Search

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., 55 pages, 20 figures. Accepted to the Astronomical Journal. Check out the code at https://github.com/rodluger/starry

This is the source code used to generate the figures and tables in The pale green dot: A method to characterize Proxima Centauri b using exo-aurorae (Luger et al. 2016, arXiv:1609.09075).

International audience; In order to properly assess the potential for habitability and prioritize target selection for the characterization of exoplanets, we need to understand the limits of orbital and rotational dynamics. Large satellites may be rare and very difficult to detect. Consequently, it is necessary to quantify the likelihood of a planet's having extreme obliquity cycles in the absence of a moon and to model the potential impact on the planet's climate. We explore the obliquity evolution of (1) known exoplanet systems that could contain Earth-like planets in the habitable zone and (2) hypothetical planets in mutually inclined, chaotic resonant configurations that experience some of the most extreme orbital evolution possible. We use a secular obliquity model coupled to either an N-body models or a 4th order secular orbital model.We find that in some known systems, planets' obliquity variations are small and unlikely to have a major effect on climate, unless undetected planets are present. Systems with three or more planets are significantly more dynamically rich, with planets that undergo obliquity changes of ~10° over 50,000 years and >30° over a few million years. In resonant configurations, Earth-like exoplanets can undergo dramatic and chaotic evolution in eccentricity and inclination while remaining stable for over 10 Gyr. In configurations in which eccentricities and inclinations stay below ~0.1 and ~10°, respectively, obliquities oscillate quasi-periodically with amplitudes similar to the non-resonant, three-planet configurations. In more dynamically active configurations, in which eccentricities and inclinations evolve to e > 0.3 and i > 15°, obliquities can extend from ~0° to well past 90°. In extreme cases eccentricities can reach >0.9999 and inclinations >179.9 degrees, driving precession rates in excess of degrees per year. However, these planets can graze or impact the stellar surface and are probably not habitable.

International audience; The orbital evolution of exoplanets in mean motion resonance and with mutual inclinations is often chaotic, with large amplitude variations of eccentricity 0 up to 0.9) and inclination 0 up to 170 degrees). Despite this strongly chaotic behavior, these systems can be stable for 10 Gyr. In cases that survive for only 0.1 to 1 Gyr, eccentricities can aperiodically reach values larger than 0.999 and inclinations larger than 179.9 degrees. Typically, the orbitalbehavior appears to switch between different modes, with the classic eccentricity-type resonance as one mode. Outside of that resonance, the motion cannot be easily characterized as eccentricity- and/or inclination-type, because both operate, with the conjunction longitude librating about specific directions. This phenomenon can affect Earth-mass planets in the habitable zone, potentially altering surface habitability. Planets with eccentricities that approach unity may be tidally circularized while the inclination is at any value, revealing a previously unknown process to produce misalignment between stellarspin axes and hot planets' orbital planes. Finally, we re-examine planet-planet scattering simulations and find they produce these types of systems with a frequency of order 0.5%. Giant planets exhibiting such behavior may be detectable by the GAIA spacecraft.

A planet's climate can be strongly affected by its orbital eccentricity and obliquity. Here we use a one-dimensional energy balance model modified to include a simple runaway greenhouse (RGH) parameterization to explore the effects of these two parameters on the climate of Earth-like aqua planets—completely ocean-covered planets—orbiting F-, G-, K-, and M-dwarf stars. We find that the range of instellations for which planets exhibit habitable surface conditions throughout an orbit decreases with increasing eccentricity. However, the appearance of temporarily habitable conditions during an orbit creates an eccentric habitable zone (EHZ) that is sensitive to orbital eccentricity and obliquity, planetary latitude, and the spectral type of the host star. We find that the fraction of a planet's orbit over which it exhibits habitable surface conditions is larger on eccentric planets orbiting M-dwarf stars, due to the lower broadband planetary albedos of these planets. Planets with larger obliquities have smaller EHZs, but exhibit warmer climates if they do not enter a snowball state during their orbits. We also find no transient RGH state on planets at all eccentricities. Rather, planets spend their entire orbits either in an RGH or not. For G-dwarf planets receiving 100% of the modern solar constant and with eccentricities above 0.55, an entire Earth ocean inventory can be lost in 3.6 Gyr. M-dwarf planets, due to their larger incident X-ray and extreme ultraviolet flux, can become desiccated in only 690 Myr with eccentricities above 0.38. This work has important implications for eccentric planets that may exhibit surface habitability despite technically departing from the traditional habitable zone as they orbit their host stars.

