--- title: "Seeing day and night on an unresolved planet" description: "How an unresolved planet reveals its bright dayside and warm nightside through changing infrared light." canonical_url: "https://sandboxphysics.com/stories/planet-phase-curves/dayside-in-starlight/" language: "en" page_type: "story" alternate_languages: zh-CN: "https://sandboxphysics.com/zh/stories/planet-phase-curves/dayside-in-starlight/" last_modified: "2026-10-28" --- [Exoplanet day and night](https://sandboxphysics.com/stories/planet-phase-curves/) AC21 · L1 # Seeing day and night on an unresolved planet Sandbox Physics · 2026-10-28 A planet can reveal a warm nightside even when a telescope cannot separate its disk from its star. As the planet travels around its orbit, different longitudes face us. Their changing infrared light traces the journey of absorbed heat. ## Before you begin No astronomy background is needed. The next chapter introduces the energy calculation. ## The night comes into view Imagine watching a glowing ball turn slowly behind a much brighter lamp. A camera records their combined light. When the ball shows its hottest face, the total rises a little. When its cooler side turns toward the camera, the total falls. Astronomers call this repeated change a phase curve. A phase tells us where the planet is in its orbit. WASP-43b completes an orbit in about nineteen and a half hours. Its rotation is expected to keep the same hemisphere facing the star. That hemisphere has a permanent day, and the opposite hemisphere a permanent night. During an orbit, however, our view changes from one side to the other. Synchronization does not keep the same side facing Earth. In December 2022, JWST's Mid-Infrared Instrument followed the system for about twenty-six and a half hours. The observation included a transit, when the planet passed in front of the star, and two secondary eclipses, when the star hid the planet. The small loss of infrared light during a secondary eclipse measured how much light the planet had been adding. Reading: Taylor J. Bell et al., Nightside clouds and disequilibrium chemistry on the hot Jupiter WASP-43b · Taylor James Bell and the 17 other named Zenodo creators, Products and Models for Nightside clouds and disequilibrium chemistry on the hot Jupiter WASP-43b ## Warm gas crosses the evening edge A motionless parcel on the nightside would keep losing heat by radiation. Its surroundings would become cold unless another source supplied energy. An atmosphere supplies a route from the day: gas absorbs starlight, moves across the evening boundary and continues radiating after direct illumination has ended. How far the gas carries its warmth depends on two competing rates. Faster flow carries it farther before it cools. A layer with more heat stored per degree also cools more slowly. The brightest region can therefore lie away from the point where the star shines straight down. In a simple eastward-flowing atmosphere, the bright region turns into view before the planet reaches secondary eclipse. That displaced bright region is often called a hotspot. The maximum of the total observed light is a weighted contribution from a whole hemisphere, so its timing need not give the exact longitude of the single hottest parcel. Even a perfectly measured curve still requires an interpretation of that projection. Reading: Nicolas B. Cowan and Eric Agol, A Model for Thermal Phase Variations of Circular and Eccentric Exoplanets · Nicolas B. Cowan and Eric Agol, Inverting Phase Functions to Map Exoplanets ## What the infrared measurement means The WASP-43b spectra gave average brightness temperatures of $1524\pm35\,\mathrm K$ on the dayside and $863\pm23\,\mathrm K$ on the nightside. Brightness temperature means the temperature a blackbody would need to produce the measured intensity in the selected spectral range. It is a way of describing light, with a specified wavelength range. An atmosphere emits from different depths at different wavelengths. A cloud can hide a warmer layer below it, changing the brightness temperature we infer. In the WASP-43b study, the observed curves and spectra were compared with atmospheric