On the XUV Luminosity Evolution of TRAPPIST-1 (The Astrophysical Journal, 2020)

We model the long-term X-ray and ultraviolet (XUV) luminosity of TRAPPIST-1 to constrain the evolving high-energy radiation environment experienced by its planetary system. Using a Markov Chain Monte Carlo (MCMC) method, we derive probabilistic constraints for TRAPPIST-1’s stellar and XUV evolution that account for observational uncertainties, degeneracies between model parameters, and empirical data of low-mass stars. We constrain TRAPPIST-1’s mass to m sstarf = 0.089 ± 0.001 M ? and find that its early XUV luminosity likely saturated at ${mathrm{log}}_{10}({L}_{mathrm{XUV}}/{L}_{mathrm{bol}})=-{3.03}_{-0.12}^{+0.23}$. From the posterior distribution, we infer that there is a ~40% chance that TRAPPIST-1 is still in the saturated phase today, suggesting that TRAPPIST-1 has maintained high activity and L XUV/L bol ? 10?3 for several gigayears. TRAPPIST-1’s planetary system therefore likely experienced a persistent and extreme XUV flux environment, potentially driving significant atmospheric erosion and volatile loss. The inner planets likely received XUV fluxes ~103–104 times that of the modern Earth during TRAPPIST-1’s ~1 Gyr long pre-main-sequence phase. Deriving these constraints via MCMC is computationally nontrivial, so scaling our methods to constrain the XUV evolution of a larger number of M dwarfs that harbor terrestrial exoplanets would incur significant computational expenses. We demonstrate that approxposterior, an open source Python machine learning package for approximate Bayesian inference using Gaussian processes, accurately and efficiently replicates our analysis using 980 times less computational time and 1330 times fewer simulations than MCMC sampling using emcee. We find that approxposterior derives constraints with mean errors on the best-fit values and 1? uncertainties of 0.61% and 5.5%, respectively, relative to emcee.

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Analytic Planetary Transit Light Curves and Derivatives for Stars With Polynomial Limb Darkening (The Astronomical Journal, 2020)

We derive analytic, closed-form solutions for the light curve of a planet transiting a star with a limb-darkening profile that is a polynomial function of the stellar elevation, up to an arbitrary integer order. We provide improved analytic expressions for the uniform, linear, and quadratic limb-darkened cases, as well as novel expressions for higher-order integer powers of limb darkening. The formulae are crafted to be numerically stable over the expected range of usage. We additionally present analytic formulae for the partial derivatives of instantaneous flux with respect to the radius ratio, impact parameter, and limb-darkening coefficients. These expressions are rapid to evaluate and compare quite favorably in speed and accuracy to existing transit light-curve codes. We also use these expressions to numerically compute the first partial derivatives of exposure-time-averaged transit light curves with respect to all model parameters. An additional application is modeling eclipsing binary or eclipsing multiple star systems in cases where the stars may be treated as spherically symmetric. We provide code which implements these formulae in C++, Python, IDL, and Julia, with tests and examples of usage (https://github.com/rodluger/Limbdark.jl).

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VPLANET: The Virtual Planet Simulator (PASP, 2020)

We describe a software package called VPLanet that simulates fundamental aspects of planetary system evolution over Gyr timescales, with a focus on investigating habitable worlds. In this initial release, eleven physics modules are included that model internal, atmospheric, rotational, orbital, stellar, and galactic processes. Many of these modules can be coupled to simultaneously simulate the evolution of terrestrial planets, gaseous planets, and stars. The code is validated by reproducing a selection of observations and past results. VPLanet is written in C and designed so that the user can choose the physics modules to apply to an individual object at runtime without recompiling, i.e., a single executable can simulate the diverse phenomena that are relevant to a wide range of planetary and stellar systems. This feature is enabled by matrices and vectors of function pointers that are dynamically allocated and populated based on user input. The speed and modularity of VPLanet enables large parameter sweeps and the versatility to add/remove physical phenomena to assess their importance. VPLanet is publicly available from a repository that contains extensive documentation, numerous examples, Python scripts for plotting and data management, and infrastructure for community input and future development.

