature well above that envisioned in isolated disks and may prevent CAIs to form in the inner disk. It will also modify the thermal structure of the disk during a few Myrs, which may lead to protracted phases of planetesimal formation (Drążkowska & Dullemond 2018). Gas and dust infall into the disk may also inseminate different regions of the disk with different isotopic compositions and explain the spatial separation of chondrites families (Pignatale et al., 2018, Nanne et al., 2019). Finally, by changing the thermal structure of the disk planetary migration may be affected. These are just hypotheses, although some of them supported by recent studies (Pignatale et al., 2018, Drążkowska & Dullemond 2018), Nanne et al., 2019, Morbidelli et al., 2020), and they must be thoroughly investigated using a multi-disciplinary approach mixing different communities (interstellar medium, planet formation, cosmochemistry) and different tools (3D non-ideal MHD, 1D planet formation models, 2D migration models) to investigate quantitatively the different timescales and spatial scales at play. All previous works suffer, in particular, from a very simplified description of the molecular cloud, neglecting magnetic effects.  So, the key aim of the project is the coupling of mature codes of planet formation, dust transport and planetary migration models to 3D non-ideal MHD simulations of molecular cloud infall. Such a coupling is beyond the current state of the art.

The DISKBUILD project is organized around three workpackages aiming at describing accurately the MHD cloud-infall and disk thermal structure (WP1), the dust and pebbles transport in the disk to identify places for planetesimals formation (WP2), and the effects of the resulting disk’s structure onto Jupiter migration (WP3). To reach these goals, we gather a strong team of experienced researchers from three different communities. We use tools that are already mature and led to several publications. DISKBUILD is an exploratory project, where clearly identified processes will be investigated. It will provide a full new framework for understanding planet formation processes in a realistic, non-isolated disk.

1.1 Introduction and state of the art: Importance of studying disks fed by the molecular cloud

1.1.1 A brief history of planet formation

In today’s emerging view, planet formation proceeds step-by-steps from dust to planets, in a series of key-events: First, there is a circum-solar disk, in hydrostatic equilibrium, accreting onto the Sun in solar composition. Then micronic dust particles coagulate and sediment in the disk’s midplane, forming pebble-sized objects (mm-cm) in a short timescale (< 104-105 years; Brauer et al., 2009, Birnstiel et al., 2011, Drążkowska et al., 2016). These pebbles rapidly drift inward. When they are concentrated enough the so-called “streaming instability” takes place and concentrates the pebbles into gravitationally bound clumps which, once contracted, lead to planetesimals with a characteristic size of ~100km (Youdin & Goodman, 2005; Johansen et al., 2006; Simon et al., 2017). After planetesimals are formed, they grow by mutual collisions and, once large enough (approximately above the size of Ceres), they start to efficiently accrete the remnant pebbles of the disk that drift from larger distances (“pebble accretion”, Ormel and Klahr, 2010; Lambrechts and Johansen, 2012). This allows some of the largest planetesimals to become protoplanets. If icy pebbles are significantly larger than refractory ones, pebble accretion is faster beyond the snowline, leading to the formation of multi-Earth-mass objects (giant planet cores), whereas within the snowline only Mars and sub-Earth protoplanets can form (Morbidelli et al., 2015). An important complication of this picture, however, is that protoplanets migrate radially as a result of their tidal interaction with the disk. The migration speed is proportional to the planetary mass for objects up to ~1 Msaturn (Type 1 migration), whereas it slows down for more massive planets that can carve a gap in the disk (Type 2 migration). These (proto)planets, as they migrate, scatter away remnant planetesimals and smaller planetary embryos mixing the Solar System material (Walsh et al. 2011, Izidoro et al. 2016). After 2-5 Myrs the gas disk is photo-evaporated. The surviving protoplanets in the inner disk take another 100Myrs to accrete through mutual giant collisions to eventually form today’s terrestrial  planets.

1.1.2 Was the protoplanetary disk isolated during the first phases of planet formation ? What sets the original composition and isotopic gradient ?

There are several problems in the general vision of planet formation outlined above. Here we highlight a few, which are at the core of our proposed research.

Solar System original solids are thought to be condensates from a gas of solar composition cooling slowly in an isolated disk. The condensed minerals follow the so-called “condensation sequence” (Grossman 1972; Ebel & Grossman 2000) where the nature of each mineral is determined by the local temperature and the remaining gas content during the cooling. Since the isolated disk is cooler further from the sun, volatile rich minerals should condense far from the sun while refractory rich (i.e. volatile poor) minerals should form closer in. 

This view collides with at least two important observations. First, the most refractory minerals, the CAIs are found to be more abundant in carbonaceous chondrites, that contain at the same time a mix of refractory and volatile minerals in their matrix (Scott & Krot 2003, Braukmüller et al., 2018 ) and which are thus thought to have formed farther from the Sun than non-carbonaceous chondrites (ordinary and enstatite chondrites, which contain only few and tiny CAIs). Second, ordinary and enstatite chondrites have Al/Si and Mg/Si ratios that are sub-solar, which should not be possible following the condensation sequence down to any planetesimal-formation temperature. 

Models of planetesimals formation based on the “streaming instability” (Johansen et al., 2007), predict early planetesimal formation (in less than 200 Kyrs) at the snow line (Ida & Guillot 2017, Drążkowska & Dullemond 2017, Charnoz et al., 2019). But observations show differently. Iron meteorites come from the core of differentiated planetesimals which should indeed have accreted early in the history of the protoplanetary disk (Kleine et al., 2009). But chondrites must have formed later, after the formation of the chondrules, which is dated to have been protracted for millions of years using several isotopic chronometers (Pb-Pb, Al-Mg; see e.g. Villeneuve et al. 2009, Connelly et al. 2017). It has been proposed (Elkins-Tanton et al., 2011) that chondrules accumulated by pebble accretion on the surface of differentiated planetesimals. This argument is supported by the measurement of paleomagnetism in CV chondrites (Weiss et al., 2010) with a geometry that argues that the magnetic field was generated inside the planetary parent body, presumably by a dynamo ongoing in a liquid core. If this is the case, chondrites would just be fragments ejected from the late-accreted surface layers of differentiated planetesimals, which instead would have formed early in agreement with the streaming instability model. However, this is unlikely to be the general solution of the chronology problem. In the asteroid belt astronomers found and characterized spectroscopically several families of fragments issued from the catastrophic fragmentation of a large (D>100km) parent body. None shows any sign of differentiation; in fact, all family members share the same spectroscopic properties. This may suggest that chondrites (possibly with the exception of CVs) come from chondritic planetesimals, which fully formed after chondrule formation, i.e. within a few Myr after CAIs. 

