30. Formation of planetary systems by pebble accretion and migration: How the radial pebble flux determines a terrestrial-planet or super-Earth growth mode.

M. Lambrechts, A. Morbidelli, S. A. Jacobson, A. Johansen, B. Bitsch, A. Izidoro & S. Raymond

Astronomy & Astrophysics 1-15 (2019)

Giant planets migrate though the protoplanetary disc as they grow their solid core and attract their gaseous envelope. Previously, we have studied the growth and migration of an isolated planet in an evolving disc. Here, we generalise such models to include the mutual gravitational interaction between a high number of growing planetary bodies. We have investigated how the formation of planetary systems depends on the radial flux of pebbles through the protoplanetary disc and on the planet migration rate. Our N-body simulations confirm previous findings that Jupiter-like planets in orbits outside the water ice line originate from embryos starting out at 20-40 AU when using nominal type-I and type-II migration rates and a pebble flux of approximately 100-200 Earth masses per million years, enough to grow Jupiter within the lifetime of the solar nebula. The planetary embryos placed up to 30 AU migrate into the inner system (rP < 1AU). There they form super-Earths or hot and warm gas giants, producing systems that are inconsistent with the configuration of the solar system, but consistent with some exoplanetary systems. We also explored slower migration rates which allow the formation of gas giants from embryos originating from the 5-10 AU region, which are stranded exterior to 1 AU at the end of the gas-disc phase. These giant planets can also form in discs with lower pebbles fluxes (50-100 Earth masses per Myr). We identify a pebble flux threshold below which migration dominates and moves the planetary core to the inner disc, where the pebble isolation mass is too low for the planet to accrete gas efficiently. In our model, giant planet growth requires a sufficiently high pebble flux to enable growth to out-compete migration. An even higher pebble flux produces systems with multiple gas giants. We show that planetary embryos starting interior to 5 AU do not grow into gas giants, even if migration is slow and the pebble flux is large. These embryos instead grow to just a few Earth masses, the mass regime of super-Earths. This stunted growth is caused by the low pebble isolation mass in the inner disc and is therefore independent of the pebble flux. Additionally, we show that the long-term evolution of our formed planetary systems can naturally produce systems with inner super-Earths and outer gas giants as well as systems of giant planets on very eccentric orbits.

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29. Formation of planetary systems by pebble accretion and migration: growth of gas giants.

B. Bitsch, A. Izidoro, A. Johansen, S. Raymond, A. Morbidelli, M. Lambrechts & S. A. Jacobson

Astronomy & Astrophysics 623, A88, 1-25 (2019)

Giant planets migrate though the protoplanetary disc as they grow their solid core and attract their gaseous envelope. Previously, we have studied the growth and migration of an isolated planet in an evolving disc. Here, we generalise such models to include the mutual gravitational interaction between a high number of growing planetary bodies. We have investigated how the formation of planetary systems depends on the radial flux of pebbles through the protoplanetary disc and on the planet migration rate. Our N-body simulations confirm previous findings that Jupiter-like planets in orbits outside the water ice line originate from embryos starting out at 20-40 AU when using nominal type-I and type-II migration rates and a pebble flux of approximately 100-200 Earth masses per million years, enough to grow Jupiter within the lifetime of the solar nebula. The planetary embryos placed up to 30 AU migrate into the inner system (rP < 1AU). There they form super-Earths or hot and warm gas giants, producing systems that are inconsistent with the configuration of the solar system, but consistent with some exoplanetary systems. We also explored slower migration rates which allow the formation of gas giants from embryos originating from the 5-10 AU region, which are stranded exterior to 1 AU at the end of the gas-disc phase. These giant planets can also form in discs with lower pebbles fluxes (50-100 Earth masses per Myr). We identify a pebble flux threshold below which migration dominates and moves the planetary core to the inner disc, where the pebble isolation mass is too low for the planet to accrete gas efficiently. In our model, giant planet growth requires a sufficiently high pebble flux to enable growth to out-compete migration. An even higher pebble flux produces systems with multiple gas giants. We show that planetary embryos starting interior to 5 AU do not grow into gas giants, even if migration is slow and the pebble flux is large. These embryos instead grow to just a few Earth masses, the mass regime of super-Earths. This stunted growth is caused by the low pebble isolation mass in the inner disc and is therefore independent of the pebble flux. Additionally, we show that the long-term evolution of our formed planetary systems can naturally produce systems with inner super-Earths and outer gas giants as well as systems of giant planets on very eccentric orbits.

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28. The timeline of the lunar bombardment---revisited.

D. P. O'Brien, A. Izidoro, S. A. Jacobson, S. N. Raymond & D. C. Rubie

Icarus 305, 262-276 (2018)

The timeline of the lunar bombardment in the first Gy of Solar System history remains unclear. Basin-forming impacts (e.g. Imbrium, Orientale), occurred 3.9-3.7 Gy ago, i.e. 600-800 My after the formation of the Moon itself. Many other basins formed before Imbrium, but their exact ages are not precisely known. There is an intense debate between two possible interpretations of the data: in the cataclysm scenario there was a surge in the impact rate approximately at the time of Imbrium formation, while in the accretion tail scenario the lunar bombardment declined since the era of planet formation and the latest basins formed in its tail-end. Here, we revisit the work of Morbidelli et al. (2012) that examined which scenario could be compatible with both the lunar crater record in the 3-4 Gy period and the abundance of highly siderophile elements (HSE) in the lunar mantle. We use updated numerical simulations of the fluxes of asteroids, comets and planetesimals leftover from the planet-formation process. Under the traditional assumption that the HSEs track the total amount of material accreted by the Moon since its formation, we conclude that only the cataclysm scenario can explain the data. The cataclysm should have started ∼ 3.95 Gy ago. However we also consider the possibility that HSEs are sequestered from the mantle of a planet during magma ocean crystallization, due to iron sulfide exsolution (O'Neil, 1991; Rubie et al., 2016). We show that this is likely true also for the Moon, if mantle overturn is taken into account. Based on the hypothesis that the lunar magma ocean crystallized about 100-150 My after Moon formation (Elkins-Tanton et al., 2011), and therefore that HSEs accumulated in the lunar mantle only after this timespan, we show that the bombardment in the 3-4 Gy period can be explained in the accretion tail scenario. This hypothesis would also explain why the Moon appears so depleted in HSEs relative to the Earth. We also extend our analysis of the cataclysm and accretion tail scenarios to the case of Mars. The accretion tail scenario requires a global resurfacing event on Mars ∼ 4.4 Gy ago, possibly associated with the formation of the Borealis basin, and it is consistent with the HSE budget of the planet. Moreover it implies that the Noachian and pre-Noachian terrains are ∼ 200 My older than usually considered.

