{'fraction_non_alphanumeric': 0.027003556364237864, 'fraction_numerical': 0.01281945248531966, 'mean_word_length': 4.8725109276347744, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
The formation of Jupiter by hybrid pebble-planetesimal accretion

The standard model for giant planet formation is based on the accretion of solids by a growing planetary embryo, followed by rapid gas accretion once the planet exceeds a so-called critical mass. The dominant size of the accreted solids (cm-size particles named pebbles or km to hundred km-size bodies named planetesimals) is, however, unknown. Recently, high-precision measurements of isotopes in meteorites provided evidence for the existence of two reservoirs in the early Solar System. These reservoirs remained separated from ~1 until ~ 3 Myr after the beginning of the Solar System's formation. This separation is interpreted as resulting from Jupiter growing and becoming a barrier for material transport. In this framework, Jupiter reached ~20 Earth masses within ~1 Myr and slowly grew to ~50 Earth masses in the subsequent 2 Myr before reaching its present-day mass. The evidence that Jupiter slowed down its growth after reaching 20 Earth masses for at least 2 Myr is puzzling because a planet of this mass is expected to trigger fast runaway gas accretion. Here, we use theoretical models to describe the conditions allowing for such a slow accretion and show that Jupiter grew in three distinct phases. First, rapid pebble accretion brought the major part of Jupiter's core mass. Second, slow planetesimal accretion provided the energy required to hinder runaway gas accretion during 2 Myr. Third, runaway gas accretion proceeded. Both pebbles and planetesimals therefore have an important role in Jupiter's formation.

