Pressure is a key parameter in the physics and chemistry of planet formation and evolution. Previous studies have erroneously assumed that internal pressures monotonically increase with the mass of a body. Using smoothed particle hydrodynamics and potential field method calculations, we demonstrate that the hot, rapidly-rotating bodies produced by giant impacts can have much lower internal pressures than cool, slowly-rotating planets of the same mass. Pressures subsequently increase due to thermal and rotational evolution of the body. Using the Moon-forming impact as an example, we show that the internal pressures after the collision could have been less than half that in present-day Earth. The current pressure profile was not established until Earth cooled and the Moon receded, a process that may take up to 10s Myr after the last giant impact. Our work defines a new paradigm for pressure evolution during accretion of terrestrial planets: stochastic changes driven by impacts.
The giant planets of the solar system likely played a large role in shaping the architecture of the terrestrial planets. Using an updated collision model, we conduct a suite of high resolution N-body integrations to probe the relationship between giant planet mass, and terrestrial planet formation and system architecture. We vary the mass of the planets that reside at Jupiter's and Saturn's orbit and examine the effects on the interior terrestrial system. We find a correlation between the mass of the exterior giant planets and the collision history of the resulting planets, which holds implica…
Many features of the outer solar system are replicated in numerical simulations if the giant planets undergo an orbital instability that ejects one or more ice giants. During this instability, Jupiter and Saturn's orbits diverge, crossing their 2:1 mean motion resonance (MMR), and this resonance-crossing can excite the terrestrial planet orbits. Using a large ensemble of simulations of this giant planet instability, we directly model the evolution of the terrestrial planet orbits during this process, paying special attention to systems that reproduce the basic features of the outer planets. In…
The migration of the giant planets due to the scattering of planetesimals causes powerful resonances to move through the asteroid belt and the terrestrial planet region. Exactly when and how the giant planets migrated is not well known. In this paper we present results of an investigation of the formation of the terrestrial planets during and after the migration of the giant planets. The latter is assumed to have occurred immediately after the dissipation of the nebular disk -- i.e. "early" with respect to the timing of the Late Heavy Bombardment (LHB). The presumed cause of our modeled early …
Evidence of mutually inclined planetary orbits has been reported for giant planets these last years. Here we aim to study the impact of eccentric and inclined massive giant planets on the terrestrial planet formation process, and investigate whether it can possibly lead to the existence of inclined terrestrial planets. We have performed 126 simulations of the late-stage planetary accretion in eccentric and inclined giant planet systems. The physical and orbital parameters of the giant planet systems result from n-body simulations of three giant planets in the late stage of the gas disc, under …
In this work, we investigate configuration formation of two inner terrestrial planets near mean motion resonance (MMRs) induced by the perturbation of a distant gas-giant for the Kepler-68 system, by conducting thousands of numerical simulations. The results show that the formation of terrestrial planets is relevant to the speed of Type I migration, the mass of planets, and the existence of giant planet. The mass and eccentricity of the giant planet may play a crucial role in shaping the final configuration of the system. The inner planet pair can be trapped in 5:3 or 7:4 MMRs if the giant pla…
We study the long term orbital evolution of a terrestrial planet under the gravitational perturbations of a giant planet. In particular, we are interested in situations where the two planets are in the same plane and are relatively close. We examine both possible configurations: the giant planet orbit being either outside or inside the orbit of the smaller planet. The perturbing potential is expanded to high orders and an analytical solution of the terrestrial planetary orbit is derived. The analytical estimates are then compared against results from the numerical integration of the full equat…
Hundreds of giant planets have been discovered so far and the quest of exo-Earths in giant planet systems has become intriguing. In this work, we aim to address the question of the possible long-term coexistence of a terrestrial companion on an orbit interior to a giant planet, and explore the extent of the stability regions for both non-resonant and resonant configurations. Our study focuses on the restricted three-body problem, where an inner terrestrial planet (massless body) moves under the gravitational attraction of a star and an outer massive planet on a circular or elliptic orbit. Usin…
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 thro…
We present models for the formation of terrestrial planets, and the collisional evolution of debris disks, in planetary systems that contain multiple unstable gas giants. We previously showed that the dynamics of the giant planets introduces a correlation between the presence of terrestrial planets and debris disks. Here we present new simulations that show that this connection is qualitatively robust to changes in: the mass distribution of the giant planets, the width and mass distribution of the outer planetesimal disk, and the presence of gas in the disk. We discuss how variations in these …