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27. The delivery of water during terrestrial planet formation.

D. P. O'Brien, A. Izidoro, S. A. Jacobson, S. N. Raymond & D. C. Rubie

Space Science Reviews 214:1, 47, 1-24 (2018)

The planetary building blocks that formed in the terrestrial planet region were likely very dry, yet water is comparatively abundant on Earth. Here we review the various mechanisms proposed for the origin of water on the terrestrial planets. Various in-situ mechanisms have been suggested, which allow for the incorporation of water into the local planetesimals in the terrestrial planet region or into the planets themselves from local sources, although all of those mechanisms have difficulties. Comets have also been proposed as a source, although there may be problems fitting isotopic constraints, and the delivery efficiency is very low, such that it may be difficult to deliver even a single Earth ocean of water this way. The most promising route for water delivery is the accretion of material from beyond the snow line, similar to carbonaceous chondrites, that is scattered into the terrestrial planet region as the planets are growing. Two main scenarios are discussed in detail. First is the classical scenario in which the giant planets begin roughly in their final locations and the disk of planetesimals and embryos in the terrestrial planet region extends all the way into the outer asteroid belt region. Second is the Grand Tack scenario, where early inward and outward migration of the giant planets implants material from beyond the snow line into the asteroid belt and terrestrial planet region, where it can be accreted by the growing planets. Sufficient water is delivered to the terrestrial planets in both scenarios. While the Grand Tack scenario provides a better fit to most constraints, namely the small mass of Mars, planets may form too fast in the nominal case discussed here. This discrepancy may be reduced as a wider range of initial conditions is explored. Finally, we discuss several more recent models that may have important implications for water delivery to the terrestrial planets.

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26. Formation, stratification, and mixing of the cores of Earth and Venus.

S. A. Jacobson, D. C. Rubie, J. Hernlund, A. Morbidelli & M. Nakajima

Earth and Planetary Science Letters 474, 375-386 (2017)

Earth possesses a persistent, internally-generated magnetic field, whereas no trace of a dynamo has been detected on Venus, at present or in the past, although a high surface temperature and recent resurfacing events may have removed paleomagnetic evidence. Whether or not a terrestrial body can sustain an internally generated magnetic field by convection inside its metallic fluid core is determined in part by its initial thermodynamic state and its compositional structure, both of which are in turn set by the processes of accretion and differentiation. Here we show that the cores of Earth- and Venus-like planets should grow with stable compositional stratification unless disturbed by late energetic impacts. They do so because higher abundances of light elements are incorporated into the liquid metal that sinks to form the core as the temperatures and pressures of metal-silicate equilibration increase during accretion. We model this process and determine that this establishes a stable stratification that resists convection and inhibits the onset of a geodynamo. However, if a late energetic impact occurs, it could mechanically stir the core creating a single homogenous region within which a long-lasting geodynamo would operate. While Earth's accretion has been punctuated by a late giant impact with likely enough energy to mix the core (e.g. the impact that formed the Moon), we hypothesize that the accretion of Venus is characterized by the absence of such energetic giant impacts and the preservation of its primordial stratifications.

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25. A Martian origin for the Mars Trojan asteroids.

D. Polishook, S. A. Jacobson, A. Morbidelli & O. Aharonson

Nature Astronomy 1, 179, 1-5 (2017)

Seven of the nine known Mars Trojan asteroids belong to an orbital cluster named after its largest member, (5261) Eureka. Eureka is probably the progenitor of the whole cluster, which formed at least 1 Gyr ago. It has been suggested that the thermal YORP (Yarkovsky-O'Keefe-Radzievskii-Paddack) effect spun up Eureka, resulting in fragments being ejected by the rotational-fission mechanism. Eureka's spectrum exhibits a broad and deep absorption band around 1 μm, indicating an olivine-rich composition. Here we show evidence that the Trojan Eureka cluster progenitor could have originated as impact debris excavated from the Martian mantle. We present new near-infrared observations of two Trojans ((311999) 2007 NS₂ and (385250) 2001 DH₄₇) and find that both exhibit an olivine-rich reflectance spectrum similar to Eureka's. These measurements confirm that the progenitor of the cluster has an achondritic composition. Olivine-rich reflectance spectra are rare amongst asteroids but are seen around the largest basins on Mars. They are also consistent with some Martian meteorites (for example, Chassigny) and with the material comprising much of the Martian mantle. Using numerical simulations, we show that the Mars Trojans are more likely to be impact ejecta from Mars than captured olivine-rich asteroids transported from the main belt. This result directly links specific asteroids to debris from the forming planets.

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24. Highly siderophile elements were stripped from Earth’s mantle by iron sulfide segregation.

