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DOE OSTI2020

Planetary Spin and Obliquity from Mergers

In planetary systems with sufficiently small inter-planet spacing, close encounters can lead to planetary collisions/mergers or ejections. Here, we study the spin property of the merger products of two giant planets in a statistical manner using numerical simulations and analytical modeling. Planetary collisions lead to rapidly rotating objects and a broad range of obliquities. We find that, under typical conditions for two-planet scatterings, the distributions of spin magnitude S and obliquity ${\theta }_{\mathrm{SL}}$ of the merger products have simple analytical forms: f S ∝ S and ${f}_{\cos {\theta }_{\mathrm{SL}}}\propto {(1-{\cos }^{2}{\theta }_{\mathrm{SL}})}^{-1/2}$. Through parameter studies, we determine the regime of validity for the analytical distributions of spin and obliquity. Since planetary mergers are a major outcome of planet–planet scatterings, observational search for the spin/obliquity signatures of exoplanets would provide important constraints on the dynamical history of planetary systems.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2023

The Variable Detection of Atmospheric Escape around the Young, Hot Neptune AU Mic b

Photoevaporation is a potential explanation for several features within exoplanet demographics. Atmospheric escape observed in young Neptune-sized exoplanets can provide insight into and characterize which mechanisms drive this evolution and at what times they dominate. AU Mic b is one such exoplanet, slightly larger than Neptune (4.19 R ⊕ ). It closely orbits a 23 Myr pre-main-sequence M dwarf with an orbital period of 8.46 days. We obtained two visits of AU Mic b at Lyα with Hubble Space Telescope (HST)/Space Telescope Imaging Spectrograph. One flare within the first HST visit is characterized and removed from our search for a planetary transit. We present a nondetection in our first visit, followed by the detection of escaping neutral hydrogen ahead of the planet in our second visit. The outflow absorbed ∼30% of the star’s Lyα blue wing 2.5 hr before the planet’s white-light transit. We estimate that the highest-velocity escaping material has a column density of 10 13.96 cm −2 and is moving 61.26 km s −1 away from the host star. AU Mic b’s large high-energy irradiation could photoionize its escaping neutral hydrogen in 44 minutes, rendering it temporarily unobservable. Our time-variable Lyα transit ahead of AU Mic b could also be explained by an intermediate stellar wind strength from AU Mic that shapes the escaping material into a leading tail. Future Lyα observations of this system will confirm and characterize the unique variable nature of its Lyα transit, which, combined with modeling, will tune the importance of stellar wind and photoionization.

Exoplanets↗

NASA NTRS2014

Science Goals and Mission Concept for the Future Exploration of Titan and Enceladus

Saturn׳s moons, Titan and Enceladus, are two of the Solar System׳s most enigmatic bodies and are prime targets for future space exploration. Titan provides an analogue for many processes relevant to the Earth, more generally to outer Solar System bodies, and a growing host of newly discovered icy exoplanets. Processes represented include atmospheric dynamics, complex organic chemistry, meteorological cycles (with methane as a working fluid), astrobiology, surface liquids and lakes, geology, fluvial and aeolian erosion, and interactions with an external plasma environment. In addition, exploring Enceladus over multiple targeted flybys will give us a unique opportunity to further study the most active icy moon in our Solar System as revealed by Cassini and to analyse in situ its active plume with highly capable instrumentation addressing its complex chemistry and dynamics. Enceladus׳ plume likely represents the most accessible samples from an extra-terrestrial liquid water environment in the Solar system, which has far reaching implications for many areas of planetary and biological science. Titan with its massive atmosphere and Enceladus with its active plume are prime planetary objects in the Outer Solar System to perform in situ investigations. In the present paper, we describe the science goals and key measurements to be performed by a future exploration mission involving a Saturn-Titan orbiter and a Titan balloon, which was proposed to ESA in response to the call for definition of the science themes of the next Large-class mission in 2013. The mission scenario is built around three complementary science goals: (A) Titan as an Earth-like system; (B) Enceladus as an active cryovolcanic moon; and (C) Chemistry of Titan and Enceladus - clues for the origin of life. The proposed measurements would provide a step change in our understanding of planetary processes and evolution, with many orders of magnitude improvement in temporal, spatial, and chemical resolution over that which is possible with Cassini-Huygens. This mission concept builds upon the successes of Cassini-Huygens and takes advantage of previous mission heritage in both remote sensing and in situ measurement technologies.

