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Our previous model (NEOMOD2) for the orbital and absolute magnitude distribution of Near Earth Objects (NEOs) was calibrated on the Catalina Sky Survey observations between 2013 and 2022. Here we extend NEOMOD2 to include visible albedo information from the Wide-Field Infrared Survey Explorer. The debiased albedo distribution of NEOs can be approximated by the sum of two Rayleigh distributions with the scale parameters p_V,dark=0.03 and p_V,bright=0.17. We find evidence for smaller NEOs having (on average) higher albedos than larger NEOs; this is likely a consequence of the size-dependent sampling of different main belt sources. These inferences and the absolute magnitude distribution from NEOMOD2 are used to construct the debiased size distribution of NEOs. We estimate 830+/-60 NEOs with diameters D>1 km and 20,000+/-2,000 NEOs with D>140 m. The new model, NEOMOD3, is available via the NEOMOD Simulator -- an easy-to-operate code that can be used to generate user-defined samples (orbits, sizes and albedos) from the model., Comment: Icarus, in press

The dynamical architecture and compositional diversity of the asteroid belt strongly constrain planet formation models. Recent Solar System formation models have shown that the asteroid belt may have been born empty and later filled with objects from the inner ($<$2~au) and outer regions (>5 au) of the solar system. In this work, we focus on the implantation of inner solar system planetesimals into the asteroid belt - envisioned to represent S and/or E- type asteroids - during the late-stage accretion of the terrestrial planets. It is widely accepted that the solar system's giant planets formed in a more compact orbital configuration and evolved to their current dynamical state due to a planetary dynamical instability. In this work, we explore how the implantation efficiency of asteroids from the terrestrial region correlates with the timing of the giant planet instability, which has proven challenging to constrain. We carried out a suite of numerical simulations of the accretion of terrestrial planets considering different initial distributions of planetesimals in the terrestrial region and dynamical instability times. Our simulations show that a giant planet dynamical instability occurring at $t\gtrapprox5$ Myr -- relative to the time of the sun's natal disk dispersal -- is broadly consistent with the current asteroid belt, allowing the total mass carried out by S-complex type asteroids to be implanted into the belt from the terrestrial region. Finally, we conclude that an instability that occurs coincident with the gas disk dispersal is either inconsistent with the empty asteroid belt scenario, or may require that the gas disk in the inner solar system have dissipated at least a few Myr earlier than the gas in the outer disk (beyond Jupiter's orbit)., Comment: Under review in Icarus

The asteroid Athor, residing today in the inner main asteroid belt, has been recently associated as the source of EL enstatite meteorites to Earth. It has been argued that Athor formed in the terrestrial region -- as indicated by similarity in isotopic compositions between Earth and EL meteorites -- and was implanted in the belt $\gtrsim$60 Myr after the formation of the solar system. A recently published study modelling Athor's implantation in the belt (Avdellidou et al 2024) further concluded, using an idealized set of numerical simulations, that Athor cannot have been scattered from the terrestrial region and implanted at its current location unless the giant planet dynamical instability occurred {\em after} Athor's implantation ($\gtrsim$60~Myr). In this work, we revisit this problem with a comprehensive suite of dynamical simulations of the implantation of asteroids into the belt during the terrestrial planet accretion. We find that Athor-like objects can in fact be implanted into the belt long after the giant planets' dynamical instability. The probability of implanting Athor analogs when the instability occurs at $\lesssim15$~Myr is at most a factor of $\sim$2 lower than that of an instability occurring at $\sim100$~Myr after the solar system formation. Moreover, Athor's implantation can occur up to $\gtrsim$100 Myr after the giant planet instability. We conclude that Athor's link to EL meteorites does not constrain the timing of the solar system's dynamical instability., Comment: Submitted. Comments welcome

The main asteroid belt (MAB) is known to be primarily composed of objects from two distinct taxonomic classes, generically defined here as S- and C-complex. The former probably originated from the inner solar system (interior to Jupiter's orbit), while the latter probably from the outer solar system. Following this definition, (4) Vesta, a V-type residing in the inner MAB (a < 2.5 au), is the sole D > 500 km object akin to S-complex that potentially formed in-situ. This provides a useful constraint on the number of D > 500 km bodies that could have formed, or grown, within the primordial MAB. In this work we numerically simulate the accretion of objects in the MAB region during the time when gas in the protoplanetary disk still existed, while assuming different MAB primordial masses. We then accounted for the depletion of that population happening after gas disk dispersal. In our analysis, we subdivided the MAB into five sub-regions and showed that the depletion factor varies throughout the MAB. This results in uneven radial- and size-dependent depletion of the MAB. We show that the MAB primordial mass has to be $\lesssim$ 2.14$\times$10$^{-3}$ Earth masses. Larger primordial masses would lead to the accretion of tens-to-thousands of S-complex objects with D > 500 km in the MAB. Such large objects would survive depletion even in the outer sub-regions (a > 2.5 au), thus being inconsistent with observations. Our results also indicate that S-complex objects with D > 200-300 km, including (4) Vesta, are likely to be terrestrial planetesimals implanted into the MAB rather than formed in-situ., Comment: Accepted for publication in PSJ, 23 pages, 7 figures, 4 tables