D. C. Rubie, V. Laurenz, S. A. Jacobson, A. Morbidelli, H. Palme, A. K. Vogel & D. J. Frost

Science 353, 6304, 1141-1144 (2016)

Highly siderophile elements (HSEs) are strongly depleted in the bulk silicate Earth (BSE) but are present in near-chondritic relative abundances. The conventional explanation is that the HSEs were stripped from the mantle by the segregation of metal during core formation but were added back in near-chondritic proportions by late accretion, after core formation had ceased. Here we show that metal-silicate equilibration and segregation during Earth's core formation actually increased HSE mantle concentrations because HSE partition coefficients are relatively low at the high pressures of core formation within Earth. The pervasive exsolution and segregation of iron sulfide liquid from silicate liquid (the "Hadean matte") stripped magma oceans of HSEs during cooling and crystallization, before late accretion, and resulted in slightly suprachondritic palladium/iridium and ruthenium/iridium ratios.

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23. Impact-induced melting during accretion of the Earth.

J. de Vries, F. Nimmo, H. J. Melosh, S. A. Jacobson, A. Morbidelli & D. C. Rubie

Progress in Earth and Planetary Science 3, 7, 1-11 (2016)

Because of the high energies involved, giant impacts that occur during planetary accretion cause large degrees of melting. The depth of melting in the target body after each collision determines the pressure and temperature conditions of metal-silicate equilibration and thus geochemical fractionation that results from core-mantle differentiation. The accretional collisions involved in forming the terrestrial planets of the inner Solar System have been calculated by previous studies using N-body accretion simulations. Here we use the output from such simulations to determine the volumes of melt produced and thus the pressure and temperature conditions of metal-silicate equilibration, after each impact, as Earth-like planets accrete. For these calculations a parameterised melting model is used that takes impact velocity, impact angle and the respective masses of the impacting bodies into account. The evolution of metal-silicate equilibration pressures (as defined by evolving magma ocean depths) during Earth’s accretion depends strongly on the lifetime of impact-generated magma oceans compared to the time interval between large impacts. In addition, such results depend on starting parameters in the N-body simulations, such as the number and initial mass of embryos. Thus, there is the potential for combining the results, such as those presented here, with multistage core formation models to better constrain the accretional history of the Earth.

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22. Matching asteroid population characteristics with a model constructed from the YORP-induced rotational fission hypothesis.

S. A. Jacobson, F. Marzari, A. Rossi & D. J. Scheeres

Icarus 277, 381-394 (2016)

From the results of a comprehensive asteroid population evolution model, we conclude that the YORP-induced rotational fission hypothesis can be consistent with the observed population statistics of small asteroids in the main belt including binaries and contact binaries. The foundation of this model is the asteroid rotation model of Marzari et al. (2011), which incorporates both the YORP effect and collisional evolution. This work adds to that model the rotational fission hypothesis and the binary evolution model of Jacobson & Scheeres (2011). The asteroid population evolution model is highly constrained by these and other previous works, and therefore it has only two significant free parameters: the ratio of low to high mass ratio binaries formed after rotational fission events and the mean strength of the binary YORP (BYORP) effect. We successfully reproduce characteristic statistics of the small asteroid population: the binary fraction, the fast binary fraction, steady-state mass ratio fraction and the contact binary fraction. We find that in order for the model to best match observations, rotational fission produces high mass ratio (> 0.2) binary components with four to eight times the frequency as low mass ratio (< 0.2) components, where the mass ratio is the mass of the secondary component divided by the mass of the primary component. This is consistent with post-rotational fission binary system mass ratio being drawn from either a flat or a positive and shallow distribution, since the high mass ratio bin is four times the size of the low mass ratio bin; this is in contrast to the observed steady-state binary mass ratio, which has a negative and steep distribution. This can be understood in the context of the BYORP-tidal equilibrium hypothesis, which predicts that low mass ratio binaries survive for a significantly longer period of time than high mass ratio systems.

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21. Did Jupiter's core form in the innermost parts of the Sun's protoplanetary disk?

S. N. Raymond, A. Izidoro, B. Bitsch & S. A. Jacobson

Monthly Notices of the Royal Astronomical Society 458:3, 2962-2972 (2016)

Jupiter's core is generally assumed to have formed beyond the snow line. Here we consider an alternative scenario, that Jupiter's core may have accumulated in the innermost parts of the protoplanetary disk. A growing body of research suggests that small particles ("pebbles") continually drift inward through the disk. If a fraction of drifting pebbles is trapped at the inner edge of the disk a several Earth-mass core can quickly grow. Subsequently, the core may migrate outward beyond the snow line via planet–disk interactions. Of course, to reach the outer Solar System Jupiter's core must traverse the terrestrial planet–forming region. We use N-body simulations including synthetic forces from an underlying gaseous disk to study how the outward migration of Jupiter's core sculpts the terrestrial zone. If the outward migration is fast (T_mig~10^4 years), the core simply migrates past resident planetesimals and planetary embryos. However, if its migration is slower (T_mig~10^5 years) the core removes solids from the inner disk by shepherding objects in mean motion resonances. In many cases the disk interior to 0.5-1 AU is cleared of embryos and most planetesimals. By generating a mass deficit close to the Sun, the outward migration of Jupiter's core may thus explain the absence of terrestrial planets closer than Mercury. Jupiter's migrating core often stimulates the growth of another large (~Earth-mass) core--that may provide a seed for Saturn's core--trapped in exterior resonance. The migrating core also may transport a fraction of terrestrial planetesimals, such as the putative parent bodies of iron meteorites, to the asteroid belt.

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20. Mechanisms and geochemical models of core formation.