future missions↗

NASA NTRS2020

Possible Climate Histories of Venus Type Worlds

There are two well-known scenarios for Venus’ climate evolution. In one Venus had a long-lived magma ocean phase in its first 100Myr with a steam and CO2 dominated atmosphere. The faint young sun with its high XUV flux would cause photodissociation of the steam atmosphere and hydrodynamic escape would cause most of the hydrogen to escape & left-over oxygen would be absorbed by the magma ocean. Hence Venus would have started out hot and dry and the high D/H ratio measured by Pioneer Venus would be from this period of water loss. The other scenario is that Venus’ magma ocean lifetime would have been roughly the same length of time as Earth’s (~1Myr) and water would have condensed on its surface in its early history and had a short period of habitability before increasing solar insolation through time drove it into a runaway greenhouse. However, results from 2016 showed that if Venus remains in the slowly rotating climate dynamics regime (as seen in exoplanet related climate studies) its cloud albedo feedback would have kept it temperate for possibly billions of years. The only way to confirm which one of these scenarios occurred for Venus is to visit it and make the necessary measurements of noble and volatile gases. But exoplanet observations of young exo-Venus type worlds around young F,G,K dwarf stars may constrain which scenario is more probable for a population of such planets. We present a vision of Venus’ climate history that places it and its exoVenus cousins in an ‘Optimistic Venus Zone’ for ~3 billion years within the conventionally named ‘Venus Zone’ and hence encourage the exoplanet communit as possible habitable environments.

Way, M. J.↗

NASA NTRS2018

Shaped Pupil Coronagraph: Disk Science Mask Experimental Verification and Testing

The Shaped Pupil Coronagraph (SPC) is one of the two operating modes of the baseline coronagraph instrument for the proposed WFIRST mission. While in SPC mode, multiple sets of shaped pupil masks and focal plane masks would be available for various imaging tasks. The disk science mask set (SPC-DSM) is designed for exozodiacal disk science. With a 360 degree high contrast field of view, extending up to 20 λ/D, the SPC-DSM provides a powerful tool to study exozodiacal dust clouds associated with stellar debris disks to gain insight of the exoplanet formation and stellar disk dynamics. We will describe the performance verification and demonstration of the SPC-DSM coronagraph as tested in the high contrast imaging testbed (HCIT) at JPL. The goal of the testbed demonstration is an average contrast of 5e-9 over a 10% bandwidth centered at 565nm, in a field of view extending from 6.5 λ/D to 20 λ/D. We will discuss electric field conjugation, performance metrics, and model agreement as applied to the SPC-DSM.

Shi, Fang↗

DOE OSTI2020

A Coupled Analysis of Atmospheric Mass Loss and Tidal Evolution in XUV Irradiated Exoplanets: The TRAPPIST-1 Case Study

Exoplanets residing close to their stars can experience evolution of both their physical structures and their orbits due to the influence of their host stars. In this work, we present a coupled analysis of dynamical tidal dissipation and atmospheric mass loss for exoplanets in X-ray and ultraviolet (XUV) irradiated environments. As our primary application, we use this model to study the TRAPPIST-1 system and place constraints on the interior structure and orbital evolution of the planets. We start by reporting on an ultraviolet continuum flux measurement (centered around ∼1900 Å) for the star TRAPPIST-1, based on 300 ks of Neil Gehrels Swift Observatory data, and which enables an estimate of the XUV-driven thermal escape arising from XUV photodissociation for each planet. We find that the X-ray flaring luminosity, measured from our X-ray detections, of TRAPPIST-1 is 5.6 × 10{sup −4} L {sub *}, while the full flux including non-flaring periods is 6.1 × 10{sup −5} L {sub *}, when L {sub *} is TRAPPIST-1's bolometric luminosity. We then construct a model that includes both atmospheric mass loss and tidal evolution and requires the planets to attain their present-day orbital elements during this coupled evolution. We use this model to constrain the ratio Q{sup ′}=3Q/2k{sub 2} for each planet. Finally, we use additional numerical models implemented with the Virtual Planet Simulator VPLanet to study ocean retention for these planets using our derived system parameters.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2020

A Coupled Analysis of Atmospheric Mass Loss and Tidal Evolution in XUV Irradiated Exoplanets: The TRAPPIST-1 Case Study

