Although conjunctions and oppositions frequently occur in planetary systems, eclipse-related phenomena are usually described from an Earth-centric perspective. Space missions to different parts of the Solar system, as well as the mounting number of known exo-planets in habitable zones and the possibility of sending featherweight robot spacecraft to them, prompt broader considerations. Here, we derive the geometry of eclipses, transits and occultations from a primarily exo-Earth viewpoint, and apply the formulation to the Solar system and three types of three-body extrasolar planetary systems: with 1 star and 2 planets (Case I), with 2 stars and 1 planet (Case II), and with 1 planet, 1 star and 1 moon (Case III). We derive the general conditions for total, partial and annular eclipses to occur at exo-syzygy, and implement them in each case in concert with stability criteria. We then apply the formalism to the TRAPPIST-1, Kepler-444 and Kepler-77 systems -- the first of which contains multiple potentially habitable planets -- and provide reference tables of both Solar system and TRAPPIST-1 syzygy properties. We conclude by detailing a basic algebraic algorithm which can be used to quickly characterize eclipse properties in any three-body system.
Solar system, exoplanet and stellar science rely on transits, eclipses and occultations for dynamical and physical insight. Often, the geometry of these configurations are modelled by assuming a particular viewpoint. Here, instead, I derive user-friendly formulae from first principles independent of viewpoint and in three dimensions. I generalise the results of Veras & Breedt (2017) by (i) characterising three-body systems which are in transit but are not necessarily perfectly aligned, and by (ii) incorporating motion. For a given snapshot in time, I derive explicit criteria to determine wheth…
Properties of planetary atmospheres, ionospheres, and magnetospheres are difficult to measure from Earth. Radio occultations are a common method for measuring these properties, but they traditionally rely on radio transmissions from a spacecraft near the planet. Here we explore whether occultations of radio emissions from a distant astrophysical radio source can be used to measure magnetic field strength, plasma density, and neutral density around planets. In a theoretical case study of Jupiter, we find that significant changes in polarization angle due to Faraday rotation occur for radio sign…
Context: When the planet transits its host star, it is possible to measure the planetary radius and (with radial velocity data) the planet mass. For the study of planetary atmospheres, it is essential to obtain transit and occultation measurements at multiple wavelengths. Aims: We aim to characterize the transiting hot Jupiter WASP-19b by deriving accurate and precise planetary parameters from a dedicated observing campaign of transits and occultations. Methods: We have obtained a total of 14 transit lightcurves in the r'-Gunn, IC, z'-Gunn and I+z' filters and 10 occultation lightcurves in z'-…
Ares is an extension of the TauREx 3 retrieval framework for the Martian atmosphere. Ares is a collection of new atmospheric parameters and forward models, designed for the European Space Agency's (ESA) Trace Gas Orbiter (TGO) Nadir and Occultation for MArs Discovery (NOMAD) instrument, Solar Occultation (SO) channel. Ares provides unique insights into the chemical composition of the Martian atmosphere by applying methods utilised in exoplanetary atmospheric retrievals, Waldmann et al. (2015), Al-Refaie et al. (2019). This insight may help unravel the true nature of $CH_{4}$ on Mars. The Ares …
We announce the detection of recurring sets of recurring starspot occultation events in the short-cadence K2 lightcurve of Qatar-2, a K dwarf star transited every 1.34 d by a hot Jupiter. In total we detect 34 individual starspot occultation events, caused by five different starspots, occulted in up to five consecutive transits or after a full stellar rotation. The longest recurring set of recurring starspot occultations spans over three stellar rotations, setting a lower limit for the longest starspot lifetime of 58 d. Starspot analysis provided a robust stellar rotational period measurement …
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 within 0.3 degrees 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 uncertainti…
Transit spectroscopy is a key tool for exoplanet atmospheric characterization. However, transit spectrum observations can be limited by aerosol extinction when gas opacities are weak. The ultraviolet wavelength range contains a variety of strong molecular and atomic features, potentially enabling gas species detection even when atmospheric hazes are present. To understand the interplay between aerosol extinction and ultraviolet molecular opacities, we investigate transmission through the atmosphere of Saturn's moon Titan during an occultation observed with the Ultraviolet Imaging Spectrometer …