D. C. Rubie & S. A. Jacobson

Deep Earth: Physics and Chemistry of the Lower Mantle and Core (Eds. H. Terasaki & R. Fischer) AGU/John Wiley & Sons, Inc., Geophysical Monograph Series 217, 181-190 (2016)

The formation of the Earth's core is a consequence of planetary accretion and processes in the Earth's interior. The mechanical process of planetary differentiation is likely to occur in large, if not global, magma oceans created by the collisions of planetary embryos. Metal-silicate segregation in magma oceans occurs rapidly and efficiently unlike grain scale percolation according to laboratory experiments and calculations. Geochemical models of the core formation process as planetary accretion proceeds are becoming increasingly realistic. Single stage and continuous core formation models have evolved into multi-stage models that are couple to the output of dynamical models of the giant impact phase of planet formation. The models that are most successful in matching the chemical composition of the Earth's mantle, based on experimentally-derived element partition coefficients, show that the temperature and pressure of metal-silicate equilibration must increase as a function of time and mass accreted and so must the oxygen fugacity of the equilibrating material. The latter can occur if silicon partitions into the core and through the late delivery of oxidized material. Coupled dynamical accretion and multi-stage core formation models predict the evolving mantle and core compositions of all the terrestrial planets simultaneously and also place strong constraints on the bulk compositions and oxidation states of primitive bodies in the protoplanetary disk.

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19. Fossilized condensation lines in the solar system protoplanetary disk.

A. Morbidelli, B. Bitsch, A. Crida, M. Gounelle, T. Guillot, S. A. Jacobson, A. Johansen, M. Lambrechts & E. Lega

Icarus 267, 368-376 (2016)

The terrestrial planets and the asteroids dominant in the inner asteroid belt are water poor. However, in the protoplanetary disk the temperature should have decreased below water-condensation level well before the disk was photo-evaporated. Thus, the global water depletion of the inner Solar System is puzling. We show that, even if the inner disk becomes cold, there cannot be direct condensation of water. This is because the snowline moves towards the Sun more slowly than the gas itself. Thus the gas in the vicinity of the snowline always comes from farther out, where it should have already condensed, and therefore it should be dry. The appearance of ice in a range of heliocentric distances swept by the snowline can only be due to the radial drift of icy particles from the outer disk. However, if a planet with a mass larger than 20 Earth mass is present, the radial drift of particles is interrupted, because such a planet gives the disk a super-Keplerian rotation just outside of its own orbit. From this result, we propose that the precursor of Jupiter achieved this threshold mass when the snowline was still around 3 AU. This effectively fossilized the snowline at that location. In fact, even if it cooled later, the disk inside of Jupiter’s orbit remained ice-depleted because the flow of icy particles from the outer system was intercepted by the planet. This scenario predicts that planetary systems without giant planets should be much more rich in water in their inner regions than our system. We also show that the inner edge of the planetesimal disk at 0.7 AU, required in terrestrial planet formation models to explain the small mass of Mercury and the absence of planets inside of its orbit, could be due to the silicate condensation line, fossilized at the end of the phase of streaming instability that generated the planetesimal seeds. Thus, when the disk cooled, silicate particles started to drift inwards of 0.7 AU without being sublimated, but they could not be accreted by any pre-existing planetesimals.

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18. Oxygen isotopic evidence for vigorous mixing during the Moon-forming giant impact.

E. D. Young, I. E. Kohl, P. H. Warren, D. C. Rubie, S. A. Jacobson & A. Morbidelli

Science 351:6272, 493-496 (2016)

Earth and Moon are shown here to be composed of oxygen isotope reservoirs that are indistinguishable, with a difference in Δ'¹⁷O of −1 +/− 5ppm (2se), in contrast to some recent measurements. Based on these data and new planet formation simulations that include a realistic model for oxygen isotopic reservoirs, our results favor vigorous mixing during the giant impact. The results indicate that the late veneer impactors had an average Δ'¹⁷O within approximately 1‰ of the terrestrial value, ruling out some proposed sources.

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17. Multiple origins of asteroid pairs.

S. A. Jacobson

Proceedings of the International Astronomical Union 318, 55-65 (2016)

Rotationally fissioned asteroids produce unbound daughter asteroids that have very similar heliocentric orbits. Backward integration of their current heliocentric orbits provides an age of closest proximity that can be used to date the rotational fission event. Most asteroid pairs follow a predicted theoretical relationship between the primary spin period and the mass ratio of the two pair members that is a direct consequence of the YORP-induced rotational fission hypothesis. If the progenitor asteroid has strength, asteroid pairs may have high mass ratios with possibly fast rotating primaries. However, secondary fission leaves the originally predicted trend unaltered. We also describe the characteristics of pair members produced by four alternative routes from a rotational fission event to an asteroid pair. Unlike direct formation from the event itself, the age of closest proximity of these pairs cannot generally be used to date the rotational fission event since considerable time may have passed.

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16. The formation of striae within cometary dust tails by a sublimation-driven YORP-like effect.

J. K. Steckloff & S. A. Jacobson

Icarus 246, 160-171 (2016)

Sublimating gas molecules scatter off of the surface of an icy body in the same manner as photons (Lambertian Scattering). This means that for every photon-driven body force, there should be a sublimation-driven analogue that affects icy bodies. Thermal photons emitted from the surfaces of asymmetrically shaped bodies in the Solar System generate net torques that change the spin rates of these bodies over time. The long-term averaging of this torque is called the YORP effect. Here we propose a sublimation-driven analogue to the YORP effect (Sublimation-YORP or SYORP), in which sublimating gas molecules emitted from the surfaces of icy bodies in the Solar System also generate net torques on the bodies. However, sublimating gas molecules carry ~10⁴-10⁵ times more momentum away from the body than thermal photons, resulting in much greater body torques. Previous studies of sublimative torques focused on emissions from highly localized sources on the surfaces of Jupiter Family Comet nuclei, and have therefore required extensive empirical observations to predict the resulting behavior of the body. By contrast, SYORP applies to non-localized emissions across the entire body, which likely dominates sublimation-drive torques on small icy chunks and Dynamically Young Comets outside the Jupiter Family, and can therefore be applied without high-resolution spacecraft observations of their surfaces. Instead, we repurpose the well-tested mathematical machinery of the YORP effect to account for sublimation-driven torques. We show how an SYORP-driven mechanism best matches observations of the rarely observed, Sun-oriented linear features (striae) in the tails of comets, whose formation mechanism has remained enigmatic for decades. The SYORP effect naturally explains why striae tend to be observed between near-perihelion and ~1 AU from the Sun for comets with perihelia less than 0.6 AU, and solves longstanding problems with moving enough material into the cometary tail to form visible striae. We show that the SYORP mechanism can form striae that match the striae of Comet West, estimate the sizes of the stria-forming chunks, and produce a power-law fit to these parent chunks with a power law index of -1.4_-0.6^+0.3. Lastly, we predict potential observables of this SYORP mechanism, which may appear as clouds or material that appear immediately prior to stria formation, or as a faint, wispy dust feature within the dust tail, between the nucleus and the striae.

