Rapid planetesimal formation in turbulent circumstellar disks

Prebiotic Vitamin B3 Synthesis in Carbonaceous Planetesimals

Aqueous chemistry within carbonaceous planetesimals is promising for synthesizing prebiotic organic matter essential to all life. Meteorites derived from these planetesimals delivered these life building blocks to the early Earth, potentially facilitating the origins of life. Here, we studied the formation of vitamin B3 as it is an important precursor of the coenzyme NAD(P)(H), which is essential for the metabolism of all life as we know it. We propose a new reaction mechanism based on known experiments in the literature that explains the synthesis of vitamin B3. It combines the sugar precursors glyceraldehyde or dihydroxyacetone with the amino acids aspartic acid or asparagine in aqueous solution without oxygen or other oxidizing agents. We performed thermochemical equilibrium calculations to test the thermodynamic favorability. The predicted vitamin B3 abundances resulting from this new pathway were compared with measured values in asteroids and meteorites. We conclude that competition for reactants and decomposition by hydrolysis are necessary to explain the prebiotic content of meteorites. In sum, our model fits well into the complex network of chemical pathways active in this environment.

TEMPus VoLA: The timed Epstein multi-pressure vessel at low accelerations

The field of planetary system formation relies extensively on our understanding of the aerodynamic interaction between gas and dust in protoplanetary disks. Of particular importance are the mechanisms triggering fluid instabilities and clumping of dust particles into aggregates, and their subsequent inclusion into planetesimals. We introduce the timed Epstein multi-pressure vessel at low accelerations, which is an experimental apparatus for the study of particle dynamics and rarefied gas under micro-gravity conditions. This facility contains three experiments dedicated to studying aerodynamic processes: (i) the development of pressure gradients due to collective particle-gas interaction, (ii) the drag coefficients of dust aggregates with variable particle-gas velocity, and (iii) the effect of dust on the profile of a shear flow and resultant onset of turbulence. The approach is innovative with respect to previous experiments because we access an untouched parameter space in terms of dust particle packing fraction, and Knudsen, Stokes, and Reynolds numbers. The mechanisms investigated are also relevant for our understanding of the emission of dust from active surfaces, such as cometary nuclei, and new experimental data will help interpreting previous datasets (Rosetta) and prepare future spacecraft observations (Comet Interceptor). We report on the performance of the experiments, which has been tested over the course of multiple flight campaigns. The project is now ready to benefit from additional flight campaigns, to cover a wide parameter space. The outcome will be a comprehensive framework to test models and numerical recipes for studying collective dust particle aerodynamics under space-like conditions.

Formation of Comets

Questions regarding how primordial or pristine the comets of the solar system are have been an ongoing controversy. In this review, we describe comets’ physical evolution from dust and ice grains in the solar nebula to the contemporary small bodies in the outer solar system. This includes the phases of dust agglomeration, the formation of planetesimals, their thermal evolution and the outcomes of collisional processes. We use empirical evidence about comets, in particular from the Rosetta Mission to comet 67P/Churyumov–Gerasimenko, to draw conclusions about the possible thermal and collisional evolution of comets.

Possible Ribose Synthesis in Carbonaceous Planetesimals

The origin of life might be sparked by the polymerization of the first RNA molecules in Darwinian ponds during wet-dry cycles. The key life-building block ribose was found in carbonaceous chondrites. Its exogenous delivery onto the Hadean Earth could be a crucial step toward the emergence of the RNA world. Here, we investigate the formation of ribose through a simplified version of the formose reaction inside carbonaceous chondrite parent bodies. Following up on our previous studies regarding nucleobases with the same coupled physico-chemical model, we calculate the abundance of ribose within planetesimals of different sizes and heating histories. We perform laboratory experiments using catalysts present in carbonaceous chondrites to infer the yield of ribose among all pentoses (5Cs) forming during the formose reaction. These laboratory yields are used to tune our theoretical model that can only predict the total abundance of 5Cs. We found that the calculated abundances of ribose were similar to the ones measured in carbonaceous chondrites. We discuss the possibilities of chemical decomposition and preservation of ribose and derived constraints on time and location in planetesimals. In conclusion, the aqueous formose reaction might produce most of the ribose in carbonaceous chondrites. Together with our previous studies on nucleobases, we found that life-building blocks of the RNA world could be synthesized inside parent bodies and later delivered onto the early Earth.