Transmission spectroscopy during planetary transits, which is based on the measurements of the variations of planet-to-star radius ratio as a function of wavelength, is a powerful technique to study the atmospheric properties of transiting planets. One of the main limitation of this technique is the effects of stellar activity, which up until now, have been taken into account only by assessing the effect of non-occulted stellar spots on the estimates of planet-to-star radius ratio. In this paper, we study, for the first time, the impact of the occultation of a stellar spot and plage on the tra…
We derive efficient, closed form, differentiable, and numerically stable solutions for the flux measured from a spherical planet or moon seen in reflected light, either in or out of occultation. Our expressions apply to the computation of scattered light phase curves of exoplanets, secondary eclipse light curves in the optical, or future measurements of planet-moon and planet-planet occultations, as well as to photometry of solar system bodies. We derive our solutions for Lambertian bodies illuminated by a point source, but extend them to model illumination sources of finite angular size and r…
Stellar activity is one of the main obstacles to high-precision exoplanet observations and has motivated extensive studies in detection and characterization problems. Most efforts focused on unocculted starspots in optical transit spectrophotometry, while the impact of starspot crossings is assumed to be negligible in the near-infrared. Here, we present \textit{HST}/WFC3 transit observations of the active star WASP-52, hosting an inflated hot Jupiter, which present a possible starspot occultation signal. By using this data set as a benchmark, we investigated whether the masking of the transit …
High altitude clouds and hazes are integral to understanding exoplanet observations, and are proposed to explain observed featureless transit spectra. However, it is difficult to make inferences from these data because of the need to disentangle effects of gas absorption from haze extinction. Here, we turn to the quintessential hazy world -- Titan -- to clarify how high altitude hazes influence transit spectra. We use solar occultation observations of Titan's atmosphere from the Visual and Infrared Mapping Spectrometer (VIMS) aboard NASA's Cassini spacecraft to generate transit spectra. Data s…
The size distribution and total mass of objects in the Oort Cloud have important implications to the theory of planets formation, including the properties of, and the processes taking place in the early solar system. We discuss the potential of space missions like Kepler and CoRoT, designed to discover transiting exo-planets, to detect Oort Cloud, Kuiper Belt and main belt objects by occultations of background stars. Relying on published dynamical estimates of the content of the Oort Cloud, we find that Kepler's main program is expected to detect between 0 and ~100 occultation events by deca-k…
When we are fortunate enough to view an exoplanetary system nearly edge-on, the star and planet periodically eclipse each other. Observations of eclipses (transits and occultations) provide a bonanza of information that cannot be obtained from radial-velocity data alone, such as the relative dimensions of the planet and its host star, as well as the orientation of the planet's orbit relative to the sky plane and relative to the stellar rotation axis. The wavelength-dependence of the eclipse signal gives clues about the the temperature and composition of the planetary atmosphere. Anomalies in t…
This paper reports the detection and the measurements of occultations of the two transiting hot giant exoplanets Kepler-5b and Kepler-6b by their parent stars. The observations are obtained in the near infrared with Spitzer Space Telescope and at optical wavelengths by combining more than a year of Kepler photometry. The investigation consists of constraining the eccentricities of these systems and of obtaining broad band emergent spectra for individual planets. For both targets, the occultations are detected at 3 sigma level at each wavelength with mid-occultation times consistent with circul…
We present HST STIS observations of two occultations of the transiting exoplanet HAT-P-1b. By measuring the planet to star flux ratio near opposition, we constrain the geometric albedo of the planet, which is strongly linked to its atmospheric temperature gradient. An advantage of HAT-P-1 as a target is its binary companion ADS 16402 A, which provides an excellent photometric reference, simplifying the usual steps in removing instrumental artifacts from HST time-series photometry. We find that without this reference star, we would need to detrend the lightcurve with the time of the exposures a…
