Stage Of Terrestrial Planet Formation Research Articles

How the presence of a giant planet affects the outcome of terrestrial planet formation simulations

The architecture and masses of planetary systems in the habitable zone could be strongly influenced by the presence of outer giant planets. Here, we investigate the impact of outer giants on terrestrial planet formation, under the assumption that the final assembly of the planetary system is set by a giant impact phase. Utilizing a state-of-the-art N-body simulation software, GENGA, we interpret how the late stage of terrestrial planet formation contributes to diversity among planetary systems. We designed two global model setups: 1) we placed a gas giant on the outer side of planetesimals and embryo disk and 2) we only included planetesimals and embryos, but no giant. For the model including the outer giant, we studied the effect of different giant initial masses in the range of 1.0–3.0 Jupiter masses, as well as a range of orbital radii from 2.0–5.8 AU. We also studied the influence of different initial positions of planetesimals and embryos on the results. Our N-body simulation time is approximately 50 Myr. The results show that the existence of an outer giant will promote the interaction between planetesimals and embryos, making the orbits of the formed terrestrial planets more compact. However, placing the giant planet too close to the planetesimals and embryo disk suppresses the formation of massive rocky planets. In addition, under the classical theory, where planetary embryos and planetesimals collide to form terrestrial planets, our results show that the presence of a giant planet actually decreases the gap complexity of the inner planetary system.

A New Database of Giant Impacts over a Wide Range of Masses and with Material Strength: A First Analysis of Outcomes

In the late stage of terrestrial planet formation, planets are predicted to undergo pairwise collisions known as giant impacts. Here, we present a high-resolution database of giant impacts for differentiated colliding bodies of iron–silicate composition, with target masses ranging from 1 × 10−4 M ⊕ up to super-Earths (5 M ⊕). We vary the impactor-to-target mass ratio, core–mantle (iron–silicate) fraction, impact velocity, and impact angle. Strength in the form of friction is included in all simulations. We find that, due to strength, the collisions with bodies smaller than about 2 ×10−3 M ⊕ can result in irregular shapes, compound-core structures, and captured binaries. We observe that the characteristic escaping velocity of smaller remnants (debris) is approximately half of the impact velocity, significantly faster than currently assumed in N-body simulations of planet formation. Incorporating these results in N-body planet formation studies would provide more realistic debris–debris and debris–planet interactions.

Orbital structure of planetary systems formed by giant impacts: stellar mass dependence

ABSTRACT Recent exoplanet surveys revealed that for solar-type stars, close-in Super-Earths are ubiquitous and many of them are in multiplanet systems. These systems are more compact than the Solar system’s terrestrial planets. However, there have been few theoretical studies on the formation of such planets around low-mass stars. In the standard model, the final stage of terrestrial planet formation is the giant impact stage, where protoplanets gravitationally scatter and collide with each other and then evolve into a stable planetary system. We investigate the effect of the stellar mass on the architecture of planetary systems formed by giant impacts. We perform N-body simulations around stars with masses of 0.1–2 times the solar mass. Using the isolation mass of protoplanets, we distribute the initial protoplanets in 0.05–0.15 au from the central star and follow the evolution for 200 million orbital periods of the innermost protoplanet. We find that for a given protoplanet system, the mass of planets increases as the stellar mass decreases, while the number of planets decreases. The eccentricity and inclination of orbits and the orbital separation of adjacent planets increase with decreasing the stellar mass. This is because as the stellar mass decreases, the relative strength of planetary scattering becomes more effective. We also discuss the properties of planets formed in the habitable zone using the minimum-mass extrasolar nebula model.