High-precision measurements of isotopes (Mo, W and Pt) in meteorites have recently been used to temporally and spatially constrain the early Solar System, by combining two main cosmochemical observations (see Methods). First, cosmochemical data of the youngest inclusions (named chondrules) in primitive meteorites constrain their accretion age. Second, distinct nucleosynthetic isotope compositions (e.g. in Mo or W) that were imprinted in dust accreted by growing bodies allow to identify regions in the protoplanetary disk with distinct dust compositions. Based on these data, the existence of two main reservoirs of small bodies that existed in the early Solar System can be infered 6,7,8 . These reservoirs remained well-separated for a period of about ~2 Myr, likely because of the formation of Jupiter 3 . These cosmochemical evidence, which were never included in Jupiter's growth models, place severe constraints on planetary formation models.
We simulate Jupiter's growth by solid and gas accretion using state-of-the art planet formation models 9 to determine the time required for Jupiter to reach 50 M ⊕ , assuming Jupiter formed in situ. We consider different values for the mass of Jupiter at 1 Myr, and for the average accretion rate of solids after 1 Myr. As the opacity and the composition of Jupiter's envelope are not precisely known, we ran models using a large range of assumptions (low or large opacity, pure Hydrogen-Helium or envelope enriched in heavier elements). Model results show that the cosmochemical constraints are met, but only with a planet mass at 1 Myr between ~5 and 16 M ⊕ depending on the assumed conditions (Fig. 1). Therefore, the minimum mass of the forming Jupiter that is required to prevent the transport of pebbles (the so-called pebble isolation mass), is somehow smaller than the 20 M ⊕ quoted above. Note that the precise value of the pebble isolation mass and the mass that Jupiter should have attained at time ~3 Myr after the beginning of the Solar System are not directly derived from cosmochemical studies, but result from theoretical interpretation 3 .
Our models also show that a relatively high solid accretion rate (at least 10 -6 M ⊕ /yr) is required to prevent rapid gas accretion after 1 Myr. Indeed, slow gas accretion is only possible through a significant thermal support of the gas-dominated envelope that can counteract the strong gravity of the planetary core. We find that the dissipation of the kinetic energy from infalling solids thermally supports the envelope and inhibits high gas accretion rates. We checked that the ranges of values of pebble isolation mass and solid accretion rates are very robust and insensitive to the envelope composition and/or the opacity values, planet's location, and disk properties (see Supplementary figures 1 and 2 in Supplementary Information).
Since Jupiter reached the pebble isolation mass around ~1 Myr, maintaining a high solid accretion rate beyond this time must result from the accretion of planetesimals, which do not feel the isolating effect of the planet as pebble do (see Supplementary Information). During the first Myr the solid accretion rate needs to be as high as ~ 10 -5 M ⊕ /yr in order for Jupiter to reach a mass of ~5 to 16 M ⊕ in only one Myr. This accretion rate is too high to result from the accretion of planetesimals, and must result from the accretion of pebbles (see Supplementary Information). On the other hand, a rate of at least 10 -6 M ⊕ / yr in planetesimal accretion is required to stall gas runaway accretion and keep the planetary mass below 50 M ⊕ for the next 2 Myr. Hence, fulfilling the cosmochemical time constraints 3 in a Jupiter formation scenario is only possible ! 2 through a hybrid accretion process, where, first, pebbles provide high accretion rates and grow a large core (~5 to 16 M ⊕ ), and second, significant planetesimal accretion sets in afterwards. This planetesimal accretion, which occurs after 1 Myr, supplies the energy required for delaying rapid gas accretion, and only modestly contributes to the core's mass.
The derived accretion rate of planetesimals onto Jupiter represents a significant flux of infalling solids. Such high accretion rates cannot be sustained by large (hundreds of km in size) planetesimals given the excitation they experience from the gravitational interaction with a growing planetary embryo and the inability of gas drag to damp the eccentricity and inclination of such big objects 10,11 . Thus, our results suggest that a significant mass of small planetesimals (km in size) was present in the Solar Nebula at 1 Myr (see Fig. 2 and Supplementary Information) in apparent contradiction to recent studies suggesting the existence of large primordial planetesimals 12,13 . These smaller objects would, therefore, be second-generation planetesimals, resulting from the fragmentation of larger primordial objects 14 . Indeed, the presence of a planet of a few M ⊕ leads to collisions that are violent enough to disrupt primordial planetesimals 14 . Moreover, the collision timescale among large planetesimals is short enough to allow the formation of small ones by fragmentation in less than 1 Myr (see Supplementary  Information). In this way, the initial growth of Jupiter by pebble accretion during the first Myr provided the conditions to fragment large primordial planetesimals into small second-generation objects in a timely manner.
Our formation scenario also provides a solution to the problem of timing of pebble accretion. Indeed, pebble accretion is so efficient that objects become quickly more massive than Jupiter unless accretion starts shortly before the dispersal of the protoplanetary disk 15,16 . This timing is inconsistent with detailed models of pebble growth, which conclude that pebbles form and accrete early 17 . In the hybrid pebble-planetesimal scenario, the formation of Jupiter-mass planets is stretched over a few Myrs, comparable to the typical lifetimes of circumstellar disks 18 . In this case, it is possible that pebbles are accreted in the early phases of the protoplanetary disk evolution, without leading necessarily to the formation of massive planets.
We conclude that Jupiter formed in a 3-step process ( Fig. 3): (1) Jupiter's core grew by pebble accretion. The contribution of primordial large planetesimals to the solid accretion was negligible. As Jupiter's core became more massive, large primordial planetesimals dynamically heated up, collided and formed second generation smaller sized planetesimals. (2) Pebble accretion ceased (Jupiter reached the pebble isolation mass) and the protoplanet grew more slowly by accretion of small planetesimals. The solid accretion rate remained high enough to provide sufficient thermal support to the gas envelope and to prevent rapid gas accretion. (3) The critical mass for gas accretion was reached, gas rapidly accreted and Jupiter reached its present-day mass. During this last phase, further solids may have been accreted increasing the final heavy-element content in Jupiter 19 .
Our simulations show that the total heavy-element mass in Jupiter (core and envelope) prior to runaway gas accretion (accounting for both pebble and planetesimal accretion) ranges from 6 to 20 M ⊕ . This value can be compared with the Jupiter's heavy-element mass as derived from structure models, which ranges from 23.6 to 46.2 M ⊕ 20 . This comparison implies that Jupiter ! 3 accreted up to ~25 M ⊕ during runaway gas accretion or at a later stage 19 . Heavy elements that accreted late do not necessarily reach the core. They can dissolve in the envelope 21 , leading to envelope enrichment and the formation of heavy element gradients 22 .
In this new hybrid pebble-planetesimal scenario, the time a protoplanet spends in the mass range of 15-50 M ⊕ extends over a few Myr before rapid gas accretion takes place. Since the final mass of a planet is determined by the dissipation of the protoplanetary disk, our new formation scenario increases the likelihood of forming intermediate-mass planets, and this provides a natural explanation for the formation of Uranus and Neptune 1,23 .  masses per year, log scale). The yellow region delimits the part of the diagram where the core growth is too slow, whereas the black region delimits the part of the diagram where the runaway gas accretion occurs too early (either because the initial core mass is too large or because the heating by incoming planetesimals is too small

