arXiv subjects

Seth A. Jacobson

Publications and source records attributed to Seth A. Jacobson.

At least 37 records · Page 2Linked to original sources

arXiv2021

The Excited Spin State of Dimorphos Resulting from the DART Impact

The NASA Double Asteroid Redirection Test (DART) mission is a planetary defense-driven test of a kinetic impactor on Dimorphos, the satellite of the binary asteroid 65803 Didymos. DART will intercept Dimorphos at a relative speed of ${\sim}6.5 \text{ km s}^{-1}$, perturbing Dimorphos's orbital velocity and changing the binary orbital period. We present three independent methods (one analytic and two numerical) to investigate the post-impact attitude stability of Dimorphos as a function of its axial ratios, $a/b$ and $b/c$ ($a \ge b \ge c$), and the momentum transfer efficiency $β$. The first method uses a novel analytic approach in which we assume a circular orbit and a point-mass primary that identifies four fundamental frequencies of motion corresponding to the secondary's mean motion, libration, precession, and nutation frequencies. At resonance locations among these four frequencies, we find that attitude instabilities are possible. Using two independent numerical codes, we recover many of the resonances predicted by the analytic model and indeed show attitude instability. With one code, we use fast Lyapunov indicators to show that the secondary's attitude can evolve chaotically near the resonance locations. Then, using a high-fidelity numerical model, we find that Dimorphos enters a chaotic tumbling state near the resonance locations and is especially prone to unstable rotation about its long axis, which can be confirmed by ESA's Hera mission arriving at Didymos in late 2026. We also show that a fully coupled treatment of the spin and orbital evolution of both bodies is crucial to accurately model the long-term evolution of the secondary's spin state and libration amplitude. Finally, we discuss the implications of a post-impact tumbling or rolling state, including the possibility of terminating BYORP evolution if Dimorphos is no longer in synchronous rotation.

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arXiv2021

The Effect of Inefficient Accretion on Planetary Differentiation

Pairwise collisions between terrestrial embryos are the dominant means of accretion during the last stage of planet formation. Hence, their realistic treatment in N-body studies is critical to accurately model the formation of terrestrial planets and to develop interpretations of telescopic and spacecraft observations. In this work, we compare the effects of two collision prescriptions on the core-mantle differentiation of terrestrial planets: a model in which collisions are always completely accretionary (``perfect merging'') and a more realistic model based on neural networks that has been trained on hydrodynamical simulations of giant impacts. The latter model is able to predict the loss of mass due to imperfect accretion and the evolution of non-accreted projectiles in hit-and-run collisions. We find that the results of the neural-network model feature a wider range of final core mass fractions and metal-silicate equilibration pressures, temperatures, and oxygen fugacities than the assumption of perfect merging. When used to model collisions in N-body studies of terrestrial planet formation, the two models provide similar answers for planets more massive than 0.1 Earth's masses. For less massive final bodies, however, the inefficient-accretion model predicts a higher degree of compositional diversity. This phenomenon is not reflected in planet formation models of the solar system that use perfect merging to determine collisional outcomes. Our findings confirm the role of giant impacts as important drivers of planetary diversity and encourage a realistic implementation of inefficient accretion in future accretion studies.

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arXiv2021

Scaling laws for the geometry of an impact-induced magma ocean

Here, we develop scaling laws for (1) the distribution of impact-induced heat within the mantle and (2) shape of the impact-induced melt based on more than 100 smoothed particle hydrodynamic (SPH) simulations. We use Legendre polynomials to describe these scaling laws and determine their coefficients by linear regression, minimizing the error between our model and SPH simulations. The input parameters are the impact angle $θ$ ($0^{\circ}, 30^{\circ}, 60^{\circ}$, and $90^{\circ}$), total mass $M_T$ ($1M_{\rm Mars}-53M_{\rm Mars}$, where $M_{\rm Mars}$ is the mass of Mars), impact velocity $v_{\rm imp}$ ($v_{\rm esc} - 2v_{\rm esc}$, where $v_{\rm esc}$ is the mutual escape velocity), and impactor-to-total mass ratio $γ$ ($0.03-0.5$). We find that the equilibrium pressure at the base of a melt pool can be higher (up to $\approx 80 \%$) than those of radially-uniform global magma ocean models. This could have a significant impact on element partitioning. These melt scaling laws are publicly available on GitHub ($\href{https://github.com/mikinakajima/MeltScalingLaw}{https://github.com/mikinakajima/MeltScalingLaw}$).