In the present research, we study the effects of a single giant planet in the dynamical evolution of water-rich embryos and planetesimals, located beyond the snow line of systems around Sun-like stars, in order to determine what kind of terrestrial-like planets could be formed in the habitable zone (hereafter HZ) of these systems. To do this, we carry out N-body simulations of planetary accretion, considering that the gas has been already dissipated from the disk and a single giant planet has been formed beyond the snow line of the system, at 3 au. We find that a giant planet with a value of m…
Evidence in the Solar System suggests that the giant planets underwent an epoch of radial migration that was very rapid, with an e-folding timescale shorter than 1~Myr. It is probable that the cause of this migration was that the giant planets experienced an orbital instability that caused them to encounter each other, resulting in radial migration. Several works suggest that this dynamical instability occurred `late', long after all the planets had formed and the solar nebula had dissipated. Assuming that the terrestrial planets had already formed, then their orbits would have been affected b…
The terrestrial planets are believed to have formed by violent collisions of tens of lunar- to Mars-size protoplanets at time t<200 Myr after the protoplanetary gas disk dispersal (t_0). The solar system giant planets rapidly formed during the protoplanetary disk stage and, after t_0, radially migrated by interacting with outer disk planetesimals. An early (t<100 Myr) dynamical instability is thought to have occurred with Jupiter having gravitational encounters with a planetary-size body, jumping inward by ~0.2-0.5 au, and landing on its current, mildly eccentric orbit. Here we investigate how…
Circumstantial evidence suggests that most known extra-solar planetary systems are survivors of violent dynamical instabilities. Here we explore how giant planet instabilities affect the formation and survival of terrestrial planets. We simulate planetary system evolution around Sun-like stars from initial conditions that comprise: an inner disk of planetesimals and planetary embryos, three giant planets at Jupiter-Saturn distances, and a massive outer planetesimal disk. We then calculate dust production rates and debris disk SEDs assuming that each planetesimal particle represents an ensemble…
Prior work has found that a variety of terrestrial planetary compositions are expected to occur within known extrasolar planetary systems. However, such studies ignored the effects of giant planet migration, which is thought to be very common in extra-solar systems. Here we present calculations of the compositions of terrestrial planets that formed in dynamical simulations incorporating varying degrees of giant planet migration. We used chemical equilibrium models of the solid material present in the disks of five known planetary host stars: the Sun, GJ 777, HD4203, HD19994 and HD213240. Giant…
The orbital distributions of currently observed extrasolar giant planets allow marginally stable orbits for hypothetical, terrestrial planets. In this paper, we propose that many of these systems may not have additional planets on these "stable" orbits, since past dynamical instability among giant planets could have removed them. We numerically investigate the effects of early evolution of multiple giant planets on the orbital stability of the inner, sub-Neptune-like planets which are modeled as test particles, and determine their dynamically unstable region. Previous studies have shown that t…
We examine the effect of giant planet migration on the formation of inner terrestrial planet systems. We consider situations in which the giant planet halts migration at semi-major axes in the range 0.13 - 1.7 AU due to gas disk dispersal. An N-body code is employed that is linked to a viscous gas disk algorithm capable of simulating: gas loss via accretion onto the central star and photoevaporation; gap formation by the giant planet; type II migration of the giant; optional type I migration of protoplanets; gas drag on planetesimals. We find that most of the inner system planetary building bl…
It has been shown that an Earth-size planet or a super-Earth, in resonance with a transiting Jupiter-like body in a short-period orbit around an M star, can create detectable TTV signals (Kirste \& Haghighipour, 2011). Given the low masses of M stars and their circumstellar disks, it is expected that such a transiting giant planet to have formed at large distances and migrated to its close-in orbit. That implies, if such systems are discovered around M stars, the terrestrial planet had to form during the migration of the giant planet. The formation of this object may be either in-situ (in a cl…
Giant planet embryos are believed to be spawned by gravitational instability in massive extended (R ~ 100 AU) protostellar discs. In a recent paper we have shown that dust can sediment inside the embryos, as argued earlier by Boss (1998) in a slightly different model. Here we study numerically the next stage of this process -- the formation of a solid core. If conditions are conducive to solid core formation, the centre of the gas cloud goes through the following sequence of phases: (i) becomes grain (and metal) rich; (ii) forms a terrestrial mass solid core via a rapid collapse driven by self…