[Abridged] The transmission of light through a planetary atmosphere can be studied as a function of altitude and wavelength using stellar or solar occultations, giving often unique constraints on the atmospheric composition. For exoplanets, a transit yields a limb-integrated, wavelength-dependent transmission spectrum of an atmosphere. When scattering haze and/or cloud particles are present in the planetary atmosphere, the amount of transmitted flux not only depends on the total optical thickness of the slant light path that is probed, but also on the amount of forward-scattering by the scatte…
The detection of lines in emission in planetary atmospheres provides direct evidence of temperature inversion. We confirm the trend of ultra-hot Jupiters orbiting A-type stars showing temperature inversions on their daysides, by detecting metals emission lines in the dayside of KELT-20b. We first detect the planetary emission by using the G2 stellar mask of the HARPS-N pipeline, which is mainly composed of neutral iron lines, as a template. Using neutral iron templates, we perform a retrieval of the atmospheric temperature-pressure profile of the planet, confirming a thermal inversion. Then we…
Predictions of Stellar Occultations by Haumea and the Event of 4 May 2026
Instituto de Astrofísica de Andalucía-CSIC（安达卢西亚天体物理研究所）；I.E.S Politécnico Hermenegildo Lanz（埃尔梅内吉尔多·兰茨理工学院）；NASA Ames Research Center（美国国家航空航天局艾姆斯研究中心）；Department of Space Sciences and Technologies, Faculty of Science, Akdeniz University（安塔利亚大学理学院空间科学与技术系）；Deutsches Zentrum für Astrophysik (DZA)（德国天体物理学中心）
Broadband flux measurements centred around [3.6 $μ$m] and [4.5 $μ$m] obtained with Spitzer during the occultation of seven extrasolar planets by their host stars have been combined with parallax measurements to compute the absolute magnitudes of these planets. Those measurements are arranged in two colour-magnitude diagrams. Because most of the targets have sizes and temperatures similar to brown dwarfs, they can be compared to one another. In principle, this should permit inferences about exo-atmospheres based on knowledge acquired by decades of observations of field brown dwarfs and ultra-co…
We observed a secondary eclipse of WASP-33b quasi-simultaneously in the optical (~0.55 μm) and the near-infrared (~1.05 μm) using the 2x8.4 m Large Binocular Telescope. WASP-33 is a δ Scuti star pulsating with periods comparable to the eclipse duration, making the determination of the eclipse depth challenging. We use previously determined oscillation frequencies to model and remove the pulsation signal from the light curves, isolating the secondary eclipse. The determined eclipse depth is dF = 1.03 +/- 0.34 parts per thousand, corresponding to a brightness temperature of Tb = 3398 +/- 302 K. …
We have added to the Chroma+ suite of stellar atmosphere and spectrum modelling codes the ability to synthesize the exo-planet transit lightcurve for planets of arbitrary size up to 10% of the host stellar radius, and arbitrary planetary and stellar mass and orbital radius (thus determining orbital velocity) and arbitrary orbital inclination. The lightcurves are computed in situ, integrated with the radiative transfer solution for the radiation field emerging from the stellar surface, and there is no limb-darkening parameterization. The lightcurves are computed for the Johnson-Bessel photometr…
The WASP-10 planetary system is intriguing because different values of radius have been reported for its transiting exoplanet. The host star exhibits activity in terms of photometric variability, which is caused by the rotational modulation of the spots. Moreover, a periodic modulation has been discovered in transit timing of WASP-10 b, which could be a sign of an additional body perturbing the orbital motion of the transiting planet. We attempt to refine the physical parameters of the system, in particular the planetary radius, which is crucial for studying the internal structure of the trans…
Since the discovery of Kepler-10, the system has received considerable interest because it contains a small, rocky planet which orbits the star in less than a day. The system's parameters, announced by the Kepler team and subsequently used in further research, were based on only 5 months of data. We have reanalyzed this system using the full span of 29 months of Kepler photometric data, and obtained improved information about its star and the planets. A detailed asteroseismic analysis of the extended time series provides a significant improvement on the stellar parameters: Not only can we stat…
