arXiv subjects

Anna C. Childs

Publications and source records attributed to Anna C. Childs.

At least 19 recordsLinked to original sources

arXiv2025

Origins of Mercury's Big Heart of Iron: Exploring Pathways to Form High Core Mass Fraction (CMF) Planets via N-body Simulations

Mercury's core mass fraction (CMF) is ~0.7, more than double that of the other rocky planets in the solar system, which have CMFs of ~0.3. The origin of Mercury's large, iron-rich core remains unknown. Adding to this mystery, an elusive population of "Exo-Mercuries" with high densities is emerging. Therefore, understanding the formation of Mercury and its exoplanetary analogs is essential to developing a comprehensive planet formation theory. Two hypotheses have been proposed to explain the high CMF of Mercury: (1) giant impacts during the latest stages of planet formation strip away mantle layers, leaving Mercury with a large core; and (2) earlier-stage iron enrichment of planetesimals closer to the Sun leads to the formation of an iron-rich planet. In this work, we conduct N-body simulations to test these two possibilities. Our simulations are focused on the solar system, however, we aim to provide a framework that can later be applied to the formation of high-CMF exoplanets. To investigate the giant impact scenario, we employ uniform initial CMF distributions. To address the other hypothesis, we use a step function with higher CMFs in the inner region. For a uniform initial CMF distribution, our results indicate that although erosive impacts produce iron-rich particles, without mechanisms that deplete stripped mantle material, these particles merge with lower-CMF objects and do not lead to Mercury's elevated CMF. However, a step function initial CMF distribution leads to the formation of a high-CMF planet alongside Earth-like planets, resembling the architecture of the terrestrial solar system.

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arXiv2025

Stellar Dynamics in Open Clusters Increases the Binary Fraction and Mass Ratios: Evidence from Photometric Binaries in 35 Open Clusters

Using the Bayesian Analysis of Stellar Evolution-9 (BASE-9) code and Gaia DR3, Pan-STARRS, and 2MASS data, we identify photometric binaries in 35 open clusters (OCs) and constrain their masses. We find a strong correlation between the binary fraction and cluster dynamical age and an even stronger correlation between core binary fraction and cluster dynamical age. We find the binary mass-ratio (q) distribution of dynamically young OCs is statistically distinct from that of the old OCs. On average, dynamically young OCs display multi-modal q distributions rising toward unity and toward our detection limit of q=0.5 while more dynamically evolved clusters display more uniform q distributions often with a peak near q=1. Interestingly, the uniform q distribution with a peak near q=1 is consistent with binaries in the field. We also observe a similar transition from multi-modal to unimodal q distributions when comparing low mass to high mass OCs in our sample. Lastly, we find a correlation between the median q of the binary population in a cluster and the cluster dynamical age. We interpret these results as an indication that dynamical encounters tend to increase the fraction of high-mass-ratio binaries within a given cluster -- particularly within the cluster's core where stellar dynamics are likely more important. This may be the result of stellar exchanges that tend to produce binaries with larger q and/or the preferential disruption or evaporation of lower q binaries.

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arXiv2025

Observational Signatures of a Previous Dynamical Instability in Multi-planet M-Dwarf Systems

We identify observational signatures suggesting a history of dynamical instability in 26 out of 34 M-dwarf multi-planet systems containing no large planets. These systems may have primarily formed in a gas-rich environment, potentially hosted more planets and were more compact. We extend previous simulations of the formation of the TRAPPIST-1 system to 100 Myr to test the stability of these systems without gas. We find the absence of a strong mean motion resonance in the innermost planet pair and the absence of three body resonances throughout the system are likely to result in the merging and ejection of planets after the gas disk disperses. The runs that experience such an instability tend to produce final systems with lower multiplicities, period ratios larger than two, increased orbital spacings, higher planetary angular momentum deficits, and slightly smaller mass ratios between adjacent planets. Remarkably, we find these same trends in the observations of M-dwarf multi-planet systems containing no large planets. Our work allows us to identify specific systems that may have experienced an instability and suggests that only ~25% of these systems formed in their current observed state while most systems were likely more compact and multiplicitous earlier in time. Previous research indicates that systems that have experienced a late stage giant impact may host planets potentially more habitable than the systems that did not. With this in mind, we suggest systems around M-dwarfs that contain period ratios larger than two be given priority in the search for habitable worlds.