Jupiter Trojans (JTs) librate about the Lagrangian stationary centers L4 and L5 associated with this planet on a typically small-eccentricity and moderate-inclination heliocentric orbits. The physical and orbital properties of JTs provide important clues about the dynamical evolution of the giant planets in the early Solar System, as well as populations of planetesimals in their source regions. Here we use decade long observations from the Catalina Sky Survey (station G96) to determine the bias-corrected orbital and magnitude distributions of JTs. We distinguish the background JT population, filling smoothly the long-term stable orbital zone about L4 and L5 points, and collisional families. We find that the cumulative magnitude distribution of JTs (the background population in our case) has a steep slope for $H\leq 9$, followed with a moderately shallow slope till $H\simeq 14.5$, beyond which the distribution becomes even shallower. At $H=15$ we find a local power-law exponent $0.38\pm 0.01$. We confirm the asymmetry between the magnitude limited background populations in L4 and L5 clouds characterized by a ratio $1.45\pm 0.05$ for $H<15$. Our analysis suggests an asymmetry in the inclination distribution of JTs, with the L4 population being tighter and the L5 population being broader. We also provide a new catalog of the synthetic proper elements for JTs with an updated identification of statistically robust families (9 at L4, and 4 at L5). The previously known Ennomos family is found to consist of two, overlapping Deiphobus and Ennomos families., Comment: 46 pages, 36 figures, 4 tables, accepted for publication in The Astronomical Journal

Catalina Sky Survey (CSS) is a major survey of Near-Earth Objects (NEOs). In a recent work, we used CSS observations from 2005-2012 to develop a new population model of NEOs (NEOMOD). CSS's G96 telescope was upgraded in 2016 and detected over 10,000 unique NEOs since then. Here we characterize the NEO detection efficiency of G96 and use G96's NEO detections from 2013-2022 to update NEOMOD. This resolves previous model inconsistencies related to the population of large NEOs. We estimate there are 936+/-29 NEOs with absolute magnitude H<17.75 (diameter D>1 km for the reference albedo p_V=0.14). The slope of the NEO size distribution for H=25-28 is found to be relatively shallow (cumulative index 2.6) and the number of H<28 NEOs (D>9 m) is determined to be (1.20+/-0.04)x10^7. Small NEOs have a different orbital distribution and higher impact probabilities than large NEOs. We estimate 0.034+/-0.002 impacts of H<28 NEOs on the Earth per year, which is near the low end of the impact flux range inferred from atmospheric bolide observations. Relative to a model where all NEOs are delivered directly from the main belt, the population of small NEOs detected by G96 shows an excess of low-eccentricity orbits with a=1--1.6 au that appears to increase with H. We suggest that the population of very small NEOs is boosted by tidal disruption of large NEOs during close encounters to the terrestrial planets. When the effect of tidal disruption is (approximately) accounted for in the model, we estimate 0.06+/-0.01 impacts of H<28 NEOs on the Earth per year, which is more in line with the bolide data., Comment: Icarus, in press. arXiv admin note: text overlap with arXiv:2306.09521

The origins of carbonaceous asteroids in the asteroid belt is not fully understood. The leading hypothesis is that they were not born at their current location but instead implanted into the asteroid belt early in the Solar System history. We investigate how the migration and growth of Jupiter and Saturn in their natal disk impact nearby planetesimals and subsequent planetesimal implantation into the asteroid belt. We account for the effects of surface ablation of planetesimals caused by thermal and frictional heating between the gas-disk medium and planetesimal surface, when planetesimals travel through the gas disk. We have performed simulations considering planetesimals of different compositions as water-ice rich planetesimals, water-ice poor planetesimals, organic-rich planetesimals, and fayalite-rich planetesimals. Our findings indicate that, regardless of the migration history of the giant planets, water-ice rich, organic-rich, and fayalite-rich planetesimals implanted into the asteroid belt generally experience surface ablation during implantation in the asteroid belt, shrinking in size. Planetesimals with enstatite-like compositions were inconsequential to surface ablation, preserving their original sizes. By assuming an initial planetesimal size-frequency distribution, our results show that -- under the effects of surface ablation -- the planetesimal population implanted into the asteroid belt shows a SFD slope slightly steeper than that of the initial one. This holds true for all migration histories of the giant planets considered in this work, but for the Grand-Tack model where the SFD slope remains broadly unchanged. Altogether, our results suggest that the largest C-type asteroids in the asteroid belt may have been born bigger. High-degree surface ablation during implantation into the asteroid belt may have even exposed the cores of early differentiated C-type planetesimals.