We present an occultation of the newly discovered hot Jupiter system WASP-19, observed with the HAWK-I instrument on the VLT, in order to measure thermal emission from the planet's dayside at ~2 um. The light curve was analysed using a Markov-Chain Monte-Carlo method to find the eclipse depth and the central transit time. The transit depth was found to be 0.366+-0.072 %, corresponding to a brightness temperature of 2540+-180 K. This is significantly higher than the calculated (zero-albedo) equilibrium temperature, and indicates that the planet shows poor redistribution of heat to the night sid…
We present sixteen occultation and three transit light curves for the ultra-short period hot Jupiter WASP-103 b, in addition to five new radial velocity measurements. We combine these observations with archival data and perform a global analysis of the resulting extensive dataset, accounting for the contamination from a nearby star. We detect the thermal emission of the planet in both the $z'$ and $K_{\mathrm{S}}$-bands, the measured occultation depths being 699$\pm$110 ppm (6.4-$σ$) and $3567_{-350}^{+400}$ ppm (10.2-$σ$), respectively. We use these two measurements together with recently pub…
The CHEOPS space mission dedicated to exoplanet follow-up was launched in December 2019, equipped with the capacity to perform photometric measurements at the 20 ppm level. As CHEOPS carries out its observations in a broad optical passband, it can provide insights into the reflected light from exoplanets and constrain the short-wavelength thermal emission for the hottest of planets by observing occultations and phase curves. Here, we report the first CHEOPS observation of an occultation, namely, that of the hot Jupiter WASP-189b, a $M_P \approx 2 M_J$ planet orbiting an A-type star. We detecte…
We present photometry of 4 transits of the exoplanet WASP-4b, each with a precision of approximately 500 ppm and a time sampling of 40-60s. We have used the data to refine the estimates of the system parameters and ephemerides. During two of the transits we observed a short-lived, low-amplitude anomaly that we interpret as the occultation of a starspot by the planet. We also find evidence for a pair of similar anomalies in previously published photometry. The recurrence of these anomalies suggests that the stellar rotation axis is nearly aligned with the orbital axis, or else the star spot wou…
We present three-band simultaneous observations of a weak-line T-Tauri star CVSO~30 (PTFO~8-8695), which is one of the youngest objects having a candidate transiting planet. The data were obtained with the Multicolor Simultaneous Camera for studying Atmospheres of Transiting exoplanets (MuSCAT) on the 188 cm telescope at Okayama Astrophysical Observatory in Japan. We observed the fading event in the $g^{\prime}_2$-, $r^{\prime}_2$-, and $z_{\rm s,2}$-bands simultaneously. As a result, we find a significant wavelength dependence of fading depths of about 3.1\%, 1.7\%, 1.0\% for the $g^{\prime}_…
We present the first ground-based detection of thermal emission from an exoplanet in the H-band. Using HAWK-I on the VLT, we observed an occultation of WASP-19b by its G8V-type host star. WASP-19b is a Jupiter-mass planet with an orbital period of only 19 h, and thus, being highly irradiated, is expected to be hot. We measure an H-band occultation depth of (0.259 +0.046 -0.044) %, which corresponds to an H-band brightness temperature of T_H = 2580 +/- 125 K. A cloud-free model of the planet's atmosphere, with no redistribution of energy from day-side to night-side, under predicts the planet/st…
The Alice instrument on NASA's New Horizons spacecraft observed an ultraviolet solar occultation by Pluto's atmosphere on 2015 July 14. The transmission vs. altitude was sensitive to the presence of N2, CH4, C2H2, C2H4, C2H6, and haze. We derived line-of-sight abundances and local number densities for the 5 molecular species, and line-of-sight optical depth and extinction coefficients for the haze. We found the following major conclusions: 1) We confirmed temperatures in Pluto's upper atmosphere that were colder than expected before the New Horizons flyby, with upper atmospheric temperatures n…
We typically measure the radii of transiting exoplanets from the transit depth, which is given by the ratio of cross-sectional areas of the planet and star. However, if a star has dark starspots (or bright regions) distributed throughout the transit chord, the transit depth will be biased towards smaller (larger) values, and thus the inferred planet radius will be smaller (larger) if unaccounted for. We reparameterize the transit light curve to account for "self-contamination" by photospheric inhomogeneities by splitting the parameter $R_p/R_\star$ into two parameters: one for the radius ratio…