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arXiv2024

Composition Tracking for Collisions Between Differentiated Bodies in REBOUND

Previous research suggests that impacts between planetary embryos and planetesimals during the late stages of planet formation can often determine the percentages of core and mantle material that compose the newly formed planets in a system. Previous studies have attempted to include the composition-changing effects of these collisions in N-body simulations of planet formation, often as post-processing codes. In this paper, we present the Differentiated Body Composition Tracker, a new post-processing tool that uses collisional data collected from the N-body integrator REBOUND to determine the amount of core and mantle material that is transferred between colliding objects and the resulting fragments during an impact. We demonstrate how this code works using the data from 50 REBOUND simulations of planet formation and explore how the parameters in the code affect the core mass fractions of the remaining objects from these simulations. We then investigate how non-uniform distributions of core material across an initial disc affect the final core mass fractions of planets. Under ideal conditions, we find that a combination of giant impacts and planetary embryos enriched in core material could create some of the iron-rich planets that have been discovered.

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arXiv2024

Investigating Mass Segregation of the Binary Stars in the Open Cluster NGC 6819

We search for mass segregation in the intermediate-aged open cluster NGC 6819 within a carefully identified sample of probable cluster members. Using photometry from the Gaia, 2MASS, and Pan-STARRS surveys as inputs for a Bayesian statistics software suite, BASE-9, we identify a rich population of (photometric) binaries and derive posterior distributions for the cluster age, distance, metallicity and reddening as well as star-by-star photometric membership probabilities, masses and mass ratios (for binaries). Within our entire sample, we find 2632 cluster members and 777 binaries. We then select a main-sequence 'primary sample' with 14.85 < G < 19.5 containing 1342 cluster members and 250 binaries with mass ratios q > 0.5, to investigate for mass segregation. Within this primary sample, we find the binary radial distribution is significantly shifted toward the cluster center as compared to the single stars, resulting in a binary fraction that increases significantly toward the cluster core. Furthermore, we find that within the binary sample, more massive binaries have more centrally concentrated radial distributions than less massive binaries. The same is true for the single stars. We verify the expectation of mass segregation for this stellar sample in NGC 6819 through both relaxation time arguments and by investigating a sophisticated N-body model of the cluster. Importantly, this is the first study to investigate mass segregation of the binaries in the open cluster NGC 6819.

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arXiv2024

Inclination instability of circumbinary planets

We analyze a tilt instability of the orbit of an outer planet in a two planet circumbinary system that we recently reported. The binary is on an eccentric orbit and the inner circumbinary planet is on a circular polar orbit that causes the the binary to undergo apsidal precession. The outer circumbinary planet is initially on a circular or eccentric orbit that is coplanar with respect to the binary. We apply a Hamiltonian in quadrupole order of the binary potential to show that the tilt instability is the result of a secular resonance in which the apsidal precession rate of the binary matches the nodal precession rate of the outer planet. Resonance is possible because the polar inner planet causes the apsidal precession of the binary to be retrograde. The outer planet periodically undergoes large tilt oscillations for which we analytically determine the initial evolution and maximum inclination. Following a typically relatively short adjustment phase, the tilt grows exponentially in time at a characteristic rate that is of order the absolute value of the binary apsidal precession rate. The analytic results agree well with numerical simulations. This instability is analogous to the Kozai-Lidov instability, but applied to a circumbinary object. The instability fails to operate if the binary mass ratio is too extreme. The instability occurs even if the outer planet is instead an object of stellar mass and involves tilt oscillations of the inner binary.

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arXiv2024

Tracing the Origins of Mass Segregation in M35: Evidence for Primordially Segregated Binaries

M35 is a young open cluster and home to an extensive binary population. Using Gaia DR3, Pan-STARRS, and 2MASS photometry with the Bayesian statistical software, BASE-9, we derive precise cluster parameters, identify single and binary cluster members, and extract their masses. We identify 571 binaries down to Gaia G = 20.3 and a lower-limit on the binary frequency of f_b = 0.41 +/- 0.02. We extend the binary demographics by many magnitudes faint-ward of previous (radial-velocity) studies of this cluster and further away from the cluster center (1.78-degrees, roughly 10 core radii). We find the binary stars to be more centrally concentrated than the single stars in the cluster. Furthermore, we find strong evidence for mass segregation within the binary population itself, with progressively more massive binary samples becoming more and more centrally concentrated. For the single stars, we find weaker evidence for mass segregation; only the most massive single stars (> 2.5MSun) appear more centrally concentrated. Given the cluster age of ~200 Myr, and our derived half-mass relaxation time for the cluster of 230 +/- 84 Myr, we estimate ~47% of the binary stars and ~12% of single stars in the cluster have had time to become dynamically mass segregated. Importantly, when we investigate only stars with mass segregation timescales greater than the cluster age, we still find the binaries to be more centrally concentrated than the singles, suggesting the binaries may have formed with a primordially different spatial distribution than the single stars.