Comets are considered a potential source of inner solar system volatiles, but the timing of this delivery relative to that of Earth's accretion is still poorly understood. Measurements of xenon isotopes in comet 67P/Churyumov-Gerasimenko revealed that comets partly contributed to the Earth's atmosphere. However, there is no conclusive evidence of a significant cometary component in the Earth's mantle. These geochemical constraints would favour a contribution of comets mainly occurring after the last stages of Earth's formation. Here, we evaluate whether dynamical simulations satisfy these constraints in the context of an Early Instability model. We perform dynamical simulations of the solar system, calculate the probability of collision between comets and Earth analogs component embryos through time and estimate the total cometary mass accreted in Earth analogs as a function of time. While our results are in excellent agreement with geochemical constraints, we also demonstrate that the contribution of comets on Earth might have been delayed with respect to the timing of the instability, due to a stochastic component of the bombardment. More importantly, we show that it is possible that enough cometary mass has been brought to Earth after it had finished forming so that the xenon constraint is not necessarily in conflict with an Early Instability scenario. However, it appears very likely that a few comets were delivered to Earth early in its accretion history, thus contributing to the mantle's budget. Finally, we compare the delivery of cometary material on Earth to Venus and Mars. These results emphasize the stochastic nature of the cometary bombardment in the inner solar system., Comment: 26 pages, 12 figures

The tumultuous early era of outer solar system evolution culminated when Neptune migrated across the primordial Kuiper belt (PKB) and triggered a dynamical instability among the giant planets. This event led to the ejection of approximately 99.9\% of the PKB (here called the destabilized population), heavy bombardment of the giant planet satellites, and the capture of Jupiter's Trojans. While this scenario has been widely tested using dynamical models, there have been fewer investigations into how the PKB, its destabilized population, and the Trojans experienced collisional evolution. Here we examined this issue for all three populations with the code Boulder. Our constraints included the size-frequency distributions (SFDs) of the Trojan asteroids and craters on the giant planet satellites. Using this combination, we solved for the unknown disruption law affecting bodies in these populations. The weakest ones, from an impact energy per mass perspective, were 20 m in diameter. Overall, collisional evolution produces a power-law-like shape for multikilometer Trojans and a wavy-shaped SFD in the PKB and destabilized populations. The latter can explain (i) the shapes of the ancient and younger crater SFDs observed on the giant planet satellites, (ii) the shapes of the Jupiter family and long-period comet SFDs, which experienced different degrees of collision evolution, and (iii) the present-day impact frequency of superbolides on Jupiter and smaller projectiles on Saturn's rings. Our model results also indicate that many observed comets, most which are smaller than 10 km in diameter, are likely to be gravitational aggregates formed by large-scale collision events., Comment: 95 pages, 19 figures. Accepted for publication in PSJ

Near Earth Objects (NEOs) are a transient population of small bodies with orbits near or in the terrestrial planet region. They represent a mid-stage in the dynamical cycle of asteroids and comets, which starts with their removal from the respective source regions -- the main belt and trans-Neptunian scattered disk -- and ends as bodies impact planets, disintegrate near the Sun, or are ejected from the Solar System. Here we develop a new orbital model of NEOs by numerically integrating asteroid orbits from main belt sources and calibrating the results on observations of the Catalina Sky Survey. The results imply a size-dependent sampling of the main belt with the $\nu_6$ and 3:1 resonances producing $\simeq 30$\% of NEOs with absolute magnitudes $H = 15$ and $\simeq 80$\% of NEOs with $H = 25$. Hence, the large and small NEOs have different orbital distributions. The inferred flux of $H<18$ bodies into the 3:1 resonance can be sustained only if the main-belt asteroids near the resonance drift toward the resonance at the maximal Yarkovsky rate ($\simeq 2 \times 10^{-4}$ au Myr$^{-1}$ for diameter $D=1$ km and semimajor axis $a=2.5$~au). This implies obliquities $\theta \simeq 0^\circ$ for $a<2.5$~au and $\theta \simeq 180^\circ$ for $a>2.5$~au, both in the immediate neighborhood of the resonance (the same applies to other resonances as well). We confirm the size-dependent disruption of asteroids near the Sun found in previous studies. An interested researcher can use the publicly available NEOMOD Simulator to generate user-defined samples of NEOs from our model., Comment: AJ