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arXiv2021

How Sublimation Delays the Onset of Dusty Debris Disk Formation Around White Dwarf Stars

Although numerous white dwarf stars host dusty debris disks, the temperature distribution of these stars differs significantly from the white dwarf population as a whole. Dusty debris disks exist exclusively around white dwarfs cooler than 27,000 K. This is all the more enigmatic given that the formation processes of dusty debris disks should favor younger, hotter white dwarfs, which likely host more dynamically unstable planetary systems. Here we apply a sophisticated material sublimation model to white dwarf systems to show that these statistics are actually a natural result of the interplay of thermal and tidal forces, and show how they define the circumstellar regions where dusty debris disks can form. We demonstrate that these processes tend to prevent stability against both sublimative destruction and reaccretion into planetesimals for rocky materials until white dwarfs cool to below ~25,000-32,000 K, in agreement with the observed limit of ~27,000 K. For pure water ice, this critical temperature is less than 2,700 K (requiring a cooling age older the universe); this precludes pure water ice-rich debris disks forming through the accepted two-step mechanism. The critical temperature is size-dependent; more massive white dwarfs could potentially host dusty debris disks at warmer temperatures. Our model suggests that the location of the disks within the PG 0010+280, GD 56, GD 362, and PG 1541+651 systems are consistent with a forsterite-dominated olivine composition. We also find that very cool white dwarfs may simultaneously host multiple, independently formed dusty debris disks, consistent with observations of the LSPM J0207+3331 system.

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arXiv2021

Formation of planetary systems by pebble accretion and migration: Hot super-Earth systems from breaking compact resonant chains

At least 30\% of main sequence stars host planets with sizes of between 1 and 4 Earth radii and orbital periods of less than 100 days. We use N-body simulations including a model for gas-assisted pebble accretion and disk--planet tidal interaction to study the formation of super-Earth systems. We show that the integrated pebble mass reservoir creates a bifurcation between hot super-Earths or hot-Neptunes ($\lesssim15M_{\oplus}$) and super-massive planetary cores potentially able to become gas giant planets ($\gtrsim15M_{\oplus}$). Simulations with moderate pebble fluxes grow multiple super-Earth-mass planets that migrate inwards and pile up at the inner edge of the disk forming long resonant chains. We follow the long-term dynamical evolution of these systems and use the period ratio distribution of observed planet-pairs to constrain our model. Up to $\sim$95\% of resonant chains become dynamically unstable after the gas disk dispersal, leading to a phase of late collisions that breaks the original resonant configurations. Our simulations naturally match observations when they produce a dominant fraction ($\gtrsim95\%$) of unstable systems with a sprinkling ($\lesssim5\%$) of stable resonant chains (the Trappist-1 system represents one such example). Our results demonstrate that super-Earth systems are inherently multiple (${\rm N\geq2}$) and that the observed excess of single-planet transits is a consequence of the mutual inclinations excited by the planet--planet instability. In simulations in which planetary seeds are initially distributed in the inner and outer disk, close-in super-Earths (abridged).

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arXiv2021

Quantitative estimates of impact induced crustal erosion during accretion and its influence on the Sm/Nd ratio of the Earth

Dynamical scenarios of terrestrial planets formation involve strong perturbations of the inner part of the solar system by the giant-planets, leading to enhanced impact velocities and subsequent collisional erosion. We quantitatively estimate the effect of collisional erosion on the resulting composition of Earth, and estimate how it may provide information on the dynamical context of its formation. We simulate and quantify the erosion of Earth's crust in the context of Solar System formation scenarios, including the classical model and Grand Tack scenario that invokes orbital migration of Jupiter during the gaseous disk phase (Walsh et al., 2011; Raymond et al., 2018). We find that collisional erosion of the early crust is unlikely to produce an excess of about 6% of the Sm/Nd ratio in terrestrial rock samples compared to chondrites for most simulations. Only Grand Tack simulations in which the last giant impact on Earth occurred later than 50 million years after the start of Solar System formation can account for such an offset. However, this time frame is consistent with current cosmochemical and dynamical estimates of the Moon forming impact (Chyba, 1991; Walker, 2009; Touboul et al.,2007, 2009, 2015; Pepin and Porcelli, 2006; Norman et al., 2003; Nyquist et al., 2006; Boyet et al.,2015). Such a late fractionation in the Sm/Nd ratio is unlikely to be responsible for a 20-ppm $^{142}$Nd excess in terrestrial rocks due to the half life of the radiogenic system. Additionally, such a large and late fractionation in the Sm/Nd ratio would accordingly induce non-observed anomalies in the $^{143}$Nd/$^{144}$Nd ratio. Considering our results, the Grand Tack model with a late Moon-forming impact cannot be easily reconciled with the Nd isotopic Earth contents.