Rethinking the role of the giant planet instability in terrestrial planet formation models

Advances in computing power and numerical methodologies over the past several decades sparked a prolific output of dynamical investigations of the late stages of terrestrial planet formation. Among other peculiar inner solar system qualities, the ability of simulations to reproduce the small mass of Mars within the planets’ geochemically inferred accretion timescale of ≲10 Myr after the appearance of calcium aluminum-rich inclusions (CAIs) is arguably considered the gold standard for judging evolutionary hypotheses. At present, a number of independent models are capable of consistently generating Mars-like planets and simultaneously satisfying various important observational and geochemical constraints. However, all models must still account for the effects of the epoch of giant planet migration and orbital instability; an event which dynamical and cosmochemical constraints indicate occurred within the first 100 Myr after nebular gas dispersal. If the instability occurred in the first few Myr of this window, the disturbance might have affected the bulk of Mars’ growth. In this manuscript, we turn our attention to a scenario where the instability took place after t≃ 50 Myr. Specifically, we simulate the instability’s effects on three nearly-assembled terrestrial systems that were generated via previous embryo accretion models and contain three large proto-planets (i.e. Earth, Venus and Theia) with 0.5 <m<1.0M⊕ and orbits interior to a collection of ∼Mars-mass embryos (a>1.3 au and m<0.2M⊕) and debris. While the instability consistently triggers a Moon-forming impact and efficiently removes excessive material from the Mars-region in our models, we find that our final systems are too dynamically excited and devoid of Mars and Mercury analogs. Thus, we conclude that, while possible, our scenario is far more improbable than one where the instability either occurred earlier, or at a time where Earth and Venus’ orbits were far less dynamically excited than considered here.

Building Terrestrial Planets: Why Results of Perfect-merging Simulations Are Not Quantitatively Reliable Approximations to Accurate Modeling of Terrestrial Planet Formation

Abstract Although it is accepted that perfect-merging is not a realistic outcome of collisions, some researchers state that perfect-merging simulations can still be considered as quantitatively reliable representations of the final stage of terrestrial planet formation. Citing the work of Kokubo &amp; Genda, they argue that the differences between the final planets in simulations with perfect-merging and those where collisions are resolved accurately are small, and it is justified to use perfect-merging results as an acceptable approximation to realistic simulations. In this paper, we show that this argument does not stand. We demonstrate that when the mass lost during collisions is taken into account, the final masses of the planets will be so different from those obtained from perfect-merging that the latter cannot be used as an approximation. We carried out a large number of smooth particle hydrodynamics simulations of embryo–embryo collisions and determined the amount of the mass and water lost in each impact. We applied the results to collisions in a typical perfect-merging simulation and showed that even when the mass loss in each collision is as small as 10%, perfect-merging can, on average, overestimate the masses of the final planets by ∼35% and their water content by more than 18%. Our analysis demonstrates that, while perfect-merging simulations are still a powerful tool in proving concepts, they cannot be used to make predictions, draw quantitative conclusions (especially about the past history of a planetary system), or serve as a valid approximation to the simulations in which collisions are resolved accurately.

Collision Chains among the Terrestrial Planets. II. An Asymmetry between Earth and Venus

Abstract During the late stage of terrestrial planet formation, hit-and-run collisions are about as common as accretionary mergers, for expected velocities and angles of giant impacts. Average hit-and-runs leave two major remnants plus debris: the target and impactor, somewhat modified through erosion, escaping at lower relative velocity. Here we continue our study of the dynamical effects of such collisions. We compare the dynamical fates of intact runners that start from hit-and-runs with proto-Venus at 0.7 au and proto-Earth at 1.0 au. We follow the orbital evolutions of the runners, including the other terrestrial planets, Jupiter, and Saturn, in an N-body code. We find that the accretion of these runners can take ≳10 Myr (depending on the egress velocity of the first collision) and can involve successive collisions with the original target planet or with other planets. We treat successive collisions that the runner experiences using surrogate models from machine learning, as in previous work, and evolve subsequent hit-and-runs in a similar fashion. We identify asymmetries in the capture, loss, and interchange of runners in the growth of Venus and Earth. Hit-and-run is a more probable outcome at proto-Venus, being smaller and faster orbiting than proto-Earth. But Venus acts as a sink, eventually accreting most of its runners, assuming typical events, whereas proto-Earth loses about half, many of those continuing to Venus. This leads to a disparity in the style of late-stage accretion that could have led to significant differences in geology, composition, and satellite formation at Earth and Venus.

