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Phase curves

Phase curves of transiting exoplanets 
from the TESS Mission

Phase curves are the holy grail of time domain exoplanet astronomy. By observing a system throughout the full orbital phase, we can measure not only the primary transit (when the planet passes in front of its host star), but also the secondary transit (when the planet is occulted) and variations in the planet’s brightness throughout its orbit. For short-period planets, which are expected to be tidally locked, these photometric modulations provide a longitudinal map of the surface brightness (see figure). 


For the most massive exoplanets, the strong mutual gravitational interaction between the planet and the star causes additional photometric variability that can be detected with visible-wavelength phase curve observations. These signals are due to the tidally distorted stellar surface (ellipsoidal distortion) and the periodic blue- and red-shifting of the stellar spectrum that results from the induced radial velocity (Doppler boosting). By probing the star’s tidal response, detailed comparisons of the measured amplitudes of these phase curve components with theoretical predictions offer an empirical test of stellar astrophysics. See, for example, my work on the ultra high-precision full Kepler phase curve of the transiting hot white dwarf system KOI-964 (Wong et al. 2020a). 

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Over the past six years, I have worked with several collaborators, including Avi Shporer (MIT), Tansu Daylan (MIT), and Björn Benneke (University of Montréal), to analyze visible-light phase curves from the TESS mission. Our first published TESS phase curve was of WASP-18 (Shporer et al. 2019; see figure), which shows phase curve components from all three physical processes: atmospheric brightness modulation, ellipsoidal distortion, and Doppler boosting. Since then, our work has expanded into a broad systematic study of all known transiting systems. Some notable targets include WASP-19, where we combined the TESS-band secondary eclipse measurement with the full body of published eclipse depths at other wavelengths to retrieve a significantly non-zero optical geometric albedo (Wong et al. 2020b). For the ultra-hot Jupiter KELT-9b, the TESS phase curve provided an extremely high signal-to-noise secondary eclipse depth and also revealed an unexpected phase curve signal at the first harmonic of the orbital phase, which we attributed to the time-varying irradiation of the planet due to the gravity darkening of the rapidly-rotating host star and the unusual polar orbit (Wong et al. 2020d).

During the TESS Primary Mission, we detected phase curve modulations and/or secondary eclipses for over two dozen systems, allowing us to search for population-level trends in our results. In our works summarizing the Year 1 and Year 2 phase curve analysis (Wong et al. 2020e, Wong et al. 2021a), we combined our TESS-band secondary eclipse measurements with previously-published Spitzer 3.6 and 4.5 micron eclipse depths to break the degeneracy between thermal emission and reflected light and derive self-consistent dayside temperatures and optical geometric albedos. We found a tentative trend between increasing dayside temperature and increasing geometric albedo for hot Jupiters between 1500 and 3000 K. The enhanced apparent albedo of these highly-irradiated planets is surprising, since all major condensate species are expected to be in the vapor phase at such high temperatures. While partial cloud cover cannot be ruled out, another possible explanation for this trend is the presence of additional high-altitude opacity sources, which can increase the thermal emission from the planet in the visible.

TESS is now in its Extended Mission, during which it has revisited most of the targets it observed in the Primary Mission. The additional photometry has greatly enhanced the precision of the measured phase-curve parameters. Furthermore, the repeated observations have allowed us to probe for possible atmospheric variability on both month- and year-long timescales. Such an analysis was recently carried out on WASP-12b (Wong et al. 2022a), where we found no evidence for significant variability in the dayside brightness of the planet. Extended Mission transit timings can also be used to refine transit ephemerides and probe for tidal orbital decay. Our study of WASP-12b leveraged the extended time baseline to derive a more precise measurement of the tidal orbital decay rate of the planet. Utilizing phase curve considerations as part of the TESS planet candidate vetting process can also uncover notable systems. For example, I led the discovery of the ultrahot Jupiter TOI-2109b, which has a 16-hour orbit that is the shortest hitherto measured for a gas giant exoplanet and shows dramatic phase-curve variations (Wong et al. 2021b).