calculations, including models with nightside clouds. The comparison gives a physical reason to study the spectrum alongside the broad rise and fall of total light. A warm nightside is an observable consequence of energy arriving there. Turning one infrared curve into an exact wind speed is harder: a slowly cooling layer and a faster wind can produce similar distributions. The next useful question is how to calculate that distribution and carry its light all the way to the telescope. Reading: Taylor J. Bell et al., Nightside clouds and disequilibrium chemistry on the hot Jupiter WASP-43b · Nicolas B. Cowan and Eric Agol, The Statistics of Albedo and Heat Recirculation on Hot Exoplanets ## Following the same heat all the way Start with the area that intercepts starlight. Subtract the fraction reflected away, allow gas to move, and calculate how each patch cools. Once the patch temperatures are known, add the emission from the visible hemisphere, giving more weight to patches that face us directly. An eclipse changes the last step. The star blocks the light on its way to us; it does not turn off the illumination that heats the planet. Keeping that distinction makes the connection between the orbit, the weather pattern and the observed curve easier to follow. The following chapters develop the areas, the moving parcel and the projected sum in that order. Reading: Nicolas B. Cowan and Eric Agol, A Model for Thermal Phase Variations of Circular and Eccentric Exoplanets · Rodrigo Luger et al., STARRY: Analytic Occultation Light Curves ## Exercises and explanations 1. Why can a tidally synchronized planet still have warm gas on its nightside? Read the explanation Synchronization fixes the same hemisphere toward the star; the atmosphere can still move relative to the body. Gas transports internal energy before radiating it away. ## Try the prediction ### [Follow the changing view](https://sandboxphysics.com/labs/exoplanet-thermal-phase-curve/) 1. Start with Eastward heat and follow the green observer direction through an orbit. 2. Switch to Observer view near secondary eclipse; compare the orange curve with the visible globe. 3. Return to Flow view and explain why the layer remains heated while its light is hidden. [Next: The areas that set a planet's temperature](https://sandboxphysics.com/stories/planet-phase-curves/areas-and-temperatures/) ## Sources and calculation scope 1. [Nicolas B. Cowan and Eric Agol, A Model for Thermal Phase Variations of Circular and Eccentric Exoplanets](https://arxiv.org/pdf/1011.0428v1) arXiv:1011.0428v1, submitted 2010-11-01. Sections 2–3, equations 1–10; section 4, equation 13; section 6; figures 1 and 6. 2. [Nicolas B. Cowan and Eric Agol, Inverting Phase Functions to Map Exoplanets](https://arxiv.org/pdf/0803.3622v1) arXiv:0803.3622v1, submitted 2008-03-25. Section 2, equations 1–4; section 3.2, equation 7; figure 1. 3. [Nicolas B. Cowan and Eric Agol, The Statistics of Albedo and Heat Recirculation on Hot Exoplanets](https://arxiv.org/pdf/1001.0012v2) arXiv:1001.0012v2, revised 2010-12-20. Sections 1, 2.1 and 2.2; equation 3. 4. [Taylor J. Bell et al., Nightside clouds and disequilibrium chemistry on the hot Jupiter WASP-43b](https://arxiv.org/pdf/2401.13027v1) arXiv:2401.13027v1, submitted 2024-01-23; dataset v1 published 2024-04-30. Main figures 1–4; Methods Observations and Data Reduction, PDF pages 12–21 including spectral binning, shadowed region, harmonics and Eureka v1 equations 1–7; Data Availability, PDF page 33. Published methods also checked for trimming and light-travel convention. 5. [Rodrigo Luger et al., STARRY: Analytic Occultation Light Curves](https://arxiv.org/pdf/1810.06559v1) arXiv:1810.06559v1, submitted 2018-10-15. Section 2.4, equation 16; section 3.1, equations 17–20; sections 3.2–3.3; section 4.2 and figure 5. 6. [Taylor James Bell and the 17 other named Zenodo creators, Products and Models for Nightside clouds and disequilibrium chemistry on the hot Jupiter WASP-43b](https://zenodo.org/records/10525170) Zenodo record 10525170, v1, published 2024-04-30. Original API metadata, archive directory, selected HDF5 arrays and attributes, S3/S4/S5 configuration and EPF.