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Jason H. Steffen

Publications and source records attributed to Jason H. Steffen.

At least 37 records · Page 2Linked to original sources
arXiv2022

The Yarkovsky effect in REBOUNDx

To more thoroughly study the effects of radiative forces on the orbits of small, astronomical bodies, we introduce the Yarkovsky effect into REBOUNDx, an extensional library for the N-body integrator REBOUND. Two different versions of the Yarkovsky effect (the "Full Version" and the "Simple Version") are available for use, depending on the needs of the user. We provide demonstrations for both versions of the effect and compare their computational efficiency with another previously implemented radiative force. In addition, we show how this effect can be used in tandem with other features in REBOUNDx by simulating the orbits of asteroids during the asymptotic giant branch phase of a 2 $M_{\odot}$ star. This effect is made freely available for use with the latest release of REBOUNDx.

astro-ph.EP↗
arXiv2022

MAGRATHEA: an open-source spherical symmetric planet interior structure code

MAGRATHEA is an open-source planet structure code that considers the case of fully differentiated spherically symmetric interiors. Given the mass of each layer and the surface temperature, the code iterates the boundary conditions of the hydrostatic equations using the method of shooting to a fitting point in order to find the planet radius. The first version of MAGRATHEA supports a maximum of four layers of iron, silicates, water, and ideal gas. With a few exceptions, the temperature profile can be chosen between isothermal, isentropic, and user-defined functions. The user has many options for the phase diagram and equation of state in each layer and we document how to add additional equations of state. We present MAGRATHEA's capabilities and discuss its applications. We encourage the community to participate in the development of MAGRATHEA at https://github.com/Huang-CL/Magrathea.

astro-ph.EP↗
arXiv2022

Maximum Temperatures in Evolving Protoplanetary Discs and Composition of Planetary Building Blocks

The maximum temperature and radial temperature profile in a protoplanetary disc are important for the condensation of different elements in the disc. We simulate the evolution of a set of protoplanetary discs from the collapse of their progenitor molecular cloud cores as well as the dust decoupling within the discs as they evolve. We show how the initial properties of the cloud cores affect the thermal history of the protoplanetary discs using a simple viscous disc model. Our results show that the maximum midplane temperature in the disc occurs within 0.5 AU. It increases with the initial cloud temperature and decreases with its angular velocity and the viscosity of the disc. From the observed properties of the molecular cloud cores we find the median value of the maximum temperature is around 1250 K, with roughly 90% of them being less than 1500 K - a value that is lower than the 50% condensation temperatures of most refractory elements. Therefore, only cloud cores with high initial temperatures or low angular velocities and/or low viscosities within the planet-forming discs will result in refractory-rich planetesimals. To reproduce the volatile depletion pattern of CM, CO, and CV chondrites and the terrestrial planets in Solar system, one must either have rare properties of the initial molecular cloud cores like high core temperature, or other sources of energy to heat the disc to sufficiently high temperatures. Alternatively, the volatile depletion observed in these chondrites may be inherited from the progenitor molecular cloud.

astro-ph.EP↗
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

astro-ph.EP↗
arXiv2022

Stellar Evolution and Tidal Dissipation in REBOUNDx

To study the post-main sequence evolution of the Solar system and exoplanetary systems more accurately and efficiently, we introduce two new features to REBOUNDx, an extended library for the N-body integrator REBOUND. The first is a convenient parameter interpolator for coupling different physics and integrators using numerical splitting schemes. The second implements a constant time lag model for tides without evolving spins. We demonstrate various uses of these features using stellar evolution data from MESA (Modules for Experiments in Stellar Astrophysics) as an example. The results of our tests agree with several studies in the literature on post-main sequence orbital evolution, and our convergence and performance studies respectively demonstrate our implementations' accuracy and efficiency. These additional effects are publicly available as of REBOUNDx's latest release.