After performing a reassessment of the known dynamical asteroid families in the inner main belt, we report a newly discovered ancient asteroid family with an estimated age of $4.3\pm1.7$ billion years. Additionally, we report the most comprehensive list of planetesimals, which are asteroids that survived since the planet forming days of the solar system., Comment: 21 pages, 13 figures

The lunar crater record features $\sim 50$ basins. The radiometric dating of Apollo samples indicates that the Imbrium basin formed relatively late -- from the planet formation perspective -- some $\simeq 3.9$ Ga. Here we develop a dynamical model for impactors in the inner solar system to provide context for the interpretation of the lunar crater record. The contribution of cometary impactors is found to be insignificant. Asteroids produced most large impacts on the terrestrial worlds in the last $\simeq 3$ Gyr. The great majority of early impactors were rocky planetesimals left behind at $\sim 0.5$--1.5 au after the terrestrial planet accretion. The population of terrestrial planetesimals was reduced by disruptive collisions in the first $t \sim 20$ Myr after the gas disk dispersal. We estimate that there were $\sim 4 \times 10^5$ diameter $d>10$ km bodies when the Moon formed (total planetesimal mass $\sim 0.015$ $M_{\rm Earth}$ at $t \sim 50$ Myr). The early bombardment of the Moon was intense. To accommodate $\sim 50$ known basins, the lunar basins that formed before $\simeq 4.35$--4.41 Ga must have been erased. The late formation of Imbrium occurs with a $\sim 15$--35\% probability in our model. About 20 $d>10$-km bodies were expected to hit the Earth between 2.5 and 3.5 Ga, which is comparable to the number of known spherule beds in the late Archean. We discuss implications of our model for the lunar/Martian crater chronologies, Late Veneer, and noble gases in the Earth atmosphere., Comment: Icarus, in press

The Moon holds important clues to the early evolution of the Solar System. Some 50 impact basins (crater diameter D>300 km) have been recognized on the lunar surface, implying that the early impact flux was much higher than it is now. The basin-forming impactors were suspected to be asteroids released from an inner extension of the main belt (1.8-2.0 au). Here we show that most impactors were instead rocky planetesimals left behind at 0.5-1.5 au after the terrestrial planet accretion. The number of basins expected from impacts of leftover planetesimals largely exceeds the number of known lunar basins, suggesting that the first 200 Myr of impacts is not recorded on the lunar surface. The Imbrium basin formation (age 3.92 Gyr; impactor diameter d~100 km) occurs with a 15-35% probability in our model. Imbrium must have formed unusually late to have only two smaller basins (Orientale and Schrodinger) forming afterwards. The model predicts 20 d>10-km impacts on the Earth 2.5-3.5 Gyr ago (Ga), which is comparable to the number of known spherule beds in the late Archean., Comment: ApJL, in press

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 with orbits interior to a collection of ~Mars-mass embryos 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., Comment: 16 pages, 7 figures, accepted for publication in Icarus

The migration history of Jupiter in the sun's natal disk remains poorly constrained. Here we consider how Jupiter's migration affects small-body reservoirs and how this constrains its original orbital distance from the Sun. We study the implications of large-scale and inward radial migration of Jupiter for the inner solar system while considering the effects of collisional evolution of planetesimals. We use analytical prescriptions to simulate the growth and migration of Jupiter in the gas disk. We assume the existence of a planetesimal disk inside Jupiter's initial orbit. This planetesimal disk received an initial total mass and size-frequency distribution (SFD). Planetesimals feel the effects of aerodynamic gas drag and collide with one another, mostly while shepherded by the migrating Jupiter. Our main goal is to measure the amount of mass in planetesimals implanted into the main asteroid belt (MAB) and the SFD of the implanted population. We also monitor the amount of dust produced during planetesimal collisions. We find that the SFD of the planetesimal population implanted into the MAB tends to resemble that of the original planetesimal population interior to Jupiter. We also find that unless very little or no mass existed between 5 au and Jupiter's original orbit, it would be difficult to reconcile the current low mass of the MAB with the possibility that Jupiter migrated from distances beyond 15 au. This is because the fraction of the original disk mass that gets implanted into the MAB is very large. Finally, we discuss the implications of our results in terms of dust production to the so-called NC-CC isotopic dichotomy., Comment: Accepted for publication in The Astrophysical Journal Letters; In press

