The astrophysics of visible-light orbital phase curves in the space age

The field of visible-light continuous time series photometry is now at its golden age, manifested by the continuum of past (CoRoT, Kepler), present (K2), and future (TESS, PLATO) space-based surveys delivering high precision data with a long baseline for a large number of stars. The availability of the high quality data has enabled astrophysical studies not possible before, including for example detailed asteroseismic investigations and the study of the exoplanet census including small planets. This has also allowed to study the minute photometric variability following the orbital motion in stellar binaries and star-planet systems which is the subject of this review. We focus on systems with a main sequence primary and a low-mass secondary, from a small star to a massive planet. The orbital modulations are induced by a combination of gravitational and atmospheric processes, including the beaming effect, tidal ellipsoidal distortion, reflected light, and thermal emission. Therefore, the phase curve shape contains information about the companion's mass and atmospheric characteristics, making phase curves a useful astrophysical tool. For example, phase curves can be used to detect and measure the mass of short-period low-mass companions orbiting hot fast-rotating stars, out of reach of other detection methods. Another interesting application of phase curves is using the orbital phase modulations to look for non-transiting systems, which comprise the majority of stellar binary and star-planet systems. We discuss the science done with phase curves, the first results obtained so far, and the current difficulties and open questions related to this young and evolving subfield.Comment: Invited Review accepted to PAS

Studying atmosphere-dominated hot Jupiter Kepler phase curves: Evidence that inhomogeneous atmospheric reflection is common

(abridged) We identify 3 Kepler transiting planets, Kepler-7b, Kepler-12b, and Kepler-41b, whose orbital phase-folded light curves are dominated by planetary atmospheric processes including thermal emission and reflected light, while the impact of non-atmospheric (i.e. gravitational) processes, including beaming (Doppler boosting) and tidal ellipsoidal distortion, is negligible. Therefore, those systems allow a direct view of their atmospheres without being hampered by the approximations used in the inclusion of both atmospheric and non-atmospheric processes when modeling the phase curve shape. Here we analyze Kepler-12b and Kepler-41b atmosphere based on their Kepler phase curve, while the analysis of Kepler-7b was presented elsewhere. The model we used efficiently computes reflection and thermal emission contributions to the phase curve, including inhomogeneous atmospheric reflection due to longitudinally varying cloud coverage. We confirm Kepler-12b and Kepler-41b show a westward phase shift between the brightest region on the planetary surface and the substellar point, similar to Kepler-7b. We find that reflective clouds located on the west side of the substellar point can explain the phase shift. The existence of inhomogeneous atmospheric reflection in all 3 of our targets, selected due to their atmosphere-dominated Kepler phase curve, suggests this phenomenon is common. Therefore it is likely to be present also in planetary phase curves that do not allow a direct view of the planetary atmosphere as they contain additional orbital processes. We discuss the implications of a bright-spot shift on the analysis of phase curves where both atmospheric and gravitational processes appear. We also discuss the potential detection of non-transiting but otherwise similar planets, whose mass is too small to show a gravitational photometric signal but their atmospheric signal is detectable.Comment: V2: Replaced with accepted version, Appendix B Figures 1 and 2 are in decreased resolutio

Time variation of Kepler transits induced by stellar rotating spots - a way to distinguish between prograde and retrograde motion I. Theory

Some transiting planets discovered by the Kepler mission display transit timing variations (TTVs) induced by stellar spots that rotate on the visible hemisphere of their parent stars. An induced TTV can be observed when a planet crosses a spot and modifies the shape of the transit light curve, even if the time resolution of the data does not allow to detect the crossing event itself. We present an approach that can, in some cases, use the derived TTVs of a planet to distinguish between a prograde and a retrograde planetary motion with respect to the stellar rotation. Assuming a single spot darker than the stellar disc, spot crossing by the planet can induce measured positive (negative) TTV, if the crossing occurs in the first (second) half of the transit. On the other hand, the motion of the spot towards (away from) the center of the stellar visible disc causes the stellar brightness to decrease (increase). Therefore, for a planet with prograde motion, the induced TTV is positive when the local slope of the stellar flux at the time of transit is negative, and vice versa. Thus, we can expect to observe a negative (positive) correlation between the TTVs and the photometric slopes for prograde (retrograde) motion. Using a simplistic analytical approximation, and also the publicly available SOAP-T tool to produce light curves of transits with spot-crossing events, we show for some cases how the induced TTVs depend on the local stellar photometric slopes at the transit timings. Detecting this correlation in Kepler transiting systems with high enough signal-to-noise ratio can allow us to distinguish between prograde and retrograde planetary motions. In coming papers we present analyses of the KOIs and Kepler eclipsing binaries, following the formalism developed here.Comment: V2: Major revision, accepted to Ap