Machine learning applied to simulations of collisions between rotating, differentiated planets

In the late stages of terrestrial planet formation, pairwise collisions between planetary-sized bodies act as the fundamental agent of planet growth. These collisions can lead to either growth or disruption of the bodies involved and are largely responsible for shaping the final characteristics of the planets. Despite their critical role in planet formation, an accurate treatment of collisions has yet to be realized. While semi-analytic methods have been proposed, they remain limited to a narrow set of post-impact properties and have only achieved relatively low accuracies. However, the rise of machine learning and access to increased computing power have enabled novel data-driven approaches. In this work, we show that data-driven emulation techniques are capable of classifying and predicting the outcome of collisions with high accuracy and are generalizable to any quantifiable post-impact quantity. In particular, we focus on the dataset requirements, training pipeline, and classification and regression performance for four distinct data-driven techniques from machine learning (ensemble methods and neural networks) and uncertainty quantification (Gaussian processes and polynomial chaos expansion). We compare these methods to existing analytic and semi-analytic methods. Such data-driven emulators are poised to replace the methods currently used in N-body simulations, while avoiding the cost of direct simulation. This work is based on a new set of 14,856 SPH simulations of pairwise collisions between rotating, differentiated bodies at all possible mutual orientations.

The Energy Budgets of Giant Impacts

AbstractGiant impacts dominate the final stages of terrestrial planet formation and set the configuration and compositions of the final system of planets. A giant impact is believed to be responsible for the formation of Earth's Moon, but the specific impact parameters are under debate. Because the canonical Moon‐forming impact is the most intensely studied scenario, it is often considered the archetypal giant impact. However, a wide range of impacts with different outcomes are possible. Here we examine the total energy budgets of giant impacts that form Earth‐mass bodies and find that they differ substantially across the wide range of possible Moon‐forming events. We show that gravitational potential energy exchange is important, and we determine the regime in which potential energy has a significant effect on the collision outcome. Energy is deposited heterogeneously within the colliding planets, increasing their internal energies, and portions of each body attain sufficient entropy for vaporization. After gravitational re‐equilibration, post‐impact bodies are strongly thermally stratified, with varying amounts of vaporized and supercritical mantle. The canonical Moon‐forming impact is a relatively low‐energy event and should not be considered the archetype of accretionary giant impacts that form Earth‐mass planets. After a giant impact, bodies are significantly inflated in size compared to condensed planets of the same mass, and there are substantial differences in the magnitudes of their potential, kinetic, and internal energy components. As a result, the conditions for metal‐silicate equilibration and the subsequent evolution of the planet may vary widely between different impact scenarios.

Planet Formation in Highly Inclined Binary Systems. II. Orbital Alignment and Planet Growth Boost in Intermediate Separation Binaries

Abstract Stars are commonly formed in binary systems, which provide a natural laboratory for studying planet formation in extreme conditions. In our first paper (Paper I) of a series, we have shown that the intermediate stage—from planetesimals to planetary embryos/cores—of planet formation can proceed even in highly inclined binaries. Following Paper I, here we numerically study the late stage of terrestrial planet formation, i.e., from embryos to full planets, in binary systems of various orbital configurations. We identify an orbital alignment effect; namely, although an inclined binary generally misaligns the planetary orbits with respect to the spin axis of the primary host star (i.e., causing large obliquity), it could align the planetary orbits with respect to the binary orbit. Such an orbital alignment effect is caused by the combination of orbital differential precession and self-damping, and it is mostly significant in cases of intermediate binary separations, i.e., a B ∼ 40–200 au for planet formation around 1 au from the primary stars. In such intermediate separation binaries, somewhat contrary to intuition, the binary companion can aid planet growth by having increased the rate of collisions, forming significantly more massive but fewer planets. On the other two ends, the companion is either too close, and thus plays a violently disruptive role, or too wide to have a significant effect on planet formation. Future observations that can discover more planet-bearing binary star systems and constrain their masses and 3D orbital motions will test our numerical findings.