Another observation that challenges the streaming instability model is that meteorites are divided in two broad groups on the basis of their non mass-dependent variations of stable isotopes (Trinquier 2008, Leya et al.,  2009, Warren 2011, Kruijer et al., 2017 and others). Carbonaceous chondrites (CC) and non-carbonaceous chondrites (NC) define the two groups. However, iron meteorites, from their isotopic anomalies, can also be partitioned in the CC and NC groups. Accounting for both iron meteorite and chondrite parent bodies, the accretion timescales of objects in the CC and NC groups overlap, which implies that they must have formed at different locations of the disk, characterized by different isotopic properties (Kruijer et al., 2017). But this is in conflict with the prediction of streaming instability models that planetesimal formation occurs at the snowline. In fact, at any time, the snowline is at one specific location of the disk, and this conflicts with the contemporary formation of planetesimals in two isotopic reservoirs separated in space. 

The observation that CAIs carry several of the isotopic anomalies of CC and that these are absent in NCs (both iron meteorites and chondrites, i.e. in planetesimals formed from ~0.1 to 2-3 My) suggest that CAIs have not resided in the inner disk at any time, challenging models of CAI formation close to the Sun, followed by radial transport (Yang & Ciesla 2012, Desch et al., 2018). 

The identification of two isotopic reservoirs in the disk, at the origin of CC and NC planetesimals, poses the problem of how these reservoirs could have been formed in first place, and then be preserved during millions of years. The preservation problem is particularly challenging given that dust drifts radially in the disk. The formation of Jupiter could have provided an effective barrier against dust-drift (Lambrechts et al., 2014; Weber et al., 2018). Thus it has been proposed that Jupiter formed early, before 1 My, in order to keep the reservoirs separated since the time of formation of the iron meteorite parent bodies (Kruijer et al., 2017). However, this poses the problem of the orbital evolution of Jupiter. Planets, once formed, are expected to migrate towards the star very rapidly. How Jupiter could have survived for millions of years near its present location is an open problem. Once Jupiter is a giant planet and Saturn is also formed, the gravitational interaction between these two planets can stop or reverse migration (Masset and Snellgrove, 2001; Morbidelli and Crida, 2007; Walsh et al., 2011) but there is a severe issue in blocking migration during Jupiter’s growth. Another proposed solution is the formation of a pressure bump in the disk, separating the dust from the two reservoirs (Brasser and Mojtzsis, 2020). However, the formation of such a pressure bump, if unrelated to Jupiter, is not explained. 

Evidence from ALMA observations of disks in star-forming regions

Millimetric and sub-millimetric observations of young and evolved disks (Class 0 to Class II) in star forming regions (Orion, Perseus, Ophiucus) show that the protostellar disk masses in dust in Orion (Class 0-I) are systematically higher by a factor > 4 than those found for Class II disks of different star forming regions (Manara et al., 2018; Tobin et al., 2020). However we note that the measurement of disks masses is still subject to large error bars due to uncertainties in the dust to flux conversion factor that depends on poorly constrained parameters (dust/gas ratio, dust size, opacity etc., see .g. Tobin et al., 2020; Galametz et al., 2019).  We remind the reader that Class 0-I disks are still embedded in the protostellar cloud and accreting from it while only Class-II disk may be isolated from the input of additional material. In addition, Class II disks may not have enough dust (detectable by ALMA at 9mm wavelength) to form planetary systems with masses comparable to the extrasolar systems typically observed (Manara et al., 2018). So two hypotheses are possible: (1) most of dust has grown above millimeter size between class 0 and II so that it can no-longer be detected or (2) most of dust has been incorporated into planets before Class II. In both cases, an important part of planet formation, if not all of it, should occur when the disk is still embedded in the molecular cloud, i.e within the proto-stellar phase that lasts about 0.1 to 1 Myr (Dunham et al. 2014). 

Conclusion : solids and planet’s building block may form during  the cloud collapse 

According to numerous precursor studies from our group or available in the literature, we do think that these conundrums can be explained if we consider that the protoplanetary disk was embedded in the parent molecular cloud and was continuously accreting material from it. The infall of the molecular cloud in the vicinity of the Sun may have formed initially a very small and hot disk, allowing the condensation of only the most refractory minerals: the CAI. The viscous expansion of the disk may have transported the refractory minerals outwards (Yang & Ciesla 2008, Pignatale et al., 2018), thus explaining their presence predominantly in CC which are supposed to be planetesimals formed in the outer disk. The continued accretion of gas from the molecular cloud, with evolving isotopic anomalies due to a change in the abundance of supernova or kilonova products (the so-called r-isotopes), while the disk was still expanding, can explain the radially heterogeneity of the disk (Nanne et al., 2019). The heating provided by the infall (Baillé et al., 2018), could also sustain a very high temperature (>1500K) for a few 105 yr, which could explain the condensation of CAIs only beyond a few AU (thus explaining their absence at any time in the inner disk). The decay of the infall would then have allowed the inner disk to cool, triggering a new condensation sequence which, fractionated by early planetesimal formation, can explain the subsolar Al/Si and Mg/Si ratios of non-carbonaceous chondrites and the correlation between Na and Al depletions (Morbidelli et al., 2020). The formation of planetesimals at different locations in the disk and different times probably requires that the disk properties are not a smooth function of heliocentric distance and time, but has several pressure/temperature bumps, again justifiable if the disk experience a protracted and inhomogeneous accretion from the molecular cloud (Baillié et al., 2019). A pressure bump at a few AU is also invoked to explain how the isotopic reservoirs of NC and CC could have remained separated in spite of the radial drift of dust grains (Brasser and Mojtszis, 2020). Pressure bumps could also have played a role in preventing the radial migration of proto-Jupiter (Baillé et al., 2018). 