astro-ph.SR↗
arXiv2021

Implications of an improved water equation of state for water-rich planets

Water (H$_{2}$O), in all forms, is an important constituent in planetary bodies, controlling habitability and influencing geological activity. Under conditions found in the interior of many planets, as the pressure increases, the H-bonds in water gradually weaken and are replaced by ionic bonds. Recent experimental measurements of the water equation of state (EOS) showed both a new phase of H-bonded water ice, ice-VII$_t$, and a relatively low transition pressure just above 30 GPa to ionic bonded ice-X, which has a bulk modulus 2.5 times larger. The higher bulk modulus of ice-X produces larger planets for a given mass, thereby either reducing the atmospheric contribution to the volume of many exoplanets or limiting their water content. We investigate the impact of the new EOS measurements on the planetary mass-radius relation and interior structure for water-rich planets. We find that the change in the planet mass-radius relation caused by the systematic differences between previous and new experimental EOS measurements are comparable to the observational uncertainties in some planet sizes -- an issue that will become more important as observations continue to improve.

astro-ph.EP↗
arXiv2020

The Occurrence of Rocky Habitable Zone Planets Around Solar-Like Stars from Kepler Data

We present occurrence rates for rocky planets in the habitable zones (HZ) of main-sequence dwarf stars based on the Kepler DR25 planet candidate catalog and Gaia-based stellar properties. We provide the first analysis in terms of star-dependent instellation flux, which allows us to track HZ planets. We define $η_\oplus$ as the HZ occurrence of planets with radius between 0.5 and 1.5 $R_\oplus$ orbiting stars with effective temperatures between 4800 K and 6300 K. We find that $η_\oplus$ for the conservative HZ is between $0.37^{+0.48}_{-0.21}$ (errors reflect 68\% credible intervals) and $0.60^{+0.90}_{-0.36}$ planets per star, while the optimistic HZ occurrence is between $0.58^{+0.73}_{-0.33}$ and $0.88^{+1.28}_{-0.51}$ planets per star. These bounds reflect two extreme assumptions about the extrapolation of completeness beyond orbital periods where DR25 completeness data are available. The large uncertainties are due to the small number of detected small HZ planets. We find similar occurrence rates using both a Poisson likelihood Bayesian analysis and Approximate Bayesian Computation. Our results are corrected for catalog completeness and reliability. Both completeness and the planet occurrence rate are dependent on stellar effective temperature. We also present occurrence rates for various stellar populations and planet size ranges. We estimate with $95\%$ confidence that, on average, the nearest HZ planet around G and K dwarfs is about 6 pc away, and there are about 4 HZ rocky planets around G and K dwarfs within 10 pc of the Sun.

astro-ph.EP↗
arXiv2020

Dust Condensation in Evolving Discs and the Composition of Planetary Building Blocks

Partial condensation of dust from the Solar nebula is likely responsible for the diverse chemical compositions of chondrites and rocky planets/planetesimals in the inner Solar system. We present a forward physical-chemical model of a protoplanetary disc to predict the chemical compositions of planetary building blocks that may form from such a disc. Our model includes the physical evolution of the disc and the condensation, partial advection, and decoupling of the dust within it. The chemical composition of the condensate changes with time and radius. We compare the results of two dust condensation models: one where an element condenses when the midplane temperature in the disc is lower than the 50\% condensation temperature ($\rm T_{50}$) of that element and the other where the condensation of the dust is calculated by a Gibbs free energy minimization technique assuming chemical equilibrium at local disc temperature and pressure. The results of two models are generally consistent with some systematic differences of $\sim 10$\% depending upon the radial distance and an element's condensation temperature. Both models predict compositions similar to CM, CO, and CV chondrites provided that the decoupling timescale of the dust is on the order of the evolution timescale of the disc or longer. If the decoupling timescale is too short, the composition deviates significantly from the measured values. These models may contribute to our understanding of the chemical compositions of chondrites, and ultimately the terrestrial planets in the solar system, and may constrain the potential chemical compositions of rocky exoplanets.

astro-ph.EP↗
arXiv2019

Bond strengthening in dense H2O and implications to planetary composition

H2O is an important constituent in planetary bodies, controlling habitability and, in geologically-active bodies, plate tectonics. At pressures within the interior of many planets, the H-bonds in H2O collapse into stronger, ionic bonds. Here we present agreement between X-ray diffraction and Raman spectroscopy for the transition from ice-VII to ice-X occurring at a pressure of approximately 30.9 GPa by means of combining grain normalizing heat treatment via direct laser heating with static compression. This is evidenced by the emergence of the characteristic Raman mode of cuprite-like ice-X and an abrupt 2.5-fold increase in bulk modulus, implying a significant increase in bond strength. This is preceded by a transition from cubic ice-VII to a structure of tetragonal symmetry, ice-VIIt at 5.1 GPa. Our results significantly shift the mass/radius relationship of water-rich planets and define a high-pressure limit for release of chemically-bound water within the Earth, making the deep mantle a potential long-term reservoir of ancient water.