The solar system's dynamical state can be explained by an orbital instability among the giant planets. A recent model has proposed that the giant planet instability happened during terrestrial planet formation. This scenario has been shown to match the inner solar system by stunting Mars' growth and preventing planet formation in the asteroid belt. Here we present a large sample of new simulations of the "Early Instability" scenario. We use an N-body integration scheme that accounts for collisional fragmentation, and also perform a large set of control simulations that do not include an early …
The eccentric orbits of the known extrasolar giant planets provide evidence that most planet-forming environments undergo violent dynamical instabilities. Here, we numerically simulate the impact of giant planet instabilities on planetary systems as a whole. We find that populations of inner rocky and outer icy bodies are both shaped by the giant planet dynamics and are naturally correlated. Strong instabilities -- those with very eccentric surviving giant planets -- completely clear out their inner and outer regions. In contrast, systems with stable or low-mass giant planets form terrestrial …
The presence of giant planets influences potentially habitable worlds in numerous ways. Massive celestial neighbors can facilitate the formation of planetary cores and modify the influx of asteroids and comets towards Earth-analogs later on. Furthermore, giant planets can indirectly change the climate of terrestrial worlds by gravitationally altering their orbits. Investigating 147 well characterized exoplanetary systems known to date that host a main sequence star and a giant planet we show that the presence of 'giant neighbors' can reduce a terrestrial planet's chances to remain habitable, e…
We present results from a suite of N-body simulations that follow the accretion history of the terrestrial planets using a new parallel treecode that we have developed. We initially place 2000 equal size planetesimals between 0.5--4.0 AU and the collisional growth is followed until the completion of planetary accretion (> 100 Myr). All the important effect of gas in laminar disks are taken into account: the aerodynamic gas drag, the disk-planet interaction including Type I migration, and the global disk potential which causes inward migration of secular resonances as the gas dissipates. We var…
The Kepler mission found hundreds of planet candidates within the habitable zones (HZ) of their host star, including over 70 candidates with radii larger than 3 Earth radii ($R_\oplus$) within the optimistic habitable zone (OHZ) (Kane et al. 2016). These giant planets are potential hosts to large terrestrial satellites (or exomoons) which would also exist in the HZ. We calculate the occurrence rates of giant planets ($R_p =$~3.0--25~$R_\oplus$) in the OHZ and find a frequency of $(6.5 \pm 1.9)\%$ for G stars, $(11.5 \pm 3.1)\%$ for K stars, and $(6 \pm 6)\%$ for M stars. We compare this with p…
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 independe…
Recent observations started revealing the compositions of protostellar discs and planets beyond the Solar System. In this paper, we explore how the compositions of terrestrial planets are affected by dynamical evolution of giant planets. We estimate the initial compositions of building blocks of these rocky planets by using a simple condensation model, and numerically study the compositions of planets formed in a few different formation models of the Solar System. We find that the abundances of refractory and moderately volatile elements are nearly independent of formation models, and that all…
With n-body simulations, we model terrestrial circumbinary planet (CBP) formation with an initial surface density profile motivated by hydrodynamic circumbinary gas disc simulations. The binary plays an important role in shaping the initial distribution of bodies. After the gas disc has dissipated, the torque from the binary speeds up the planet formation process by promoting body-body interactions but also drives the ejection of planet building material from the system at an early time. Fewer but more massive planets form around a close binary compared to a single star system. A sufficiently …
In this work, we extensively investigate the formation of near 4:2:1 mean motion resonances (MMRs) configuration by performing two sets of N-body simulations. We model the eccentricity damping, gas drag, type I and type II planetary migration of planetesimals, planetary embryos and giant planets in the first sets. For the simulations of giant planets with type II migration, the massive terrestrial planets, with a mass up to several Earth masses, are likely produced in the systems. We further show that by shepherding and/or scattering mechanisms through Jovian planet's type II migration, the te…
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 embry…
We present a new scaling law to predict the loss of atmosphere from planetary collisions for any speed, angle, impactor mass, target mass, and body compositions, in the regime of giant impacts onto broadly terrestrial planets with relatively thin atmospheres. To this end, we examine the erosion caused by a wide range of impacts, using 3D smoothed particle hydrodynamics simulations with sufficiently high resolution to directly model the fate of low-mass atmospheres around 1% of the target's mass. Different collision scenarios lead to extremely different behaviours and consequences for the plane…
