Giant Impact Stage Research Articles

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.

The New Generation Planetary Population Synthesis (NGPPS)

Context.Planetary formation and evolution is a combination of multiple interlinked processes. Constraining the mechanisms observationally requires statistical comparison to a large diversity of planetary systems.Aims.We want to understand global observable consequences of different physical processes (accretion, migration, and interactions) and initial properties (like disc masses and metallicities) on the demographics of the planetary population. We also want to study the convergence of our scheme with respect to one initial condition, the initial number of planetary embryo in each disc.Methods.We selected distributions of initial conditions that are representative of known protoplanetary discs. Then, we used the Generation III Bern model to perform planetary population synthesis. We synthesise five populations with each a different initial number of Moon-mass embryos per disc: 1, 10, 20, 50, and 100. The last is our nominal population consisting of 1000 stars (systems) that was used for an extensive statistical analysis of planetary systems around 1M⊙stars.Results.The properties of giant planets do not change much as long as there are at least ten embryos in each system. The study of giants can thus be done with simulations requiring less computational resources. For inner terrestrial planets, only the 100-embryos population is able to attain the giant-impact stage. In that population, each planetary system contains, on average, eight planets more massive than 1M⊕. The fraction of systems with giants planets at all orbital distances is 18%, but only 1.6% are at >10 au. Systems with giants contain on average 1.6 such planets. The planetary mass function varies asM−2between 5 and 50M⊕. Both at lower and higher masses, it follows approximatelyM−1. The frequency of terrestrial and super-Earth planets peaks at a stellar [Fe/H] of −0.2 and 0.0, respectively, being limited at lower [Fe/H] by a lack of building blocks, and by (for them) detrimental growth of more massive dynamically active planets at higher [Fe/H]. The frequency of more massive planets (Neptunian, giants) increases monotonically with [Fe/H]. The fast migration of planets in the 5–50M⊕range is reduced by the presence of multiple lower-mass inner planets in the multi-embryos populations. To assess the impact of parameters and model assumptions, we also study two non-nominal populations: insitu formation without gas-driven migration, and a different initial planetesimal surface density.Conclusions.We present one of the most comprehensive simulations of (exo)planetary system formation and evolution to date. For observations, the syntheses provides a large data set to search for comparison synthetic planetary systems that show how these systems have come into existence. The systems, including their full formation and evolution tracks are available online. For theory, they provide the framework to observationally test the global statistical consequences of theoretical models for specific physical processes. This is an important ingredient towards the development of a standard model of planetary formation and evolution.

Ejection of close-in super-Earths around low-mass stars in the giant impact stage

Context.Earth-sized planets were observed in close-in orbits around M dwarfs. While more and more planets are expected to be uncovered around M dwarfs, theories of their formation and dynamical evolution are still in their infancy.Aims.We investigate the giant impact stage for the growth of protoplanets, which includes strong scattering around low-mass stars. The aim is to clarify whether strong scattering around low-mass stars affects the orbital and mass distributions of the planets.Methods.We performed anN-body simulation of protoplanets by systematically surveying the parameter space of the stellar mass and surface density of protoplanets.Results.We find that protoplanets are often ejected after twice or three times the close-scattering around late M dwarfs. The ejection sets the upper limit of the largest planet mass. By adopting the surface density that linearly scales with the stellar mass, we find that as the stellar mass decreases, less massive planets are formed in orbits with higher eccentricities and inclinations. Under this scaling, we also find that a few close-in protoplanets are generally ejected.Conclusions.The ejection of protoplanets plays an important role in the mass distribution of super-Earths around late M dwarfs. The mass relation of observed close-in super-Earths and their central star mass is reproduced well by ejection.

Formation of Close-in Super-Earths by Giant Impacts: Effects of Initial Eccentricities and Inclinations of Protoplanets

Abstract Recent observations have revealed the eccentricity and inclination distributions of close-in super-Earths. These distributions have the potential to constrain their formation processes. In the in situ formation scenario, the eccentricities and inclinations of planets are determined by gravitational scattering and collisions between protoplanets on the giant impact stage. We investigate the effect of the initial eccentricities and inclinations of protoplanets on the formation of close-in super-Earths. We perform N-body simulations of protoplanets in gas-free disks, changing the initial eccentricities and inclinations systematically. We find that while the eccentricities of protoplanets are well relaxed through their evolution, the inclinations are not. When the initial inclinations are small, they are not generally pumped up since scattering is less effective and collisions occur immediately after orbital crossing. On the other hand, when the initial inclinations are large, they tend to be kept large since collisional damping is less effective. Not only the resultant inclinations of planets, but also their number, eccentricities, angular momentum deficit, and orbital separations are affected by the initial inclinations of protoplanets.