The CoPhyLab comet-simulation chamber

The Comet Physics Laboratory (CoPhyLab) is an international research program to study the physical properties of cometary analog materials under simulated space conditions. The project is dedicated to studying, with the help of multiple instruments and the different expertise and background from the different partners, the physics of comets, including the processes inside cometary nuclei, the activity leading to the ejection of dust and gas, and the sub-surface and surface evolution of cometary nuclei when exposed to solar illumination. CoPhyLab will provide essential information on the formation and evolution of comets and insights into the origins of primitive Solar System bodies. To this end, we constructed a new laboratory that hosts several small-scale experiments and a large-scale comet-simulation chamber (L-Chamber). This chamber has been designed and constructed to host ice-dust samples with a diameter of up to 250 mm and a variable height between 100 and 300 mm. The cometary-analog samples will be kept at temperatures below 120 K and pressures around 10^-6 mbar to ensure cometary-like conditions. In total, 14 different scientific instruments are attached to the L-Chamber to study the temporal evolution of the physical properties of the sample under different insolation conditions. Due to the implementation of a scale inside the L-Chamber that can measure weight changes of the samples with high precision, the cooling system is mechanically decoupled from the sample holder and cooling of the samples occurs by radiation only. The constructed chamber allows us to conduct uninterrupted experiments at low temperatures and pressures up to several weeks.

Bifurcation of planetary building blocks during Solar System formation

Geochemical and astronomical evidence demonstrates that planet formation occurred in two spatially and temporally separated reservoirs. The origin of this dichotomy is unknown. We use numerical models to investigate how the evolution of the solar protoplanetary disk influenced the timing of protoplanet formation and their internal evolution. Migration of the water snow line can generate two distinct bursts of planetesimal formation that sample different source regions. These reservoirs evolve in divergent geophysical modes and develop distinct volatile contents, consistent with constraints from accretion chronology, thermochemistry, and the mass divergence of inner and outer Solar System. Our simulations suggest that the compositional fractionation and isotopic dichotomy of the Solar System was initiated by the interplay between disk dynamics, heterogeneous accretion, and internal evolution of forming protoplanets.

The birth environment of planetary systems

Star and planet formation are inextricably linked. In the earliest phases of the collapse of a protostar, a disc forms around the young star and such discs are observed for the first several million years of a star's life. It is within these circumstellar, or protoplanetary, discs that the first stages of planet formation occur. Recent observations from the Atacama large millimetre array (ALMA) suggest that planet formation may already be underway after only 1 Myr of a star's life. However, stars do not form in isolation; they form from the collapse and fragmentation of giant molecular clouds several parsecs in size. This results in young stars forming in groups-often referred to as 'clusters'. In these star-forming regions, the stellar density is much higher than the location of the Sun and other stars in the Galactic disc that host exoplanets. As such, the environment where stars form has the potential to influence the planet formation process. In star-forming regions, protoplanetary discs can be truncated or destroyed by interactions with passing stars, as well as photoevaporation from the radiation fields of very massive stars. Once formed, the planets themselves can have their orbits altered by dynamical encounters-either directly from passing stars or through secondary effects such as the Kozai-Lidov mechanism. In this contribution, I review the different processes that can affect planet formation and stability in star-forming regions. I discuss each process in light of the typical range of stellar densities observed for star-forming regions. I finish by discussing these effects in the context of theories for the birth environment of the Solar System.

Accretion of a large LL parent planetesimal from a recently formed chondrule population

Chondritic meteorites, derived from asteroidal parent bodies and composed of millimeter-sized chondrules, record the early stages of planetary assembly. Yet, the initial planetesimal size distribution and the duration of delay, if any, between chondrule formation and chondrite parent body accretion remain disputed. We use Pb-phosphate thermochronology with planetesimal-scale thermal models to constrain the minimum size of the LL ordinary chondrite parent body and its initial allotment of heat-producing ²⁶Al. Bulk phosphate ²⁰⁷Pb/²⁰⁶Pb dates of LL chondrites record a total duration of cooling ≥75 Ma, with an isothermal interior that cools over ≥30 Ma. Since the duration of conductive cooling scales with parent body size, these data require a ≥150-km radius parent body and a range of bulk initial ²⁶Al/²⁷Al consistent with the initial ²⁶Al/²⁷Al ratios of constituent LL chondrules. The concordance suggests that rapid accretion of a large LL parent asteroid occurred shortly after a major chondrule-forming episode.

Color, composition, and thermal environment of Kuiper Belt object (486958) Arrokoth

The outer Solar System object (486958) Arrokoth (provisional designation 2014 MU₆₉) has been largely undisturbed since its formation. We studied its surface composition using data collected by the New Horizons spacecraft. Methanol ice is present along with organic material, which may have formed through irradiation of simple molecules. Water ice was not detected. This composition indicates hydrogenation of carbon monoxide-rich ice and/or energetic processing of methane condensed on water ice grains in the cold, outer edge of the early Solar System. There are only small regional variations in color and spectra across the surface, which suggests that Arrokoth formed from a homogeneous or well-mixed reservoir of solids. Microwave thermal emission from the winter night side is consistent with a mean brightness temperature of 29 ± 5 kelvin.

