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Co-orbital systems contain two or more bodies sharing the same orbit around a planet or star. The best-known flavors of co-orbital systems are tadpoles (in which two bodies' angular separations oscillate about the L4/L5 Lagrange points $60^\circ$ apart) and horseshoes (with two bodies periodically exchanging orbital energy to trace out a horseshoe shape in a co-rotating frame). Here, we use N-body simulations to explore the parameter space of many-planet horseshoe systems. We show that up to 24 equal-mass, Earth-mass planets can share the same orbit at 1 au, following a complex pattern in which neighboring planets undergo horseshoe oscillations. We explore the dynamics of horseshoe constellations, and show that they can remain stable for billions of years and even persist through their stars' post-main sequence evolution. With sufficient observations, they can be identified through their large-amplitude, correlated transit timing variations. Given their longevity and exotic orbital architectures, horseshoe constellations may represent potential SETI beacons., 10 pages, 10 figures. Published in MNRAS. YouTube playlist with animations of horseshoe constellation systems here: https://www.youtube.com/playlist?list=PLelMZVM3ka3F335LGLxkxrD1ieiLJYQ5N . Blog post here: https://planetplanet.net/2023/04/20/constellations-of-co-orbital-planets/

We analyze 5108 AFGKM stars with at least five high precision radial velocity points as well as Gaia and Hipparcos astrometric data utilizing a novel pipeline developed in previous work. We find 914 radial velocity signals with periods longer than 1000\,d. Around these signals, 167 cold giants and 68 other types of companions are identified by combined analyses of radial velocity, astrometry, and imaging data. Without correcting for detection bias, we estimate the minimum occurrence rate of the wide-orbit brown dwarfs to be 1.3\%, and find a significant brown dwarf valley around 40 $M_{\rm Jup}$. We also find a power-law distribution in the host binary fraction beyond 3 au similar to that found for single stars, indicating no preference of multiplicity for brown dwarfs. Our work also reveals nine sub-stellar systems (GJ 234 B, GJ 494 B, HD 13724 b, HD 182488 b, HD 39060 b and c, HD 4113 C, HD 42581 d, HD 7449 B, and HD 984 b) that have previously been directly imaged, and many others that are observable at existing facilities. Depending on their ages we estimate that an additional 10-57 sub-stellar objects within our sample can be detected with current imaging facilities, extending the imaged cold (or old) giants by an order of magnitude., 39 pages, 14 figures, 5 tables, published in The Astrophysical Journal Supplement Series

The inner solar system's modern orbital architecture provides inferences into the epoch of terrestrial planet formation; a ~100 Myr time period of planet growth via collisions with planetesimals and other proto-planets. While classic numerical simulations of this scenario adequately reproduced the correct number of terrestrial worlds, their semi-major axes and approximate formation timescales, they struggled to replicate the Earth-Mars and Venus-Mercury mass ratios. In a series of past independent investigations, we demonstrated that Mars' mass is possibly the result of Jupiter and Saturn's early orbital evolution, while Mercury's diminutive size might be the consequence of a primordial mass deficit in the region. Here, we combine these ideas in a single modeled scenario designed to simultaneously reproduce the formation of all four terrestrial planets and the modern orbits of the giant planets in broad strokes. By evaluating our Mercury analogs' core mass fractions, masses, and orbital offsets from Venus, we favor a scenario where Mercury forms through a series of violent erosive collisions between a number of ~Mercury-mass embryos in the inner part of the terrestrial disk. We also compare cases where the gas giants begin the simulation locked in a compact 3:2 resonant configuration to a more relaxed 2:1 orientation and find the former to be more successful. In 2:1 cases, the entire Mercury-forming region is often depleted due to strong sweeping secular resonances that also tend to overly excite the orbits of Earth and Venus as they grow. While our model is quite successful at replicating Mercury's massive core and dynamically isolated orbit, the planets' low mass remains extremely challenging to match. Finally, we discuss the merits and drawbacks of alternative evolutionary scenarios and initial disk conditions., Comment: 23 pages, 9 figures, 3 tables, accepted for publication in Icarus

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, 16 pages, 7 figures, accepted for publication in Icarus