NATURE ASTR
rived accretion rate of planetesimals onto Jupiter reprebstantial flux of infalling solids. Such high accretion rates sustained by large (hundreds of kilometres in size) planeiven the excitation they experience from the gravitational n with a growing planetary embryo and the inability of gas mp the eccentricity and inclination of such big objects 10,11 . results suggest that a substantial mass of small planetesimetres in size) was present in the solar nebula at 1 Myr 2 and Supplementary Information), in apparent contrarecent studies suggesting the existence of large primortesimals 12,13 . These smaller objects would, therefore, be it is possible that pebbles are accreted in the early phas planetary disk evolution, without leading necessarily to tion of massive planets. We conclude that Jupiter formed in a three-step proc (1) Jupiter's core grew by pebble accretion. The contribu primordial planetesimals to the solid accretion was ne Jupiter's core became more massive, large primordia mals dynamically heated, collided and formed second smaller planetesimals. (2) Pebble accretion ceased (Jup the pebble isolation mass), and the protoplanet grew m by the accretion of small planetesimals. The solid ac  39 . Upper right: non-enriched envelope and opacity reduced by a factor of ten compared with the ISM value. Lower left: enrich acity. Lower right: enriched envelope and reduced opacity. The yellow region delimits where the core growth is too slow; the black ere the runaway gas accretion occurs too early (because either the initial core mass is too large or the heating by incoming planete ours between purple and orange indicate the region that is compatible with the growth timescale of Jupiter as obtained from cosmo ote that in all cases, the parameter space that is consistent with the cosmochemical constraints 3 is small.

Fig. 2. Accretion rate of planetesimals as a function of the solid mass fraction and the core mass at 1 Myr. The green region delimits the parameters that allow matching the cosmochemical constraints 3 , i.e., a core mass between 4 and ~16 M ⊕ and accretion rate of solids between 10 -6 M ⊕ /yr and 10 -5 M ⊕ /y). The white shaded area delimits the likely solid mass fraction according to the standard MMSN model for the lowest value 25 and the dust-to-planetesimal formation models for the highest value 26 . The left panel is for large planetesimals (100 km in size), whereas the right panel is for small planetesimals (1 km in size).
! 8 LE ASTRONOMY final mass of a planet is determined by the dissipati toplanetary disk, our formation scenario increases th forming intermediate-mass planets, which provides a nation for the formation of Uranus and Neptune 1,23 .

Methods
Meteoritic constraints. Kruijer et al. 3 constrained Jupiter's growth by combining two main cosmochemical observations. First, cosm data of the youngest inclusions (chondrules) in primitive meteori the maximum accretion age for small primitive bodies, while the 182 Hf to 182 W decay system dates metal-silicate separation and, as accretion timescales of small differentiated bodies and planets. Se nucleosynthetic isotope compositions (for example, of molybdenu that were imprinted in dust accreted by planetary bodies allow reg protoplanetary disk with originally distinct dust compositions to On the basis of this, cosmochemical data constrain two main rese bodies that existed in the early Solar System 6-8 . They remained we about 2-4 Myr (refs 3,24 ). The separation of these two reservoirs oc million years after the beginning of the Solar System, as defined b of the oldest Solar System materials (Ca-Al-rich inclusions). It wa that this separation was initiated by the growth of proto-Jupiter re isolation mass (20 M ⊕ ), thereby isolating the population of pebble outside its orbit. The two reservoirs remained separated until Jupi enough to scatter small bodies, reconnecting the reservoirs. This o Jupiter reached 50 M ⊕ , and not earlier than 3-4 Myr after Ca-Al-r formation 3 . While cosmochemical evidence constrains the timesc   Fig. 3 | The three stages of the hybrid pebble-planetesimal formation model. Stage 1 (up to 1 Myr): Jupiter (black) grows by pebble accretion (small circles), and planetesimal accretion is negligible. Large primordial planetesimals (large circles) are excited by the growing planet and suffer high collision velocities (large arrows), leading to destructive collisions (yellow), which produce small, second-generation planetesimals (medium circles). Stage 2 (1-3 Myr): Jupiter is massive enough to prevent pebble accretion. The energy associated with the accretion of small planetesimals is large enough to prevent rapid gas accretion (grey arrows). Stage 3 (after 3 Myr): Jupiter is massive enough to accrete large amounts of gas (hydrogen, helium). Nearby pebbles and small planetesimals can be gravitationally captured. Ultimately, a gap (white) is opened in the solar nebula, stopping further gas accretion. Red and blue indicate the two reservoirs of small bodies (inside and outside Jupiter's orbit, respectively), which are separated by Jupiter's growth in stage 2 and reconnected in stage 3. The Sun is shown on the left.