The solar nebula origin of (486958) Arrokoth, a primordial contact binary in the Kuiper Belt

The New Horizons spacecraft's encounter with the cold classical Kuiper Belt object (486958) Arrokoth (provisional designation 2014 MU₆₉) revealed a contact-binary planetesimal. We investigated how Arrokoth formed and found that it is the product of a gentle, low-speed merger in the early Solar System. Its two lenticular lobes suggest low-velocity accumulation of numerous smaller planetesimals within a gravitationally collapsing cloud of solid particles. The geometric alignment of the lobes indicates that they were a co-orbiting binary that experienced angular momentum loss and subsequent merger, possibly because of dynamical friction and collisions within the cloud or later gas drag. Arrokoth's contact-binary shape was preserved by the benign dynamical and collisional environment of the cold classical Kuiper Belt and therefore informs the accretion processes that operated in the early Solar System.

On the Origin and Evolution of the Material in 67P/Churyumov-Gerasimenko

Primitive objects like comets hold important information on the material that formed our solar system. Several comets have been visited by spacecraft and many more have been observed through Earth- and space-based telescopes. Still our understanding remains limited. Molecular abundances in comets have been shown to be similar to interstellar ices and thus indicate that common processes and conditions were involved in their formation. The samples returned by the Stardust mission to comet Wild 2 showed that the bulk refractory material was processed by high temperatures in the vicinity of the early sun. The recent Rosetta mission acquired a wealth of new data on the composition of comet 67P/Churyumov-Gerasimenko (hereafter 67P/C-G) and complemented earlier observations of other comets. The isotopic, elemental, and molecular abundances of the volatile, semi-volatile, and refractory phases brought many new insights into the origin and processing of the incorporated material. The emerging picture after Rosetta is that at least part of the volatile material was formed before the solar system and that cometary nuclei agglomerated over a wide range of heliocentric distances, different from where they are found today. Deviations from bulk solar system abundances indicate that the material was not fully homogenized at the location of comet formation, despite the radial mixing implied by the Stardust results. Post-formation evolution of the material might play an important role, which further complicates the picture. This paper discusses these major findings of the Rosetta mission with respect to the origin of the material and puts them in the context of what we know from other comets and solar system objects.

The magnetorotational instability prefers three dimensions

The magnetorotational instability (MRI) occurs when a weak magnetic field destabilizes a rotating, electrically conducting fluid with inwardly increasing angular velocity. The MRI is essential to astrophysical disc theory where the shear is typically Keplerian. Internal shear layers in stars may also be MRI-unstable, and they take a wide range of profiles, including near-critical. We show that the fastest growing modes of an ideal magnetofluid are three-dimensional provided the shear rate, S, is near the two-dimensional onset value, S _c . For a Keplerian shear, three-dimensional modes are unstable above S ≈ 0.10S _c , and dominate the two-dimensional modes until S ≈ 2.05S _c . These three-dimensional modes dominate for shear profiles relevant to stars and at magnetic Prandtl numbers relevant to liquid-metal laboratory experiments. Significant numbers of rapidly growing three-dimensional modes remainy well past 2.05S _c . These finding are significant in three ways. First, weakly nonlinear theory suggests that the MRI saturates by pushing the shear rate to its critical value. This can happen for systems, such as stars and laboratory experiments, that can rearrange their angular velocity profiles. Second, the non-normal character and large transient growth of MRI modes should be important whenever three-dimensionality exists. Finally, three-dimensional growth suggests direct dynamo action driven from the linear instability.

Discovery of fossil asteroidal ice in primitive meteorite Acfer 094

Carbonaceous chondrites are meteorites believed to preserve our planet's source materials, but the precise nature of these materials still remains uncertain. To uncover pristine planetary materials, we performed synchrotron radiation-based x-ray computed nanotomography of a primitive carbonaceous chondrite, Acfer 094, and found ultraporous lithology (UPL) widely distributed in a fine-grained matrix. UPLs are porous aggregates of amorphous and crystalline silicates, Fe─Ni sulfides, and organics. The porous texture must have been formed by removal of ice previously filling pore spaces, suggesting that UPLs represent fossils of primordial ice. The ice-bearing UPLs formed through sintering of fluffy icy dust aggregates around the H₂O snow line in the solar nebula and were incorporated into the Acfer 094 parent body, providing new insight into asteroid formation by dust agglomeration.

Mineralogy, Structure, and Habitability of Carbon-Enriched Rocky Exoplanets: A Laboratory Approach