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arXiv2023

Goodbye to Chi-by-Eye: A Bayesian Analysis of Photometric Binaries in Six Open Clusters

We present a robust methodology for identifying photometric binaries in star clusters. Using Gaia DR3, Pan-STARRS and 2MASS data, we self-consistently define the cluster parameters and binary demographics for the open clusters (OCs) NGC 2168 (M35), NGC 7789, NGC 6819, NGC 2682 (M67), NGC 188, and NGC 6791. These clusters span in age from ~200 Myr (NGC 2168) to more than ~8 Gyr (NGC 6791) and have all been extensively studied in the literature. We use the Bayesian Analysis of Stellar Evolution software suite (BASE-9) to derive the age, distance, reddening, metallicity, binary fraction, and binary mass-ratio posterior distributions for each cluster. We perform a careful analysis of our completeness and also compare our results to previous spectroscopic surveys. For our sample of main-sequence stars with masses between 0.6 - 1 M_Sun, we find that these OCs have similar binary fractions that are also broadly consistent with the field multiplicity fraction. Within the clusters, the binary fraction increases dramatically toward the cluster centers, likely a result of mass segregation. Furthermore nearly all clusters show evidence of mass segregation within the single and binary populations, respectively. The OC binary fraction increases significantly with cluster age in our sample, possibly due to a combination of mass-segregation and cluster dissolution processes. We also find a hint of an anti-correlation between binary fraction and cluster central density as well as total cluster mass, possibly due to an increasing frequency of higher energy close stellar encounters that inhibit long-period binary survival and/or formation.

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arXiv2023

Relativistic Effects on Circumbinary Disk Evolution: Breaking the Polar Alignment around Eccentric Black Hole Binary Systems

We study the effects of general relativity (GR) on the evolution and alignment of circumbinary disks around binaries on all scales. We implement relativistic apsidal precession of the binary into the hydrodynamics code {\sc phantom}. We find that the effects of GR can suppress the stable polar alignment of a circumbinary disk, depending on how the relativistic binary apsidal precession timescale compares to the disk nodal precession timescale. Studies of circumbinary disk evolution typically ignore the effects of GR which is an appropriate simplification for low mass or widely separated binary systems. In this case, polar alignment occurs providing that the disks initial misalignment is sufficiently large. However, systems with a very short relativistic precession timescale cannot polar align and instead move toward coplanar alignment. In the intermediate regime where the timescales are similar, the outcome depends upon the properties of the disk. Polar alignment is more likely in the wavelike disk regime (where the disk viscosity parameter is less than the aspect ratio, $α<H/r$) since the disk is in good radial communication. In the viscous disk regime disk breaking is more likely. Multiple rings can destructively interact with one another resulting in short disk lifetimes, and the disk moving towards coplanar alignment. Around main-sequence star or stellar mass black hole binaries, polar alignment may be suppressed far from the binary but in general the inner parts of the disk can align to polar. Polar alignment may be completely suppressed for disks around supermassive black holes for close binary separations.

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arXiv2023

Mergers of black hole binaries driven by misaligned circumbinary discs

With hydrodynamical simulations we examine the evolution of a highly misaligned circumbinary disc around a black hole binary including the effects of general relativity. We show that a disc mass of just a few percent of the binary mass can significantly increase the binary eccentricity through von-Zeipel--Kozai-Lidov (ZKL) like oscillations provided that the disc lifetime is longer than the ZKL oscillation timescale. The disc begins as a relatively narrow ring of material far from the binary and spreads radially. When the binary becomes highly eccentric, disc breaking forms an inner disc ring that quickly aligns to polar. The polar ring drives fast retrograde apsidal precession of the binary that weakens the ZKL effect. This allows the binary eccentricity to remain at a high level and may significantly shorten the black hole merger time. The mechanism requires the initial disc inclination relative to the binary to be closer to retrograde than to prograde.