Thus, it is now urgent to study quantitatively the injection path of ISM dust and gas and the resulting disk structure (WP1), the radial transport of dust, pebbles and gas coupled with chemistry and accretion (WP2) and the migration of planet embryos in a fed disk (WP3).

1.2 Previous studies of planet formation in a disk fed by the infalling cloud

Only a handful of works have attempted to study planet formation during the infall of the molecular cloud, including some of the members of the DISKBUILD project (see Pignatale et al., 2018, 2019, Charnoz et al., 2019; Morbidelli et al., 2020). A family of 1D models have investigated this question assuming the Shu (1977), or Ulrich (1976) self-similar infall models of the molecular cloud.  Angular momentum conservation inside the system is always assumed: this is a severe approximation in which the interaction of the ionized gas with the magnetic field is neglected. Several works (Nakamoto & Nakagawa 1994, Hueso and Guillot 2005) show that when neglecting magnetic forces and assuming self-similar collapse, disks may form with characteristics similar to the MMSN (Nakamoto & Nakagawa 1994) or to disks observed in young stars clusters (Hueso & Guillot 2005). However observations show that the cloud infall is not as simple but rather follows “arms'' of accretion only explained via MHD effects. It was also shown that CAIs could form close to the star, from condensing gas, and be transported away (Yang & Cielsa 2012, Pignatale et al., 2012) due to viscous spreading of the disk. Drążkowska and Dullemond (2018) show that planetesimals may form during the gas infall at different locations as the snow-line moves first outward then inward. Pignatale et al. (2018) using a detailed multi-species model including condensation and sublimation in a stratified disk with dead zones and nebular infall, shows that disk spreading coupled to cloud infall can explain the CAIs overabundance in carbonaceous chondrites consistent with meteoritic records. 

3D numerical models of cloud collapse and disk assembling have also been published, but cover a much shorter time evolution than 1D models, however with a much more detailed physics based on first principles. Kuffmeier et al. (2017) studies the collapse of a molecular cloud with initial size of 40 pc using zoom-in techniques. They do find formation of disks around protostars during the 100 Kyrs of the simulation, but no rotationally supported disk. However, despite its qualities, this work uses ideal MHD, and it was demonstrated in recent years (Hennebelle et al. 2016, Masson et al. 2016,, Bethune & Lesur 2017 ) that non ideal MHD processes drastically change the picture of the flow in circumstellar disks. More recently Wurster and Bate (2019) use non-ideal MHD in a SPH simulation of cloud collapse and demonstrate that non-ideal MHD effects promote disk formation. However the simulation spans only 16 kyr, a small fraction of the infall time (a few 100 Kyrs) and the spatial resolution does not allow to investigate the flow structure in the terrestrial planets regions. Finally they do not consider dust and gas differential dynamics which may be at play (Bate & Loren-Aguilar 2017, Lebreuilly et al. 2019) and stellar irradiation to determine the disk thermal structure. Hybrid approaches have been also proposed: Kadam et al. (2020) run a simulation of cloud collapse onto a disk using essentially a 2D Navier Stokes simulation in the thin disk limit with a parametrization of the turbulent viscosity due to magnetic effect. 

To go beyond these works, we plan to run (and we have already partially done it, see below) simulations of molecular cloud collapse forming a disk, using non ideal MHD simulations, up to several 100 Kyrs including dust and gas differential dynamics as well as protostellar irradiation (WP1).

1.4 Outstanding questions at the heart of the DISKBUILD project

Following the above arguments, the questions below are the most urgent to answer in this project. As described in the introduction we mainly want to determine if the infall of the nebula heats-up the dust in the whole inner Solar System, up to a few AU as this may bring a solution to several meteoritic measurements. So a special emphasis is given to thermodynamics and dust transport. Determining if Jupiter migrates is also a key question as it is thought to have a pivotal role to isolate isotopic reservoirs.

1) Where is ISM material injected into the disk ? 

The Shu (1977) and Ulrich (1979) solutions predict that cloud material is injected initially in the inner regions of the disk, and lately in the outer regions due to the expansion of the so-called ‘centrifugal radius’. So the place where pristine material is injected evolves with time. This has major implications for the formation of CAIs and potentially for the establishment of different nucleosynthetic isotopic differences between the NC and CC reservoirs (Nanne et al. , 2019). However non ideal MHD effects change the inflow structure as material’s  angular momentum is redistributed into the envelope (Hennebelle & Fromang 2008, Li et al. 2014; Wurster & Bate 2016, Hennebelle  et al. 2020). This leads in general to the formation of a stratified flow (Bethune & Lesur 2017) due to the coupling of magnetic forces with non-ideal effects (ohmic diffusion, hall effect, ambipolar diffusion). In this stratified flow we wish to track where the pristine material coming from the ISM is injected in the disk and if it is preserved from heating or is vaporized. We will use 3D RMHD simulations.Thus  we will determine the “Source function” for the disk of injected material  as a function of space and time (S(r,t)). This will be done in WP1.

2) What is the thermal structure of the young disk ? Where is the snow-line ?

In the same study we will determine the thermal radial evolution of the disk T(r,t) and track the location of the snow-line as a function of time. The thermal structure of the disk is a fundamental parameter that controls (1) the radial transport and vertical settling of dust in the midplane through diffusion coefficients (2) the growth rate of pebbles and (3) in turn the growth rate of planetesimals (that need concentration and growth of dust in the midplane for the onset of the streaming-instability) and (4) the migration rate of protoplanets. It has been suggested that planetesimals form preferentially at the snow-line (due to water vapor retro-diffusion and traffic jam effect, see e.g. Drążkowska et al., 2014, 2018, Charnoz et al., 2019) but noting that either chondrites formation times or iron meteorites differentiation ages span different epochs, this suggests either that the snow-line may have evolved with time and space, or that another process that accumulates material (like a pressure-bump) may have occurred at several places. Thus we will determine the (P,T) profile of the young disk fed by the molecular cloud,  with time and space.