In their model for the origin of the parent bodies of iron meteorites, Bottke et al proposed differentiated planetesimals that were formed in the region of 1-2 AU during the first 1.5 Myr, as the parent bodies, and suggested that these objects and their fragments were scattered into the asteroid belt as a result of interactions with planetary embryos. Although viable, this model does not include the effect of a giant planet that might have existed or been growing in the outer regions. We present the results of a concept study where we have examined the effect of a planetary body in the orbit o…
Given the tendency of planets to form in multiples, and the observational evidence in support of the existence of potential planet-hosting stars in binaries or clusters, it is expected that extrasolar terrestrial planes are more likely to be found in multiple body systems. This paper discusses the prospects of the detection of terrestrial/habitable planets in multibody systems by presenting the results of a study of the long-term stability of these objects in systems with multiple giant planets (particularly those in eccentric and/or in mean-motion resonant orbits), systems with close-in Jupit…
We review the state of the field of terrestrial planet formation with the goal of understanding the formation of the inner Solar System and low-mass exoplanets. We review the dynamics and timescales of accretion from planetesimals to planetary embryos and from embryos to terrestrial planets. We discuss radial mixing and water delivery, planetary spins and the importance of parameters regarding the disk and embryo properties. Next, we connect accretion models to exoplanets. We first explain why the observed hot Super Earths probably formed by in situ accretion or inward migration. We show how t…
This paper reviews our current understanding of terrestrial planets formation. The focus is on computer simulations of the dynamical aspects of the accretion process. Throughout the chapter, we combine the results of these theoretical models with geochemical, cosmochemical and chronological constraints, in order to outline a comprehensive scenario of the early evolution of our Solar System. Given that the giant planets formed first in the protoplanetary disk, we stress the sensitive dependence of the terrestrial planet accretion process on the orbital architecture of the giant planets and on t…
Many dynamical aspects of the solar system can be explained by the outer planets experiencing a period of orbital instability sometimes called the Nice Model. Though often correlated with a perceived delayed spike in the lunar cratering record known as the Late Heavy Bombardment (LHB), recent work suggests that this event may have occurred much earlier; perhaps during the epoch of terrestrial planet formation. While current simulations of terrestrial accretion can reproduce many observed qualities of the solar system, replicating the small mass of Mars requires modification to standard planet …
The formation of planets like Earth is expected to conclude with a series of late-stage giant impacts that generate warm dusty debris, the most anticipated visible signpost of terrestrial planet formation in progress. While there is now evidence that Earth-sized terrestrial planets orbit a significant fraction of solar-type stars, the anticipated dusty debris signature of their formation is rarely detected. Here we discuss several ways in which our current ideas about terrestrial planet formation imply transport mechanisms capable of erasing the anticipated debris signature. A tenuous gas disk…
Water condensed as ice beyond the water snowline, the location in the Sun's natal gaseous disk where temperatures were below 170 K. As the disk evolved and cooled, the snowline moved inwards. A low temperature in the terrestrial planet-forming region is unlikely to be the origin of water on the planets, and the distinct isotopic compositions of planetary objects formed in the inner and outer disks suggest limited early mixing of inner and outer Solar System materials. Water in our terrestrial planets has rather been derived from H-bearing materials indigenous to the inner disk and delivered by…
We analyze two new sets of coagulation calculations for solid particles orbiting within the terrestrial zone of a solar-type star. In models of collisional cascades, numerical simulations demonstrate that the total mass, the mass in 1 mm and smaller particles, and the dust luminosity decline with time more rapidly than predicted by analytic models, $\propto t^{-n}$ with $n \approx$ 1.1-1.2 instead of 1. Size distributions derived from the numerical calculations follow analytic predictions at radii less than 0.1 km but are shallower than predicted at larger sizes. In simulations of planet forma…
The giant impact hypothesis for Moon formation successfully explains the dynamic properties of the Earth-Moon system but remains challenged by the similarity of isotopic fingerprints of the terrestrial and lunar mantles. Moreover, recent geochemical evidence suggests that the Earth's mantle preserves ancient (or "primordial") heterogeneity that predates the Moon-forming giant impact. Using a new hydrodynamical method, we here show that Moon-forming giant impacts lead to a stratified starting condition for the evolution of the terrestrial mantle. The upper layer of the Earth is compositionally …
Discoveries of exoplanets using the radial velocity method are progressively reaching out to increasingly longer orbital periods as the duration of surveys continues to climb. The improving sensitivity to potential Jupiter analogs is revealing a diversity of orbital architectures that are substantially different from that found in our solar system. An excellent example of this is the recent discovery of HR 5183b; a giant planet on a highly eccentric ($e = 0.84$) $\sim$75~year orbit. The presence of such giant planet orbits are intrinsically interesting from the perspective of the dynamical his…