The formation of the solar system's giant planets predated the ultimate epoch of massive impacts that concluded the process of terrestrial planet formation. Following their formation, the giant planets' orbits evolved through an episode of dynamical instability. Several qualities of the solar system have recently been interpreted as evidence of this event transpiring within the first ~100 Myr after the Sun's birth; around the same time as the final assembly of the inner planets. In a series of recent papers we argued that such an early instability could resolve several problems revealed in classic numerical studies of terrestrial planet formation; namely the small masses of Mars and the asteroid belt. In this paper, we revisit the early instability scenario with a large suite of simulations specifically designed to understand the degree to which Earth and Mars' formation are sensitive to the specific evolution of Jupiter and Saturn's orbits. By deriving our initial terrestrial disks directly from recent high-resolution simulations of planetesimal accretion, our results largely confirm our previous findings regarding the instability's efficiency of truncating the terrestrial disk outside of the Earth-forming region in simulations that best replicate the outer solar system. Moreover, our work validates the primordial 2:1 Jupiter-Saturn resonance within the early instability framework as a viable evolutionary path for the solar system. While our simulations elucidate the fragility of the terrestrial system during the epoch of giant planet migration, many realizations yield outstanding solar system analogs when scrutinized against a number of observational constraints. Finally, we highlight the inability of models to form adequate Mercury-analogs and the low eccentricities of Earth and Venus as the most significant outstanding problems for future numerical studies to resolve., 24 pages, 10 figures, 6 tables, accepted for publication in Icarus

Trans-Neptunian Objects (TNOs) in the scattered disk with 50 < a < 100 au are thought to cluster near Neptune's n:1 resonances (e.g: 3:1, 4:1, and so on). While these objects spend lengthy periods of time at large heliocentric distances, if their perihelia remain less than around 40 au, their dynamical evolution is still largely coupled to Neptune's. Conversely, around a dozen extreme TNOs with a > 250 au and detached perihelia seem to exist in a regime where they are too distant to be affected by the giant planets, and too close for their dynamics to be governed by external forces. Recent work suggests that the apparent alignment of these orbits in physical space is a signature of gravitational shepherding by a distant massive planet. In this paper, we investigate the evolution of TNOs in each of Neptune's n:1 resonances between the 3:1 and 14:1. We conclude that both resonant and non-resonant objects beyond the 12:1 near ~157 au are removed rather efficiently via perturbations from the hypothetical Planet Nine. Additionally, we uncover a population of simulated TNOs with a < 100 au, 40 < q < 45 au and low inclinations that experience episodes of resonant interactions with both Neptune and Planet Nine. Finally, we simulate the evolution of observed objects with a > 100 au and identify several TNOs that are potentially locked in n:1 resonances with Neptune; including the most distant known resonant candidates 2014 JW80 and 2014 OS394 that appear to be in the 10:1 and 11:1 resonances, respectively. Our results suggest that the detection of similar remote objects might provide a useful constraint on hypotheses invoking the existence of additional distant planets., 18 pages, 12 figures, 1 table, AJ in press, corrected minor typographical errors

The absence of planets interior to Mercury continues to puzzle terrestrial planet formation models, particularly when contrasted with the relatively high derived occurrence rates of short-period planets around Sun-like stars. Recent work proposed that the majority of systems hosting hot super-Earths attain their orbital architectures through an epoch of dynamical instability after forming in quasi-stable, tightly packed configurations. Isotopic evidence seems to suggest that the formation of objects in the super-Earth mass regime is unlikely to have occurred in the solar system as the terrestrial-forming disk is thought to have been significantly mass-deprived starting around 2 Myr after CAI; a consequence of either Jupiter's growth or an intrinsic disk feature. Nevertheless, terrestrial planet formation models and high-resolution investigations of planetesimal dynamics in the gas disk phase occasionally find that quasi-stable proto-planets with masses comparable to that of Mars emerge in the vicinity of Mercury's modern orbit. In this paper, we investigate whether it is possible for a primordial configuration of such objects to be cataclysmically destroyed in a manner that leaves Mercury behind as the sole survivor without disturbing the other terrestrial worlds. We use numerical simulations to show that this scenario is plausible. In many cases, the surviving Mercury analog experiences a series of erosive impacts; thereby boosting its Fe/Si ratio. A caveat of our proposed genesis scenario for Mercury is that Venus typically experiences at least one late giant impact., 18 pages, 15 figures, 1 table, accepted for publication in AJ. Summary available at https://youtu.be/Mu762MjRxtE (video)