2) Where did CAIs form and where nucleosynthetic anomalies were implanted and isolated ?

By implementing the Source function (WP1) in 1D disk models (accounting for My-long integration and including grain-growth physics; see WP2) we will identify the most likely formation time and place of CAIs and their dominant transport mechanism to the outer disk. We will also track the implantation and diffusion of gases or solid carriers of nucleosynthetic anomalies to see how long the disk can remain heterogeneous. Our 1D code (Charnoz et al., 2019) can do that as it is a multi-material and multi-layered disk model (see WP2 for details).  

3) Where and when pebbles and planetesimal form ? For how long ?

Pebbles and planetesimals are the key “ingredients to form planets”. Modeling accurately the flow of pebbles requires a good knowledge of the young protoplanetary disk. In the present work we will use a similar approach as in Drążkowska et al. (2016) and Charnoz et al. (2019), but starting with realistic initial conditions provided by the RAMSES code (WP1), to investigate the formation of pebbles and their flow and, in turn, the location and timing of planetesimal formation. This will be done in WP2 to compute the growth rate as a function of space and time, while considering a realistic model of cloud infall and disk structure given by WP1. We will map using 1D simulations the timing and location of dust and pebble growth. 

4) How proto-planets migrate in a disk fed by the molecular cloud ? 

Planetary migration is a key process of planet formation and may explain the over abundance of short-period planets found in exoplanetary systems. In our Solar System, it is still not clear if Jupiter has suffered migration. In a particular the early formation of Jupiter is invoked to separate the inner from the outer Solar System to explain both the low abundance of water in the inner Solar System (Morbidelli et al., 2015) and the separation of mass-independent isotopic reservoirs (Kruijer et al. 2017). However this requires that Jupiter did not migrate during at least 1 Myr. How is that possible ? A speculative possibility is that accretion inflow from le molecular cloud may have modified the conditions for migration, however whereas the migration theory is well established, the effect of an inflow onto migration is unknown. We will study here planetary migration processes concerning planet embryos, especially in the case of Jupiter for which an early formation and no migration are necessary ingredients to explain the structure of the Solar System. This will be done with the 3D hydrodynamic code FARGOCA especially designed for planet migration studies. FARGOCA will be modified to include the molecular cloud source function and the disk thermal structure obtained in WP1. This will be the work of WP3.

1.4 Structure of the DISKBUILD Project

In order to answer the above outstanding questions, the project is built around 3 complementary workpackages (WP). WP1 will run radiation non-ideal MHD collapse simulations , to investigate separately the gas-flow and dust-flow structure around the star during the molecular cloud collapse and quantify the protoplanetary disk properties: WP1 will provide realistic initial and boundary conditions (in the form of source functions) for WP2 and WP3. WP2 will compute the growth, transport and mixing of dust, pebbles and the accretion of planetesimals. In WP3 migration of planetary embryos inside the disk will be studied, with a special emphasis on Jupiter.

Thanks to our array of consultants in cosmochemistry and in observations, the modelisation efforts of WP1, 2 and 3 will be confronted to meteoritic records and observational data. Results of WP1 will be confronted to ALMA dust continuum and polarized emission observations (Maury et al., 2019) of disk size and mass distribution (collaborating with our external expert collaborator Anaelle MAURY). The results of WP2 will be confronted to meteoritic data for the CAI distribution across different chondrites families. Results of WP3 are more theoretical and will assess the conditions under which the proto-Jupiter may stay on its orbit to isolate isotopic reservoirs, under cloud infall.  

Figure 1: Structure of the DISKBUILD project

1.5 Detailed description of the 3 work-packages 

1.5.1 WP1: How are interstellar dust and gas brought to the disk ? What is the disk structure ?  WP1 aims to characterize how the accretion flow from the ISM into the disk using 3D non ideal MHD code and tracking separately dust and gas. The disk structure will be characterized: density, temperature, dust-size distribution, and structure of turbulence. We will track the location and the movement of the snow-line.

We will simulate the cloud infall using multi-scale (adaptive-mesh-refinement)  zoom on the forming disk, to characterize this accretion flow and in particular the source function, F(r,t) and the resulting PPD structure. We want to determine: What is the mass flux injected vertically and from the equatorial plane ? Is there “late” accretion, beyond 1 Myr ? Is the flux spatially confined by a “centrifugal radius” (like in the Shu solution) ? We will also characterize the resulting properties of protoplanetary disks in terms of (i) surface density (ii) temperature (iii) dust distribution and track the location of the snow-line (iv) size and and (v) accretion rate.

An important aspect of WP1 is the computation of the thermal structure of the flow. For this a special effort will be put on the computation of radiative transfer using state-of-the-art algorithms which accounts for the anisotropy of protostellar irradiation (Commerçon et al. 2011, 2014, Mignon-Risse et al. 2020).Also, as dust is a key parameter to be confronted to (sub-)millimetric observation, dust dynamics will be introduced in the numerical model (see below). 

Numerical methods

We will perform 3D radiative non-ideal magneto-hydrodynamical simulations of molecular cloud collapse. with the Adaptive-MeshRefinement (AMR) code RAMSES For this purpose we will benefit from all the numerical developments that the group has been carrying out over the years making RAMSES a state-of-the-art tool for this project. Indeed non-ideal MHD (Masson et al. 2012, Masson et al. 2016), state-of-the-art magnetic resistivities based on chemistry networks (Marchand et al. 2016), multi-species dust dynamics (Lebreuilly et al. 2019), as well as radiative transfer (Commerçon et al. 2011, 2014, Mignon-Risse et al 2020) have all been included so that we will take great benefit from this unique tool. The only development to be done before the start of the scientific exploitation is the introduction of a three-temperature solver to track the gas, dust, and radiation temperatures separately (Pavlyuchenkov & Zhilkin 2013). The combination of all the physical modules with the AMR scheme make it a very powerful tool to tackle the problem under investigation. In particular, the AMR scheme allows to alleviate if not solve the initial conditions and boundary problems. Indeed the group is routinely performing molecular cloud simulations (e.g. Hennebelle 2018, Commerçon et al. 2019) from which it is easy to zoom up to the desired resolution. Initial conditions are thus self-consistently obtained from large scale simulations. All-together, our numerical methods is well suited to our purposes and will go beyond the state-of-the-art in the field. 