The newly formed giant planets may have migrated and crossed a number of mutual mean motion resonances (MMRs) when smaller objects (embryos) were accreting to form the terrestrial planets. We investigated the effects of the planetesimal-driven migration of Jupiter and Saturn, and the influence of their mutual 1:2 MMR crossing on terrestrial planet formation for the first time, by performing N-body simulations. These simulations considered distinct timescales of MMR crossing and planet migration. In total, 68 high-resolution simulation runs using 2000 disk planetesimals were performed, which wa…
The detection of many extrasolar gas giants with high eccentricities indicates that dynamical instabilities in planetary systems are common. These instabilities can alter the orbits of gas giants as well as the orbits of terrestrial planets and therefore eject or move a habitable planet out of the habitable zone. In this work 423 simulations with 153 different hypothetical planetary systems with gas giants and terrestrial planets have been modelled to explore the orbital stability of habitable planets. The initial parameter variations include the number, distances and masses of the giant plane…
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 generat…
We examine the mechanisms by which atmosphere can be eroded by giant impacts onto Earth-like planets with thin atmospheres, using 3D smoothed particle hydrodynamics simulations with sufficient resolution to directly model the fate of low-mass atmospheres. We present a simple scaling law to estimate the fraction lost for any impact angle and speed in this regime. In the canonical Moon-forming impact, only around 10% of the atmosphere would have been lost from the immediate effects of the collision. There is a gradual transition from removing almost none to almost all of the atmosphere for a gra…
We investigate the dynamical evolution of the terrestrial planets during the planetesimal-driven migration of the giant planets. A basic assumption of this work is that giant planet migration occurred after the completion of terrestrial planet formation, such as in the models that link the former to the origin of the Late Heavy Bombardment. The divergent migration of Jupiter and Saturn causes the g5 eigenfrequency to cross resonances of the form g5=gk with k ranging from 1 to 4. Consequently these secular resonances cause large-amplitude responses in the eccentricities of the terrestrial plane…
Exomoons orbiting terrestrial or super-terrestrial exoplanets have not yet been discovered; their possible existence and properties are therefore still an unresolved question. Here we explore the collisional formation of exomoons through giant planetary impacts. We make use of smooth particle hydrodynamical (SPH) collision simulations and survey a large phase-space of terrestrial/super-terrestrial planetary collisions. We characterize the properties of such collisions, finding one rare case in which an exomoon forms through a graze&capture scenario, in addition to a few graze&merge or hit&run …
We investigate formation of close-in terrestrial planets from planetary embryos under the influence of a hot Jupiter (HJ) using gravitational N-body simulations that include gravitational interactions between the gas disk and the terrestrial planet (e.g., type I migration). Our simulations show that several terrestrial planets efficiently form outside the orbit of the HJ, making a chain of planets, and all of them gravitationally interact directly or indirectly with the HJ through resonance, which leads to inward migration of the HJ. We call this mechanism of induced migration of the HJ as "cr…
The classical scenario of terrestrial planet formation is characterized by a phase of giant impacts among Moon-to-Mars mass planetary embryos. While the classic model and its adaptations have produced adequate analogs of the outer three terrestrial planets, Mercury's origin remains elusive. Mercury's high-core mass fraction compared to the Earth's is particularly outstanding. Among collisional hypotheses, this feature has been long interpreted as the outcome of an energetic giant impact among two massive protoplanets. Here, we revisit the classical scenario of terrestrial planet formation with…
We present integrations of a model Solar System with five terrestrial planets (beginning ~30-50 Myr after the formation of primitive Solar System bodies) in order to determine the preferred regions of parameter space leading to a giant impact that resulted in the formation of the Moon. Our results indicate which choices of semimajor axes and eccentricities for Theia (the proto-Moon) at this epoch can produce a late Giant Impact, assuming that Mercury, Venus, and Mars are near the current orbits. We find that the likely semimajor axis of Theia, at the epoch when our simulations begin, depends o…
Building the terrestrial planets has been a challenge for planet formation models. In particular, classical theories have been unable to reproduce the small mass of Mars and instead predict that a planet near 1.5 AU should roughly be the same mass as the Earth. Recently, a new model called Viscous Stirred Pebble Accretion (VSPA) has been developed that can explain the formation of the gas giants. This model envisions that the cores of the giant planets formed from 100 to 1000 km bodies that directly accreted a population of pebbles --- sub-meter sized objects that slowly grew in the protoplane…