In this work, we model the collisional evolution of the Jupiter Trojans and determined under which conditions the Eurybates-Queta system survives. We show that the collisional strength of the Jupiter Trojans and the age of the Eurybates family and by extension Queta are correlated. The collisional grinding of the Jupiter Trojan population over 4.5 Gy results in a size-frequency distribution (SFD) that remains largely unaltered at large sizes (>10 km) but is depleted at small sizes (10 m to 1 km). This results in a turnover in the SFD, the location of which depends on the collisional strength of the material. It is to be expected that the Trojan SFD bends between 1 and 10 km. Based on the SFD of the Eurybates family, we find that the family was likely the result of a catastrophic impact onto a 100 km rubble pile target. This corresponds to objects with a rather low collisional strength (10 times weaker than that of basaltic material studied in Benz & Asphaug1999). Assuming this weak strength, and an initial cumulative slope of the size frequency distribution of 2.1 between diameters of 2 m and 100 km when the Trojans were captured, the existence of Queta, the satellite of Eurybates, implies an upper limit for the family age of 3.7 Gy. Alternatively, we demonstrate that an unconventional collisional strength with a minimum at 20 m is a plausible candidate to ensure the survival of Queta over the age of the Solar System. Finally, we show how different collisional histories change the expected number of craters on the targets of the Lucy mission and that Lucy will be able to differentiate between them., Comment: 19 pages, 13 figures

Astronomical observations reveal that protoplanetary disks around young stars commonly have ring- and gap-like structures in their dust distributions. These features are associated with pressure bumps trapping dust particles at specific locations, which simulations show are ideal sites for planetesimal formation. Here we show that our Solar System may have formed from rings of planetesimals -- created by pressure bumps -- rather than a continuous disk. We model the gaseous disk phase assuming the existence of pressure bumps near the silicate sublimation line (at $T \sim$1400~K), water snowline (at $T \sim$170~K), and CO-snowline (at $T \sim$30~K). Our simulations show that dust piles up at the bumps and forms up to three rings of planetesimals: a narrow ring near 1~au, a wide ring between $\sim$3-4~au and $\sim$10-20~au, and a distant ring between $\sim$20~au and $\sim$45~au. We use a series of simulations to follow the evolution of the innermost ring and show how it can explain the orbital structure of the inner Solar System and provides a framework to explain the origins of isotopic signatures of Earth, Mars and different classes of meteorites. The central ring contains enough mass to explain the rapid growth of the giant planets' cores. The outermost ring is consistent with dynamical models of Solar System evolution proposing that the early Solar System had a primordial planetesimal disk beyond the current orbit of Uranus., Comment: Published in Nature Astronomy on Dec 30, 2021. Authors' version including Methods and Supplementary Information

Planets between 1-4 Earth radii with orbital periods <100 days are strikingly common. The migration model proposes that super-Earths migrate inwards and pile up at the disk inner edge in chains of mean motion resonances. After gas disk dispersal, simulations show that super-Earth's gravitational interactions can naturally break their resonant configuration leading to a late phase of giant impacts. The instability phase is key to matching the orbital spacing of observed systems. Yet, most previous simulations have modelled collisions as perfect accretion events, ignoring fragmentation. In this work, we investigate the impact of imperfect accretion on the breaking the chains scenario. We performed N-body simulations starting from distributions of planetary embryos and modelling the effects of pebble accretion and migration in the gas disk. Our simulations also follow the long-term dynamical evolution of super-Earths after the gas disk dissipation. We compared the results of simulations where collisions are treated as perfect merging events with those where imperfect accretion and fragmentation are allowed. We concluded that the perfect accretion is a suitable approximation in this regime, from a dynamical point of view. Although fragmentation events are common, only ~10% of the system mass is fragmented during a typical "late instability phase", with fragments being mostly reacreted by surviving planets. This limited total mass in fragments proved to be insufficient to alter qualitatively the final system dynamical configuration -- e.g. promote strong dynamical friction or residual migration -- compared to simulations where fragmentation is neglected., Comment: 13 pages, 8 figures and 1 table. Accepted for publication in MNRAS

A planetary instability occurring at time $<100$ My after formation of the giant planets in our solar system can be responsible for some characteristics of the inner solar system. However, the actual influence of the instability on the terrestrial planet formation is not well understood. The simulations of terrestrial planet formation are very CPU-expensive, and this limits the exploration of different instability scenarios. To include the effects of the giant planets instability in the simulations of terrestrial planets formation in a feasible way, we approach the problem in two steps. First, we model and record an evolution of the giant planets that replicates the present outer solar system in the end. Then, we use that orbital record, properly interpolated, as the input for a second step to simulate its effects on the terrestrial planet formation. For this second step, we developed iSyMBA, a symplectic massive bodies algorithm, where ``i'' stands for interpolation. iSyMBA is a very useful code to accurately evaluate the effects of planetary instabilities on minor body reservoirs, while accounting for close encounters among massive objects. We provide a detailed description of how iSyMBA was developed and implemented to study terrestrial planet formation. Adapting iSyMBA for other problems that demand interpolation from previous simulations can be done following the method described here.