Photopolarimetric Characteristics of Brown Dwarfs. I. Uniform Cloud Decks

This work is a theoretical exploration facilitating the interpretation of polarimetric observations in terms of cloudiness, rotational velocities, and effective temperatures of brown dwarfs (BDs). An envelope of scatterers like free electrons, atoms/molecules, or haze/clouds affects the Stokes vector of the radiation emitted by oblate bodies. Due to high rotation rates, BDs can be considerably oblate. We present a conics-based radiative transfer scheme for computing the disk-resolved and disk-integrated polarized emission of an oblate BD or extrasolar giant planet bearing homogeneous or patchy clouds. Assuming a uniform gray atmosphere, we theoretically examine the sensitivity of photopolarimetry to the atmosphere's scattering properties, like cloud optical thickness and grain size, concurrently with BD properties, like oblateness, inclination, and effective temperature, which are all treated as free parameters. Additionally, we examine the potential effects of gravitational darkening (GD), revealing that it could significantly amplify disk-integrated polarization. GD imparts a nonlinear inverse temperature dependence to the resulting polarization. Photopolarimetric observations are sensitive to oblateness and inclination. The degree of polarization increases in response to both, making it potentially useful for assessing the spatial orientation of the BD. Under our model assumptions, increasing droplet size in optically thick clouds causes a blueward shift in the near-infrared colors of BDs, which is interesting in light of the observed J – K brightening in the L/T transition. For large cloud grains, polarization decreases sharply, while the transmitted intensity shows a steady increase. BD polarization is thus a potential indicator not only of the presence of clouds but also provides information on cloud grain size

Kepler-47: A Transiting Circumbinary Multiplanet System

We report the detection of Kepler-47, a system consisting of two planets orbiting around an eclipsing pair of stars. The inner and outer planets have radii 3.0 and 4.6 times that of Earth, respectively. The binary star consists of a Sun-like star and a companion roughly one-third its size, orbiting each other every 7.45 days. With an orbital period of 49.5 days, 18 transits of the inner planet have been observed, allowing a detailed characterization of its orbit and those of the stars. The outer planet’s orbital period is 303.2 days, and although the planet is not Earth-like, it resides within the classical "habitable zone," where liquid water could exist on an Earth-like planet. With its two known planets, Kepler-47 establishes that close binary stars can host complete planetary systems

Accelerated Tidal Circularization Via Resonance Locking in KIC 8164262

Tidal dissipation in binary star and planetary systems is poorly understood. Fortunately, eccentric binaries known as heartbeat stars often exhibit tidally excited oscillations, providing observable diagnostics of tidal circularization mechanisms and timescales. We apply tidal theories to observations of the heartbeat star KIC 8164262, which contains an F-type primary in a very eccentric orbit that exhibits a prominent tidally excited oscillation. We demonstrate that the prominent oscillation is unlikely to result from a chance resonance between tidal forcing and a stellar oscillation mode. However, the oscillation has a frequency and amplitude consistent with the prediction of resonance locking, a mechanism in which coupled stellar and orbital evolution maintain a stable resonance between tidal forcing and a stellar oscillation mode. The resonantly excited mode produces efficient tidal dissipation (corresponding to an effective tidal quality factor $Q \sim 5 \times 10^4$), such that tidal orbital decay/circularization proceeds on a stellar evolution time scale.Comment: Published in MNRAS Letters. For an interactive 3D model of the system, go to http://www.glowscript.org/#/user/slantburns/folder/Public/program/KIC816426

The Pseudosynchronization of Binary Stars Undergoing Strong Tidal Interactions

Eccentric binaries known as heartbeat stars experience strong dynamical tides as the stars pass through periastron, providing a laboratory to study tidal interactions. We measure the rotation periods of 24 heartbeat systems, using the Kepler light curves to identify rotation peaks in the Fourier transform. Where possible, we compare the rotation period to the pseudosynchronization period derived by Hut 1981. Few of our heartbeat stars are pseudosynchronized with the orbital period. For four systems, we were able to identify two sets of rotation peaks, which we interpret as the rotation from both stars in the binary. The majority of the systems have a rotation period that is approximately 3/2 times the pseudosynchronization period predicted by Hut 1981, suggesting that other physical mechanisms influence the stars' rotation, or that stars typically reach tidal spin equilibrium at a rotation period slightly longer than predicted.Comment: 9 pages, 4 figures, 1 table