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

Modern terrestrial planet formation models are highly successful at consistently generating planets with masses and orbits analogous to those of Earth and Venus. In stark contrast to classic theoretical predictions and inferred demographics of multi-planet systems of rocky exoplanets, the mass (>10) and orbital period (>2) ratios between Venus and Earth and the neighboring Mercury and Mars are not common outcomes in numerically generated systems. While viable solutions to the small-Mars problem are abundant in the literature, Mercury's peculiar origin remains rather mysterious. In this paper, we investigate the possibility that Mercury formed in a mass-depleted, inner region of the terrestrial disk (a < 0.5 au). This regime is often neglected in terrestrial planet formation models because of the high computational cost of resolving hundreds of short-period objects over ~100 Myr timescales. By testing multiple disk profiles and mass distributions, we identify several promising sets of initial conditions that lead to remarkably successful analog systems. In particular, our most successful simulations consider moderate total masses of Mercury-forming material (0.1-0.25 Earth masses). While larger initial masses tend to yield disproportionate Mercury analogs, smaller values often inhibit the planets' formation as the entire region of material is easily accreted by Venus. Additionally, we find that shallow surface density profiles and larger inventories of small planetesimals moderately improve the likelihood of adequately reproducing Mercury., 20 pages, 10 figures, 3 tables, accepted for publication in AJ. Summary available at https://youtu.be/Mu762MjRxtE (video)

In recent years a paradigm shift has occurred in exoplanet science, wherein low-mass stars are increasingly viewed as a foundational pillar of the search for potentially habitable worlds in the solar neighborhood. However, the formation processes of this rapidly accumulating sample of planet systems are still poorly understood. Moreover, it is unclear whether tenuous primordial atmospheres around these Earth-analogs could have survived the intense epoch of heightened stellar activity that is typical for low-mass stars. We present new simulations of in-situ planet formation across the M-dwarf mass spectrum, and derive leftover debris populations of small bodies that might source delayed volatile delivery. We then follow the evolution of this debris with high-resolution models of real systems of habitable zone planets around low-mass stars such as TRAPPIST-1, Proxima Centauri and TOI-700. While debris in the radial vicinity of the habitable zone planets is removed rapidly, thus making delayed volatile delivery highly unlikely, we find that material ubiquitously scattered into an exo-asteroid belt region during the planet formation process represents a potentially lucrative reservoir of icy small bodies. Thus, the presence of external ~Neptune-Saturn mass planets capable of dynamically perturbing these asteroids would be a sign that habitable zone worlds around low-mass stars might have avoided complete desiccation. However, we also find that such giant planets significantly limit the efficiency of asteroidal implantation during the planet formation process. In the coming decade, long-baseline radial velocity studies and Roman Space Telescope microlensing observations will undoubtedly further constrain this process., 19 pages, 9 figures, 3 tables, accepted for publication in ApJ

We present the discovery and validation of a three-planet system orbiting the nearby (31.1 pc) M2 dwarf star TOI-700 (TIC 150428135). TOI-700 lies in the TESS continuous viewing zone in the Southern Ecliptic Hemisphere; observations spanning 11 sectors reveal three planets with radii ranging from 1 R$_\oplus$ to 2.6 R$_\oplus$ and orbital periods ranging from 9.98 to 37.43 days. Ground-based follow-up combined with diagnostic vetting and validation tests enable us to rule out common astrophysical false-positive scenarios and validate the system of planets. The outermost planet, TOI-700 d, has a radius of $1.19\pm0.11$ R$_\oplus$ and resides in the conservative habitable zone of its host star, where it receives a flux from its star that is approximately 86% of the Earth's insolation. In contrast to some other low-mass stars that host Earth-sized planets in their habitable zones, TOI-700 exhibits low levels of stellar activity, presenting a valuable opportunity to study potentially-rocky planets over a wide range of conditions affecting atmospheric escape. While atmospheric characterization of TOI-700 d with the James Webb Space Telescope (JWST) will be challenging, the larger sub-Neptune, TOI-700 c (R = 2.63 R$_\oplus$), will be an excellent target for JWST and beyond. TESS is scheduled to return to the Southern Hemisphere and observe TOI-700 for an additional 11 sectors in its extended mission, which should provide further constraints on the known planet parameters and searches for additional planets and transit timing variations in the system., Accepted for publication in AJ (30 pages, 13 figures, 4 tables, 2 appendices)