Carbon-enriched rocky exoplanets have been proposed to occur around dwarf stars as well as binary stars, white dwarfs, and pulsars. However, the mineralogical make up of such planets is poorly constrained. We performed high-pressure high-temperature laboratory experiments (P = 1-2 GPa, T = 1523-1823 K) on chemical mixtures representative of C-enriched rocky exoplanets based on calculations of protoplanetary disk compositions. These P-T conditions correspond to the deep interiors of Pluto- to Mars-sized planets and the upper mantles of larger planets. Our results show that these exoplanets, when fully differentiated, comprise a metallic core, a silicate mantle, and a graphite layer on top of the silicate mantle. Graphite is the dominant carbon-bearing phase at the conditions of our experiments with no traces of silicon carbide or carbonates. The silicate mineralogy comprises olivine, orthopyroxene, clinopyroxene, and spinel, which is similar to the mineralogy of the mantles of carbon-poor planets such as the Earth and largely unaffected by the amount of carbon. Metals are either two immiscible iron-rich alloys (S-rich and S-poor) or a single iron-rich alloy in the Fe-C-S system with immiscibility depending on the S/Fe ratio and core pressure. We show that, for our C-enriched compositions, the minimum carbon abundance needed for C-saturation is 0.05-0.7 wt% (molar C/O ∼0.002-0.03). Fully differentiated rocky exoplanets with C/O ratios more than that needed for C-saturation would contain graphite as an additional layer on top of the silicate mantle. For a thick enough graphite layer, diamonds would form at the bottom of this layer due to high pressures. We model the interior structure of Kepler-37b and show that a mere 10 wt% graphite layer would decrease its derived mass by 7%, which suggests that future space missions that determine both radius and mass of rocky exoplanets with insignificant gaseous envelopes could provide quantitative limits on their carbon content. Future observations of rocky exoplanets with graphite-rich surfaces would show low albedos due to the low reflectance of graphite. The absence of life-bearing elements other than carbon on the surface likely makes them uninhabitable.

Understanding droplet collisions through a model flow: Insights from a Burgers vortex

We investigate the role of intense vortical structures, similar to those in a turbulent flow, in enhancing collisions (and coalescences) which lead to the formation of large aggregates in particle-laden flows. By using a Burgers vortex model, we show, in particular, that vortex stretching significantly enhances sharp inhomogeneities in spatial particle densities, related to the rapid ejection of particles from intense vortices. Furthermore our work shows how such spatial clustering leads to an enhancement of collision rates and extreme statistics of collisional velocities. We also study the role of polydisperse suspensions in this enhancement. Our work uncovers an important principle, which, if valid for realistic turbulent flows, may be a factor in how small nuclei water droplets in warm clouds can aggregate to sizes large enough to trigger rain.

Heavy Metal Rules. I. Exoplanet Incidence and Metallicity

The discovery of only a handful of exoplanets required establishing a correlation between giant planet occurrence and metallicity of their host stars. More than 20 years have already passed from that discovery, however, many questions are still under lively debate: (1) What is the origin of that relation?; (2) What is the exact functional form of the giant planet–metallicity relation (in the metal-poor regime)?; and (3) Does such a relation exist for terrestrial planets? All of these questions are very important for our understanding of the formation and evolution of (exo)planets of different types around different types of stars and are the subject of the present manuscript. Besides making a comprehensive literature review about the role of metallicity on the formation of exoplanets, I also revisited most of the planet–metallicity related correlations reported in the literature using a large and homogeneous data provided by the SWEET-Cat catalog. This study led to several new results and conclusions, two of which I believe deserve to be highlighted in the abstract: (i) the hosts of sub-Jupiter mass planets (∼0.6–0.9 M♃) are systematically less metallic than the hosts of Jupiter-mass planets. This result might be related to the longer disk lifetime and the higher amount of planet building materials available at high metallicities, which allow a formation of more massive Jupiter-like planets; (ii) contrary to the previous claims, our data and results do not support the existence of a breakpoint planetary mass at 4 M♃ above and below which planet formation channels are different. However, the results also suggest that planets of the same (high) mass can be formed through different channels depending on the (disk) stellar mass i.e., environmental conditions.

Dynamics of nonspherical, fractal-like water-ice particles in a plasma environment

Plasmas containing small solid-state particles (also known as dust particles) are ubiquitous in nature and laboratories. Existing models typically assume that the dust particles are spherical but several observations and simulations indicate that a significant amount of dust particles are nonspherical. Because dust particles are not spherical they show different dynamics from spherical particles in a plasma environment namely, they align in the direction perpendicular to the force equilibrium line, rotate about their alignment axis due to the interaction between the dipole moment and the surrounding electric field, and show vortex motion while maintaining their alignment and rotation when they are exposed to a nonconservative drag force.

Free Cooling of a Granular Gas of Rodlike Particles in Microgravity

Granular gases as dilute ensembles of particles in random motion are at the basis of elementary structure-forming processes in the Universe, involved in many industrial and natural phenomena, and also excellent models to study fundamental statistical dynamics. The essential difference to molecular gases is the energy dissipation in particle collisions. Its most striking manifestation is the so-called granular cooling, the gradual loss of mechanical energy E(t) in the absence of external excitation. We report an experimental study of homogeneous cooling of three-dimensional granular gases in microgravity. The asymptotic scaling E(t)∝t^{-2} obtained by Haff's minimal model [J. Fluid Mech. 134, 401 (1983)JFLSA70022-112010.1017/S0022112083003419] proves to be robust, despite the violation of several of its central assumptions. The shape anisotropy of the grains influences the characteristic time of energy loss quantitatively but not qualitatively. We compare kinetic energies in the individual degrees of freedom and find a slight predominance of translational motions. In addition, we observe a preferred rod alignment in the flight direction, as known from active matter or animal flocks.