Exoplanets residing close to their stars can experience evolution of both their physical structures and their orbits due to the influence of their host stars. In this work, we present a coupled analysis of dynamical tidal dissipation and atmospheric mass loss for exoplanets in X-ray and ultraviolet (XUV) irradiated environments. As our primary application, we use this model to study the TRAPPIST-1 system and place constraints on the interior structure and orbital evolution of the planets. We start by reporting on an ultraviolet continuum flux measurement (centered around ∼1900 Å) for the star TRAPPIST-1, based on 300 ks of Neil Gehrels Swift Observatory data, and which enables an estimate of the XUV-driven thermal escape arising from XUV photodissociation for each planet. We find that the X-ray flaring luminosity, measured from our X-ray detections, of TRAPPIST-1 is 5.6 × 10(exp −4) L(*), while the full flux including non-flaring periods is 6.1 × 10(exp −5) L*, when L(*) is TRAPPIST-1ʼs bolometric luminosity. We then construct a model that includes both atmospheric mass loss and tidal evolution and requires the planets to attain their present-day orbital elements during this coupled evolution. We use this model to constrain the ratio Q' = 3Q/2k2 for each planet. Finally, we use additional numerical models implemented with the Virtual Planet Simulator VPLanet to study ocean retention for these planets using our derived system parameters.

Juliette Becker↗

DOE OSTI2021

Precise Dynamical Masses and Orbital Fits for β Pic b and β Pic c

We present a comprehensive orbital analysis to the exoplanets β Pictoris b and c that resolves previously reported tensions between the dynamical and evolutionary mass constraints on β Pic b. We use the Markov Chain Monte Carlo orbit code orvara to fit 15 years of radial velocities and relative astrometry (including recent GRAVITY measurements), absolute astrometry from Hipparcos and Gaia, and a single relative radial velocity measurement between β Pic A and b. We measure model-independent masses of 9.3{sub −2.5}{sup +2.6} M {sub Jup} for β Pic b and 8.3 ± 1.0 M {sub Jup} for β Pic c. These masses are robust to modest changes to the input data selection. We find a well-constrained eccentricity of 0.119 ± 0.008 for β Pic b, and an eccentricity of 0.21{sub −0.09}{sup +0.16} for β Pic c, with the two orbital planes aligned to within ∼05. Both planets’ masses are within ∼1σ of the predictions of hot-start evolutionary models and exclude cold starts. We validate our approach on N-body synthetic data integrated using REBOUND. We show that orvara can account for three-body effects in the β Pic system down to a level ∼5 times smaller than the GRAVITY uncertainties. Systematics in the masses and orbital parameters from orvara’s approximate treatment of multiplanet orbits are a factor of ∼5 smaller than the uncertainties we derive here. Future GRAVITY observations will improve the constraints on β Pic c’s mass and (especially) eccentricity, but improved constraints on the mass of β Pic b will likely require years of additional radial velocity monitoring and improved precision from future Gaia data releases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2018

ModelE Orbits & Calendars

The GISS climate model, ModelE, [an atmosphere-ocean model] has been extended to support the simulation of climates for exoplanets. As part of this process, a more general calendaring system has been implemented that is derived from orbital parameters. The calendar design attempts to preserve the basic notions of the 4 seasons as well as the time of day. These slides provide the basic underlying assumptions for the design and detail how to configure the model to use non-Earth orbital parameters. [One of a series of videos taken of the ROCKE-3D (Resolving Orbital and Climate Keys of Earth and Extraterrestrial Environments with Dynamics), a 3-Dimensional General Circulation Model (GCM) exoplanet modeling tutorial sessions, May 21-22, 2018, (this slide set was prepared for Day 2, Parts 1 and 2, May 22, 2018) on YouTube (https://www.youtube.com)]

Clune, Tom↗

NASA NTRS2016

Engineering Considerations Applied to Starshade Repointing

Engineering analysis has been carried out on orbit dynamics that drive the delta-v budget for repointing a free-flying starshade occulter for viewing exoplanets with a space telescope. This analysis has application to the design of starshade spacecraft and yield calculations of observations of exoplanets using a space telescope and a starshade. Analysis was carried out to determine if there may be some advantage for the global delta-v budget if the telescope performs orbit changing delta-v maneuvers as part of the telescope-starshade alignment for observing exoplanets. Analysis of the orbit environmental forces at play found no significant advantage in having the telescope participate in delta-v maneuvers for exoplanet observation repointing. A separate analysis of starshade delta-v for repointing found that the orbit dynamics of the starshade is driven by multiple simultaneous variables that need to be considered together in order to create an effective estimate of delta-v over an exoplanet observation campaign. These include area of the starshade, dry mass of the starshade spacecraft, and propellant mass of the starshade spacecraft. Solar radiation pressure has the potential to play a dominant role in the orbit dynamics and delta-v budget. SRP effects are driven by the differences in the mass, area, and coefficients of reflectivity of the observing telescope and the starshade. The propellant budget cannot be effectively estimated without a conceptual design of a starshade spacecraft including the propulsion system. The varying propellant mass over the mission is a complexity that makes calculating the propellant budget less straightforward.