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arXiv2023

Composition constraints of the TRAPPIST-1 planets from their formation

We study the formation of the TRAPPIST-1 (T1) planets starting shortly after Moon-sized bodies form just exterior to the ice line. Our model includes mass growth from pebble accretion and mergers, fragmentation, type-I migration, and eccentricity and inclination dampening from gas drag. We follow the composition evolution of the planets fed by a dust condensation code that tracks how various dust species condense out of the disc as it cools. We use the final planet compositions to calculate the resulting radii of the planets using a new planet interior structure code and explore various interior structure models. Our model reproduces the broader architecture of the T1 system and constrains the initial water mass fraction of the early embryos and the final relative abundances of the major refractory elements. We find that the inner two planets likely experienced giant impacts and fragments from collisions between planetary embryos often seed the small planets that subsequently grow through pebble accretion. Using our composition constraints we find solutions for a two-layer model, a planet comprised of only a core and mantle, that match observed bulk densities for the two inner planets b and c. This, along with the high number of giant impacts the inner planets experienced, is consistent with recent observations that these planets are likely dessicated. However, two-layer models seem unlikely for most of the remaining outer planets which suggests that these planets have a primordial hydrosphere. Our composition constraints also indicate that no planets are consistent with a core-free interior structure.

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arXiv2023

Coplanar circumbinary planets can be unstable to large tilt oscillations in the presence of an inner polar planet

Mutually misaligned circumbinary planets may form in a warped or broken gas disc or from later planet-planet interactions. With numerical simulations and analytic estimates we explore the dynamics of two circumbinary planets with a large mutual inclination. A coplanar inner planet causes prograde apsidal precession of the binary and the stationary inclination for the outer planet is higher for larger outer planet orbital radius. In this case a coplanar outer planet always remains coplanar. On the other hand, a polar inner planet causes retrograde apsidal precession of the binary orbit and the stationary inclination is smaller for larger outer planet orbital radius. For a range of outer planet semi-major axes, an initially coplanar orbit is librating meaning that the outer planet undergoes large tilt oscillations. Circumbinary planets that are highly inclined to the binary are difficult to detect -- it is unlikely for a planet to have an inclination below the transit detection limit in the presence of a polar inner planet. These results suggest that there could be a population of circumbinary planets that are undergoing large tilt oscillations.

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arXiv2022

Formation of super-Earths in icy dead zones around low-mass stars

While giant planet occurrence rates increase with stellar mass, occurrence rates of close-in super-Earths decrease. This is in contradiction to the expectation that the total mass of the planets in a system scale with the protoplanetary disc mass and hence the stellar mass. Since the snow line plays an important role in the planet formation process we examine differences in the temperature structure of protoplanetary gas discs around stars of different mass. Protoplanetary discs likely contain a dead zone at the midplane that is sufficiently cold and dense for the magneto-rotational instability to be suppressed. As material builds up, the outer parts of the dead zone may be heated by self-gravity. The temperature in the disc can be below the snow line temperature far from the star and in the inner parts of a dead zone. The inner icy region has a larger radial extent around smaller mass stars. The increased mass of solid icy material may allow for the in situ formation of larger and more numerous planets close to a low-mass star. Super-Earths that form in the inner icy region may have a composition that includes a significant fraction of volatiles.

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arXiv2022

Life on Exoplanets In the Habitable Zone of M-Dwarfs?

Exoplanets orbiting in the habitable zone around M-dwarf stars have been prime targets in the search for life due to the long lifetimes of the host star, the prominence of such stars in the galaxy, and the apparent excess of terrestrial planets found around M-dwarfs. However, the heightened stellar activity of M-dwarfs and the often tidally locked planets in these systems have raised questions about the habitability of these planets. In this letter we examine another significant challenge that may exist: these systems seem to lack the architecture necessary to deliver asteroids to the habitable terrestrial planets, and asteroid impacts may play a crucial role in the origin of life. The most widely accepted mechanism for producing a stable asteroid belt and the late stage delivery of asteroids after gas disk dissipation requires a giant planet exterior to the snow line radius. We show that none of the observed systems with planets in the habitable zone of their star also contain a giant planet and therefore are unlikely to have stable asteroid belts. We consider the locations of observed giant planets relative to the snow line radius as a function of stellar mass and find that there is a population of giant planets outside of the snow line radius around M-dwarfs. Therefore, asteroid belt formation around M-dwarfs is generally possible. However, we find that multi-planetary system architectures around M-dwarfs can be quite different from those around more massive stars.