Origin and evolution of the atmospheres of early Venus, Earth and Mars

We review the origin and evolution of the atmospheres of Earth, Venus and Mars from the time when their accreting bodies were released from the protoplanetary disk a few million years after the origin of the Sun. If the accreting planetary cores reached masses $$\ge 0.5 M_\mathrm{Earth}$$ before the gas in the disk disappeared, primordial atmospheres consisting mainly of H $$_2$$ form around the young planetary body, contrary to late-stage planet formation, where terrestrial planets accrete material after the nebula phase of the disk. The differences between these two scenarios are explored by investigating non-radiogenic atmospheric noble gas isotope anomalies observed on the three terrestrial planets. The role of the young Sun’s more efficient EUV radiation and of the plasma environment into the escape of early atmospheres is also addressed. We discuss the catastrophic outgassing of volatiles and the formation and cooling of steam atmospheres after the solidification of magma oceans and we describe the geochemical evidence for additional delivery of volatile-rich chondritic materials during the main stages of terrestrial planet formation. The evolution scenario of early Earth is then compared with the atmospheric evolution of planets where no active plate tectonics emerged like on Venus and Mars. We look at the diversity between early Earth, Venus and Mars, which is found to be related to their differing geochemical, geodynamical and geophysical conditions, including plate tectonics, crust and mantle oxidation processes and their involvement in degassing processes of secondary $$\hbox {N}_2$$ atmospheres. The buildup of atmospheric $$\hbox {N}_2$$ , $$\hbox {O}_2$$ , and the role of greenhouse gases such as $$\hbox {CO}_2$$ and $$\hbox {CH}_4$$ to counter the Faint Young Sun Paradox (FYSP), when the earliest life forms on Earth originated until the Great Oxidation Event $$\approx $$ 2.3 Gyr ago, are addressed. This review concludes with a discussion on the implications of understanding Earth’s geophysical and related atmospheric evolution in relation to the discovery of potential habitable terrestrial exoplanets.

THE FREQUENCY OF GIANT IMPACTS ON EARTH-LIKE WORLDS

ABSTRACT The late stages of terrestrial planet formation are dominated by giant impacts that collectively influence the growth, composition, and habitability of any planets that form. Hitherto, numerical models designed to explore these late stage collisions have been limited by assuming that all collisions lead to perfect accretion, and many of these studies lack the large number of realizations needed to account for the chaotic nature of N-body systems. We improve on these limitations by performing 280 simulations of planet formation around a Sun-like star, half of which used an N-body algorithm that has recently been modified to include fragmentation and hit-and-run (bouncing) collisions. We find that when fragmentation is included, the final planets formed are comparable in terms of mass and number; however, their collision histories differ significantly and the accretion time approximately doubles. We explored impacts onto Earth-like planets, which we parameterized in terms of their specific impact energies. Only 15 of our 164 Earth-analogs experienced an impact that was energetic enough to strip an entire atmosphere. To strip about half of an atmosphere requires energies comparable to recent models of the Moon-forming giant impact. Almost all Earth-analogs received at least one impact that met this criteria during the 2 Gyr simulations and the median was three giant impacts. The median time of the final giant impact was 43 Myr after the start of the simulations, leading us to conclude that the time-frame of the Moon-forming impact is typical among planetary systems around Sun-like stars.

Formation of terrestrial planets in disks with different surface density profiles