Identification of a primordial asteroid family constrains the original planetesimal population

A quarter of known asteroids is associated with more than 100 distinct asteroid families, meaning that these asteroids originate as impact fragments from the family parent bodies. The determination of which asteroids of the remaining population are members of undiscovered families, or accreted as planetesimals from the protoplanetary disk, would constrain a critical phase of planetary formation by unveiling the unknown planetesimal size distribution. We discovered a 4-billion-year-old asteroid family extending across the entire inner part of the main belt whose members include most of the dark asteroids previously unlinked to families. This allows us to identify some original planetesimals, which are all larger than 35 kilometers, supporting the view of asteroids being born big. Their number matches the known distinct meteorite parent bodies.

Giant ripples on comet 67P/Churyumov-Gerasimenko sculpted by sunset thermal wind

Explaining the unexpected presence of dune-like patterns at the surface of the comet 67P/Churyumov-Gerasimenko requires conceptual and quantitative advances in the understanding of surface and outgassing processes. We show here that vapor flow emitted by the comet around its perihelion spreads laterally in a surface layer, due to the strong pressure difference between zones illuminated by sunlight and those in shadow. For such thermal winds to be dense enough to transport grains-10 times greater than previous estimates-outgassing must take place through a surface porous granular layer, and that layer must be composed of grains whose roughness lowers cohesion consistently with contact mechanics. The linear stability analysis of the problem, entirely tested against laboratory experiments, quantitatively predicts the emergence of bedforms in the observed wavelength range and their propagation at the scale of a comet revolution. Although generated by a rarefied atmosphere, they are paradoxically analogous to ripples emerging on granular beds submitted to viscous shear flows. This quantitative agreement shows that our understanding of the coupling between hydrodynamics and sediment transport is able to account for bedform emergence in extreme conditions and provides a reliable tool to predict the erosion and accretion processes controlling the evolution of small solar system bodies.

Collision velocity of dust grains in self-gravitating protoplanetary discs

We have conducted the first comprehensive numerical investigation of the relative velocity distribution of dust particles in self-gravitating protoplanetary discs with a view to assessing the viability of planetesimal formation via direct collapse in such environments. The viability depends crucially on the large sizes that are preferentially collected in pressure maxima produced by transient spiral features (Stokes numbers, St ∼ 1); growth to these size scales requires that collision velocities remain low enough that grain growth is not reversed by fragmentation. We show that, for a single-sized dust population, velocity driving by the disc's gravitational perturbations is only effective for St > 3, while coupling to the gas velocity dominates otherwise. We develop a criterion for understanding this result in terms of the stopping distance being of the order of the disc scaleheight. Nevertheless, the relative velocities induced by differential radial drift in multi-sized dust populations are too high to allow the growth of silicate dust particles beyond St ∼ 10^{- 2} or 10^-1 (10 cm to m sizes at 30 au), such Stokes numbers being insufficient to allow concentration of solids in spiral features. However, for icy solids (which may survive collisions up to several 10 m s^-1), growth to St ∼ 1 (10 m size) may be possible beyond 30 au from the star. Such objects would be concentrated in spiral features and could potentially produce larger icy planetesimals/comets by gravitational collapse. These planetesimals would acquire moderate eccentricities and remain unmodified over the remaining lifetime of the disc.

Abrupt growth of large aggregates by correlated coalescences in turbulent flow

Smoluchowski's coagulation kinetics is here shown to fail when the coalescing species are dilute and transported by a turbulent flow. The intermittent Lagrangian motion involves correlated violent events that lead to an unexpected rapid occurrence of the largest particles. This new phenomena is here quantified in terms of the anomalous scaling of turbulent three-point motion, leading to significant corrections in macroscopic processes that are critically sensitive to the early-stage emergence of large embryonic aggregates, as in planet formation or rain precipitation.

Linking the Origin of Asteroids to Planetesimal Formation in the Solar Nebula

The asteroids (more precisely: objects of the main asteroid belt) and Kuiper Belt objects (more precisely: objects of the cold classical Kuiper Belt) are leftovers of the building material for our earth and all other planets in our solar system from more than 4.5 billion years ago. At the time of their formation those were typically 100 km large objects. They were called planetesimals, built up from icy and dusty grains. In our current paradigm of planet formation it was turbulent flows and metastable flow patterns, like zonal flows and vortices, that concentrated mm to cm sized icy dust grains in sufficient numbers that a streaming instability followed by a gravitational collapse of these particle clump was triggered. The entire picture is sometimes referred to as gravoturbulent formation of planetesimals. What was missing until recently, was a physically motivated prediction on the typical sizes at which planetesimals should form via this process. Our numerical simulations in the past had only shown a correlation between numerical resolution and planetesimal size and thus no answer was possible (Johansen et al.2011). But with the lastest series of simulations on JUQUEEN (Stephan & Doctor 2015), covering all the length scales down to the physical size of actual planetesimals, we were able to obtain values for the turbulent particle diffusion as a function of the particle load in the gas. Thus, we have all necessary data at hand to feed a 'back of the envelope' calculation that predicts the size of planetesimals as result of a competition between gravitational concentration and turbulent diffusion. Using the diffusion values obtained in the numerical simulations it predicts planetesimal sizes on the order of 100 km, which suprisingly coincides with the measured data from both asteroids (Bottke et al.2005) as well from Kuiper Belt objects (Nesvorny et al.2011).