Meteoritic constraints
High-precision measurements of isotopes (Mo, W and Pt) in meteorites have been used by other authors to constrain Jupiter's growth history 3 by combining two main cosmochemical observations. First, cosmochemical data of the youngest inclusions (i.e. chondrules) in primitive meteorites constrain the maximum accretion age for small primitive bodies, while the short-lived 182 Hf-182 W decay system dates metal-silicate separation and as such the accretion timescales of small differentiated bodies and planets. Second, distinct nucleosynthetic isotope compositions (e.g. in Mo or W) that were imprinted in dust accreted by planetary bodies allow to identify regions in the protoplanetary disk with originally distinct dust compositions. Based on this, cosmochemical data constrain two main reservoirs of small bodies that existed in the early Solar System 4,5,6 . They remained well-separated for a period of about 2-4 Myr 3,27 . The separation of these two reservoirs occurred within the first Myr after the beginning of the Solar System as defined by the formation of the oldest Solar System materials (Calcium Aluminium rich Inclusions (CAIs)). It was proposed 3 that this separation was initiated by the growth of proto-Jupiter reaching pebble isolation mass (20 M ⊕ ), thereby isolating the population of pebbles inside and outside of its orbit. The two reservoirs remained separated until Jupiter grew massive enough to scatter small bodies, reconnecting the reservoirs. This occurred when Jupiter reached 50 M ⊕ , and not earlier than 3-4 Myr after CAI formation 3 . While cosmochemical evidence constrain the timescale of the separation of the reservoirs, it does not constrain the mass that Jupiter had at these epochs.

Modelling the planetary growth
We compute the planetary growth in the framework of the core accretion model, by solving the planetary internal structure equations 4,5,6 , assuming the luminosity results from the accretion of solids and gas contraction.
We consider two limiting cases regarding the fate of solids accreted by proto-Jupiter. In the first case, the so-called non-enriched case, all the accreted heavy elements are assumed to sink to the center (core). In this case the envelope is made of pure H and He. In the second case, the enriched case, we assume that the volatile fraction of the accreted solids is deposited in the envelope, whereas the refractory component reaches the core 20,28 . The volatile fraction is assumed to be 50 wt%, following recent condensation models 29 . The luminosity in this case is the one provided just by the refractory material, since the volatiles are assumed to remain mixed in the envelope and contribute to the luminosity generated by its contraction 20,28 . In all the models presented here, we treat the accretion rate of solids between 1 Myr and 3 Myr as a free parameter that varies from 10 -8 M ⊕ /yr to 10 -5 M ⊕ /yr.

! 10
The internal structure equations 4,5,6 are solved, using as boundary conditions the pressure and temperature in the protoplanetary disk at the position of the planetary embryo and defining the planetary radius as a combination of the Hill and Bondi radii 30 . The evolution of the planetary envelope depends on the used EOS and opacity. For the non-enriched case, we use the EOS of H and He 31 . For the enriched case, the envelope is assumed to be composed of H, He and water, and we take into account the mixture of the three components 28, 31,32 . For the opacity, we use either interstellar medium (ISM) opacity 21 , or a reduced opacity in which we multiply the ISM opacity by 1/10, in order to mimic the possible opacity reduction due to grain growth 33,34 . The calculations do not include the effect of destruction and replenishment of pebbles in Jupiter's envelope 35,36 , since the growth of Jupiter after 1 Myr is dominated by accretion of planetesimals for which the effect of destruction in the planetary envelope is less important 36 .