We present the results of an extensive study of the final stage of terrestrial planet formation in disks with different surface density profiles and for different orbits of Jupiter and Saturn. We carried out simulations for disk densities proportional to r^-0.5, r^-1, and r^-1.5, and also for partially depleted disks as in the recent model of Mars formation by Izidoro et al (2014). The purpose of our study is to determine how the final assembly of planets and their physical properties are affected by the total mass of the disk and its radial profile. Because of the important roles of secular resonances in orbits and properties of the final planets, we studied the effects of these resonances as well. We have divided this study into two parts. In Part 1, we are interested in examining the effects of secular resonances on the formation of Mars and orbital stability of terrestrial planets. In Part 2, our goal is to determine trends that may exist between the disk surface density profile and the final properties of terrestrial planets. In the context of the depleted disk model, results show that the nu_5 resonance does not have a significant effect on the final orbits of terrestrial planets. However, nu_6 and nu_16 resonances play important roles in clearing their affected areas ensuring that no additional mass will be scattered into the accretion zone of Mars so that it can maintain its mass and orbital stability. In Part 2, our results indicate that despite some small correlations, in general, no trend seems to exist between the disk surface density profile and the mean number of the final planets, their masses, time of formation, and distances to the central star. We present the results of our simulations and discuss their implications for the formation of Mars and other terrestrial planets, as well as the physical properties of these objects such as their masses and water contents.

WARM DEBRIS DISKS PRODUCED BY GIANT IMPACTS DURING TERRESTRIAL PLANET FORMATION

In our solar system, Mars-sized protoplanets frequently collided with each other during the last stage of terrestrial planet formation called the giant impact stage. Giant impacts eject a large amount of material from the colliding protoplanets into the terrestrial planet region, which may form debris disks with observable infrared excesses. Indeed, tens of warm debris disks around young solar-type stars have been observed. Here, we quantitatively estimate the total mass of ejected materials during the giant impact stages. We found that $\sim$0.4 times the Earth's mass is ejected in total throughout the giant impact stage. Ejected materials are ground down by collisional cascade until micron-sized grains are blown out by radiation pressure. The depletion timescale of these ejected materials is determined primarily by the mass of the largest body among them. We conducted high-resolution simulations of giant impacts to accurately obtain the mass of the largest ejected body. We then calculated the evolution of the debris disks produced by a series of giant impacts and depleted by collisional cascades to obtain the infrared excess evolution of the debris disks. We found that the infrared excess is almost always higher than the stellar infrared flux throughout the giant impact stage ($\sim$100 Myr) and is sometimes $\sim$10 times higher immediately after a giant impact. Therefore, giant impact stages would explain the infrared excess from most observed warm debris disks. The observed fraction of stars with warm debris disks indicates that the formation probability of our solar system-like terrestrial planets is approximately 10%.

The feeding zones of terrestrial planets and insights into Moon formation

The final stage of terrestrial planet formation consists of several hundred approximately lunar mass bodies accreting into a few terrestrial planets. This final stage is stochastic, making it hard to predict which parts of the original planetesimal disk contributed to each of our terrestrial planets. Here we present an extensive suite of terrestrial planet formation simulations that allows quantitative analysis of this process. Although there is a general correlation between a planet’s location and the initial semi-major axes of its constituent planetesimals, we concur with previous studies that Venus, Earth, and Mars analogs have overlapping, stochastic feeding zones. We quantify the feeding zone width, Δa, as the mass-weighted standard deviation of the initial semi-major axes of the planetary embryos and planetesimals that make up the final planet. The size of a planet’s feeding zone in our simulations does not correlate with its final mass or semi-major axis, suggesting there is no systematic trend between a planet’s mass and its volatile inventory. Instead, we find that the feeding zone of any planet more massive than 0.1M⊕ is roughly proportional to the radial extent of the initial disk from which it formed: Δa≈0.25(amax-amin), where amin and amax are the inner and outer edge of the initial planetesimal disk. These wide stochastic feeding zones have significant consequences for the origin of the Moon, since the canonical scenario predicts the Moon should be primarily composed of material from Earth’s last major impactor (Theia), yet its isotopic composition is indistinguishable from Earth. In particular, we find that the feeding zones of Theia analogs are significantly more stochastic than the planetary analogs. Depending on our assumed initial distribution of oxygen isotopes within the planetesimal disk, we find a ∼5% or less probability that the Earth and Theia will form with an isotopic difference equal to or smaller than the Earth and Moon’s. In fact we predict that every planetary mass body should be expected to have a unique isotopic signature. In addition, we find paucities of massive Theia analogs and high velocity Moon-forming collisions, two recently proposed explanations for the Moon’s isotopic composition. Our work suggests that there is still no scenario for the Moon’s origin that explains its isotopic composition with a high probability event.