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arXiv2022

Misaligned circumbinary disks as efficient progenitors of interstellar asteroids

Gaseous circumbinary disks (CBDs) that are highly inclined to the binary orbit are commonly observed in nature. These disks harbor particles that can reach large mutual inclinations as a result of nodal precession once the gas disk has dissipated. With n-body simulations that include fragmentation we demonstrate that misaligned disks of particles can be efficient progenitors of interstellar asteroids (ISAs). Collisions that take place between particles with large mutual inclinations have large impact velocities which can result in mass ejection, with a wide range of fragment sizes and ejection velocities. We explore the binary parameters for which the majority of the terrestrial planet forming material is ejected rather than accreted into planets. The misalignment required to eject significant material decreases with binary eccentricity. If the distribution of binary eccentricity is uniform and the initial particle CBD orientation relative to the binary orbit is isotropic, about 59% of binaries are more likely to eject the majority of their CBD terrestrial planet disk mass through high velocity body-body collisions rather than retain this material and build terrestrial planets. However, binary--disk interactions during the gas disk phase with non-zero disk viscosity will reduce this fraction. The composition, small size, highly elongated shape, and tumbling motion of `Oumuamua is consistent with ISAs generated by misaligned CBDs.

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arXiv2022

A radial limit on polar circumbinary orbits from general relativity

A particle orbiting a misaligned eccentric orbit binary undergoes nodal precession either around the binary angular momentum vector (a circulating orbit) or around a stationary inclination (a librating orbit). In the absence of general relativity, the stationary inclination is inclined by 90 degrees to the binary angular momentum vector (aligned with the binary eccentricity vector) and does not depend on the particle semi-major axis. General relativity causes apsidal precession of the binary orbit. Close to the binary, the behaviour of the particle is not significantly affected, a librating particle precesses with the binary. However, we find that the stationary inclination and the minimum inclination required for libration both increase with the particle semi-major axis. There is a critical radius beyond which there are no librating orbits, only circulating orbits, and therefore there is a maximum orbital radius for a stationary polar orbiting body. The critical radius is within planet forming regions around binaries with semi-major axis <= 1 au. This has implications for the search for misaligned circumbinary planets and the radial extent of polar circumbinary disks.

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arXiv2022

Misalignment of terrestrial circumbinary planets as an indicator of their formation mechanism

Circumbinary gas disks are often observed to be misaligned to the binary orbit suggesting that planet formation may proceed in a misaligned disk. With N-body simulations we consider the formation of circumbinary terrestrial planets from a particle disk that is initially misaligned. We find that if terrestrial planets form in this way, in the absence of gas, they can only form close to coplanar or close to polar to the binary orbit. Planets around a circular binary form coplanar while planets around an eccentric binary can form coplanar or polar depending on the initial disk misalignment and the binary eccentricity. The more massive a terrestrial planet is, the more aligned it is (to coplanar or polar) since it has undergone more mergers that lead on average to smaller misalignment angles. Nodal precession of particle disks with very large initial inclinations lead to high mutual inclinations between the particles. This produces high relative velocities between particles that leads to mass ejections that can completely inhibit planet formation. Misaligned terrestrial circumbinary planets may be able to form in the presence of a misaligned circumbinary gas disk that may help to nodally align the particle orbits and maintain the inclination of the planets during their formation.

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arXiv2022

Collisional fragmentation and bulk composition tracking in REBOUND

We present a fragmentation module and a composition tracking code for the $n$-body code REBOUND. Our fragmentation code utilises previous semi-analytic models and follows an implementation method similar to fragmentation for the $n$-body code MERCURY. In our $n$-body simulations with fragmentation, we decrease the collision and planet formation timescales by inflating the particle radii by an expansion factor $f$ and experiment with various values of $f$ to understand how expansion factors affect the collision history and final planetary system. As the expansion factor increases, so do the rate of mergers which produces planetary systems with more planets and planets at larger orbits. Additionally, we present a composition tracking code which follows the compositional change of homogeneous bodies as a function of mass exchange and use it to study how fragmentation and the use of an expansion factor affects volatile delivery to the inner terrestrial disc. We find that fragmentation enhances radial mixing relative to perfect merging and that on average, as $f$ increases so does the average water mass fraction of the planets. Radial mixing decreases with increasing $f$ as collisions happen early on, before the bodies have time to grow to excited orbits and move away from their original location

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