In a recent paper we proposed that the giant planets' primordial orbits may have been eccentric (~0.05), and used a suite of dynamical simulations to show outcomes of the giant planet instability that are consistent with their present-day orbits. In this follow-up investigation, we present more comprehensive simulations incorporating superior particle resolution, longer integration times, and eliminating our prior means of artificially forcing instabilities to occur at specified times by shifting a planets' position in its orbit. While we find that the residual phase of planetary migration only minimally alters the the planets' ultimate eccentricities, our work uncovers several intriguing outcomes in realizations where Jupiter and Saturn are born with extremely large eccentricities (~0.10 and ~0.25, respectively). In successful simulations, the planets' orbits damp through interactions with the planetesimal disk prior to the instability, thus loosely replicating the initial conditions considered in our previous work. Our results therefore suggest an even wider range of plausible evolutionary pathways are capable of replicating Jupiter and Saturn's modern orbital architecture., Comment: 12 pages, 3 figures, 2 tables, accepted for publication in Icarus

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 the giant planet instability affected formation of the terrestrial planets. We study several instability cases that were previously shown to match many solar system constraints. We find that resonances with the giant planets help to remove solids available for accretion near ~1.5 au, thus stalling the growth of Mars. It does not matter, however, whether the giant planets are placed on their current orbits at t_0 or whether they realistically evolve in one of our instability models; the results are practically the same. The tight orbital spacing of Venus and Earth is difficult to reproduce in our simulations, including cases where bodies grow from a narrow annulus at 0.7-1 au, because protoplanets tend to radially spread during accretion. The best results are obtained in the narrow-annulus model when protoplanets emerging from the dispersing gas nebula are assumed to have (at least) the Mars mass. This suggests efficient accretion of the terrestrial protoplanets during the first ~10 Myr of the solar system., Comment: AJ, in press

Following the break up of a parent body, the Yarkovsky effect causes asteroid family members to spread in orbital semimajor axis with a rate often inversely proportional to their diameter. This size dependent semimajor axis drift causes family members to form structures in the semimajor axis vs inverse diameter plane that have the shape of the letter V. The V-shape method consists in finding the borders of such V-shapes of unknown center and opening. Although successfully employed to find some very old families in the inner main asteroid belt, the V-shape searching method is very sensitive to many parameters. In this work, we first created and evolved a synthetic asteroid family over billions of years. Then, by adding uncertainties to semimajor axis and diameter of the evolved synthetic family components, we randomly generated additional 99 similar, but not perfectly V-shaped, family clones. We chose a fairly low initial velocity dispersion of 20 m/s for our family. Thus, we can more easily relate the spreading in semimajor axis with the family's age (slope of the evolving V). A synthetic background with an initially randomly distributed components was also created and evolved for 100 Myr. Thus, by setting different levels of ratio of the synthetic family and background asteroids, we derived a detection efficiency map for the V-shape method and determined how sensitive the results can be based on signal-to-noise levels. We also determined optimal parameter values for the method's efficiency. We found that, families older than ~3 Gyr are likely undetectable, with a method efficiency of 50% or less, whereas younger families (0.5--2.5 Gyr) are more easily detected by the method, with an efficiency of >80%., Comment: 21 pages, 16 figures, Accepted for publication in Icarus

An episode of dynamical instability is thought to have sculpted the orbital structure of the outer solar system. When modeling this instability, a key constraint comes from Jupiter's fifth eccentric mode (quantified by its amplitude M55), which is an important driver of the solar system's secular evolution. Starting from commonly-assumed near-circular orbits, the present-day giant planets' architecture lies at the limit of numerically generated systems, and M55 is rarely excited to its true value. Here we perform a dynamical analysis of a large batch of artificially triggered instabilities, and test a variety of configurations for the giant planets' primordial orbits. In addition to more standard setups, and motivated by the results of modern hydrodynamical simulations of the giant planets' evolution within the primordial gaseous disk, we consider the possibility that Jupiter and Saturn emerged from the nebular gas locked in 2:1 resonance with non-zero eccentricities. We show that, in such a scenario, the modern Jupiter-Saturn system represents a typical simulation outcome, and M55 is commonly matched. Furthermore, we show that Uranus and Neptune's final orbits are determined by a combination of the mass in the primordial Kuiper belt and that of an ejected ice giant., Comment: 35 pages, 21 figures, 8 tables, accepted for publication in AJ