The atmospheric temperatures of the ultra-hot Jupiter KELT-9b straddle the transition between gas giants and stars, and therefore between two traditionally distinct regimes of atmospheric chemistry. Previous theoretical studies assume the atmosphere of KELT-9b to be in chemical equilibrium. Despite the high ultraviolet flux from KELT-9, we show using photochemical kinetic calculations that the observable atmosphere of KELT-9b is predicted to be close to chemical equilibrium, which greatly simplifies any theoretical interpretation of its spectra. It also makes the atmosphere of KELT-9b, which is expected to be cloud-free, a tightly constrained chemical system that lends itself to a clean set of theoretical predictions. Due to the lower pressures probed in transmission (compared to emission) spectroscopy, we predict the abundance of water to vary by several orders of magnitude across the atmospheric limb depending on temperature, which makes water a sensitive thermometer. Carbon monoxide is predicted to be the dominant molecule under a wide range of scenarios, rendering it a robust diagnostic of the metallicity when analyzed in tandem with water. All of the other usual suspects (acetylene, ammonia, carbon dioxide, hydrogen cyanide, methane) are predicted to be subdominant at solar metallicity, while atomic oxygen, iron, and magnesium are predicted to have relative abundances as high as 1 part in 10,000. Neutral atomic iron is predicted to be seen through a forest of optical and near-infrared lines, which makes KELT-9b suitable for high-resolution ground-based spectroscopy with HARPS-N or CARMENES. We summarize future observational prospects of characterizing the atmosphere of KELT-9b.

To constrain the formation history of an exoplanet, we need to know its chemical composition. With an equilibrium temperature of about 4,050 kelvin, the exoplanet KELT-9b (also known as HD 195689b) is an archetype of the class of ultrahot Jupiters that straddle the transition between stars and gas-giant exoplanets and are therefore useful for studying atmospheric chemistry. At these high temperatures, iron and several other transition metals are not sequestered in molecules or cloud particles and exist solely in their atomic forms5. However, despite being the most abundant transition metal in nature, iron has not hitherto been detected directly in an exoplanet because it is highly refractory. The high temperatures of KELT-9b imply that its atmosphere is a tightly constrained chemical system that is expected to be nearly in chemical equilibrium and cloud-free, and it has been predicted that spectral lines of iron should be detectable in the visible range of wavelengths. Here we report observations of neutral and singly ionized atomic iron (Fe and Fe⁺) and singly ionized atomic titanium (Ti⁺) in the atmosphere of KELT-9b. We identify these species using cross-correlation analysis of high-resolution spectra obtained as the exoplanet passed in front of its host star. Similar detections of metals in other ultrahot Jupiters will provide constraints for planetary formation theories.

Weathering of silicate rocks at a planetary surface can draw down CO2 from the atmosphere for eventual burial and long-term storage in the planetary interior. This process is thought to provide essential negative feedback to the carbonate-silicate cycle (carbon cycle) to maintain clement climates on Earth and potentially similar temperate exoplanets. We implement thermodynamics to determine weathering rates as a function of surface lithology (rock type). These rates provide upper limits that allow the maximum rate of weathering in regulating climate to be estimated. This modeling shows that the weathering of mineral assemblages in a given rock, rather than individual minerals, is crucial to determine weathering rates at planetary surfaces. By implementing a fluid-transport-controlled approach, we further mimic chemical kinetics and thermodynamics to determine weathering rates for three types of rocks inspired by the lithologies of Earthʼs continental and oceanic crust, and its upper mantle. We find that thermodynamic weathering rates of a continental crust-like lithology are about one to two orders of magnitude lower than those of a lithology characteristic of the oceanic crust. We show that when the CO2 partial pressure decreases or surface temperature increases, thermodynamics rather than kinetics exerts a strong control on weathering. The kinetically and thermodynamically limited regimes of weathering depend on lithology, whereas the supply-limited weathering is independent of lithology. Our results imply that the temperature sensitivity of thermodynamically limited silicate weathering may instigate a positive feedback to the carbon cycle, in which the weathering rate decreases as the surface temperature increases.

Using an energy balance model with ice sheets, we examine the climate response of an Earth-like planet orbiting a G-dwarf star and experiencing large orbital and obliquity variations. We find that ice caps couple strongly to the orbital forcing, leading to extreme ice ages. In contrast with previous studies, we find that such exo-Milankovitch cycles tend to impair habitability by inducing snowball states within the habitable zone. The large amplitude changes in obliquity and eccentricity cause the ice edge, the lowest latitude extent of the ice caps, to become unstable and grow to the equator. We apply an analytical theory of the ice edge latitude to show that obliquity is the primary driver of the instability. The thermal inertia of the ice sheets and the spectral energy distribution of the G-dwarf star increase the sensitivity of the model to triggering runaway glaciation. Finally, we apply a machine learning algorithm to demonstrate how this technique can be used to extend the power of climate models. This work illustrates the importance of orbital evolution for habitability in dynamically rich planetary systems. We emphasize that as potentially habitable planets are discovered around G-dwarfs, we need to consider orbital dynamics.