cond-mat.mtrl-sci↗
arXiv2019

The discovery and legacy of Kepler's multi-transiting planetary systems

We revisit the discovery and implications of the first candidate systems to contain multiple transiting exoplanets. These systems were discovered using data from the Kepler space telescope. The initial paper, presenting five systems (Steffen et al. 2010), was posted online at the time the project released the first catalog of Kepler planet candidates. The first extensive analysis of the observed population of multis was presented in a follow-up paper published the following year (Lissauer et al. 2011a). Multiply-transiting systems allow us to answer a variety of important questions related to the formation and dynamical evolution of planetary systems. These two papers addressed a wide array of topics including: the distribution of orbital period ratios, planet size ratios, system architectures, mean-motion resonance, orbital eccentricities, planet validation and confirmation, and the identification of different planet populations. They set the stage for many subsequent, detailed studies by other groups. Intensive studies of individual multiplanet systems provided some of Kepler's most important exoplanet discoveries. As we examine the scientific impact of the first of these systems, we also present some history of the people and circumstances surrounding their discoveries.

astro-ph.EP↗
arXiv2019

Long-Period Giant Companions to Three Compact, Multiplanet Systems

Understanding the relationship between long-period giant planets and multiple smaller short-period planets is critical for formulating a complete picture of planet formation. This work characterizes three such systems. We present Kepler-65, a system with an eccentric (e=0.28+/-0.07) giant planet companion discovered via radial velocities (RVs) exterior to a compact, multiply-transiting system of sub-Neptune planets. We also use precision RVs to improve mass and radius constraints on two other systems with similar architectures, Kepler-25 and Kepler-68. In Kepler-68 we propose a second exterior giant planet candidate. Finally, we consider the implications of these systems for planet formation models, particularly that the moderate eccentricity in Kepler-65's exterior giant planet did not disrupt its inner system.

astro-ph.EP↗
arXiv2019

Giant planet effects on terrestrial planet formation and system architecture

The giant planets of the solar system likely played a large role in shaping the architecture of the terrestrial planets. Using an updated collision model, we conduct a suite of high resolution N-body integrations to probe the relationship between giant planet mass, and terrestrial planet formation and system architecture. We vary the mass of the planets that reside at Jupiter's and Saturn's orbit and examine the effects on the interior terrestrial system. We find a correlation between the mass of the exterior giant planets and the collision history of the resulting planets, which holds implications for the planet's properties. More massive giants also produce terrestrial planets that are on smaller, more circular orbits. We do not find a strong correlation between exterior giant planet mass and the number of Earth-analogs (analogous in mass and semi-major axis) produced in the system. These results allow us to make predictions on the nature of terrestrial planets orbiting distant Sun-like star systems that harbor giant planet companions on long orbits---systems which will be a priority for NASA's upcoming Wide-Field Infrared Space Telescope (WFIRST) mission.

astro-ph.EP↗
arXiv2019

Dynamical instability and its implications for planetary system architecture

We examine the effects that dynamical instability has on shaping the orbital properties of exoplanetary systems. Using N-body simulations of non-EMS (Equal Mutual Separation), multi-planet systems we find that the lower limit of the instability timescale $t$ is determined by the minimal mutual separation $K_{\rm min}$ in units of the mutual Hill radius. Planetary systems showing instability generally include planet pairs with period ratio $<1.33$. Our final period ratio distribution of all adjacent planet pairs shows dip-peak structures near first-order mean motion resonances similar to those observed in the \kepler\ planetary data. Then we compare the probability density function (PDF) of the de-biased \kepler\ period ratios with those in our simulations and find a lack of planet pairs with period ratio $> 2.1$ in the observations---possibly caused either by inward migration before the dissipation of the disk or by planet pairs not forming with period ratios $> 2.1$ with the same frequency they do with smaller period ratios. By comparing the PDF of the period ratio between simulation and observation, we obtain an upper limit of 0.03 on the scale parameter of the Rayleigh distributed eccentricities when the gas disk dissipated. Finally, our results suggest that a viable definition for a `packed' or `compact' planetary system be one that has at least one planet pair with a period ratio less than 1.33. This criterion would imply that 4\% of the \kepler\ systems (or 6\% of the systems with more than two planets) are compact.