Ejection of iron-bearing giant-impact fragments and the dynamical and geochemical influence of the fragment re-accretion

The Earth was born in violence. Many giant collisions of protoplanets are thought to have occurred during the terrestrial planet formation. Here we investigated the giant impact stage by using a hybrid code that consistently deals with the orbital evolution of protoplanets around the Sun and the details of processes during giant impacts between two protoplanets. A significant amount of materials (up to several tens of percent of the total mass of the protoplanets) is ejected by giant impacts. We call these ejected fragments the giant-impact fragments (GIFs). In some of the erosive hit-and-run and high-velocity collisions, metallic iron is also ejected, which comes from the colliding protoplanets' cores. From ten numerical simulations for the giant impact stage, we found that the mass fraction of metallic iron in GIFs ranges from ∼1 wt% to ∼25 wt%. We also discussed the effects of the GIFs on the dynamical and geochemical characteristics of formed terrestrial planets. We found that the GIFs have the potential to solve the following dynamical and geochemical conflicts: (1) The Earth, currently in a near circular orbit, is likely to have had a highly eccentric orbit during the giant impact stage. The GIFs are large enough in total mass to lower the eccentricity of the Earth to its current value via their dynamical friction. (2) The concentrations of highly siderophile elements (HSEs) in the Earth's mantle are greater than what was predicted experimentally. Re-accretion of the iron-bearing GIFs onto the Earth can contribute to the excess of HSEs. In addition, Iron-bearing GIFs provide significant reducing agent that could transform primitive CO2–H2O atmosphere and ocean into more reducing H2-bearing atmosphere. Thus, GIFs are important for the origin of Earth's life and its early evolution.

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%.

Giant Impacts and Debris Disks

AbstractDuring the last stage of terrestrial planet formation, Mars-sized protoplanets often collides with each other. Our high-resolution impact simulations show that such giant impacts produce a significant amount of fragments within the terrestrial planet region. These ejected fragments form a hot debris disk around the central star. We calculated the evolution of the surface density and size distribution of the debris disk using the analytical model of collision disruption, and estimated its infrared excess emission. We found that 24 μm flux from the debris disk is higher than stellar flux throughout the giant impact stage (~ 108 years), which can explain the infrared excess recently observed around the star with the age of 107 – 108 years.

THE LAST STAGES OF TERRESTRIAL PLANET FORMATION: DYNAMICAL FRICTION AND THE LATE VENEER

The final stage of terrestrial planet formation consists of the cleanup of residual planetesimals after the giant impact phase. Dynamically, a residual planetesimal population is needed to damp the high eccentricities of the terrestrial planets after the giant impact stage. Geochemically, highly siderophile element (HSE) abundance patterns inferred for the terrestrial planets and the Moon suggest that a total of about 0.01 M_Earth of chondritic material was delivered as `late veneer' by planetesimals to the terrestrial planets after the end of giant impacts. Here we combine these two independent lines of evidence for a leftover population of planetesimals and show that: 1) A residual planetesimal population containing 0.01 M_Earth is able to damp the eccentricities of the terrestrial planets after giant impacts to their observed values. 2) At the same time, this planetesimal population can account for the observed relative amounts of late veneer added to the Earth, Moon and Mars provided that the majority of the late veneer was delivered by small planetesimals with radii <10m. These small planetesimal sizes are required to ensure efficient damping of the planetesimal's velocity dispersion by mutual collisions, which in turn ensures that the planets' accretion cross sections are significantly enhanced by gravitational focusing above their geometric values. Specifically we find, in the limit that the relative velocity between the terrestrial planets and the planetesimals is significantly less than the terrestrial planets' escape velocities, that gravitational focusing yields an accretion ratio Earth/Mars~17, which agrees well with the accretion ratio inferred from HSEs of 12-23. For the Earth-Moon system, we find an accretion ratio of ~200, which is consistent with estimates of 150-700 derived from HSE abundances that include the lunar crust as well as mantle component. (Abridged)

MERGING CRITERIA FOR GIANT IMPACTS OF PROTOPLANETS

At the final stage of terrestrial planet formation, known as the giant impact stage, a few tens of Mars-sized protoplanets collide with one another to form terrestrial planets. Almost all previous studies on the orbital and accretional evolution of protoplanets in this stage have been based on the assumption of perfect accretion, where two colliding protoplanets always merge. However, recent impact simulations have shown that collisions among protoplanets are not always merging events, that is, two colliding protoplanets sometimes move apart after the collision (hit-and-run collision). As a first step towards studying the effects of such imperfect accretion of protoplanets on terrestrial planet formation, we investigated the merging criteria for collisions of rocky protoplanets. Using the smoothed particle hydrodynamic (SPH) method, we performed more than 1000 simulations of giant impacts with various parameter sets, such as the mass ratio of protoplanets, $\gamma$, the total mass of two protoplanets, $M_{\rm T}$, the impact angle, $\theta$, and the impact velocity, $v_{\rm imp}$. We investigated the critical impact velocity, $v_{\rm cr}$, at the transition between merging and hit-and-run collisions. We found that the normalized critical impact velocity, $v_{\rm cr}/v_{\rm esc}$, depends on $\gamma$ and $\theta$, but does not depend on $M_{\rm T}$, where $v_{\rm esc}$ is the two-body escape velocity. We derived a simple formula for $v_{\rm cr}/v_{\rm esc}$ as a function of $\gamma$ and $\theta$, and applied it to the giant impact events obtained by \textit{N}-body calculations in the previous studies. We found that 40% of these events should not be merging events.