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arXiv2020

Small Bodies Tell the Story of the Solar System: A Scientific Rationale for a Multi-Target Small Body Sample Return Program including the Earth-based Laboratory Analysis of Returned Samples

Small bodies are time-capsules of different eras of solar system history from the most primitive materials within the solar system to evolved pieces of larger bodies. A small body sample return program is an essential component of small body exploration, and such a program should include opportunities for both missions and laboratory analysis.

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arXiv2020

Chemical Diversity of Super-Earths As a Consequence of Formation

Recent observations of rocky super-Earths have revealed an apparent wider distribution of Fe/Mg ratios, or core to mantle ratios, than the planets in our Solar System. This study aims to understand how much of the chemical diversity in the super-Earth population can arise from giant impacts during planetary formation. Planet formation simulations have only recently begun to treat collisions more realistically in an attempt to replicate the planets in our Solar System. We investigate planet formation more generally by simulating the formation of rocky super-Earths with varying initial conditions using a version of SyMBA, a gravitational N-body code, that incorporates realistic collisions. We track the maximum plausible change in composition after each impact. The final planets span a range of Fe/Mg ratios similar to the Solar System planets, but do not completely match the distribution in super-Earth data. We only form a few planets with minor iron-depletion, suggesting other mechanisms are at work. The most iron-rich planets have a lower Fe/Mg ratio than Mercury, and are less enriched than planets such as Kepler-100b. This indicates that further work on our understanding of planet formation and further improvement of precision of mass and radius measurements are required to explain planets at the extremes of this Fe/Mg distribution.

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arXiv2019

Formation of compact systems of super-Earths via dynamical instabilities and giant impacts

NASA's Kepler mission discovered $\sim700$ planets in multi-planet systems containing 3 or more transiting bodies, many of which are super-Earths and mini-Neptunes in compact configurations. Using $N$-body simulations, we examine the in situ, final stage assembly of multi-planet systems via the collisional accretion of protoplanets. Our initial conditions are constructed using a subset of the Kepler 5-planet systems as templates. Two different prescriptions for treating planetary collisions are adopted. The simulations address numerous questions: do the results depend on the accretion prescription?; do the resulting systems resemble the Kepler systems, and do they reproduce the observed distribution of planetary multiplicities when synthetically observed?; do collisions lead to significant modification of protoplanet compositions, or to stripping of gaseous envelopes?; do the eccentricity distributions agree with those inferred for the Kepler planets? We find the accretion prescription is unimportant in determining the outcomes. The final planetary systems look broadly similar to the Kepler templates adopted, but the observed distributions of planetary multiplicities or eccentricities are not reproduced, because scattering does not excite the systems sufficiently. In addition, we find that $\sim 1$% of our final systems contain a co-orbital planet pair in horseshoe or tadpole orbits. Post-processing the collision outcomes suggests they would not significantly change the ice fractions of initially ice-rich protoplanets, but significant stripping of gaseous envelopes appears likely. Hence, it may be difficult to reconcile the observation that many low mass Kepler planets have H/He envelopes with an in situ formation scenario that involves giant impacts after dispersal of the gas disc.

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arXiv2019

Constraints on terrestrial planet formation timescales and equilibration processes in the Grand Tack scenario from Hf-W isotopic evolution

We examine 141 N-body simulations of terrestrial planet late-stage accretion that use the Grand Tack scenario, coupling the collisional results with a hafnium-tungsten (Hf-W) isotopic evolution model. Accretion in the Grand Tack scenario results in faster planet formation than classical accretion models because of higher planetesimal surface density induced by a migrating Jupiter. Planetary embryos that grow rapidly experience radiogenic ingrowth of mantle $^{182}$W that is inconsistent with the measured terrestrial composition, unless much of the tungsten is removed by an impactor core that mixes thoroughly with the target mantle. For physically Earth-like surviving planets, we find that the fraction of equilibrating impactor core $k_\text{core} \geq 0.6$ is required to produce results agreeing with observed terrestrial tungsten anomalies (assuming equilibration with relatively large volumes of target mantle material; smaller equilibrating mantle volumes would require even larger $k_\text{core}$). This requirement of substantial core re-equilibration may be difficult to reconcile with fluid dynamical predictions and hydrocode simulations of mixing during large impacts, and hence this result does not favor the rapid planet building that results from Grand Tack accretion.