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15. Asteroid systems: binaries, triples, and pairs.

J.-L. Margot, P. Pravec, P. A. Taylor, B. Carry & S. A. Jacobson

Asteroids IV (Eds. P. Michel, F. E. DeMeo & W. F. Bottke) University of Arizona Press, Space Science Series, 355-374 (2015)

In the past decade, the number of known binary near-Earth asteroids has more than quadrupled and the number of known large main belt asteroids with satellites has doubled. Half a dozen triple asteroids have been discovered, and the previously unrecognized populations of asteroid pairs and small main belt binaries have been identified. The current observational evidence confirms that small (<20 km) binaries form by rotational fission and establishes that the YORP effect powers the spin-up process. A unifying paradigm based on rotational fission and post-fission dynamics can explain the formation of small binaries, triples, and pairs. Large (>20 km) binaries with small satellites are most likely created during large collisions.

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14. Formation and evolution of binary asteroids.

K. J. Walsh & S. A. Jacobson

Asteroids IV (Eds. P. Michel, F. E. DeMeo & W. F. Bottke) University of Arizona Press, Space Science Series, 375-393 (2015)

Satellites of asteroids have been discovered in nearly every known small body population, and a remarkable aspect of the known satellites is the diversity of their properties. They tell a story of vast differences in formation and evolution mechanisms that act as a function of size, distance from the Sun, and the properties of their nebular environment at the beginning of Solar System history and their dynamical environment over the next 4.5 Gyr. The mere existence of these systems provides a laboratory to study numerous types of physical processes acting on asteroids and their dynamics provide a valuable probe of their physical properties otherwise possible only with spacecraft. Advances in understanding the formation and evolution of binary systems have been assisted by: 1) the growing catalog of known systems, increasing from 33 to nearly 250 between the Merline et al. (2002) Asteroids III chapter and now, 2) the detailed study and long-term monitoring of individual systems such as 1999 KW4 and 1996 FG3, 3) the discovery of new binary system morphologies and triple systems, 4) and the discovery of unbound systems that appear to be end-states of binary dynamical evolutionary paths. Specifically for small bodies (diameter smaller than 10 km), these observations and discoveries have motivated theoretical work finding that thermal forces can efficiently drive the rotational disruption of small asteroids. Long-term monitoring has allowed studies to constrain the system's dynamical evolution by the combination of tides, thermal forces and rigid body physics. The outliers and split pairs have pushed the theoretical work to explore a wide range of evolutionary end-states.

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13. The great dichotomy of the Solar System: small terrestrial embryos and massive giant planet cores.

A. Morbidelli, M. Lambrechts, S. A. Jacobson & B. Bitsch

Icarus 258, 418-429 (2015)

The basic structure of the Solar System is set by the presence of low-mass terrestrial planets in its inner part and giant planets in its outer part. This is the result of the formation of a system of multiple embryos with approximately the mass of Mars in the inner disk and of a few multi-Earth-mass cores in the outer disk, within the lifetime of the gaseous component of the protoplanetary disk. What was the origin of this dichotomy in the mass distribution of embryos/cores? We show in this paper that the classic processes of runaway and oligarchic growth from a disk of planetesimals cannot explain this dichotomy, even if the original surface density of solids increased at the snowline. Instead, the accretion of drifting pebbles by embryos and cores can explain the dichotomy, provided that some assumptions hold true. We propose that the mass-flow of pebbles is two-times lower and the characteristic size of the pebbles is approximately ten times smaller within the snowline than beyond the snowline (respectively at heliocentric distance r < r_ice and r >r_ice , where r_ice is the snowline heliocentric distance), due to ice sublimation and the splitting of icy pebbles into a collection of chondrule-size silicate grains. In this case, objects of original sub-lunar mass would grow at drastically different rates in the two regions of the disk. Within the snowline these bodies would reach approximately the mass of Mars while beyond the snowline they would grow to ∼20 Earth masses. The results may change quantitatively with changes to the assumed parameters, but the establishment of a clear dichotomy in the mass distribution of protoplanets appears robust provided that there is enough turbulence in the disk to prevent the sedimentation of the silicate grains into a very thin layer.

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12. Earth and terrestrial planet formation.

S. A. Jacobson & K. J. Walsh

The early Earth: accretion and differentiation (Eds. J. Badro & M. J. Walter) AGU/John Wiley & Sons, Inc., Geophysical Monograph Series 212, 49-70 (2015)

The growth and composition of Earth is a direct consequence of planet formation throughout the Solar System. We discuss the known history of the Solar System, the proposed stages of growth and how the early stages of planet formation may be dominated by pebble growth processes. Pebbles are small bodies whose strong interactions with the nebula gas lead to remarkable new accretion mechanisms for the formation of planetesimals and the growth of planetary embryos. Many of the popular models for the later stages of planet formation are presented. The classical models with the giant planets on fixed orbits are not consistent with the known history of the Solar System, fail to create a high Earth/Mars mass ratio, and, in many cases, are also internally inconsistent. The successful Grand Tack model creates a small Mars, a wet Earth, a realistic asteroid belt and the mass-orbit structure of the terrestrial planets. In the Grand Tack scenario, growth curves for Earth most closely match a Weibull model. The feeding zones, which determine the compositions of Earth and Venus follow a particular pattern determined by Jupiter, while the feeding zones of Mars and Theia, the last giant impactor on Earth, appear to randomly sample the terrestrial disk. The late accreted mass samples the disk nearly evenly.