delta-V↗

NASA NTRS2019

Prospects for TTV Detection and Dynamical Constraints with TESS

We consider the potential for the Transiting Exoplanet Survey Satellite (TESS) to detect transit timing variations (TTVs) during both its nominal and extended mission phases. Building on previous estimates of the overall yield of planetary systems from the TESS mission, we predict that during its nominal two-year mission, TESS will observe measurable TTVs in ~30 systems, from which planet will get precise mass measurements from TTVs alone, ~5 planets will have significant constraints placed on their masses from TTVs, and over a dozen systems will be singly transiting TTV systems. We consider a number of different extended mission scenarios, and predict that in a typical scenario, an extended mission will allow TESS to increase the number of systems with measurable TTVs to a total of ~90, from which ~15 planets will have precise mass measurements, another ~15 will have significant constraints placed on their masses, and ~60 will be singly transiting TTV systems. We also describe how follow-up transit observations of multiplanet systems discovered by the TESS mission can be optimally planned to maximize TTV mass and eccentricity constraints.

planets↗

NASA NTRS2020

Mass Determinations of the Three Mini-Neptunes Transiting TOI-125

The Transiting Exoplanet Survey Satellite, TESS, is currently carrying out an all-sky search for small planets transiting bright stars. In the first year of the TESS survey, a steady progress was made in achieving the mission’s primary science goal of establishing bulk densities for 50 planets smaller than Neptune. During that year, the TESS’s observations were focused on the southern ecliptic hemisphere, resulting in the discovery of three mini-Neptunes orbiting the star TOI-125, a V = 11.0 K0 dwarf. We present intensive HARPS radial velocity observations, yielding precise mass measurements for TOI-125b, TOI-125c, and TOI-125d. TOI-125b has an orbital period of 4.65 d, a radius of 2.726 ± 0.075 R(E), a mass of 9.50 ± 0.88 M(E), and is near the 2:1 mean motion resonance with TOI-125c at 9.15 d. TOI-125c has a similar radius of 2.759 ± 0.10 R(E) and a mass of 6.63 ± 0.99 M(E), being the puffiest of the three planets. TOI-125d has an orbital period of 19.98 d and a radius of 2.93 ± 0.17 R(E) and mass 13.6 ± 1.2 M(E). For TOI-125b and d, we find unusual high eccentricities of 0.19 ± 0.04 and 0.17(sup +0.08, sub −0.06), respectively. Our analysis also provides upper mass limits for the two low-SNR planet candidates in the system; for TOI-125.04 (R(P) = 1.36 R(E), P = 0.53 d), we find a 2σ upper mass limit of 1.6 M(E), whereas TOI-125.05 (R(P) = 4.2(sup +2.4, sub −1.4 R(E), P = 13.28 d) is unlikely a viable planet candidate with an upper mass limit of 2.7 M(E). We discuss the internal structure of the three confirmed planets, as well as dynamical stability and system architecture for this intriguing exoplanet system.

L D Nielsen↗

DOE OSTI2025

Cation Disorder of ${\text{Mg}}_{\mathbf{2}}{\text{SiO}}_{\mathbf{4}}$ in Super‐Earth Mantles