All water-covered rocky planets in the inner habitable zones of solar-type stars will inevitably experience a catastrophic runaway climate due to increasing stellar luminosity and limits to outgoing infrared radiation from wet greenhouse atmospheres. Reflectors or scatterers placed near Earth's inner Lagrange point (L1) have been proposed as a 'geo-engineering" solution to anthropogenic climate change and an advanced version of this could modulate incident irradiation over many Gyr or "rescue" a planet from the interior of the habitable zone. The distance of the starshade from the planet that …
After observing WASP-12 in the second year of the primary mission, the Transiting Exoplanet Survey Satellite (TESS) revisited the system in late 2021 during its extended mission. In this paper, we incorporate the new TESS photometry into a reanalysis of the transits, secondary eclipses, and phase curve. We also present a new $K_s$-band occultation observation of WASP-12b obtained with the Palomar/Wide-field Infrared Camera instrument. The latest TESS photometry spans three consecutive months, quadrupling the total length of the TESS WASP-12 light curve and extending the overall time baseline b…
NASA's Kepler Space Telescope has successfully discovered thousands of exoplanet candidates using the transit method, including hundreds of stars with multiple transiting planets. In order to estimate the frequency of these valuable systems, it is essential to account for the unique geometric probabilities of detecting multiple transiting extrasolar planets around the same parent star. In order to improve on previous studies that used numerical methods, we have constructed an efficient, semi-analytical algorithm called CORBITS which, given a collection of conjectured exoplanets orbiting a star…
We use solar occultations observed by the Visual and Infrared Mapping Spectrometer aboard the Cassini Spacecraft to extract the 1 to 5 micron transmission spectrum of Saturn, as if it were a transiting exoplanet. We detect absorption from methane, ethane, acetylene, aliphatic hydrocarbons, and possibly carbon monoxide with peak-to-peak features of up to 90 parts-per-million despite the presence of ammonia clouds. We also find that atmospheric refraction, as opposed to clouds or haze, determines the minimum altitude that could be probed during mid-transit. Self-consistent exoplanet atmosphere m…
Mapping distant worlds is the next frontier for exoplanet infrared photometry studies. Ultimately, constraining spatial and temporal properties of an exoplanet atmosphere will provide further insight into its physics. For tidally-locked hot Jupiters that transit and are eclipsed by their host star, the first steps are now possible. Our aim is to constrain an exoplanet's shape, brightness distribution (BD) and system parameters from its light curve. Notably, we rely on the eclipse scanning. We use archived Spitzer 8-μm data of HD189733 (6 transits, 8 secondary eclipses, and a phase curve) in a …
Among the four known transneptunian dwarf planets, Haumea is an exotic, very elongated, and fast rotating body. In contrast to the other dwarf planets, its size, shape, albedo, and density are not well constrained. Here we report results of a multi-chord stellar occultation, observed on 2017 January 21. Secondary events observed around the main body are consistent with the presence of a ring of opacity 0.5, width 70 km, and radius 2,287$_{-45}^{+75}$ km. The Centaur Chariklo was the first body other than a giant planet to show a ring system and the Centaur Chiron was later found to possess som…
The James Webb Space Telescope (JWST) will provide an opportunity to investigate the atmospheres of potentially habitable planets. Aerosols, significantly mute molecular features in transit spectra because they prevent light from probing the deeper layers of the atmosphere. Earth occasionally has stratospheric/high tropospheric clouds at 15-20 km that could substantially limit the observable depth of the underlying atmosphere. We use solar occultations of Earth's atmosphere to create synthetic JWST transit spectra of Earth analogs orbiting dwarf stars. Unlike previous investigations, we consid…
WASP-80b is a missing link in the study of exo-atmospheres. It falls between the warm Neptunes and the hot Jupiters and is amenable for characterisation, thanks to its host star's properties. We observed the planet through transit and during occultation with Warm Spitzer. Combining our mid-infrared transits with optical time series, we find that the planet presents a transmission spectrum indistinguishable from a horizontal line. In emission, WASP-80b is the intrinsically faintest planet whose dayside flux has been detected in both the 3.6 and 4.5 $μ$m Spitzer channels. The depths of the occul…