Hypotheses and assumptions.

It is a ‘first principle” approach, so that it relies on a small set of assumptions. First, we will follow the dynamics of the neutral dust grains only. The fluid description of charged dust grains requires heavy theoretical and numerical developments that go beyond the scope of the project. The dust dynamics solver developed by the team in RAMSES accounts for dust backreaction onto the gas dynamics and allows it to follow multiple small dust grain species with Stokes number St<<1, which corresponds to a size of a few millimeters in the disk. For larger grain, we will use a bi-fluid approach in which the dust grains are treated as Lagrangean tracer particles (e.g. Hopkins & Lee 2016). The back reaction of the large dust grain will thus be neglected. Second, we will use the dust distribution from the smaller grains in the opacity estimate for the radiative transfer, which is a good approximation since most of the surface is in the small grains. The stellar irradiation will be treated using the hybrid scheme of Mignon-Risse et al. (2020) which performed well in the estimate of the temperature in star-disk systems. 

Main difficulties and an innovative strategies

The difficulty that must be addressed in this problem is the large range of spatial and temporal scales that needs to be covered. Typically the disk formation from the parent cloud requires about 100 kyr and one is willing to follow the disk evolution for about 1 Myr. On the other hand, the typical timescale within the disk is below 1 yr implying that the timesteps to be solved is much smaller, on the order of one minute or so. This would imply that a formidable number of timesteps should be performed, which clearly is not possible with current computers and numerical schemes. To address this question, we have developed an original methodology which consists in simulating the disk at a somewhat coarse numerical resolution (1-2 AU) which allows us to form and follow it self-consistently for hundreds of kyr. Then at regular time interval (say every 10 kyr or so), the simulation is restarted at much higher resolution (typically at least 0.1 AU or so) allowing to describe the inner part of the disk and to get accurate values of the disk structure and transport coefficient (such as the effective alpha viscosity, the magnetic flux through the disk, etc…). We have verified by running simulations at various resolutions that this method is providing reliable results. The reason is that the early disk properties such as its radius, accretion rate and magnetic field are largely controlled by the collapsing envelope that is continuously delivering material onto the disk. While the method is now in use, there are several developments that need to be conducted. First we have established that the disk properties, in particular their mass, sensitively depend on the sink particles that are introduced to mimic the star (Hennebelle et al. 2020). A sink particle is a Lagrangian particle, which interacts with the gas through gravity and can accrete dense material. It is therefore simply a subgrid model that needs to be introduced because stars are too small scale objects in this context. However, the parameters that control its introduction and the accretion are somehow arbitrary and influence the disk properties. To avoid this we need to develop a specific strategy that consists in zooming further toward the stars before introducing the sink particle. Obviously the timesteps are going to be very small, but the grid can be de-refined once the sink has been introduced making the high refinement phase only transient. This would lead to a much higher accuracy regarding when the sink is being introduced. We will implement this procedure within the course of DISKBUILD.

Runs already performed

We stress that we have already some preliminary results (Lee et al., 2020, submitted) that will allow the other workpackage to start using the results of workpackage 1 immediately. This consists in a run corresponding to a one solar mass cloud with a few percent of rotation initially as well as a magnetic field  with a substantial, but not dominant magnetic field (mass-to-flux over critical mass-to-flux ratio of 3). This simulation neglects dust dynamics and does not benefit from the new radiative transfer solver of Mignon-Risse et al. (2020). 

Figure 2 : First results we have obtained with RAMSES by zooming onto the disk. Left: edge-on disk, right : face on disk. The colors scales with the gas density. The surrounding molecular cloud is not displayed. (Lee et al., 2020)

Within the course of DISKBUILD we will build upon this first simulation and improve the physics described to perform a systematic parameter survey by changing the mass of the core, the magnetic flux and the initial rotation and turbulence. We will also explore the influence of magnetic resistivities as their values remain largely uncertain.

1.5.2 WP2 : How dust of the protoplanetary material is mixed? Where do refractory and volatile material (either injected from ISM pristine or condensed) end-up in the disk ? When and where pebbles and planetesimals are formed and transported? Is it possible to keep separated different reservoirs of isotopic anomalies ? What is the composition of the first planetesimals ?  Can we form the CC and NC groups, with timescales of formation coherent with iron meteorites measurements and is it possible to separate them during the course of planet formation ?

In order to do that, we have already published a 1D code (Pignatale et al., 2018, Charnoz et al., 2019, Pignatale et al., 2019, Jacquet et al., 2019). It will be modified to implement the molecular cloud infall source function (S(r,t)) that will be determined in WP1. So we will have a gas-disk model coupled to the cloud allowing us to study the disk evolution over several million years of evolution, in which the different species (dust, gas, isotopic anomalies, pebbles, planetesimals) will be tracked.   

The advantage of a 1D code is that it can be evolved during the lifetime of the disk (up to 10 Myrs). Of course it relies on a number of simplifications: the α model, axisymmetric, and its mono-layer description of the disk. However the α model is known to be flexible through the parameterization of α. We will explore several α laws to find which better match the short-term RAMSES simulations, and extend the run up to Myrs. Dust grows through binary collisions in the disk, and the growth speed depends strongly on the local turbulence state and dust to gas ratio (Brauer et a., 2009, Birnstiel et al., 2011). Dust growth and diffusion, pebbles formation and planetesimal formation will be tracked using our 1D code (Charnoz et al., 2019) that is at the state-of-the-art and compares well with the Drążkowska’s code for instance (Drążkowska & Dullemond 2018).

We will simulate all of these processes, and their formation timing considering a disk fed by the molecular cloud in order to understand how the solid material is distributed in the disk, form pebbles and planetesimals, and how the different chemical species will be distributed among the different planetesimal families.