The solar system's terrestrial planets are thought to have accreted over millions of years out of a sea of smaller embryos and planetesimals. Because it is impossible to know the surface density profile for solids and size frequency distribution in the primordial solar nebula, distinguishing between the various proposed evolutionary schemes has been historically difficult. Nearly all previous simulations of terrestrial planet formation assume that Moon to Mars massed embryos formed throughout the inner solar system during the primordial gas-disk phase. However, validating this assumption through models of embryo accretion is computationally challenging because of the large number of bodies required. Here, we reevaluate this problem with GPU-accelerated, direct N-body simulations of embryo growth starting from r~100 km planetesimals. We find that embryos emerging from the primordial gas phase at a given radial distance already have masses similar to the largest objects at the same semi-major axis in the modern solar system. Thus, Earth and Venus attain ~50% of their modern mass, Mars-massed embryos form in the Mars region, and Ceres-massed objects are prevalent throughout asteroid belt. Consistent with other recent work, our new initial conditions for terrestrial accretion models produce markedly improved solar system analogs when evolved through the giant impact phase of planet formation. However, we still conclude that an additional dynamical mechanism such as giant planet migration is required to prevent Earth-massed Mars analogs from growing., 16 pages, 13 figures, 4 tables, accepted for publication in The Planetary Science Journal

The longitudes of perihelia and orbital poles of the solar system's dozen or so most remote detected objects are clustered in a manner inconsistent with that of a random sample of uniformly distributed orbits. While small number statistics and observational biases may explain these features, the statistical significance of the clustering has led to the recent development of the "Planet Nine hypothesis." In the proposed scenario, orbits in the distant solar system are shepherded via secular perturbations from an undetected massive planet on an eccentric orbit. However, the precession of perihelia and nodes in the outer Kuiper Belt and inner Oort Cloud are also affected by the the giant planets, passing stars, and the galactic tide. We perform a large suite of numerical simulations designed to study the orbital alignment of Extreme Trans-Neptunian Objects (ETNOs) and Inner Oort Cloud Objects (IOCOs). In our various integrations that include Planet Nine, we consistently find that >60% of ETNOs and IOCOs that are detectable after 4 Gyr are also anti-aligned in perihelia with the distant massive perturber. However, when we randomly select 17 objects from this sample of remaining orbits, there is significant scatter in the degree of longitude of perihelion and orbital pole clustering that might be observed. Furthermore, we argue that, in the absence of Planet Nine, 17 randomly drawn orbits should still exhibit some clustering even if the underlying distribution is uniform. Thus, we find that still more ETNO and IOCO detections are required to confidently infer the presence of Planet Nine., 11 pages, 7 figures, 4 tables, accepted for publication in AJ

The asteroid belt is characterized by an extreme low total mass of material on dynamically excited orbits. The Nice Model explains many peculiar qualities of the solar system, including the belt's excited state, by invoking an orbital instability between the outer planets. However, previous studies of the Nice Model's effect on the belt's structure struggle to reproduce the innermost asteroids' orbital inclination distribution. Here, we show how the final phase of giant planet migration sculpts the asteroid belt, in particular its inclination distribution. As interactions with leftover planetesimals cause Saturn to move away from Jupiter, its rate of orbital precession slows as the two planets' mutual interactions weaken. When the planets approach their modern separation, where Jupiter completes just short of five orbits for every two of Saturn's, Jupiter's eccentric forcing on Saturn strengthens. We use numerical simulations to show that the absence of asteroids with orbits that precess between 24-28 arcsec/yr is related to the inclination problem. As Saturn's precession speeds back up, high inclination asteroids are excited on to planet crossing orbits and removed from the inner main belt. Through this process, the asteroid belt's orbital structure is reshaped, leading to markedly improved simulation outcomes., 5 pages, 4 figures, 2 tables, accepted for publication in MRNAS Letters

Earth-sized planets in the habitable zones of M dwarfs are good candidates for the study of habitability and detection of biosignatures. To search for these planets, we analyze all available radial velocity data and apply four signal detection criteria to select the optimal candidates. We find 10 strong candidates satisfying these criteria and three weak candidates showing inconsistency over time due to data samplings. We also confirm three previous planet candidates and improve their orbital solutions through combined analyses of updated data sets. Among the strong planet candidates, HIP 38594 b is a temperate super-Earth with a mass of 8.2 ± 1.7 M ⊕ and an orbital period of 60.7 ± 0.1 days, orbiting around an early-type M dwarf. Early-type M dwarfs are less active and thus are better hosts for habitable planets than mid-type and late-type M dwarfs. Moreover, we report the detection of five two-planet systems, including two systems made up of a warm or cold Neptune and a cold Jupiter, consistent with a positive correlation between these two types of planets. We also detect three temperate Neptunes, four cold Neptunes, and four cold Jupiters, contributing to a rarely explored planet population. Due to their proximity to the Sun, these planets on wide orbits are appropriate targets for direct imaging by future facilities such as the Habitable Exoplanet Observatory and the Extremely Large Telescope.