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Detection of Hundreds of New Planet Candidates and Eclipsing Binaries in K2 Campaigns 0-8 (The Astrophysical Journal Supplement Series, 2019)

We implement a search for exoplanets in campaigns zero through eight (C0–8) of the K2 extension of the Kepler spacecraft. We apply a modified version of the QATS planet search algorithm to K2 light curves produced by the EVEREST pipeline, carrying out the C0–8 search on 1.5 × 105 target stars with magnitudes in the range of Kp = 9?15. We detect 818 transiting planet candidates, of which 374 were undiscovered by prior searches, with {64, 15, 5, 2, 1} in {2, 3, 4, 5, 6}-planet multiplanet candidate systems, respectively. Of the new planets detected, 100 orbit M dwarfs, including one that is potentially rocky and in the habitable zone. A total of 154 of our candidates reciprocally transit with our solar system: they are geometrically aligned to see at least one solar system planet transit. We find candidates that display transit timing variations and dozens of candidates on both period extremes with single transits or ultrashort periods. We point to evidence that our candidates display similar patterns in frequency and size–period relation to confirmed planets, such as tentative evidence for the radius gap. Confirmation of these planet candidates with follow-up studies will increase the number of K2 planets by up to 50%, and characterization of their host stars will improve statistical studies of planet properties. Our sample includes many planets orbiting bright stars amenable for radial velocity follow-up and future characterization with JWST. We also list the 579 eclipsing binary systems detected as part of this search.

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STARRY: Analytic Occultation Light Curves (The Astronomical Journal, 2019)

We derive analytic, closed form, numerically stable solutions for the total flux received from a spherical planet, moon, or star during an occultation if the specific intensity map of the body is expressed as a sum of spherical harmonics. Our expressions are valid to arbitrary degree and may be computed recursively for speed. The formalism we develop here applies to the computation of stellar transit light curves, planetary secondary eclipse light curves, and planet–planet/planet–moon occultation light curves, as well as thermal (rotational) phase curves. In this paper, we also introduce starry, an open-source package written in C++ and wrapped in Python that computes these light curves. The algorithm in starry is six orders of magnitude faster than direct numerical integration and several orders of magnitude more precise. starry also computes analytic derivatives of the light curves with respect to all input parameters for use in gradient-based optimization and inference, such as Hamiltonian Monte Carlo (HMC), allowing users to quickly and efficiently fit observed light curves to infer properties of a celestial body’s surface map. (Please see https://github.com/rodluger/starry, https://rodluger.github.io/starry/, and https://doi.org/10.5281/zenodo.1312286).

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Evolved Climates and Observational Discriminants for the TRAPPIST-1 Planetary System (The Astrophysical Journal, 2018)

The TRAPPIST-1 planetary system provides an unprecedented opportunity to study terrestrial exoplanet evolution with the James Webb Space Telescope (JWST) and ground-based observatories. Since M dwarf planets likely experience extreme volatile loss, the TRAPPIST-1 planets may have highly evolved, possibly uninhabitable atmospheres. We used a versatile, 1D terrestrial planet climate model with line-by-line radiative transfer and mixing length convection (VPL Climate) coupled to a terrestrial photochemistry model to simulate environmental states for the TRAPPIST-1 planets. We present equilibrium climates with self-consistent atmospheric compositions and observational discriminants of postrunaway, desiccated, 10–100 bar O2- and CO2-dominated atmospheres, including interior outgassing, as well as for water-rich compositions

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The Habitability of Proxima Centauri b: Environmental States and Observational Discriminants (Astrobiology, 2018)

Proxima Centauri b provides an unprecedented opportunity to understand the evolution and nature of terrestrial planets orbiting M dwarfs. Although Proxima Cen b orbits within its star’s habitable zone, multiple plausible evolutionary paths could have generated different environments that may or may not be habitable. Here, we use 1-D coupled climate-photochemical models to generate self-consistent atmospheres for several evolutionary scenarios, including high-O2, high-CO2, and more Earth-like atmospheres, with both oxic and anoxic compositions. We show that these modeled environments can be habitable or uninhabitable at Proxima Cen b’s position in the habitable zone. We use radiative transfer models to generate synthetic spectra and thermal phase curves for these simulated environments, and use instrument models to explore our ability to discriminate between possible planetary states.