Understanding the mineralogy of exoplanets is essential for unraveling their interior structures, dynamics, and evolution. For large super-Earths, the post-post spinel ${\text{Mg}}_{\mathbf{2}}{\text{SiO}}_{\mathbf{4}}$, one of the major mantle phases, may undergo the order-disorder transition (ODT) at high temperatures. However, the ODT phase boundary of ${\text{Mg}}_{\mathbf{2}}{\text{SiO}}_{\mathbf{4}}$ has not been rigorously constrained. Additionally, fundamental thermodynamic properties of the disordered ${\text{Mg}}_{\mathbf{2}}{\text{SiO}}_{\mathbf{4}}$ remain poorly investigated. Here, we develop a unified machine learning potential (MLP) for ${\text{Mg}}_{\mathbf{2}}{\text{SiO}}_{\mathbf{4}}$ of ab initio accuracy under super-Earth mantle conditions. With the efficient MLP, we extensively calculate the free energy of post-post spinel ${\text{Mg}}_{\mathbf{2}}{\text{SiO}}_{\mathbf{4}}$ via the thermodynamic integration method. The results are used to constrain the ODT phase boundary. Furthermore, we report the P-V-T equation of state and Grüneisen parameters for post-post spinel ${\text{Mg}}_{\mathbf{2}}{\text{SiO}}_{\mathbf{4}}$ across various degrees of disorder. These thermodynamic properties are further applied to update the adiabatic thermal profiles and the mass-radius relation of super-Earths.

36 MATERIALS SCIENCE↗

NASA NTRSDate not supplied

ROCKE-3D 2.0: An Updated General Circulation Model for Simulating the Climates of Rocky Planets

We present the second generation of ROCKE-3D (Resolving Orbital and Climate Keys of Earth and Extraterrestrial Environments with Dynamics), the generalized 3-dimensional General Circulation Model (GCM) for use in Solar System and exoplanetary simulations of rocky planet climates. ROCKE-3D version 2.0 is a descendant of GISS ModelE2.1, the flagship GCM of the NASA Goddard Institute for Space Studies (GISS) used in the most recent Intergovernmental Panel for Climate Change (IPCC) assessment. ROCKE-3D is a continuous effort to expand the capabilities of GISS ModelE to handle a broader range of atmospheric conditions, including different atmospheric planet sizes, gravities, pressures, rotation rates, more diverse chemistries and atmospheric compositions, diverse ocean and land distributions and topographies, and potential basic biosphere functions. We present in this release many more supported configurations which can serve as starting points to simulate terrestrial planets of interest. Two different radiation schemes are supported, the GISS radiation, valid for Earth-like planets, and SOCRATES, which is more generalized but requires more CPU resources. In addition, three different atmospheric compositions are supported, three ocean configurations (prescribed, q-flux, and dynamic), and two resolutions: the medium resolution (4 x 5 degrees in latitude x longitude) used in ROCKE-3D 1.0, and the fine resolution, which has double the resolution in the atmosphere and 4 times the resolution in the ocean. We quantify how the different component choices affect model results, and discuss strengths and limitations of using each component, together with how one can select which component to use. ROCKE-3D is publicly available and tutorial sessions are available for the community, greatly facilitating its use by any interested group.

ROCKE-3D↗

NASA NTRS2018

Climates of Warm Earth-Like Planets. I. 3D Model Simulations

We present a large ensemble of simulations of an Earth-like world with increasing insolation and rotation rate. Unlike previous work utilizing idealized aquaplanet congurations we focus our simulations on modern Earth-like topography. The orbital period is the same as modern Earth, but with zero obliquity and eccentricity. The atmosphere is 1 bar N2-dominated with CO2=400 ppmv and CH4=1 ppmv. The simulations include two types of oceans; one without ocean heat transport (OHT) between grid cells as has been commonly used in the exoplanet literature, while the other is a fully coupled dynamic bathtub type ocean. The dynamical regime transitions that occur as day length increases induce climate feedbacks producing cooler temperatures, rst via the reduction of water vapor with increasing rotation period despite decreasing shortwave cooling by clouds, and then via decreasing water vapor and increasing shortwave cloud cooling, except at the highest insolations. Simulations without OHT are more sensitive to insolation changes for fast rotations while slower rotations are relatively insensitive to ocean choice. OHT runs with faster rotations tend to be similar with gyres transporting heat poleward making them warmer than those without OHT. For slower rotations OHT is directed equator-ward and no high latitude gyres are apparent. Uncertainties in cloud parameterization preclude a precise determination of habitability but do not a affect robust aspects of exoplanet climate sensitivity. This is the first paper in a series that will investigate aspects of habitability in the simulations presented herein. The datasets from this study are open source and publicly available.