Small bodies

Characterizing minor planets in the 

middle and outer Solar System

Beyond the Main Belt asteroids lie several enigmatic populations of small bodies:

  • Hildas: asteroids in the 3:2 mean motion resonance with Jupiter, orbiting at roughly 4 AU from the Sun.

  • Jupiter Trojans: two large swarms of minor planets confined to the L4 and L5 Lagrangian points in Jupiter’s orbit.

  • Kuiper belt objects (KBOs): a vast, diverse collection of icy bodies extending beyond the orbit of Neptune

  • Centaurs: inward-scattered former KBOs that lie on unstable, eccentric orbits that cross the giant planet region.


With recent developments in our understanding of solar system formation and evolution, these far-flung small body populations have entered the spotlight. Current models diverge from the classical in situ planet formation paradigm and posit a drastically different scenario in which the outer planets initially formed in a more compact orbital configuration (e.g., Morbidelli et al. 2005). A subsequent period of dynamical instability drastically altered the architecture of the middle and outer solar system. A major consequence of such dynamical instability models is the disruption of the large reservoir of planetesimals located beyond the ice giants. While the majority of the surviving objects migrated outward to populate the present-day KBO region, a small fraction of these bodies were scattered inward to be captured by Jupiter into the Hilda and Trojan groups. Thus, dynamical instability models predict that the Trojans, Hildas, and KBOs originate from a single primordial population of outer solar system planetesimals and should share similar chemical compositions. 


Since 2014, I have carried out a multifaceted observational and modeling campaign to further our understanding of these small body populations. Some highlights from this work include the discovery and/or confirmation of the optical color bimodality among Hildas, Trojans, and similarly-sized KBOs (see figure above), and the characterization of the size distributions for all three populations using a combination of archival data from the Sloan Digital Sky Survey and new photometric observations with the Subaru Telescope (Wong et al. 2014, Wong & Brown 2015, Wong & Brown 2017a, Wong & Brown 2017b). 

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In addition, we proposed a hypothesis to explain the color bimodalities and thermal/collisional evolution of all middle and outer solar system asteroid populations within the dynamical instability framework (Wong & Brown 2016; see figure). In short, we posit that sublimation-driven volatile loss from the outermost layers of ice-rich bodies in the primordial outer solar system planetesimal disk led to the development of two distinct surface compositions — the objects situated closer to the Sun experienced higher surface temperatures and became depleted of H₂S on their surfaces, while objects farther out retained H₂S. Solar irradiation reddened the surfaces of these two populations to different extents, and the subsequent dynamical instability spread these bodies throughout the Solar System to become the present-day Trojans, Hildas, and KBOs, which thereby inherited the color bimodality. 

My subsequent work focused on spectroscopic characterization of Hildas and Trojans. Near-infrared spectra of Hildas were found to be largely identical to those of Trojans, and crucially, they show a clear bimodality in spectral shape that aligns with the aforementioned optical color bimodalities (Wong et al. 2017). UV observations with Hubble likewise revealed a clear distinction in spectral behavior between less-red and red Trojans (Wong et al. 2019a). The reflectance spectra of the two Trojan subpopulations are now characterized across the 0.3-5.0 micron wavelength range (see figure). Simultaneously, I worked on improving our understanding of active Centaurs — an enigmatic subclass of the Centaurs that show cometary activity. By expanding the catalog of measured active Centaur colors with new photometric measurements and examining their orbital distribution relative to the inactive Centaurs (Wong et al. 2019b), we seek to use the Centaurs as a proxy for inward-scattered primordial icy bodies, with important implications for understanding the composition and evolution of Jupiter Trojans within the framework of dynamical instability models.