On the origin and composition of Theia: Constraints from new models of the Giant Impact

Knowing the isotopic composition of Theia, the proto-planet which collided with the Earth in the Giant Impact that formed the Moon, could provide interesting insights on the state of homogenization of the inner Solar System at the late stages of terrestrial planet formation. We use the known isotopic and modeled chemical compositions of the bulk silicate mantles of Earth and Moon and combine them with different Giant Impact models, to calculate the possible ranges of isotopic composition of Theia in O, Si, Ti, Cr, Zr and W in each model. We compare these ranges to the isotopic composition of carbonaceous chondrites, Mars, and other Solar System materials. In the absence of post-impact isotopic re-equilibration, the recently proposed high angular momentum models of the Giant Impact (“impact-fission”, Cúk, M., Stewart, S.T. [2012]. Science 338, 1047; and “merger”, Canup, R.M. [2012]. Science 338, 1052) allow – by a narrow margin – for a Theia similar to CI-chondrites, and Mars. The “hit-and-run” model (Reufer, A., Meier, M.M.M., Benz, W., Wieler, R. [2012]. Icarus 221, 296–299) allows for a Theia similar to enstatite-chondrites and other Earth-like materials. If the Earth and Moon inherited their different mantle FeO contents from the bulk mantles of the proto-Earth and Theia, the high angular momentum models cannot explain the observed difference. However, both the hit-and-run as well as the classical or “canonical” Giant Impact model naturally explain this difference as the consequence of a simple mixture of two mantles with different FeO. Therefore, the simplest way to reconcile the isotopic similarity, and FeO dissimilarity, of Earth and Moon is a Theia with an Earth-like isotopic composition and a higher (∼20%) mantle FeO content.

THE EFFECT OF PLANETS BEYOND THE ICE LINE ON THE ACCRETION OF VOLATILES BY HABITABLE-ZONE ROCKY PLANETS

Models of planet formation have shown that giant planets have a large impact on the number, masses and orbits of terrestrial planets that form. In addition, they play an important role in delivering volatiles from material that formed exterior to the snow-line (the region in the disk beyond which water ice can condense) to the inner region of the disk where terrestrial planets can maintain liquid water on their surfaces. We present simulations of the late stages of terrestrial planet formation from a disk of protoplanets around a solar-type star, and we include a massive planet (from 1 Earth mass to 1 Jupiter mass) in Jupiter's orbit at ~5.2 AU in all but one set of simulations. Two initial disk models are examined with the same mass distribution and total initial water content, but with different distributions of water content. We compare the accretion rates and final water mass fraction of the planets that form. Remarkably, all of the planets that formed in our simulations without giant planets were water-rich, showing that giant planet companions are not required to deliver volatiles to terrestrial planets in the habitable zone. In contrast, an outer planet at least several times the mass of Earth may be needed to clear distant regions from debris truncating the epoch of frequent large impacts. Observations of exoplanets from radial velocity surveys suggest that outer Jupiter-like planets may be scarce, therefore the results presented here suggest the number of habitable planets that reside in our galaxy may be more than previously thought.

Dynamics of the terrestrial planets from a large number of N-body simulations

The agglomeration of planetary embryos and planetesimals was the final stage of terrestrial planet formation. This process is modeled using N-body accretion simulations, whose outcomes are tested by comparing to observed physical and chemical Solar System properties. The outcomes of these simulations are stochastic, leading to a wide range of results, which makes it difficult at times to identify the full range of possible outcomes for a given dynamic environment. We ran fifty high-resolution simulations each with Jupiter and Saturn on circular or eccentric orbits, whereas most previous studies ran an order of magnitude fewer. This allows us to better quantify the probabilities of matching various observables, including low probability events such as Mars formation, and to search for correlations between properties. We produce many good Earth analogues, which provide information about the mass evolution and provenance of the building blocks of the Earth. Most observables are weakly correlated or uncorrelated, implying that individual evolutionary stages may reflect how the system evolved even if models do not reproduce all of the Solar System's properties at the end. Thus individual N-body simulations may be used to study the chemistry of planetary accretion as particular accretion pathways may be representative of a given dynamic scenario even if that simulation fails to reproduce many of the other observed traits of the Solar System.

