skip to main content

This content will become publicly available on June 6, 2023

Title: Analytic Light Curves in Reflected Light: Phase Curves, Occultations, and Non-Lambertian Scattering for Spherical Planets and Moons
Abstract 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 rough surfaces with phase-dependent scattering. Our algorithm is implemented in Python within the open-source starry mapping framework and is designed with efficient gradient-based inference in mind. The algorithm is ∼4–5 orders of magnitude faster than direct numerical evaluation methods and ∼10 orders of magnitude more precise. We show how the techniques developed here may one day lead to the construction of two-dimensional maps of terrestrial planet surfaces, potentially enabling the detection of continents and oceans on exoplanets in the habitable zone. 6 6
; ; ;
Award ID(s):
Publication Date:
Journal Name:
The Astronomical Journal
Page Range or eLocation-ID:
Sponsoring Org:
National Science Foundation
More Like this

    Eclipsing binaries are important benchmark objects to test and calibrate stellar structure and evolution models. This is especially true for binaries with a fully convective M-dwarf component for which direct measurements of these stars’ masses and radii are difficult using other techniques. Within the potential of M-dwarfs to be exoplanet host stars, the accuracy of theoretical predictions of their radius and effective temperature as a function of their mass is an active topic of discussion. Not only the parameters of transiting exoplanets but also the success of future atmospheric characterization relies on accurate theoretical predictions. We present the analysis of five eclipsing binaries with low-mass stellar companions out of a subsample of 23, for which we obtained ultra-high-precision light curves using the CHEOPS satellite. The observation of their primary and secondary eclipses are combined with spectroscopic measurements to precisely model the primary parameters and derive the M-dwarfs mass, radius, surface gravity, and effective temperature estimates using the PYCHEOPS data analysis software. Combining these results to the same set of parameters derived from TESS light curves, we find very good agreement (better than 1 per cent for radius and better than 0.2 per cent for surface gravity). We also analyse the importance of precisemore »orbits from radial velocity measurements and find them to be crucial to derive M-dwarf radii in a regime below 5 per cent accuracy. These results add five valuable data points to the mass–radius diagram of fully convective M-dwarfs.

    « less

    A new window to observing individual stars and other small sources at cosmological distances was opened recently, with the detection of several caustic-crossing events in galaxy cluster fields. Many more such events are expected soon from dedicated campaigns with the Hubble Space Telescope and the James Webb Space Telescope. These events can not only teach us about the lensed sources themselves, such as individual high-redshift stars, star clusters, or accretion discs, but through their light curves they also hold information about the point-mass function of the lens, and thus, potentially, the composition of dark matter. We present here a simple method for simulating light curves of such events, i.e. the change in apparent magnitude of the source as it sweeps over the net of caustics generated by microlenses embedded around the critical region of the lens. The method is recursive and so any reasonably sized small source can be accommodated, down to sub-solar scales, in principle. We compare the method, which we dub Adaptive Boundary Method, with other common methods such as simple inverse ray shooting, and demonstrate that it is significantly more efficient and accurate in the small-source and high-magnification regime of interest. A python version of themore »code is made publicly available in an open-source fashion for simulating future events.

    « less
  3. Abstract

    We present a solution for the light curve of two bodies mutually transiting a star with polynomial limb darkening. The term “mutual transit” in this work refers to a transit of the star during which overlap occurs between the two transiting bodies. These could be an exoplanet with an exomoon companion, two exoplanets, an eclipsing binary and a planet, or two stars eclipsing a third in a triple-star system. We include analytic derivatives of the light curve with respect to the positions and radii of both bodies. We provide code that implements a photodynamical model for a mutual transit. We include two dynamical models, one for hierarchical systems in which a secondary body orbits a larger primary (e.g., an exomoon system) and a second for confocal systems in which two bodies independently orbit a central mass (e.g., two planets in widely separated orbits). Our code is fast enough to enable inference with Markov Chain Monte Carlo algorithms, and the inclusion of derivatives allows for the use of gradient-based inference methods such as Hamiltonian Monte Carlo. While applicable to a variety of systems, this work was undertaken primarily with exomoons in mind. It is our hope that making this codemore »publicly available will reduce barriers for the community to assess the detectability of exomoons, conduct searches for exomoons, and attempt to validate existing exomoon candidates. We also anticipate that our code will be useful for studies of planet–planet transits in exoplanetary systems, transits of circumbinary planets, and eclipses in triple-star systems.

    « less
  4. Context. The origin of ultra-rapid flares of very high-energy radiation from active galactic nuclei remains elusive. Magnetospheric processes, occurring in the close vicinity of the central black hole, could account for these flares. Aims. Our aim is to bridge the gap between simulations and observations by synthesizing gamma-ray light curves in order to characterize the activity of a black hole magnetosphere, using kinetic simulations. Methods. We performed global axisymmetric 2D general-relativistic particle-in-cell simulations of a Kerr black hole magnetosphere. We included a self-consistent treatment of radiative processes and plasma supply, as well as a realistic magnetic configuration, with a large-scale equatorial current sheet. We coupled our particle-in-cell code with a ray-tracing algorithm in order to produce synthetic light curves. Results. These simulations show a highly dynamic magnetosphere, as well as very efficient dissipation of the magnetic energy. An external supply of magnetic flux is found to maintain the magnetosphere in a dynamic state, otherwise the magnetosphere settles in a quasi-steady Wald-like configuration. The dissipated energy is mostly converted to gamma-ray photons. The light curves at low viewing angle (face-on) mainly trace the spark gap activity and exhibit high variability. On the other hand, no significant variability is found at highmore »viewing angle (edge-on), where the main contribution comes from the reconnecting current sheet. Conclusions. We observe that black hole magnetospheres with a current sheet are characterized by a very high radiative efficiency. The typical amplitude of the flares in our simulations is lower than is detected in active galactic nuclei. These flares could result from the variation in parameters external to the black hole.« less
  5. Abstract

    Recent work has revealed that the light curves of hydrogen-poor (Type I) superluminous supernovae (SLSNe), thought to be powered by magnetar central engines, do not always follow the smooth decline predicted by a simple magnetar spin-down model. Here we present the first systematic study of the prevalence and properties of “bumps” in the post-peak light curves of 34 SLSNe. We find that the majority (44%–76%) of events cannot be explained by a smooth magnetar model alone. We do not find any difference in supernova properties between events with and without bumps. By fitting a simple Gaussian model to the light-curve residuals, we characterize each bump with an amplitude, temperature, phase, and duration. We find that most bumps correspond with an increase in the photospheric temperature of the ejecta, although we do not see drastic changes in spectroscopic features during the bump. We also find a moderate correlation (ρ≈ 0.5;p≈ 0.01) between the phase of the bumps and the rise time, implying that such bumps tend to happen at a certain “evolutionary phase,” (3.7 ± 1.4)trise. Most bumps are consistent with having diffused from a central source of variable luminosity, although sources further out in the ejecta are not excluded.more »With this evidence, we explore whether the cause of these bumps is intrinsic to the supernova (e.g., a variable central engine) or extrinsic (e.g., circumstellar interaction). Both cases are plausible, requiring low-level variability in the magnetar input luminosity, small decreases in the ejecta opacity, or a thin circumstellar shell or disk.

    « less