Accretion timescales and style of asteroidal differentiation in an 26Al-poor protoplanetary disk

The decay of radioactive ²⁶Al to ²⁶Mg (half-life of 730,000 years) is postulated to have been the main energy source promoting asteroidal melting and differentiation in the nascent solar system. High-resolution chronological information provided by the ²⁶Al-²⁶Mg decay system is, therefore, intrinsically linked to the thermal evolution of early-formed planetesimals. In this paper, we explore the timing and style of asteroidal differentiation by combining high-precision Mg isotope measurements of meteorites with thermal evolution models for planetesimals. In detail, we report Mg isotope data for a suite of olivine-rich [Al/Mg ~ 0] achondritic meteorites, as well as a few chondrites. Main Group, pyroxene and the Zinder pallasites as well as the lodranite all record deficits in the mass-independent component of μ²⁶Mg (μ²⁶Mg*) relative to chondrites and Earth. This isotope signal is expected for the retarded ingrowth of radiogenic ²⁶Mg* in olivine-rich residues produced through partial silicate melting during ²⁶Al decay and consistent with their marginally heavy Mg isotope composition relative to ordinary chondrites, which may reflect the early extraction of isotopically light partial melts from the source rock. We propose that their parent planetesimals started forming within ~250,000 years of solar system formation from a hot (>~500 K) inner protoplanetary disk region characterized by a reduced initial (²⁶Al/²⁷Al)₀ abundance (~1-2 × 10^-5) relative to the (²⁶Al/²⁷Al)₀ value in CAIs of 5.25 × 10^-5. This effectively reduced the total heat production and allowed for the preservation of solid residues produced through progressive silicate melting with depth within the planetesimals. These 'non-carbonaceous' planetesimals acquired their mass throughout an extended period (>3 Myr) of continuous accretion, thereby generating onion-shell structures of incompletely differentiated zones, consisting of olivine-rich residues, overlaid by metachondrites and undifferentiated chondritic crusts. In contrast, individual olivine crystals from Eagle Station pallasites record variable μ²⁶Mg* excesses, suggesting that these crystals captured the ²⁶Mg* evolution of a magmatic reservoir controlled by fractional crystallization processes during the lifespan of ²⁶Al. Similar to previous suggestions based on isotopic evidence, we suggest that Eagle Station pallasites formed from precursor material similar in composition to carbonaceous chondrites from a cool outer protoplanetary disk region characterized by (²⁶Al/²⁷Al)₀ ≥ 2.7 × 10^-5. Protracted planetesimal accretion timescales at large orbital distances, with onset of accretion 0.3-1 Myr post-CAIs, may have resulted in significant radiative heat loss and thus efficient early interior cooling of slowly accreting 'carbonaceous' planetesimals.

Tungsten isotopic constraints on the age and origin of chondrules

Chondrules may have played a critical role in the earliest stages of planet formation by mediating the accumulation of dust into planetesimals. However, the origin of chondrules and their significance for planetesimal accretion remain enigmatic. Here, we show that chondrules and matrix in the carbonaceous chondrite Allende have complementary (183)W anomalies resulting from the uneven distribution of presolar, stellar-derived dust. These data refute an origin of chondrules in protoplanetary collisions and, instead, indicate that chondrules and matrix formed together from a common reservoir of solar nebula dust. Because bulk Allende exhibits no (183)W anomaly, chondrules and matrix must have accreted rapidly to their parent body, implying that the majority of chondrules from a given chondrite group formed in a narrow time interval. Based on Hf-W chronometry on Allende chondrules and matrix, this event occurred ∼2 million years after formation of the first solids, about coeval to chondrule formation in ordinary chondrites.

Continuous Growth of Droplet Size Variance due to Condensation in Turbulent Clouds

We use a stochastic model and direct numerical simulation to study the impact of turbulence on cloud droplet growth by condensation. We show that the variance of the droplet size distribution increases in time as t^{1/2}, with growth rate proportional to the large-to-small turbulent scale separation and to the turbulence integral scales but independent of the mean turbulent dissipation. Direct numerical simulations confirm this result and produce realistically broad droplet size spectra over time intervals of 20 min, comparable with the time of rain formation.