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Planet-Planet Occultations in TRAPPIST-1 and Other Exoplanet Systems (Astrophysical Journal, 2017)

We explore the occurrence and detectability of planet-planet occultations (PPOs) in exoplanet systems. These are events during which a planet occults the disk of another planet in the same system, imparting a small photometric signal as its thermal or reflected light is blocked. We focus on the planets in TRAPPIST-1, whose orbital planes we show are aligned to < 0\buildrel{\circ}\over{.} 3 at 90% confidence. We present a photodynamical model for predicting and computing PPOs in TRAPPIST-1 and other systems for various assumptions of the planets’ atmospheric states. When marginalizing over the uncertainties on all orbital parameters, we find that the rate of PPOs in TRAPPIST-1 is about 1.4 per day. We investigate the prospects for detection of these events with the James Webb Space Telescope, finding that ∼10-20 occultations per year of b and c should be above the noise level at 12-15 μm. Joint modeling of several of these PPOs could lead to a robust detection. Alternatively, observations with the proposed Origins Space Telescope should be able to detect individual PPOs at high signal-to-noise ratios. We show how PPOs can be used to break transit timing variation degeneracies, imposing strong constraints on the eccentricities and masses of the planets, as well as to constrain the longitudes of nodes and thus the complete three-dimensional structure of the system. We further show how modeling of these events can be used to reveal a planet’s day/night temperature contrast and construct crude surface maps. We make our photodynamical code available on github (https://github.com/rodluger/planetplanet).

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Identifying Planetary Biosignature Impostors: Spectral Features of CO and O4 Resulting from Abiotic O2/O3 Production (The Astrophysical Journal, 2016)

O2 and O3 have been long considered the most robust individual biosignature gases in a planetary atmosphere, yet multiple mechanisms that may produce them in the absence of life have been described. However, these abiotic planetary mechanisms modify the environment in potentially identifiable ways. Here we briefly discuss two of the most detectable spectral discriminants for abiotic O2/O3: CO and O4. We produce the first explicit self-consistent simulations of these spectral discriminants as they may be seen by James Webb Space Telescope (JWST). If JWST-NIRISS and/or NIRSpec observe CO (2.35, 4.6 μm) in conjunction with CO2 (1.6, 2.0, 4.3 μm) in the transmission spectrum of a terrestrial planet it could indicate robust CO2 photolysis and suggest that a future detection of O2 or O3 might not be biogenic. Strong O4 bands seen in transmission at 1.06 and 1.27 μm could be diagnostic of a post-runaway O2-dominated atmosphere from massive H-escape. We find that for these false positive scenarios, CO at 2.35 μm, CO2 at 2.0 and 4.3 μm, and O4 at 1.27 μm are all stronger features in transmission than O2/O3 and could be detected with S/Ns gsim 3 for an Earth-size planet orbiting a nearby M dwarf star with as few as 10 transits, assuming photon-limited noise. O4 bands could also be sought in UV/VIS/NIR reflected light (at 0.345, 0.36, 0.38, 0.445, 0.475, 0.53, 0.57, 0.63, 1.06, and 1.27 μm) by a next generation direct-imaging telescope such as LUVOIR/HDST or HabEx and would indicate an oxygen atmosphere too massive to be biologically produced.

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The Three-dimensional Architecture of the Υ Andromedae Planetary System (the Astrophysical Journal, 2015)

The υ Andromedae system is the first exoplanetary system to have the relative inclination of two planets’ orbital planes directly measured, and therefore offers our first window into the three-dimensional configurations of planetary systems. We present, for the first time, full three-dimensional, dynamically stable configurations for the three planets of the system consistent with all observational constraints. While the outer two planets, c and d, are inclined by ~30°, the inner planet’s orbital plane has not been detected.

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Extreme Water Loss and Abiotic O2 Buildup on Planets Throughout the Habitable Zones of M Dwarfs (Astrobiology, 2015)

We show that terrestrial planets in the habitable zones of M dwarfs older than ∼1 Gyr could have been in runaway greenhouses for several hundred million years following their formation due to the star’s extended pre-main sequence phase, provided they form with abundant surface water. Such prolonged runaway greenhouses can lead to planetary evolution divergent from that of Earth. During this early runaway phase, photolysis of water vapor and hydrogen/oxygen escape to space can lead to the loss of several Earth oceans of water from planets throughout the habitable zone, regardless of whether the escape is energy-limited or diffusion-limited.

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