In 2021, NASA launched the Lucy spacecraft on a flyby mission to the Trojans. I am actively collaborating with the science team to carry out ground- and space-based observations of the mission targets in preparation for the encounters. An example of this supporting research is our multi-band photometric observations of a mutual event in the Patroclus-Menoetius binary system (Wong & Brown 2019). I have also leveraged the capabilities of JWST to obtain spectra of both Trojans and KBOs, uncovering diagnostic absorption features that have yielded improved constraints on their surface compositions. As part of the JWST Solar System Guaranteed Time Observations team, I am working on a wide range of Cycle 1 and Cycle 2 data products, focusing on NIRSpec reflectance spectroscopy and MIRI emission spectroscopy. I've led and/or contributed to over a dozen papers based on JWST data to date; see my CV for a full list. Results from a Cycle 1 program that observed the Trojan targets of the Lucy Mission with the NIRSpec instrument have recently been published (Wong et al. 2024), revealing evidence for OH absorption, aliphatic organics and a peculiar CO₂ feature on the collisional fragment Eurybates. I am also venturing into examining interesting individual targets that may be particularly diagnostic of underlying physics. Recently, I completed a photometric campaign to confirm and characterize the Ennomos collisional family in the Trojans, revealing a small group of unusually blue objects that are spectrally distinct from the background population (Wong & Brown 2023).

Atmospheric characterization of cool gas giants

Over the past decade, transmission spectroscopy has emerged as a powerful tool for studying the chemical composition of exoplanet atmospheres. The opacity of the atmosphere across different wavelengths is affected by the absorption features of the component molecules. Measurements of the transmission spectrum can reveal variations in transit depth as a function of wavelength and thereby detect the presence of a whole suite of molecular species within the optically-thin part of the atmosphere near the day-night terminator. As telescope capabilities and analysis methodologies improve, the field continues to strive for more and more detailed compositional characterization of an increasingly diverse range of exoplanets.


A frequent complicating factor in transmission spectroscopy is the presence of clouds and/or hazes. Even small amounts of condensates in the atmosphere can strongly attenuate the absorption features in the transmission spectrum, constraining our ability to place meaningful constraints on many atmospheric properties. At the same time, the important role of clouds in driving atmospheric chemistry and dynamics, as well as the great diversity of condensate species found on exoplanets, has motivated increasingly complex microphysical models for describing the formation, composition, and thermochemical effects of clouds. On a practical note, a more refined understanding of the conditions under which clouds and hazes occur will be crucial in the selection of optimal targets with clear atmospheres for intensive observations using the limited time allocation available on next-generation telescopes, such as the James Webb Space Telescope (JWST).

As part of the effort to better understand clouds in exoplanet atmospheres, I have analyzed the transmission spectra of several cool gas giants. While many hot Jupiters have been intensely observed in transmission, cooler and smaller planets, especially those with dayside temperatures below 1000 K, provide a hitherto poorly-explored region in the mass-temperature distribution for detailed atmospheric characterization. These planets can serve as proxies for studying the atmospheres of super Earths, which have similar dayside temperatures and are therefore likely to host similar kinds of clouds.

Our work on the sub-Saturn HAT-P-12b, combining Hubble and Spitzer transit observations with Spitzer secondary eclipses, produced a transmission spectrum spanning 0.3-5.0 microns (Wong et al. 2020c; see figure). We detected a salient water vapor absorption feature around 1.4 microns attenuated by clouds and a prominent Rayleigh scattering slope in the optical. We interpreted the spectrum using both state-of-the-art atmospheric retrievals from SCARLET and forward models generated by the aerosol microphysics code CARMA. These models indicate that the atmosphere of HAT-P-12b is consistent with a broad range of super-solar metallicities, a roughly solar C/O ratio, a near-isothermal upper atmosphere, and moderately efficient vertical mixing. Photochemical hazes consisting of soot and/or tholins were shown to provide the additional short-wavelength opacity necessary to match the observed Rayleigh scattering feature at visible wavelengths.


In a recently published analogous analysis of two more cool gas giants, WASP-29b and WASP-80b (Wong et al. 2022b), we measured transmission spectra that suggest drastically different cloud opacity levels, despite the planets being at very similar temperatures. While the flat and featureless spectrum of WASP-29b indicates strong cloud opacity, the spectrum of WASP-80b shows a prominent water vapor absorption, evidence of enhanced atmospheric metallicity, and signs of fine-particle aerosols.

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Transmission spectra
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