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arXiv2019

Population control of Mars Trojans by the Yarkovsky & YORP effects

We explore the hypothesis that the population of Martian Trojans is the result of a balance between the production of new asteroids ("YORPlets") through the YORP effect and their eventual escape from the Trojan clouds through Yarkovsky-driven orbital evolution. Our principal observables are: (5261) Eureka, its family of 8 asteroids and the family-less Trojans (101429) 1998 VF31 & (121514) 1999 UJ7. We model the population evolution as a birth-death random process and assume it is in a steady state. We then simulate the discovery of Trojans to-date and find that family members of 101429 and 121514, if they exist, are intrinsically more difficult to detect than Eureka's. Their non-discovery can be used as evidence of their non-existence only under the assumption that their brightness relative to the parent asteroid is similar to that in the Eureka family. To find out how efficiently Mars Trojans are lost from the Trojan clouds due to the Yarkovsky effect, we carry out dynamical simulations of test particles originating from these parent bodies. We find that objects originating from Eureka and 121514 begin escaping after ~1 Gyr, but that those from 101429 are already lost by that time, probably due to that asteroid's proximity to an eccentricity-type secular resonance within Mars's co-orbital region. This is the likely cause behind the absence of Trojans in the orbital vicinity of 101429. In contrast, the solitary status of 121514 points to an intrinsic inability of the asteroid to produce YORPlets during the most recent ~20% of the solar system's history, a finding potentially related to 121514's present, low angular momentum rotational state, unless the Eureka family formed rapidly during a single fission event.

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arXiv2019

Astro2020: Training the Future Generation of Computational Researchers

The current disparity in computational knowledge is a critical hindrance to the diversity and success of the field. Recommendations are outlined for policies and funding models to enable the growth and retention of a new generation of computational researchers that reflect the demographics of the undergraduate population in Astronomy and Physics.

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arXiv2019

Formation of planetary systems by pebble accretion and migration: Growth of gas giants

Giant planets migrate though the protoplanetary disc as they grow. We investigate 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 100-200 Earth masses per million years, enough to grow Jupiter within the lifetime of the solar nebula. The planetary embryos placed up to 30AU migrate into the inner system (r<1AU) and 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 explore slower migration rates which allow the formation of gas giants from embryos originating from the 5-10AU region, which are stranded exterior to 1 AU at the end of the gas-disc phase. 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. Giant planet growth requires a sufficiently-high pebble flux to enable growth to out-compete migration. Even higher pebble fluxes produce systems with multiple gas giants. We show that planetary embryos starting interior to 5AU do not grow into gas giants, even if migration is slow and the pebble flux is large. Instead they grow to the mass regime of super-Earths. This stunted growth is caused by the low pebble isolation mass in the inner disc and is independent of the pebble flux. Additionally we show that the long term evolution of our formed planetary systems can produce systems with hot super-Earths and outer gas giants as well as systems of giants on eccentric orbits (abridged).

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arXiv2019

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

Super-Earths are found in tighter orbits than the Earth's around more than one third of main sequence stars. It has been proposed that super-Earths are scaled-up terrestrial planets that formed similarly, through mutual accretion of planetary embryos, but in discs much denser than the solar protoplanetary disc. We argue instead that terrestrial planets and super-Earths have two distinct formation pathways that are regulated by the disc's pebble reservoir. Through numerical integrations, which combine pebble accretion and N-body gravity between embryos, we show that a difference of a factor of two in the pebble mass-flux is enough to change the evolution from the terrestrial to the super-Earth growth mode. If the pebble mass-flux is small, then the initial embryos within the ice line grow slowly and do not migrate substantially, resulting in a widely spaced population of Mars-mass embryos when the gas disc dissipates. Without gas being present, the embryos become unstable and a small number of terrestrial planets are formed by mutual collisions. The final terrestrial planets are at most 5 Earth masses. Instead, if the pebble mass-flux is high, then the initial embryos within the ice line rapidly become sufficiently massive to migrate through the gas disc. Embryos concentrate at the inner edge of the disc and growth accelerates through mutual merging. This leads to the formation of a system of closely spaced super-Earths in the 5 to 20 Earth-mass range, bounded by the pebble isolation mass. Generally, instabilities of these super-Earth systems after the disappearance of the gas disc trigger additional merging events and dislodge the system from resonant chains. The pebble flux - which controls the transition between the two growth modes - may be regulated by the initial reservoir of solids in the disc or the presence of more distant giant planets that can halt the radial flow of pebbles.

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arXiv2018

The Delivery of Water During Terrestrial Planet Formation

The planetary building blocks that formed in the terrestrial planet region were likely very dry, yet water is comparatively abundant on Earth. 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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arXiv2017

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

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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arXiv2017

A Martian Origin for the Mars Trojan Asteroids

Seven of the nine known Mars Trojan asteroids belong to an orbital cluster named after its largest member 5261 Eureka. Eureka is likely the progenitor of the whole cluster, which formed at least 1 Gyr ago. It was suggested that the thermal YORP effect spun-up Eureka resulting with 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 (e.g. 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 links directly specific asteroids to debris from the forming planets.

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arXiv2016

Highly siderophile elements were stripped from Earth's mantle by iron sulfide segregation

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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