Growing the terrestrial planets from the gradual accumulation of submeter-sized objects

Building the terrestrial planets has been a challenge for planet formation models. In particular, classical theories have been unable to reproduce the small mass of Mars and instead predict that a planet near 1.5 astronomical units (AU) should roughly be the same mass as Earth. Recently, a new model called Viscously Stirred Pebble Accretion (VSPA) has been developed that can explain the formation of the gas giants. This model envisions that the cores of the giant planets formed from 100- to 1,000-km bodies that directly accreted a population of pebbles-submeter-sized objects that slowly grew in the protoplanetary disk. Here we apply this model to the terrestrial planet region and find that it can reproduce the basic structure of the inner solar system, including a small Mars and a low-mass asteroid belt. Our models show that for an initial population of planetesimals with sizes similar to those of the main belt asteroids, VSPA becomes inefficient beyond ∼ 1.5 AU. As a result, Mars's growth is stunted, and nothing large in the asteroid belt can accumulate.

Growing the gas-giant planets by the gradual accumulation of pebbles

It is widely held that the first step in forming gas-giant planets, such as Jupiter and Saturn, was the production of solid 'cores' each with a mass roughly ten times that of the Earth. Getting the cores to form before the solar nebula dissipates (in about one to ten million years; ref. 3) has been a major challenge for planet formation models. Recently models have emerged in which 'pebbles' (centimetre-to-metre-sized objects) are first concentrated by aerodynamic drag and then gravitationally collapse to form objects 100 to 1,000 kilometres in size. These 'planetesimals' can then efficiently accrete left-over pebbles and directly form the cores of giant planets. This model is known as 'pebble accretion'; theoretically, it can produce cores of ten Earth masses in only a few thousand years. Unfortunately, full simulations of this process show that, rather than creating a few such cores, it produces a population of hundreds of Earth-mass objects that are inconsistent with the structure of the Solar System. Here we report that this difficulty can be overcome if pebbles form slowly enough to allow the planetesimals to gravitationally interact with one another. In this situation, the largest planetesimals have time to scatter their smaller siblings out of the disk of pebbles, thereby stifling their growth. Our models show that, for a large and physically reasonable region of parameter space, this typically leads to the formation of one to four gas giants between 5 and 15 astronomical units from the Sun, in agreement with the observed structure of the Solar System.

Mechanisms for the clustering of inertial particles in the inertial range of isotropic turbulence

In this paper, we consider the physical mechanism for the clustering of inertial particles in the inertial range of isotropic turbulence. We analyze the exact, but unclosed, equation governing the radial distribution function (RDF) and compare the mechanisms it describes for clustering in the dissipation and inertial ranges. We demonstrate that in the limit Str≪1, where Str is the Stokes number based on the eddy turnover time scale at separation r, the clustering in the inertial range can be understood to be due to the preferential sampling of the coarse-grained fluid velocity gradient tensor at that scale. When Str≳O(1) this mechanism gives way to a nonlocal clustering mechanism. These findings reveal that the clustering mechanisms in the inertial range are analogous to the mechanisms that we identified for the dissipation regime [see New J. Phys. 16, 055013 (2014)]. Further, we discuss the similarities and differences between the clustering mechanisms we identify in the inertial range and the "sweep-stick" mechanism developed by Coleman and Vassilicos [Phys. Fluids 21, 113301 (2009)]. We show that the idea that initial particles are swept along with acceleration stagnation points is only approximately true because there always exists a finite difference between the velocity of the acceleration stagnation points and the local fluid velocity. This relative velocity is sufficient to allow particles to traverse the average distance between the stagnation points within the correlation time scale of the acceleration field. We also show that the stick part of the mechanism is only valid for Str≪1 in the inertial range. We emphasize that our clustering mechanism provides the more fundamental explanation since it, unlike the sweep-stick mechanism, is able to explain clustering in arbitrary spatially correlated velocity fields. We then consider the closed, model equation for the RDF given in Zaichik and Alipchenkov [Phys. Fluids 19, 113308 (2007)] and use this, together with the results from our analysis, to predict the analytic form of the RDF in the inertial range for Str1, which, unlike that in the dissipation range, is not scale invariant. The results are in good agreement with direct numerical simulations, provided the separations are well within the inertial range.