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11. Accretion and differentiation of the terrestrial planets with implications for the compositions of early-formed Solar System bodies and accretion of water.

D. C. Rubie, S. A. Jacobson, A. Morbidelli, D. P. O'Brien, E. D. Young, J. de Vries, F. Nimmo, H. Palme & D. J. Frost

Icarus 248, 89-108 (2015)

In order to test accretion simulations as well as planetary differentiation scenarios, we have integrated a multistage core-mantle differentiation model with N-body accretion simulations. Impacts between embryos and planetesimals are considered to result in magma ocean formation and episodes of core formation. The core formation model combines rigorous chemical mass balance with metal-silicate element partitioning data and requires that the bulk compositions of all starting embryos and planetesimals are defined as a function of their heliocentric distances of origin. To do this, we assume that non-volatile elements are present in Solar System (CI) relative abundances in all bodies and that oxygen and H2O contents are the main compositional variables. The primary constraint on the combined model is the composition of the Earth's primitive mantle. In addition, we aim to reproduce the composition of the martian mantle and the mass fractions of the metallic cores of Earth and Mars. The model is refined by least squares minimization with up to five fitting parameters that consist of the metal-silicate equilibration pressure and 1-4 parameters that define the starting compositions of primitive bodies. This integrated model has been applied to six Grand Tack N-body accretion simulations. Investigations of a broad parameter space indicate that: (1) accretion of Earth was heterogeneous, (2) metal-silicate equilibration pressures increase as accretion progresses and are, on average, 60-70% of core-mantle boundary pressures at the time of each impact, and (3) a large fraction (70-100%) of the metal of impactor cores equilibrates with a small fraction of the silicate mantles of proto-planets during each core formation event. Results are highly sensitive to the compositional model for the primitive starting bodies and several accretion/core-formation models can thus be excluded. Acceptable fits to the Earth's mantle composition are obtained only when bodies that originated close to the Sun, at <0.9-1.2 AU, are highly reduced and those from beyond this distance are increasingly oxidized. Reasonable concentrations of H2O in Earth's mantle are obtained when bodies originating from beyond 6-7 AU contain 20 wt% water ice (icy bodies that originated between the snow line and this distance did not contribute to Earth's accretion because they were swept up by Jupiter and Saturn). In the six models examined, water is added to the Earth mainly after 60-80% of its final mass has accreted. The compositional evolution of the mantles of Venus and Mars are also constrained by the model. The FeO content of the martian mantle depends critically on the heliocentric distance at which the Mars-forming embryo originated. Finally, the Earth's core is predicted to contain 8-9 wt% silicon, 2-4 wt% oxygen and 10-60 ppm hydrogen, whereas the martian core is predicted to contain low concentrations (<1 wt%) of Si and O.

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10. The binary near-Earth asteroid 175706 (1996 FG₃)--an observational constraint on its orbital evolution.

P. Scheirich, P. Pravec, S. A. Jacobson, J. Ďurech, P. Kušnirák, K. Hornoch, S. Mottola, M. Mommert, S. Hellmich, D. Pray, D. Polishook, Yu. N. Krugly, R. Ya. Inasaridze, O. I. Kvaratskhelia, V. Ayvazian, I. Slyusarev, J. Pittichová, E. Jehin, J. Manfroid, M. Gillon, A. Galád, J. Pollock, J. Licandro, V. Alí-Lagoa, J. Brinsfeld & I. E. Molotov

Icarus 245, 56-63 (2015)

Using our photometric observations taken between April 1996 and January 2013 and other published data, we derived properties of the binary near-Earth Asteroid (175706) 1996 FG3 including new measurements constraining evolution of the mutual orbit with potential consequences for the entire binary asteroid population. We also refined previously determined values of parameters of both components, making 1996 FG3 one of the most well understood binary asteroid systems. With our 17-year long dataset, we determined the orbital vector with a substantially greater accuracy than before and we also placed constraints on a stability of the orbit. Specifically, the ecliptic longitude and latitude of the orbital pole are 266° and -83°, respectively, with the mean radius of the uncertainty area of 4°, and the orbital period is 16.1508 ± 0.0002 h (all quoted uncertainties correspond to 3σ). We looked for a quadratic drift of the mean anomaly of the satellite and obtained a value of 0.04 ± 0.20°/yr² , i.e., consistent with zero. The drift is substantially lower than predicted by the pure binary YORP (BYORP) theory of McMahon and Scheeres (McMahon, J., Scheeres, D. [2010]. Icarus 209, 494-509) and it is consistent with the tigidity and quality factor of μQ = 1.3 × 10⁷ Pa using the theory that assumes an elastic response of the asteroid material to the tidal forces. This very low value indicates that the primary of 1996 FG3 is a 'rubble pile', and it also calls for a re-thinking of the tidal energy dissipation in close asteroid binary systems.

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9. Post-main-sequence debris from rotation-induced YORP break-up of small bodies.