Planetary systems↗

NASA NTRS2016

Secure Mass Measurements From Transit Timing: 10 Kepler Exoplanets Between 3 and 8M⊕ with Diverse Densities and Incident Fluxes

We infer dynamical masses in eight multiplanet systems using transit times measured from Keplerʼs complete dataset, including short-cadence data where available. Of the 18 dynamical masses that we infer, 10 pass multiple tests for robustness. These are in systems Kepler-26 (KOI-250), Kepler-29 (KOI-738), Kepler-60 (KOI-2086), Kepler-105 (KOI-115), and Kepler-307 (KOI-1576). Kepler -105 c has a radius of 1.3R⊕ and a density consistent with an Earth-like composition. Strong transit timing variation (TTV) signals were detected from additional planets, but their inferred masses were sensitive to outliers or consistent solutions could not be found with independently measured transit times, including planets orbiting Kepler-49 (KOI-248), Kepler-57 (KOI-1270), Kepler-105 (KOI-115), and Kepler-177 (KOI-523). Nonetheless, strong upper limits on the mass of Kepler-177 cimply an extremely low density of 0.1 g cm−3. In most cases, individual orbital eccentricities were poorly constrained owing to degeneracies in TTV inversion. For five planet pairs in our sample, strong secular interactions imply a moderate to high likelihood of apsidal alignment over a wide range of possible eccentricities. We also find solutions for the three planets known to orbit Kepler-60 in a Laplace-like resonance chain. However, nonlibrating solutions also match the transit timing data. For six systems, we calculate more precise stellar parameters than previously known, enabling useful constraints on planetary densities where we have secure mass measurements. Placing these exoplanets on the mass–radius diagram, we find that a wide range of densities is observed among sub-Neptune-mass planets and that the range in observed densities is anticorrelated with incident flux.

Stars individual↗

NASA NTRS2019

Standard Evaluation of exoplanet Yield for the LUVOIR and HabEx Concept Studies

The HabEx and LUVOIR mission concepts aim to directly image and spectrally characterize potentially habitable exoplanets. We use EXOSIMS to simulate design reference missions with observation scheduling to determine yield of exoplanets detected, spectrally characterized, and orbits determined. EXOSIMS performs dynamically responsive scheduling with realistic mission observing constraints on Monte Carlo universes of synthetic planets around known nearby stars. We use identical astrophysical inputs and the individual observing scenarios of each concept to evaluate a common comparison of the detection and spectral characterization yields of HabEx and LUVOIR. HabEx is evaluated for the 4m hybrid starshade and coronagraph architecture, the 4m coronagraph only architecture, and the 4 m starshade only architecture. LUVOIR is evaluated for the 8 m architecture of their final report. Yield analysis shows that both concepts can directly image and spectrally characterize earth-like planets in the habitable zone and that each concept has complementary strengths.

Keithly, Dean↗

NASA NTRS2016

Secure Mass Measurements From Transit Timing: 10 Kepler Exoplanets Between 3 and 8 M⊕ With Diverse Densities and Incident Fluxes

We infer dynamical masses in eight multiplanet systems using transit times measured from Keplerʼs complete data set, including short-cadence data where available. Of the 18 dynamical masses that we infer, 10 pass multiple tests for robustness. These are in systems Kepler-26 (KOI-250), Kepler-29 (KOI-738), Kepler-60 (KOI-2086), Kepler-105 (KOI-115), and Kepler-307 (KOI-1576). Kepler-105 c has a radius of 1.3 R(sub ⨁) and a density consistent with an Earth-like composition. Strong transit timing variation (TTV) signals were detected from additional planets, but their inferred masses were sensitive to outliers or consistent solutions could not be found with independently measured transit times, including planets orbiting Kepler-49 (KOI-248), Kepler-57 (KOI-1270), Kepler-105 (KOI-115), and Kepler-177 (KOI-523). Nonetheless, strong upper limits on the mass of Kepler-177 c imply an extremely low density of ∽0.1 g cm(exp −3). In most cases, individual orbital eccentricities were poorly constrained owing to degeneracies in TTV inversion. For five planet pairs in our sample, strong secular interactions imply a moderate to high likelihood of apsidal alignment over a wide range of possible eccentricities. We also find solutions for the three planets known to orbit Kepler-60 in a Laplace-like resonance chain. However, nonlibrating solutions also match the transit timing data. For six systems, we calculate more precise stellar parameters than previously known, enabling useful constraints on planetary densities where we have secure mass measurements. Placing these exoplanets on the mass–radius diagram, we find that a wide range of densities is observed among sub-Neptune-mass planets and that the range in observed densities is anticorrelated with incident flux.

Individual stars↗