A special attention will be given to the description of the cloud infall. Some works have already attempted it (Drążkowska & Dullemond 2018, Pignatale et al., 2018, 2019) but both considering MHD-Free infall, or by using a non-layered disk , that is at odds with MHD simulations. Our code (Charnoz et al., 2019) is a two-layers model, and can be easily coupled to the cloud-source function given by WP1.

Most of the tools needed to perform the study mentioned above have been developed and are functioning (Pignatale et al., 2018, Charnoz et al., 2019). We will also implement also condensation processes (using the HSC thermochemistry code) in order to track the condensation of CAIs in the disk and their transport, to describe precisely the effect of the snow-line(water vapor condenses into solids at the snow-line, and pebbles that drift inward produce vapor). The vapor and solid forms of all relevant species (Si, Mg, H2O, Al etc..) will be tracked individually allowing the computation of the local dust composition, the composition of pebbles and planetesimals.

Hypotheses and assumptions.

The disk is assumed to be axisymmetric, and the turbulence is described as a multi-layered diffusive process : the so-called ‘α model’ linking the diffusivity to the local temperature. There is a very abundant literature on this type of model and they are routinely used to study long term evolution of planet forming disk, but they always need to be confronted to MHD simulations, when possible to check their validity;

Method:  Our 1D model will be used first to first have a large scale description of the disk with correct gas flux. To match the 3D simulations on short timescales, we will measure diffusion coefficients (radial, vertical) in the 3D disks simulations (RAMSES) in order to put them in 1D and 2D models. Our 1D model is multi-material and multi-layered. It is described in Charnoz et al. (2019). It includes: transport of gas and dust (following Yang & Ciesla 2011); viscous and radiative heating (following Hueso & Guillot 2016); Multi-materials, in order to track the local composition (H2O solid and gas ,SIO2 solid and gas, CO solid and gas, H2 and He gas, Al, Fe, S ), dust growth (Birnstiel et al., 2011); planetesimal formation conditions (using the prescription from Drążkowska et al., 2016); thermodynamic vaporization calculation (using the HSC thermochemistry code).

1.5.3 WP3: How protoplanets migrate in a non isolated disk?

How gas infall modifies planetary migration ? How fast and in what direction terrestrial and giant protoplanets migrate in the disk?  How an early formed proto-Jupiter would migrate in a fed disk ? Can it stay on its orbit (and then prevent mixing of dust and pebbles formed in the inner and outer solar System, as suggested by several works, see Kruijer et al., 2017, Nanne et al., 2019), or will Jupiter migration prevent such an isolation process ? 

Workpackage 3 aims to characterize the migration of macroscopic planetary bodies in a non-isolated disk: As gas infall changes the disk dynamics (temperature, turbulence, gas flow), in turn protoplanets migration will be affected. The 3D hydrocode FARGOCA will be used for this purpose.

Migration state-of-the-art: We know that migration is a key process for the protoplanets’ early dynamical evolution, either in our Solar System (Morbidelli et al. 2007, Crida 2009) or for exoplanetary systems (see Baruteau et al. 2014 for a recent review). Planet migration is a key process especially to understand water abundance in the inner Solar System as well as the isolation of nucleosynthetic isotopic reservoirs. In both cases the early formation of Jupiter and its capacity to create a dynamical barrier in the early S.S is invoked in numerous papers (Morbidelli et al., 2015, Kruijer et al., 2017). However we do not know if it is possible to maintain Jupiter on its orbit despite migration processes. Planetary migration in non-isolated disks, with nebular infall has never been studied.

The torque a planet feels from the disk depends on its mass, but also critically on the disk parameters. The gas surface density, the slope of the surface density and temperature profiles, the aspect ratio of the protoplanetary disk all set the so-called Lindblad torque, which pushes small planets inwards. The corotation torque can in some conditions push a planet outwards ; it also scales linearly in the planet’s mass, but has a different dependence on the radial density and temperature profile of the disk. Moreover the viscosity of the protoplanetary disk dictates the degree of saturation of the corotation torque. From the possible structures of disks obtained in WP1 and the known dependencies of the Lindblad and corotation torques (Paardekooper et al., 2010, 2011), we will create migration maps, that show the torque felt by a planet as a function of its mass and location in the disk. The work by Bitsch et al. (2013, 2014a,b), that was developed in the Nice team, has shown the importance of this concept. However, it was developed on isolated disks, supposed to be in steady state. Baillié et al. (2019) have started to explore the concept of migration maps in a disk whose evolution depends on the infall of gas, and have shown that new “planet traps” appear, where migration stalls and planets may accumulate. But their infall model is too simplistic, as explained above. We will also revisit the migration of giant planets (Type II migration, proportional to the disk’s viscosity) at the light of the effective viscosity generated in the disk from the infalling gas (determined in WP1), as a function of time.

Main objectives:

To understand the fate of the first formed planetary embryos, which could appear early after planetesimal formation (as suggested by Manara et al., 2108), we need new migration maps corresponding to the first phases of a disk experiencing an infall. The outcome of this WP will be to understand how protoplanets forming early can survive migration in a non-isolated disk. How gas accretion of the PPD changes the picture of planetary migration ? For the moment, these are open questions. New disk structures may revolutionize our understanding of the role of planetary migration (e.g. Ogihara et al. 2018). It has been increasingly evident that small changes in the disk structure may lead to big changes in the architecture of a planetary system, e.g. construction (or not) of stable (or not) chains of resonance of super-Earths, outward migration (or not) of giant plant cores. In parallel, the architecture of the exoplanetary systems is also amazingly diverse. By exploiting the diversity of the conditions provided by WP1, we will assess whether we can explain the observed diversity of planetary systems.

Numerical Method:  

We will use the FARGOCA code, which has been developed in the Nice group on the basis of Frédéric Masset’s FARGO code. It is a 3D eulerian Hydro-code, working on a spherical geometry grid, centred on the star, that encompasses the protoplanetary disk. The dynamics of the disk is computed solving the Navier-Stokes equations plus the gravity from the star and the planet(s), and the orbital evolutions of planets is computed using a Runge Kutta 5 algorithm, taking the force from the disk into account. This code has been thoroughly tested, is fast, efficient, and has already been used in several publications (Lega et al., 2014).The effect of gas infall will be included through the implementation of a vertical boundary condition source function S(r,t) that will be provided from WP1. The first thing to do will be to measure how the infall heats the (inner) disk, by adiabatic compression. The whole structure of the protoplanetary disk will then be analysed with a finer resolution as in WP1.