D. Veras, S. A. Jacobson & B. T. Gänsicke

Monthly Notices of the Royal Astronomical Society 445:3, 2794-2799 (2014)

Although discs of dust and gas have been observed orbiting white dwarfs, the origin of this circumstellar matter is uncertain. We hypothesize that the in situ break-up of small bodies such as asteroids spun to fission during the giant branch phases of stellar evolution provides an important contribution to this debris. The YORP (Yarkovsky-O'Keefe-Radviesvki-Paddock) effect, which arises from radiation pressure, accelerates the spin rate of asymmetric asteroids, which can eventually shear themselves apart. This pressure is maintained and enhanced around dying stars because the outward push of an asteroid due to stellar mass loss is insignificant compared to the resulting stellar luminosity increase. Consequently, giant star radiation will destroy nearly all bodies with radii in the range 100 m-10 km that survive their parent star's main-sequence lifetime within a distance of about 7 au; smaller bodies are spun apart to their strongest, competent components. This estimate is conservative and would increase for highly asymmetric shapes or incorporation of the inward drag due to giant star stellar wind. The resulting debris field, which could extend to thousands of au, may be perturbed by remnant planetary systems to reproduce the observed dusty and gaseous discs which accompany polluted white dwarfs.

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8. Lunar and terrestrial planet formation in the Grand Tack scenario.

S. A. Jacobson & A. Morbidelli

Philosophical Transactions of the Royal Society A 372:2024, 0174, 1-26 (2014)

We present conclusions from a large number of N-body simulations of the giant impact phase of terrestrial planet formation. We focus on new results obtained from the recently proposed Grand Tack model, which couples the gas-driven migration of giant planets to the accretion of the terrestrial planets. The giant impact phase follows the oligarchic growth phase, which builds a bi-modal mass distribution within the disc of embryos and planetesimals. By varying the ratio of the total mass in the embryo population to the total mass in the planetesimal population and the mass of the individual embryos, we explore how different disc conditions control the final planets. The total mass ratio of embryos to planetesimals controls the timing of the last giant (Moon forming) impact and its violence. The initial embryo mass sets the size of the lunar impactor and the growth rate of Mars. After comparing our simulated outcomes with the actual orbits of the terrestrial planets (angular momentum deficit, mass concentration) and taking into account independent geochemical constraints on the mass accreted by the Earth after the Moon forming event and on the timescale for the growth of Mars, we conclude that the protoplanetary disc at the beginning of the giant impact phase must have had most of its mass in Mars-sized embryos and only a small fraction of the total disc mass in the planetesimal population. From this, we infer that the Moon forming event occurred between ~60 and ~130 My after the formation of the first solids, and was caused most likely by an object with a mass similar to that of Mars.

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7. Small asteroid system evolution.

S. A. Jacobson

Proceedings of the International Astronomical Union 9:S310, 108-117 (2014)

Recently, the discovery of small unbound asteroid systems called asteroid pairs have revolutionized the study of small asteroid systems. Observations with radar, photometric and direct imaging techniques have discovered that multiple asteroid systems can be divided clearly into a handful of different morphologies. Simultaneously, new theoretical advances have demonstrated that solar radiation dictates the evolution of small asteroids with strong implications for asteroid internal structure. We review our current understanding of how small asteroid systems evolve and point to the future.

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6. Highly siderophile elements in Earth's mantle as a clock for the Moon-forming impact.

S. A. Jacobson, A. Morbidelli, S. N. Raymond, D. P. O'Brien, K. J. Walsh & D. C. Rubie

Nature 508:7494, 84-87 (2014)

According to the generally accepted scenario, the last giant impact on Earth formed the Moon and initiated the final phase of core formation by melting Earth's mantle. A key goal of geochemistry is to date this event, but different ages have been proposed. Some argue for an early Moon-forming event, approximately 30 million years (Myr) after the condensation of the first solids in the Solar System, whereas others claim a date later than 50 Myr (and possibly as late as around 100 Myr) after condensation. Here we show that a Moon-forming event at 40 Myr after condensation, or earlier, is ruled out at a 99.9 per cent confidence level. We use a large number of N-body simulations to demonstrate a relationship between the time of the last giant impact on an Earth-like planet and the amount of mass subsequently added during the era known as Late Accretion. As the last giant impact is delayed, the late-accreted mass decreases in a predictable fashion. This relationship exists within both the classical scenario and the Grand Tack scenario of terrestrial planet formation, and holds across a wide range of disk conditions. The concentration of highly siderophile elements (HSEs) in Earth's mantle constrains the mass of chondritic material added to Earth during Late Accretion. Using HSE abundance measurements, we determine a Moon-formation age of 95 +/- 32 Myr after condensation. The possibility exists that some late projectiles were differentiated and left an incomplete HSE record in Earth's mantle. Even in this case, various isotopic constraints strongly suggest that the late-accreted mass did not exceed 1 per cent of Earth's mass, and so the HSE clock still robustly limits the timing of the Moon-forming event to significantly later than 40 Myr after condensation.

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5. Effect of rotational disruption on the size-frequency distribution of the Main Belt asteroid population.

S. A. Jacobson, F. Marzari, A. Rossi, D. J. Scheeres & D. R. Davis

Monthly Notices of the Royal Astronomical Society: Letters 439:1, L95-L99 (2014)

The size distribution of small asteroids in the Main Belt is assumed to be determined by an equilibrium between the creation of new bodies out of the impact debris of larger asteroids and the destruction of small asteroids by collisions with smaller projectiles. However, for a diameter less than 6 km, we find that YORP-induced rotational disruption significantly contributes to the erosion even exceeding the effects of collisional fragmentation. Including this additional grinding mechanism in a collision evolution model for the asteroid belt, we generate size-frequency distributions from either an accretional or an 'Asteroids were born big' initial size-frequency distribution that are consistent with observations reported in Gladman et al. Rotational disruption is a new mechanism that must be included in all future collisional evolution models of asteroids.

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4. Formation of the wide asynchronous binary asteroid population.