Containing only a few percent the mass of the moon, the current asteroid belt is around three to four orders of magnitude smaller that its primordial mass inferred from disk models. Yet dynamical studies have shown that the asteroid belt could not have been depleted by more than about an order of magnitude over the past ~4 Gyr. The remainder of the mass loss must have taken place during an earlier phase of the solar system's evolution. An orbital instability in the outer solar system occurring during the process of terrestrial planet formation can reproduce the broad characteristics of the inner solar system. Here, we test the viability of this model within the constraints of the main belt's low present-day mass and orbital structure. While previous studies modeled asteroids as massless test particles because of limited computing power, our work uses GPU (Graphics Processing Unit) acceleration to model a fully self-gravitating asteroid belt. We find that depletion in the main belt is related to the giant planets' exact evolution within the orbital instability. Simulations that produce the closest matches to the giant planets' current orbits deplete the main belt by two to three orders of magnitude. These simulated asteroid belts are also good matches to the actual asteroid belt in terms of their radial mixing and broad orbital structure., Comment: 12 pages, 7 figures, 2 tables, accepted for publication in AJ corrected minor typographical errors

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 formation models. Here we use 800 dynamical simulations to show that an early instability in the outer solar system strongly influences terrestrial planet formation and regularly yields properly sized Mars analogs. Our most successful outcomes occur when the terrestrial planets evolve an additional 1-10 million years (Myr) following the dispersal of the gas disk, before the onset of the giant planet instability. In these simulations, accretion has begun in the Mars region before the instability, but the dynamical perturbation induced by the giant planets' scattering removes large embryos from Mars' vicinity. Large embryos are either ejected or scattered inward toward Earth and Venus (in some cases to deliver water), and Mars is left behind as a stranded embryo. An early giant planet instability can thus replicate both the inner and outer solar system in a single model., 18 pages, 9 figures, accepted for publication in Icarus

The formation of the solar system’s terrestrial planets has been numerically modeled in various works, and many other studies have been devoted to characterizing our modern planets’ chaotic dynamical state. However, it is still not known whether our planets fragile chaotic state is an expected outcome of terrestrial planet accretion. We use a suite of numerical simulations to present a detailed analysis and characterization of the dynamical chaos in 145 different systems produced via terrestrial planet formation in Kaib and Cowan (2015). These systems were created in the presence of a fully formed Jupiter and Saturn, using a variety of different initial conditions. They are not meant to provide a detailed replication of the actual present solar system, but rather serve as a sample of similar systems for comparison and analysis. We find that dynamical chaos is prevalent in roughly half of the systems we form. We show that this chaos disappears in the majority of such systems when Jupiter is removed, implying that the largest source of chaos is perturbations from Jupiter. Chaos is most prevalent in systems that form 4 or 5 terrestrial planets. Additionally, an eccentric Jupiter and Saturn is shown to enhance the prevalence of chaos in systems. Furthermore, systems in our sample with a center of mass highly concentrated between ∼0.8–1.2 AU generally prove to be less chaotic than systems with more exotic mass distributions. Through the process of evolving systems to the current epoch, we show that late instabilities are quite common in our systems. Of greatest interest, many of the sources of chaos observed in our own solar system (such as the secularly driven chaos between Mercury and Jupiter) are shown to be common outcomes of terrestrial planetary formation. Thus, consistent with previous studies such as Laskar (1996), the solar system’s marginally stable, chaotic state may naturally arise from the process of terrestrial planet formation.

Of the solar system's four terrestrial planets, the origin of Mercury is perhaps the most mysterious. Modern numerical simulations designed to model the dynamics of terrestrial planet formation systematically fail to replicate Mercury; which possesses just 5% the mass of Earth and the highest orbital eccentricity and inclination among the planets. However, Mercury's large iron-rich core and low volatile inventory stand out among the inner planets, and seem to imply a violent collisional origin. Because most algorithms used for simulating terrestrial accretion do not consider the effects of collisional fragmentation, it has been difficult to test these collisional hypotheses within the larger context of planet formation. Here, we analyze a large suite of terrestrial accretion models that account for the fragmentation of colliding bodies. We find that planets with core mass fractions boosted as a result of repeated hit-and-run collisions are produced in 90% of our simulations. While many of these planets are similar to Mercury in mass, they rarely lie on Mercury-like orbits. Furthermore, we perform an additional batch of simulations designed to specifically test the single giant impact origin scenario. We find less than a 1% probability of simultaneously replicating the Mercury-Venus dynamical spacing and the terrestrial system's degree of orbital excitation after such an event. While dynamical models have made great strides in understanding Mars' low mass, their inability to form accurate Mercury analogs remains a glaring problem., 11 pages, 7 figures, 2 tables, accepted for publication in AJ