2. Originality and relevance in relation to the state of the art

2.1  Originality : Bringing together different scientific communities

This is an ambitious project, because it aims to make a direct and continuous link, using both high end modern numerical simulations (RAMSES, WP1), 2D hydromodels (FARGOCA, WP3) and  1D  dust growth and transport models (WP2), between topics that have always been separated in the literature : (1) The molecular cloud infall physics,  (2) The injection of material in the protoplanetary disk, (3) The subsequent evolution of this material into planetary bodies through growth  (4) The chemical evolution of solid material in the disk and link with chondrites  (5) The dynamical evolution of the disk and protoplanets under the infall of gas.

In the literature, points (1) and (2) are investigated by researchers working on the Interstellar medium and star formation. Points (3) and (5) are classically investigated by people from planet formation. Points (4) is mostly investigated for cosmochemists and people from Earth Science. Most of the time these communities do not work together and speak a different language. Inside the DISKBUILD project we gather, at the national Level, a strong team of people from the three communities : Star Formation and ISM, planet formation and migration and cosmochemists (as consultants). 

2.2 Relevance : (1) Change the paradigm for Solar Nebula initial conditions, and (2) define a realistic context and timescale for the condensation and accretion of Solar System primitive material.

As mentioned in section 1, most studies of planet formation start with the model of the minimum Solar Nebula that is an ad-hoc model disconnected from its origin (the cloud infall). In DISKBUILD we will build a realistic MHD infall disk model for dust and gas. It will also provide a realistic Solar Nebula (P,T) structure  to be used as initial conditions for planet formation studies. In addition, it will provide for the first time a time-frame that can be linked clearly to the timescale of the Sun’s formation and chondrites accretion history.DISKBUILD may lead to a major revision of the Solar System history: it will put for the first time solid bases to understand the heritage of the ISM into the Solar Nebula and the radial mixing of dust and isolation of isotopic reservoirs. This will provide a new frame to interpret the large array of laboratory measurements available today on extraterrestrial material.

 2.3 Already obtained results in the context of previously obtained projects.

 One of the strength of our project, which makes it particularly realistic to achieve on time, is that we start the project with already developed mature tools (the RAMSES code, the 1D disk models including dust transport and planetesimal formation, the FARGOCA code) that will necessitate only minors modifications. The DISKBUILD project may be seen as the “grand-final” that will allow to re-use the past experience, and for the first time. We got in the last years 

* An ANR project “CRADLE” (2015-2019, PI: M. Chaussidon) devoted to the study of the dust transport in a 1D protoplanetary fed by a non realistic self-similarly infalling cloud as described by Shu (1977). Our results are published in Pignatale et al. (2018, 2019), Charnoz et al., (2019)

*A DIM-ACAV project (2019-2021, PI: S. Charnoz), funding (only) the postdoc of F. Pignatale? devoted to compute the chemistry of Carbon species in the molecular cloud and protoplanetary disk. This project is complementary to the DISKBUILD project and will come in support of it for all chemical aspects.

*A LABEX-UNIVEARTHS funding (2017-2019, PI: P. Hennebelle) devoted to study the hydrodynamic collapse of a molecular cloud. The main outcome of this project was to define an appropriate set-up for studying protoplanetary assembling. The set-up is now ready (2 years of work)  and it will be used as the starting point of the DISKBUILD project. A paper is submitted to A&A  (Lee et al., 2020).

All the different bricks of the DISKBUILD project are in place, and we now need to start the final work of assembling those bricks, along the lines of our three Worpackages.

3. Methodology and risk management

3.1 Methodology          

The methods used inside each WP are described in section 2. Most technical decisions have been already taken and evaluated (thanks to our work in the last year) and we are now ready to start the study proposed here. Simulations we will start from a collapsing cloud using non-ideal RMHD (radiation  magneto hydro dynamics). It will progressively form a disk structure (at small scale) around an accreting star. To simulate the presence of the star, a sink particle will be put in the middle of the disk. High-resolution on the disk’s structure will be achieved using a dedicated ‘re-zooming’ procedure (see WP1’s description). Simulations will be run first in a “fast” mode, using the barotropic equation of state, where some radiative transfer processes are “absorbed” in the equation of state to make computation faster. Then we can go to full physical resolution using the diffusion limited heat transport flux and stellar irradiation, in order to have real treatment of heat flux. For WP2 and WP3 the methodologies are quite standards and mature. They have been published in several papers (see WP2 and WP3 descriptions). WP1,WP2 and WP3 are tightly coupled via the implementation into WP2 and WP3 of the cloud-collapse source function (S(r,t)) and disk thermal structure (that will be both provided by WP1).

3.2 Risk Management.  

Thanks to our experience already acquired on the subject by the different members of the team, we do not see “risks” of not obtaining a result, or not achieving our objectives are quite low. Each leader is an expert in his domain. However, we still see a potential threat to our project worth to mention: The main outcome of WP1 is to provide to WP2 and WP3 a simple, parameterized 1Dl description of the cloud collapse: S(r,t) the material infall source term onto the disk, as a function of r and t,  α(r,t) the turbulence intensity parameter, as a function of r and time. If these functions are too complex, we will tabulate them by saving disk structure, directly extracted from RAMSES simulation outputs, in a collection of 1D grids (through vertical averaging), saved on the disk. So the evolution of disks will be directly read from the computer memory, and we will transport the different species using the method described in WP2 and in Charnoz et al. (2019). 

4.Project organisation and means implemented
4.1 Scientific coordinator and its consortium: The team

The PI and coordinator of WP2 is Sebastien Charnoz. He is an expert on planet and satellite formation with a lot of experience in numerical computing of dust growth and transport, with several innovative code already published, in particular the first codes that couple dynamics and grain growth without growth parameterization (Charnoz et al., 2014, Pignatale et al., 2018, 2019). He is working at IPGP that is the ideal place for leading this project: it is a multidisciplinary laboratory mixing world leading cosmochemists (F. Moynier, M. Chaussidon) thermodynamicists (J. Siebert) taking part in the project they will bring their expertise on meteoritic data and condensation processes and will act as consultants on all cosmochemical aspects related to chondrites families.  