Disk structure
The disk model provides the pressure and temperature at the formation location of Jupiter, which serve as boundary conditions for the computation of the internal structure. This model is designed to fit 2-D radiative hydrodynamic simulations of protoplanetary disks 37 .

Planetesimal Accretion
In early planet formation models, it was assumed that the accreted solids were large planetesimals 4 (with sizes of hundreds of km), in agreement with several theoretical and observational constraints 9,10 . These planetesimal-based formation models still face the problem that the time required to reach rapid gas accretion is comparable to or even longer than the disk's lifetime 4,15 . This challenge is even more severe if dynamical heating (increased eccentricity and inclination) of the planetesimals by the gravity of a proto-Jupiter is considered 7,38 (see also Supplementary Information) since this hinders the core growth. Dynamical heating is counteracted by damping caused from gas drag and thus primarily affects small planetesimals. Hence, accreting solids of only a few km in size can relieve the timescale problem 7,8 . Numerical simulations, however, predict much larger typical sizes for primordial planetesimal, on the order of tens to hundreds of km 9 , with most of the mass stored in the largest bodies, in agreement with the constraints from the asteroid belt 10 . Therefore, km-sized planetesimals are likely generated by collisional fragmentation of large primordial planetesimals. This in turn requires high collision velocities, which results from the gravitational stirring of primordial planetesimals by objects with masses of a few M ⊕ 11 . Planetesimal accretion depends on three factors: the amount of planetesimals near the planet, the mass of the forming planet, and the degree of planetesimals excitation. In particular, the planetesimal accretion rate depends on the gravitational focussing factor Fgrav, itself depending inversely on the relative velocity vrel between planetesimals and the growing Jupiter. When planetesimals are dynamically excited (i.e, have large eccentricity and inclination), vrel increases and the planetesimals are accreted less efficiently. Planetesimals are excited by the forming planet and by planetesimal-planetesimal interactions, and also damped by gas drag.

! 11
Large planetesimals are more excited than small ones, because gas drag is less active on the formers. Therefore, the relative velocity between planetesimals and the growing Jupiter is larger for large planetesimals, leading to smaller accretion rates than for small planetesimals. We compute the accretion rate of planetesimals 11 , for planetesimals of 100 km or 1 km in size, as a function of the planet mass, and planetesimal-to-gas mass ratio. The properties of the gas disk that are required for this calculation (e.g. gas density) are taken form the disk model at a radial distance of 5.2 AU and an age of 1 Myr (when planetesimal accretion begins).

Fragmentation of large planetesimals
Two conditions are required in order to account for the formation of small planetesimals from the fragmentation of large ones before 1 Myr (when the accretion of pebbles stops). Collisions must be frequent enough (so that small planetesimals are produced rapidly enough), and violent enough (so that collisions lead to fragmentation). We estimate the collision timescale 39,40 between planetesimals of 100 km in size, as a function of the protoplanet's mass, and the solid surface density at 5 AU. The collision frequencies are calculated for a single sized population of planetesimals. The calculation includes the stirring of planetesimals by the growing Jupiter, but not the interaction between planetesimals, which is negligible for planets a few M ⊕ in mass 11 . Including this effect would increase the excitation of planetesimals, leading to even more violent collisions, and further fragmentation. We also include the gas drag that decreases the eccentricity and inclination of planetesimals, and therefore their collision velocity. In order to determine in which case the collisions lead to the destruction of planetesimals, we compared the specific energy of the collision with the one required for disruption Q * D. We chose for this value a very conservative estimate of 6. 10 9 erg/g, which corresponds to the highest value found for any set of compositional parameters 41 . As a result, for all collisions involving an energy larger than Q * D, planetesimals are expected to be destroyed and to fragment into much smaller objects. More details on the calculation of the fragmentation of large planetesimals is given in the Supplementary Information.

Data availability statement:
The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. ! 12