astro-ph.EP↗
arXiv2018

Detecting circumbinary exoplanets and hierarchical stellar triples with the LISA gravitational radiation mission

We investigate the possibility of detecting planetary or stellar companions orbiting white dwarf binaries using the LISA gravitational radiation detector. Specifically, we consider the acceleration of the barycenter of the white dwarf binary due to the orbiting third body as well as the effect of changes in the tidal field across the binary due to the perturber's eccentric orbit. We find that the movement of the barycenter is detectable for both stellar and planetary mass objects. If circumbinary planets occur with frequencies similar to gas giant planets around isolated main sequence stars, then we expect to find of order 10 such planets in four years of LISA observations. For a longer, ten-year mission the accessible parameter space for planetary mass, orbital period, and binary orbital period grows and LISA's associated yield increases to ~100 expected detections.

astro-ph.EP↗
arXiv2018

Survivability of Moon Systems Around Ejected Gas Giants

We examine the effects that planetary encounters have on the moon systems of ejected gas giant planets. We conduct a suite of numerical simulations of planetary systems containing three Jupiter-mass planets (with the innermost planet at 3 AU) up to the point where a planet is ejected from the system. The ejected planet has an initial system of 100 test-particle moons. We determine the survival probability of moons at different distances from their host planet, measure the final distribution of orbital elements, examine the stability of resonant configurations, and characterize the properties of moons that are stripped from the planets. We find that moons are likely to survive in orbits with semi-major axes out beyond 200 planetary radii (0.1 AU in our case). The orbital inclinations and eccentricities of the surviving moons are broadly distributed and include nearly hyperbolic orbits and retrograde orbits. We find that a large fraction of moons in two-body and three-body mean-motion resonances also survive planetary ejection with the resonance intact. The moon-planet interactions, especially in the presence of mean-motion resonance, can keep the interior of the moons molten for billions of years via tidal flexing, as is seen in the moons of the gas giant planets in the solar system. Given the possibility that life may exist in the subsurface ocean of the Galilean satellite Europa, these results have implications for life on the moons of rogue planets---planets that drift through the galaxy with no host star.

astro-ph.EP↗
arXiv2018

Survival of non-coplanar, closely-packed planetary systems after a close encounter

Planetary systems with more than two bodies will experience orbital crossings at a time related to the initial orbital separations of the planets. After a crossing, the system enters a period of chaotic evolution ending in the reshaping of the system's architecture via planetary collisions or ejections. We carry out N-body integrations on a large number of systems with equally-spaced planets (in units of the Hill radius) to determine the distribution of instability times for a given planet separation. We investigate both the time to the initiation of instability through a close encounter and the time to a planet-planet collision. We find that a significant portion of systems with non-zero mutual inclinations survive after a close encounter and do not promptly experience a planet-planet collision. Systems with significant inclinations can continue to evolve for over 1,000 times longer than the encounter time. The fraction of long lived systems is dependent on the absolute system scale and the initial inclination of the planets. These results have implications to the assumed stability of observed planetary systems.

astro-ph.EP↗
arXiv2018

Systematic mischaracterization of exoplanetary system dynamical histories from a model degeneracy near mean-motion resonance

There is a degeneracy in the radial velocity exoplanet signal between a single planet on an eccentric orbit and a two-planet system with a period ratio of 2:1. This degeneracy could lead to misunderstandings of the dynamical histories of planetary systems as well as measurements of planetary abundances if the correct architecture is not established. We constrain the rate of mischaracterization by analyzing a sample of 60 non-transiting, radial velocity systems orbiting main sequence stars from the NASA Exoplanet Archive (NASA Archive) using a new Bayesian model comparison pipeline. We find that 15 systems (25% of our sample) show compelling evidence for the two-planet case with a confidence level of 95%.

astro-ph.EP↗