A planet's emission spectrum contains information about atmospheric composition and structure. We compare the Bayesian Information Criterion (BIC) of blackbody fits and idealized spectral retrieval fits for the 44 planets with published eclipse measurements in multiple thermal wavebands, mostly obtained with the Spitzer Space Telescope. The evidence for spectral features depends on eclipse depth uncertainties. Spitzer has proven capable of eclipse precisions better than 1E-4 when multiple eclipses are analyzed simultaneously, but this feat has only been performed four times. It is harder to se…
[Abridged] Distant stars and planets will remain spatially unresolved for the foreseeable future. It is nonetheless possible to infer aspects of their brightness markings and viewing geometries by analyzing disk-integrated rotational and orbital brightness variations. We compute the harmonic lightcurves, F_l^m(t), resulting from spherical harmonic maps of intensity or albedo, Y_l^m(theta,phi), where l and m are the total and longitudinal order. Notably, odd m>1 are present in an inclined lightcurve, but not seen by an equatorial observer. We therefore suggest that the Fourier spectrum of a the…
We present a theoretical analysis of the optical light curves (LCs) for short-period high-mass transiting extrasolar planet systems. Our method considers the primary transit, the secondary eclipse, and the overall phase shape of the LC between the occultations. Phase variations arise from (i) reflected and thermally emitted light by the planet, (ii) the ellipsoidal shape of the star due to the gravitational pull of the planet, and (iii) the Doppler shift of the stellar light as the star orbits the center of mass of the system. Our full model of the out-of-eclipse variations contains informatio…
Studies of planetary systems of stars in star-forming regions and young clusters open a window on the formative stages of planetary evolution. We obtained high-cadence high-resolution infrared spectroscopy of the solar-mass Taurus association-member V1298 Tau during a transit of its 10R$_{\oplus}$-size "b" planet. We measured the systemic radial velocity and find that the kinematics of V1298 Tau suggest an affiliation with a $\gtrsim$6 Myr-old subgroup. A comparison of V1298 Tau and the nearby, co-moving star 2M0405 with stellar evolution models suggests an age of $\sim$10-25 Myr. We measured …
As revealed by its peculiar Kepler light curve, the enigmatic star KIC 8462852 undergoes short and deep flux dimmings at a priori unrelated epochs. It presents nonetheless all other characteristics of a quiet 1 Gyr old F3V star. These dimmings resemble the absorption features expected for the transit of dust cometary tails. The exocomet scenario is therefore most commonly advocated. We reanalyzed the Kepler data and extracted a new high-quality light curve to allow for the search of shallow signature of single or a few exocomets. We discovered that among the 22 flux dimming events that we iden…
Atmospheric refraction affects to various degrees exoplanet transit, lunar eclipse, as well as stellar occultation observations. Exoplanet retrieval algorithms often use analytical expressions for the column abundance along a ray traversing the atmosphere as well as for the deflection of that ray, which are first order approximations valid for low densities in a spherically symmetric homogeneous isothermal atmosphere. We derive new analytical formulae for both of these quantities, which are valid for higher densities, and use them to refine and validate a new ray tracing algorithm which can be…
We report the discovery of HAT-P-14b, a fairly massive transiting extrasolar planet orbiting the moderately bright star GSC 3086-00152 (V = 9.98), with a period of P = 4.627669 +/- 0.000005 days. The transit is close to grazing (impact parameter 0.891 +0.007/-0.008) and has a duration of 0.0912 +/- 0.0017 days, with a reference epoch of mid transit of Tc = 2454875.28938 +/- 0.00047 (BJD). The orbit is slightly eccentric (e = 0.107 +/- 0.013), and the orientation is such that occultations are unlikely to occur. The host star is a slightly evolved mid-F dwarf with a mass of 1.386 +/- 0.045 M(Sun…
To date, more than 750 planets have been discovered orbiting stars other than the Sun. Two sub-classes of these exoplanets, "hot Jupiters" and their less massive counterparts "hot Neptunes," provide a unique opportunity to study the extended atmospheres of planets outside of our solar system. We describe here the first far-ultraviolet transit study of a hot Neptune, specifically GJ436b, for which we use HST/STIS Lyman-$α$ spectra to measure stellar flux as a function of time, observing variations due to absorption from the planetary atmosphere during transit. This analysis permits us to derive…