WP1 is led by Benoît Commerçon, based in CRAL (LYON). B. Commerçon is a renowned  expert on star formation and interstellar medium dynamics, and also expert of high end numerical simulations, especially using the RAMSES code. He has been developing radiative transfer codes now implemented into RAMSES that couple properly thermodynamics with MHD effect, as the temperature distribution of dust and gas in the disk will be a first important parameter to determine. 

WP3 is led by Alessandro Morbidelli at Laboratoire Lagrange at OCA. A. Morbidelli is a world leading expert in planet formation and migration processes and has been deeply involved in the development of the code FARGOCA that will be used for the current project. He will work with his colleague Aurélien CRIDA on the task of studying migration processes in a disk fed by the Solar Nebula. Elena Lega, who wrote the FARGOCA code will work with Aurélien to modify FARGOCA to implement disk infall. 

We will work also in close contact with external collaborators : our colleagues from CEA Patrick HENNEBELLE (a world leading expert of star formation and interstellar medium) and Anaelle MAURY  that is a world famous observer of star forming regions and at the international level  ELSI / TOKYO TECH : Shigeru IDA, Hidenori GENDA, Ryuki HYODO, and Yueh-Ning LEE at the Taipei Normal University. She is an expert of RAMSES. 

REFERENCES

Andrews, S. M. et al.  2005, ApJ, 631, 1134; Baillié K. et al., 2019, A&A 624, A93 ; Bate & Lorén-Aguilar, 2017, MNRAS 465, 1089; Birnstiel T.,  et al.  2011. A&A 525, id.A11; Birnstiel, T., et al. 2012, A&A, 539, A148; Bollard et al., 2017. Sci. Adv. 3 :e1700407; Brauer, et al. 2008, A&A, 480, 859; Braukmüller et al., 2018  Geoch. Acta. 239, 17 Charnoz S.. et al. 2019 A&A 627 id.A50  Chikako et al., 2009. ApJ 705, 54-63;  Ciesla F.J. & Cuzzi J.N., 2006. Icarus 81, 178-204; Commerçon et al., 2010, A&A 510, id.L3 ; Commerçon et al., 2011. ApJL 742, id. L9; Connelly J.N. et al., 2017, Geoch. Cosmochim. Acta 201,345 ; Desch S. J., et al.,  2018. ApJS 238, id.11; Drążkowska, et al. 2016, A&A, 594, A105; Drążkowska  J. & Dullemond, C. P. 2018, A&A, 614, A62 ; Dunham et al., 2014 MNRAS 444, 887; Elkins-Tanton L.T. et al. 2011, EPSL 305, 1; Galametz M., et al., 2019, A&A 632, id.A5; Gerber S. et al., 2017, ApJL 841:L17; Grossman L., 1972 Geo. & Cosm. Ac. 36, 597 Hayashi, C. 1981, Progress of Theoretical Physics Supplement, 70, 35 ; Hennebelle et al., 2016. ApJL 830, L8; Hennebelle et al., 2017, A&A 599, id.A86;  Hennebelle P. & Fromang S. 2008, A&A 477, 9; Hennebelle et al. 2020, A&A 635, id.A67 ; Hueso R. & Guillot T., 2005. A&A 442, 703-25; IzidoroA., et al., 2016. ApJ 833, id.40; Johansen A. et al. 2006. ApJ 1136, 1121-34; Klein et al., 2009 Geoch. Cosm. Acta 73, 4963 ; Kuffmeier M. et al., 2017, ApJ 846; Kööp et al., 2018 Geochem. and. Cosmochim. acta. 211, 296-317, Kruijer et al. 2017. PNAS 114, 6712-16; Lambrechts & Johansen 2012, A&A 544, id.A32; Lebreuilly et al., 2019, A&A 626, A96;  Lee Y-N, 2020.,Submitted to A&A , Lega E. et al., 2014, 2014, MNRAS, 440, 683; Manara C.F.,  et al., 2018. A&A 618, id.L3; Masson et al., 2016, A&A 587, id.A32; Masset F. & Snellgrove M., 2001 MNRAS 320, I.55 ;  Marchand et al., 2016, A&A 592, id.A18; Maury A. et al., 2019, A&A 621, Id.A76; Mikouchi et al., 2014. Earth. Pl. Sp. 66, id.82; Morbidelli A. & Crida A. 2007, Icarus 191, 158 ;  Morbidelli et al., 2015, Icarus 258, 418; Morbidelli et al., 2020, PNAS (under press) ; Murillo N.M., Lai S-P, Bruderer, et al.,, 2013. A&A 560, A103; Nakamoto T., et al. 1994. ApJ 421, 640-50; Nanne J., al.  2019. EPSL 511, 54-44; Ormel & Klahr 2010, A&A 520 id.A43;  Padoan P., et al. 2014. ApJ 797, id.32; Pignatale F., et al. 2018. ApJ 867, L23; Shu, F. H. 1977, ApJ, 214, 488; Tobin et al., 2020 ApJ 890 id. 130; Scott E.R.D. & Krot A.N. 2003, Treat. Geochem. V1, Elsevier, 143; Simon et al., 2017, ApJL 847 L12; Villeneuve et al.,2009, Science 325, 985;  Walsh et al., 2011 Nature 475 , 206; Walsh et al.  2001. Nature, 206; Warren 2011, EPSL 311, 1;  Weber B. et al., 2018, ApJ 854, 153;  Weidenschilling, S. J. 1977, MNRAS, 180, 57; Weiss B.J. et al., 2010, SSRev. 152, 341; Wurster J. & Bate 2016 M.R. MNRAS 457, 1037; Wurster J. & Bate 2019 M.R. MNRAS 486, 2587; Ulrich R.K., 1976. ApJ 210, 377-91; Yang& Ciesla 2012. M&PS 47, 99-119, Youdin & Goodman 2005, ApJ 620, 459