The growth time scales of planetary embryos and their formation process are imperative for our understanding on how planetary systems form and develop. They determine the subsequent growth mechanisms during the life stages of a circumstellar disk. We quantify the timescales and spatial distribution of planetary embryos via collisional growth and fragmentation of dynamically forming 100km sized planetesimals. In our study, the formation timescales of viscous disk evolution and planetesimal formation are linked to the formation of planetary embryos in the terrestrial planet zone. We connect a one dimensional model for viscous gas evolution, dust and pebble dynamics and pebble flux regulated planetesimal formation to the N-body code LIPAD. Our framework enables us to study the formation, growth, fragmentation and evolution of planetesimals with an initial size of 100km in diameter for the first million years of a viscous disk. Our study shows the effect of the planetesimal surface density evolution on the preferential location and timescales of planetary embryo formation. A one dimensional analytically derived model for embryo formation based on the local planetesimal surface density evolution is presented. This model manages to reproduce the spatial distribution, formation rate and total number of planetary embryos at a fraction of the computational cost of the N-body simulations. The formation of planetary embryos in the terrestrial planet zone occurs simultaneously to the formation of planetesimals. The local planetesimal surface density evolution and the orbital spacing of planetary embryos in the oligarchic regime serve well as constraints to model planetary embryo formation analytically. Our embryo formation model will be a valuable asset in future studies regarding planet formation.

The accretion of pebbles on planetary cores has been widely studied in recent years and is found to be a highly effective mechanism for planetary growth. While most studies assume planetary cores as an initial condition in their simulation, the question how, where and when these cores form is often neglected. We study the impact of pebble accretion during the formation phase and subsequent evolution of planetary embryos in the early stages of circumstellar disk evolution. In doing so we aim to quantify the timescales and local dependency of planetary embryo formation, based on the solid evolution of the disk. We connect a one dimensional two population model for solid evolution and pebble flux regulated planetesimal formation to the N-body code LIPAD. In our study we focus on the growth of planetesimals with an initial size of 100 km in diameter by planetesimal collisions and pebble accretion for the first 1 million years of a viscously evolving disk. We compare 18 different N-body simulations in which we vary the total planetesimal mass after 1 million years, the surface density profile of the planetesimal disk, the radial pebble flux and the possibility of pebble accretion. Pebble accretion leads to the formation of fewer, but substantially more massive embryos. The area of possible embryo formation is weakly influenced by the accretion of pebbles and the innermost embryos tend to form slightly earlier compared to the simulations in which pebble accretion is neglected. Pebble accretion strongly enhances the formation of super earths in the terrestrial planet region, but it does not enhance the formation of embryos at larger distances.

The main asteroid belt (MB) is low in mass but dynamically excited. Here we propose a new mechanism to excite the MB during the giant planet ('Nice model') instability, which is expected to have featured repeated close encounters between Jupiter and one or more ice giants ('Jumping Jupiter' -- JJ). We show that, when Jupiter temporarily reaches a high enough level of excitation, both in eccentricity and inclination it induces strong forced vectors of eccentricity and inclination across the MB region. Because during the JJ instability Jupiter's orbit `jumps' around, the forced vectors keep changing both in magnitude and phase throughout the whole MB region. The entire cold primordial MB is thus excited as a natural outcome of the JJ instability. The level of such an excitation, however, is typically larger than the current orbital excitation observed in the MB. We show that the subsequent evolution of the Solar System is capable of reshaping the resultant over-excited MB to its present day orbital state, and that a strong mass depletion ($\sim$90$\%$) is associated to the JJ instability phase and its subsequent evolution throughout the age of the Solar System., Comment: Accepted for publication in The Astrophysical Journal

The origin of the orbital structure of the cold component of the Kuiper belt is still a hot subject of investigation. Several features of the solar system suggest that the giant planets underwent a phase of global dynamical instability, but the actual dynamical evolution of the planets during the instability is still debated. To explain the structure of the cold Kuiper belt, Nesvorny (2015, AJ 150,68) argued for a soft instability, during which Neptune never achieved a very eccentric orbit. Here we investigate the possibility of a more violent instability, from an initially more compact fully resonant configuration of 5 giant planets. We show that the orbital structure of the cold Kuiper belt can be reproduced quite well provided that the cold population formed in situ, with an outer edge between 44 and 45 au and never had a large mass.

Recent works on planetary migration show that the orbital structure of the Kuiper belt can be very well reproduced if before the onset of the planetary instability Neptune underwent a long-range planetesimal-driven migration up to $\sim$28 au. However, considering that all giant planets should have been captured in mean motion resonances among themselves during the gas-disk phase, it is not clear whether such a very specific evolution for Neptune is possible, nor whether the instability could have happened at late times. Here, we first investigate which initial resonant configuration of the giant planets can be compatible with Neptune being extracted from the resonant chain and migrating to $\sim$28 au before that the planetary instability happened. We address the late instability issue by investigating the conditions where the planets can stay in resonance for about 400 My. Our results indicate that this can happen only in the case where the planetesimal disk is beyond a specific minimum distance $\delta_{stab}$ from Neptune. Then, if there is a sufficient amount of dust produced in the planetesimal disk, that drifts inwards, Neptune can enter in a slow dust-driven migration phase for hundreds of Mys until it reaches a critical distance $\delta_{mig}$ from the disk. From that point, faster planetesimal-driven migration takes over and Neptune continues migrating outward until the instability happens. We conclude that, although an early instability reproduces more easily the evolution of Neptune required to explain the structure of the Kuiper belt, such evolution is also compatible with a late instability., Comment: Accepted for publication in AJ