Early accretion of protoplanets inferred from a reduced inner solar system 26Al inventory

The mechanisms and timescales of accretion of 10-1000 km sized planetesimals, the building blocks of planets, are not yet well understood. With planetesimal melting predominantly driven by the decay of the short-lived radionuclide ²⁶Al (²⁶Al→²⁶Mg; t_1/2 = 0.73 Ma), its initial abundance determines the permissible timeframe of planetesimal-scale melting and its subsequent cooling history. Currently, precise knowledge about the initial ²⁶Al abundance [(²⁶Al/²⁷Al)₀] exists only for the oldest known solids, calcium aluminum-rich inclusions (CAIs) - the so-called canonical value. We have determined the ²⁶Al/²⁷Al of three angrite meteorites, D'Orbigny, Sahara 99555 and NWA 1670, at their time of crystallization, which corresponds to (3.98 ± 0.15)×10^-7, (3.64 ± 0.18)×10^-7, and (5.92 ± 0.59)×10^-7, respectively. Combined with a newly determined absolute U-corrected Pb-Pb age for NWA 1670 of 4564.39 ± 0.24 Ma and published U-corrected Pb-Pb ages for the other two angrites, this allows us to calculate an initial (²⁶Al/²⁷Al)₀ of [Formula: see text] for the angrite parent body (APB) precursor material at the time of CAI formation, a value four times lower than the accepted canonical value of 5.25 × 10^-5. Based on their similar ⁵⁴Cr/⁵²Cr ratios, most inner solar system materials likely accreted from material containing a similar ²⁶Al/²⁷Al ratio as the APB precursor at the time of CAI formation. To satisfy the abundant evidence for widespread planetesimal differentiation, the subcanonical ²⁶Al budget requires that differentiated planetesimals, and hence protoplanets, accreted rapidly within 0.25 ± 0.15 Ma of the formation of canonical CAIs.

Jupiter's decisive role in the inner Solar System's early evolution

The statistics of extrasolar planetary systems indicate that the default mode of planet formation generates planets with orbital periods shorter than 100 days and masses substantially exceeding that of the Earth. When viewed in this context, the Solar System is unusual. Here, we present simulations which show that a popular formation scenario for Jupiter and Saturn, in which Jupiter migrates inward from a > 5 astronomical units (AU) to a ≈ 1.5 AU before reversing direction, can explain the low overall mass of the Solar System's terrestrial planets, as well as the absence of planets with a < 0.4 AU. Jupiter's inward migration entrained s ≳ 10-100 km planetesimals into low-order mean motion resonances, shepherding and exciting their orbits. The resulting collisional cascade generated a planetesimal disk that, evolving under gas drag, would have driven any preexisting short-period planets into the Sun. In this scenario, the Solar System's terrestrial planets formed from gas-starved mass-depleted debris that remained after the primary period of dynamical evolution.

Growth of asteroids, planetary embryos, and Kuiper belt objects by chondrule accretion

Chondrules are millimeter-sized spherules that dominate primitive meteorites (chondrites) originating from the asteroid belt. The incorporation of chondrules into asteroidal bodies must be an important step in planet formation, but the mechanism is not understood. We show that the main growth of asteroids can result from gas drag-assisted accretion of chondrules. The largest planetesimals of a population with a characteristic radius of 100 km undergo runaway accretion of chondrules within ~3 My, forming planetary embryos up to Mars's size along with smaller asteroids whose size distribution matches that of main belt asteroids. The aerodynamical accretion leads to size sorting of chondrules consistent with chondrites. Accretion of millimeter-sized chondrules and ice particles drives the growth of planetesimals beyond the ice line as well, but the growth time increases above the disc lifetime outside of 25 AU. The contribution of direct planetesimal accretion to the growth of both asteroids and Kuiper belt objects is minor. In contrast, planetesimal accretion and chondrule accretion play more equal roles in the formation of Moon-sized embryos in the terrestrial planet formation region. These embryos are isolated from each other and accrete planetesimals only at a low rate. However, the continued accretion of chondrules destabilizes the oligarchic configuration and leads to the formation of Mars-sized embryos and terrestrial planets by a combination of direct chondrule accretion and giant impacts.

Origin of the imbalance between energy cascade and dissipation in turbulence

It is shown in direct numerical simulations of homogeneous isotropic non-stationary turbulence that there is a systematic and significant imbalance between the non-linear energy cascade to fine scales and its dissipation. This imbalance stems from the power required to induce or annihilate fine-scale motions in order to change the level of dissipation. The imbalance is present regardless of transfer time-lags and is applicable to a wide range of Reynolds numbers.

Clustering, fronts, and heat transfer in turbulent suspensions of heavy particles

Heavy inertial particles transported by a turbulent flow are shown to concentrate in the regions where an advected passive scalar, such as temperature, displays very strong frontlike discontinuities. This novel effect is responsible for extremely high levels of fluctuations for the passive field sampled by the particles that impacts the heat fluxes exchanged between the particles and the surrounding fluid. Instantaneous and averaged heat fluxes are shown to follow strongly intermittent statistics and anomalous scaling laws.

Planetary system formation in thermally evolving viscous protoplanetary discs

Observations of extrasolar planets are providing new opportunities for furthering our understanding of planetary formation processes. In this paper, we review planet formation and migration scenarios and describe some recent simulations that combine planetary accretion and gas-disc-driven migration. While the simulations are successful at forming populations of low- and intermediate-mass planets with short orbital periods, similar to those that are being observed by ground- and space-based surveys, our models fail to form any gas giant planets that survive migration into the central star. The simulation results are contrasted with observations, and areas of future model development are discussed.