S. A. Jacobson, D. J. Scheeres & J. McMahon

The Astrophysical Journal 780:1, 60, 1-22 (2014)

We propose and analyze a new mechanism for the formation of the wide asynchronous binary population. These binary asteroids have wide semimajor axes relative to most near-Earth and main belt asteroid systems. Confirmed members have rapidly rotating primaries and satellites that are not tidally locked. Previously suggested formation mechanisms from impact ejecta, from planetary flybys, and directly from rotational fission events cannot satisfy all of the observations. The newly hypothesized mechanism works as follows: (1) these systems are formed from rotational fission, (2) their satellites are tidally locked, (3) their orbits are expanded by the binary Yarkovsky-O'Keefe-Radzievskii-Paddack (BYORP) effect, (4) their satellites desynchronize as a result of the adiabatic invariance between the libration of the secondary and the mutual orbit, and (5) the secondary avoids resynchronization because of the YORP effect. This seemingly complex chain of events is a natural pathway for binaries with satellites that have particular shapes, which define the BYORP effect torque that acts on the system. After detailing the theory, we analyze each of the wide asynchronous binary members and candidates to assess their most likely formation mechanism. Finally, we suggest possible future observations to check and constrain our hypothesis.

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3. Long-term stable equilibria for synchronous binary asteroids.

S. A. Jacobson & D. J. Scheeres

The Astrophysical Journal: Letters 736:1, L19, 1-5 (2011)

Synchronous binary asteroids may exist in a long-term stable equilibrium, where the opposing torques from mutual body tides and the binary YORP (BYORP) effect cancel. Interior of this equilibrium, mutual body tides are stronger than the BYORP effect and the mutual orbit semimajor axis expands to the equilibrium; outside of the equilibrium, the BYORP effect dominates the evolution and the system semimajor axis will contract to the equilibrium. If the observed population of small (0.1-10 km diameter) synchronous binaries are in static configurations that are no longer evolving, then this would be confirmed by a null result in the observational tests for the BYORP effect. The confirmed existence of this equilibrium combined with a shape model of the secondary of the system enables the direct study of asteroid geophysics through the tidal theory. The observed synchronous asteroid population cannot exist in this equilibrium if described by the canonical "monolithic" geophysical model. The "rubble pile" geophysical model proposed by Goldreich & Sari is sufficient, however it predicts a tidal Love number directly proportional to the radius of the asteroid, while the best fit to the data predicts a tidal Love number inversely proportional to the radius. This deviation from the canonical and Goldreich & Sari models motivates future study of asteroid geophysics. Ongoing BYORP detection campaigns will determine whether these systems are in an equilibrium, and future determination of secondary shapes will allow direct determination of asteroid geophysical parameters.

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2. Dynamics of rotationally fissioned asteroids: source of observed small asteroid systems.

S. A. Jacobson & D. J. Scheeres

Icarus 214:1, 161-178 (2011)

We present a model of near-Earth asteroid (NEA) rotational fission and ensuing dynamics that describes the creation of synchronous binaries and all other observed NEA systems including: doubly synchronous binaries, high-e binaries, ternary systems, and contact binaries. Our model only pre-supposes the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect, "rubble pile" asteroid geophysics, and gravitational interactions. The YORP effect torques a "rubble pile" asteroid until the asteroid reaches its fission spin limit and the components enter orbit about each other (Scheeres, D.J. [2007]. Icarus 189, 370-385). Non-spherical gravitational potentials couple the spin states to the orbit state and chaotically drive the system towards the observed asteroid classes along two evolutionary tracks primarily distinguished by mass ratio. Related to this is a new binary process termed secondary fission - the secondary asteroid of the binary system is rotationally accelerated via gravitational torques until it fissions, thus creating a chaotic ternary system. The initially chaotic binary can be stabilized to create a synchronous binary by components of the fissioned secondary asteroid impacting the primary asteroid, solar gravitational perturbations, and mutual body tides. These results emphasize the importance of the initial component size distribution and configuration within the parent asteroid. NEAs may go through multiple binary cycles and many YORP-induced rotational fissions during their approximately 10 Myr lifetime in the inner Solar System. Rotational fission and the ensuing dynamics are responsible for all NEA systems including the most commonly observed synchronous binaries.

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1. Formation of asteroid pairs by rotational fission.

P. Pravec, D. Vokrouhlický, D. Polishook, D. J. Scheeres, A. W. Harris, A. Galád, O. Vaduvescu, F. Pozo, A. Barr, P. Longa, F. Vachier, F. Colas, D. P. Pray, J. Pollock, D. Reichart, K. Ivarsen, J. Haislip, A. Lacluyze, P. Kušnirák, T. Henych, F. Marchis, B. Macomber, S. A. Jacobson, Yu. N. Krugly, A. V. Sergeev & A. Leroy

Nature 466, 1085-1088 (2010)

Pairs of asteroids sharing similar heliocentric orbits, but not bound together, were found recently. Backward integrations of their orbits indicated that they separated gently with low relative velocities, but did not provide additional insight into their formation mechanism. A previously hypothesized rotational fission process may explain their formation-critical predictions are that the mass ratios are less than about 0.2 and, as the mass ratio approaches this upper limit, the spin period of the larger body becomes long. Here we report photometric observations of a sample of asteroid pairs, revealing that the primaries of pairs with mass ratios much less than 0.2 rotate rapidly, near their critical fission frequency. As the mass ratio approaches 0.2, the primary period grows long. This occurs as the total energy of the system approaches zero, requiring the asteroid pair to extract an increasing fraction of energy from the primary's spin in order to escape. We do not find asteroid pairs with mass ratios larger than 0.2. Rotationally fissioned systems beyond this limit have insufficient energy to disrupt. We conclude that asteroid pairs are formed by the rotational fission of a parent asteroid into a proto-binary system, which subsequently disrupts under its own internal system dynamics soon after formation.

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