FORMATION OF TERRESTRIAL PLANETS FROM PROTOPLANETS UNDER A REALISTIC ACCRETION CONDITION

The final stage of terrestrial planet formation is known as the giant impact stage where protoplanets collide with one another to form planets. So far this stage has been mainly investigated by N-body simulations with an assumption of perfect accretion in which all collisions lead to accretion. However, this assumption breaks for collisions with high velocity and/or a large impact parameter. We derive an accretion condition for protoplanet collisions in terms of impact velocity and angle and masses of colliding bodies, from the results of numerical collision experiments. For the first time, we adopt this realistic accretion condition in N-body simulations of terrestrial planet formation from protoplanets. We compare the results with those with perfect accretion and show how the accretion condition affects terrestrial planet formation. We find that in the realistic accretion model, about half of collisions do not lead to accretion. However, the final number, mass, orbital elements, and even growth timescale of planets are barely affected by the accretion condition. For the standard protoplanetary disk model, typically two Earth-sized planets form in the terrestrial planet region over about 100 M years in both realistic and perfect accretion models. We also find that for the realistic accretion model, the spin angular velocity is about 30% smaller than that for the perfect accretion model that is as large as the critical spin angular velocity for rotational instability. The spin angular velocity and obliquity obey Gaussian and isotropic distributions, respectively, independently of the accretion condition.

Formation and Accretion History of Terrestrial Planets from Runaway Growth through to Late Time: Implications for Orbital Eccentricity

Remnant planetesimals might have played an important role in reducing the orbital eccentricities of the terrestrial planets after their formation via giant impacts. However, the population and the size distribution of remnant planetesimals during and after the giant impact stage are unknown, because simulations of planetary accretion in the runaway growth and giant impact stages have been conducted independently. Here we report results of direct N-body simulations of the formation of terrestrial planets beginning with a compact planetesimal disk. The initial planetesimal disk has a total mass and angular momentum as observed for the terrestrial planets, and we vary the width (0.3 and 0.5 AU) and the number of planetesimals (1000-5000). This initial configuration generally gives rise to three final planets of similar size, and sometimes a fourth small planet forms near the location of Mars. Since a sufficient number of planetesimals remains, even after the giant impact phase, the final orbital eccentricities are as small as those of the Earth and Venus.

Formation of Terrestrial Planets from Protoplanets. II. Statistics of Planetary Spin

The final stage of terrestrial planet formation is known as the giant impact stage, where protoplanets collide with one another to form planets. The initial spin state of terrestrial planets is determined at this stage. We statistically investigate the spin parameters of terrestrial planets assembled from protoplanets using N-body simulations. As initial conditions, we adopt the oligarchic growth model of protoplanets. For the standard disk model, typically two Earth-sized planets form in the terrestrial planet region. We find that the spin angular velocity of the planets is well expressed by a Gaussian distribution, and their obliquity is well expressed by an isotropic distribution. The typical spin angular velocity is given by the critical spin angular velocity for rotational instability under the assumption of perfect accretion in collisions. We show the dependencies of the spin parameters on the initial protoplanet system parameters. The initial orbital separation and velocity anisotropy of protoplanets barely affect the spin parameters. The bulk density of protoplanets does not affect the obliquity distribution, while the spin angular velocity increases with the bulk density.

Formation of Terrestrial Planets from Protoplanets. I. Statistics of Basic Dynamical Properties

The final stage of terrestrial planet formation is known as the giant impact stage, where protoplanets collide with one another to form planets. As this process is stochastic, in order to clarify it, it is necessary to quantify it statistically. We investigate this final assemblage of terrestrial planets from protoplanets using N-body simulations. As initial conditions, we adopt the oligarchic growth model of protoplanets. We systematically change the surface density, surface density profile, and orbital separation of the initial protoplanet system, and the bulk density of protoplanets, while the initial system radial range is fixed at 0.5-1.5 AU. For each initial condition, we perform 20 runs, and from their results we derive the statistical properties of the assembled planets. For the standard disk model, typically two Earth-sized planets form in the terrestrial planet region. We show the dependences of the masses and orbital elements of planets on the initial protoplanet system parameters and give their simple empirical fits. The number of planets slowly decreases as the surface density of the initial protoplanets increases, while the masses of individual planets increase almost linearly. For a steeper surface density profile, large planets tend to form closer to the star. For the parameter ranges that we test, the basic structure of planetary systems depends only slightly on the initial distribution of protoplanets and the bulk density as long as the total mass is fixed.