Adiabatic release measurements inα-quartz between 300 and 1200 GPa: Characterization ofα-quartz as a shock standard in the multimegabar regime

$\ensuremath{\alpha}$-quartz has been used prolifically in recent years as an impedance matching standard in the multimegabar regime (1 Mbar $=$ 100 GPa). This is due to the fact that above $\ensuremath{\sim}$90--100 GPa along the principal Hugoniot $\ensuremath{\alpha}$-quartz becomes reflective, and thus shock velocities can be measured to high precision using velocity interferometry. This property allows for high-precision measurements, however, the accuracy of impedance matching measurements depends upon the knowledge of both the Hugoniot and the release or reshock response of $\ensuremath{\alpha}$-quartz. Here, we present the results of several adiabatic release measurements of $\ensuremath{\alpha}$-quartz from $\ensuremath{\sim}$300--1200 GPa states along the principal Hugoniot using full density polymethylpentene (commonly known as TPX), and both $\ensuremath{\sim}$190 and $\ensuremath{\sim}$110 mg/cc silica aerogel standards. These data were analyzed within the framework of a simple, analytical model that was motivated by a first-principles molecular dynamics investigation into the release response of $\ensuremath{\alpha}$-quartz. Combined, this theoretical and experimental study provides a method to perform impedance matching calculations without the need to appeal to any tabular equation of state for $\ensuremath{\alpha}$-quartz. As an analytical model, this method allows for propagation of all uncertainty, including the random measurement uncertainties and the systematic uncertainties of the Hugoniot and release response of $\ensuremath{\alpha}$-quartz. This work establishes $\ensuremath{\alpha}$-quartz for use as a high-precision standard for impedance matching in the multimegabar regime. We also note that the experimentally validated model framework should prove to be useful in the development of wide range equations of state for silica, a major constituent in the Earth's crust and mantle. Such models are crucial for accurate simulations of high-velocity giant impacts that are thought to be prevalent in the final stages of terrestrial planet formation.

Shock response of low-density silica aerogel in the multi-Mbar regime

Low-density silica aerogels have found several applications in high-pressure research due to the ability for aerogel to be made over a wide range of initial densities with very small and uniform pore sizes. Here, we present plate-impact, shock wave experiments on nominally 110 and 200 mg/cc silica aerogel over the pressure range of ∼30-100 and ∼30-200 GPa, respectively. Direct measurement of the shock velocity in the aerogel using velocity interferometry enabled the Hugoniot to be inferred with very high precision, more than an order of magnitude improvement with respect to previously reported data for similar density silica aerogel. These results establish aerogel as a useful low impedance shock wave standard and provide data at high-entropy, high-pressure, and relatively low-density states to aid in the development of wide range equations of state for silica, a major constituent in the Earth's crust and mantle. Such models are crucial for accurate simulations of high-velocity giant impacts that are thought to be prevalent in the final stages of terrestrial planet formation.

Dynamics and accretion of planetesimals

We review the basic dynamics and accretion of planetesimals by showing N-body simulations. The orbits of planetesimals evolve through two-body gravitational relaxation: viscous stirring increases the random velocity and dynamical friction realizes the equiparation of the random energy. In the early stage of planetesimal accretion the growth mode of planetesimals is runaway growth where larger planetesimals grow faster than smaller ones. When a protoplanet (runaway-growing planetesimal) exceeds a critical mass the growth mode shifts to oligarchic growth where similar-sized protoplanets grow keeping a certain orbital separation. The final stage of terrestrial planet formation is collision among protoplanets known as giant impacts. We also summarize the dynamical effects of disk gas on planets and the core accretion model for formation of gas giants and discuss the diversity of planetary systems.