The Asteroid Belt is characterized by the radial mixing of bodies with different physical properties, a very low mass compared to Minimum Mass Solar Nebula expectations and has an excited orbital distribution. Models of the evolution of the Asteroid Belt show that the origin of its structure is strongly linked to the process of terrestrial planet formation. The Grand Tack model presents a possible solution to the conundrum of reconciling the small mass of Mars with the properties of the Asteroid Belt, including the mass depletion, radial mixing and orbital excitation. However, while the inclination distribution produced in the Grand Tack model is in good agreement with the one observed, the eccentricity distribution is skewed towards values larger than those found today. Here, we evaluate the evolution of the orbital properties of the Asteroid Belt from the end of the Grand Tack model (at the end of the gas nebula phase when planets emerge from the dispersing gas disk), throughout the subsequent evolution of the Solar System including an instability of the Giant Planets approximately 400 My later. Before the instability, the terrestrial planets were modeled on dynamically cold orbits with Jupiter and Saturn locked in a 3:2 mean motion resonance. The model continues for an additional 4.1 Gy after the giant planet instability. Our results show that the eccentricity distribution obtained in the Grand Tack model evolves towards one very similar to that currently observed, and the semimajor axis distribution does the same. The inclination distribution remains nearly unchanged with a slight preference for depletion at low inclination; this leads to the conclusion that the inclination distribution at the end of the Grand Tack is a bit over-excited., Comment: published on Icarus

We evaluate the effects of a distant planet, commonly known as planet 9, on the dynamics of the giant planets of the Solar System. We find that, given the large distance of planet 9, the dynamics of the inner giant planets can be decomposed into a classic Lagrange-Laplace dynamics relative to their own invariant plane (the plane orthogonal to their total angular momentum vector) and a slow precession of said plane relative to the total angular momentum vector of the Solar System, including planet 9. Under some specific configurations for planet 9, this precession can explain the current tilt of approximately 6 degrees between the invariant plane of the giant planets and the solar equator. An analytical model is developed to map the evolution of the inclination of the inner giant planets' invariant plane as a function of the planet 9's mass, inclination, eccentricity and semimajor axis, and some numerical simulations of the equations of motion of the giant planets and planet 9 are performed to validate our analytical approach. The longitude of the ascending node of planet 9 is found to be linked to the longitude of the ascending node of the giant planets' invariant plane, which also constrain the longitude of the node of planet 9 on the ecliptic. Some of the planet 9 configurations that allow explaining the current solar tilt are compatible with those proposed to explain the orbital confinement of the most distant Kuiper belt objects. Thus, this work on the one hand gives an elegant explanation for the current tilt between the invariant plane of the inner giant planets and the solar equator and, on the other hand, adds new constraints to the orbital elements of planet 9., Comment: manuscript #: AAS01708, submitted on July 12, 2016

Saturn's moon Iapetus has an orbit in a transition region where the Laplace surface is bending from the equator to the orbital plane of Saturn. The orbital inclination of Iapetus to the local Laplace plane is ~8 deg, which is unexpected, because the inclination should be ~0 if Iapetus formed from a circumplanetary disk on the Laplace surface. It thus appears that some process has pumped up Iapetus's inclination while leaving its eccentricity near zero (e=0.03 at present). Here we examined the possibility that Iapetus's inclination was excited during the early solar system instability when encounters between Saturn and ice giants occurred. We found that the dynamical effects of planetary encounters on Iapetus's orbit sensitively depend on the distance of the few closest encounters. In four out of ten instability cases studied here, the orbital perturbations were too large to be plausible. In one case, Iapetus's orbit was practically unneffected. In the remaining five cases, the perturbations of Iapetus's inclination were adequate to explain its present value. In three of these cases, however, Iapetus's eccentricity was excited to 0.1-0.25, and it is not clear whether it could have been damped to its present value (0.03) by some subsequent process (e.g., tides and dynamical friction from captured irregular satellites do not seem to be strong enough). Our results therefore imply that only 2 out of 10 instability cases (~20%) can excite Iapetus's inclination to its present value (~30% of trials lead to >5 deg) while leaving its orbital eccentricity low., Comment: Astronomical Journal