Reflected-light Phase Curves with PICASO: A Kepler-7b Case Study

Alexandria V. Johnson; Colin D. Hamill; Danica Adams; Natasha Batalha; Peter Gao; Rowan Nag; Tiffany Kataria

REVIEW 3 major objections 5 minor 2 references

Reflected-light Phase Curves with PICASO: A Kepler-7b Case Study

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This paper claims that PICASO can now model reflected-light phase curves from GCM atmospheres, and that for Kepler-7b a three-cloud, low-sedimentation scenario best matches the observed phase curve but under-predicts its brightness by…

desk verdict A genuinely new reflected-light phase-curve mode for PICASO, but the missing known-answer test for the new geometry means the factor-of-three Kepler under-prediction could be a code bug rather than missing physics. read the letter →

arxiv 2411.14225 v1 pith:JMJ6WJXH submitted 2024-11-21 astro-ph.EP

Colin D. Hamill , Alexandria V. Johnson , Natasha Batalha , Rowan Nag , Peter Gao , Danica Adams , Tiffany Kataria This is my paper · ORCID

classification astro-ph.EP

keywords reflectedlightphasecurvesPICASOVirgaKepler-7bhotJupiterexoplanetcloudsradiativetransfergeneralcirculationmodels

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper introduces a new routine in the open-source radiative transfer code PICASO that computes reflected-light phase curves directly from three-dimensional GCM atmospheres, with clouds supplied post hoc by the Virga cloud model. The authors apply it to Kepler-7b, a hot Jupiter whose optical phase curve is dominated by starlight reflected off clouds. They find that the best match to the Kepler data comes from a three-condensate scenario (Mg2SiO4, Al2O3, TiO2) with low sedimentation efficiency (fsed = 0.03, reduced chi-square 1.94), but every model under-predicts the observed brightness by about a factor of three. The work matters because reflected-light phase curves will be a primary observable for the next generation of direct-imaging and phase-curve telescopes, and this tool makes such predictions possible from published GCM output.

What carries the argument

The load-bearing machinery is the new reflected-phase-curve routine in PICASO, which adapts the thermal phase-curve method by tracking how much of the illuminated dayside is visible at each orbital phase and integrating facet intensities with Chebyshev-Gauss weights. Cloud optical properties (single-scattering albedo, asymmetry parameter, optical depth per pressure level) are computed by Virga at every GCM grid point and rotated/regridded onto a 20 x 20 dayside facet grid before radiative transfer; the choice of 20 x 20 keeps errors below two percent versus 30 x 30.

What would settle it

Measure a spatially resolved dayside brightness map of Kepler-7b at near-infrared wavelengths (e.g., with JWST) and compare the longitude and contrast of the bright western region with the model's cloud map; if the observed bright region is substantially broader or brighter than the Virga predictions, the paper's factor-of-three gap is explained, and if not, the missing brightness must come from something else such as zonal transport or non-spherical particles.

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Extended reading notes

Core claim

The central claim is that PICASO can now take a GCM's temperature-pressure and eddy-diffusion fields, run Virga to compute equilibrium condensate clouds, and produce a full-orbit reflected-light phase curve whose shape and offset are set by the three-dimensional cloud distribution. For Kepler-7b, the model reproduces the expected cloud bank west of the substellar point, high-latitude and eastern-limb magnesium silicate clouds, and Al2O3/TiO2 clouds near the substellar point; the low-fsed three-cloud models match the observed phase-curve shape best, yet yield intensities roughly one-third of the observed values. The paper's proposed explanations for the shortfall are an under-bright or undersized western cloud region, missing zonal transport of cloud particles, neglected cloud radiative feedback, and the assumption of spherical particles.

Load-bearing premise

The GCM thermal structure from Adams et al. (2022), which does not include cloud radiative feedback, is a faithful representation of Kepler-7b's atmosphere, because that temperature field determines where Virga places clouds and therefore the shape and amplitude of the phase curve.

Editorial extensions

If this is right

The community gets a validated, open-source path from GCM output to reflected-light phase curves, applicable to any exoplanet with a 3D climate model.
Kepler-7b's albedo appears to require multiple cloud species: Al2O3 and TiO2 can contribute up to half of the reflected light, despite magnesium silicates dominating the western cloud bank.
Phase-curve offsets are directly readable as cloud-location diagnostics: low-fsed, multi-cloud models place the offset at about 30 degrees westward, matching observations.
Future Roman and Habitable Worlds Observatory reflected-light observations can be interpreted with physical cloud models rather than free-parameter albedo fits.
Thermal phase-curve and reflected-light capabilities now share one code, enabling joint visible and infrared modeling of the same planet.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Including cloud radiative feedback in the GCM would likely brighten the dayside and may close part of the factor-of-three gap, since the paper notes feedback is neglected.
Zonal transport of cloud particles from the nightside toward the substellar point is a testable extension: a GCM coupled to a transport-aware cloud microphysics scheme could be compared against the Virga static-cloud prediction.
The factor-of-three shortfall suggests assuming spherical, compact particles underestimates scattering; computing scattering with porous or aggregate particles would give a quantitative check.
The paper's resolution tests show 20 x 20 is a reasonable default; a 10 x 10 grid introduces more than five percent errors at some phases, so future users should not drop below 20 x 20.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The useful thing here is a real new capability: PICASO can now turn GCM output into reflected-light phase curves, tracking the waxing and waning dayside as the planet orbits. The paper is open about what it does, ships code and a tutorial, and the Kepler-7b comparison is transparent, including the honest admission that the models peak at ~11–14 ppm against 50±2 ppm observed. The new cloud maps, with Al2O3 and TiO2 opacity near the substellar point and magnesium silicates at the limbs, are also genuinely new and worth having.

The soft spot is the one the stress-test flags, and it is real. The new geometry in Section 2.2.1 is the whole point of the paper, yet nothing validates its absolute normalization. The only benchmark is Kepler-7b, which misses by a factor of three. The authors attribute that gap to zonal transport, cloud radiative feedback, and nonspherical particles, and those are plausible. But a normalization error or an integration bug in the Chebyshev–Gauss weighting of Equation (6) would produce exactly the same symptom. The appendix shows grid convergence, not absolute correctness. I would want a known-answer test: a Lambertian sphere phase curve, or a simple 1D radiative-transfer comparison at a few phase angles, before trusting the code's absolute fluxes. Without that, the 'enhanced capability' claim is not fully supported.

Two smaller issues. First, the fsed conclusion is a post-hoc chi-square selection on the same dataset, so the 'best fit' is a fit result, not a prediction. The paper mostly frames it that way, but the abstract overstates the preference for low fsed. Second, the GCM without cloud radiative feedback and Virga without zonal transport are acknowledged limitations, and they likely explain part of the amplitude gap. Those are fine as stated, but they make the Kepler-7b comparison a demonstration, not a validation.

The paper deserves a serious referee. The community needs exactly this kind of open-source tool for Roman and HWO planning, and the core geometry change is worth scrutiny. But I would send it back demanding the validation test, and I would not cite the absolute phase-curve amplitudes in my own work until that test is in the literature.

Referee Report

3 major / 5 minor

Summary. The paper introduces a new capability in the open-source radiative transfer code PICASO for computing reflected-light phase curves from three-dimensional GCM atmospheres. The routine rotates and regrids GCM temperature, chemistry, and Virga cloud fields onto the visible dayside hemisphere using Chebyshev–Gauss integration. The authors apply it to Kepler-7b using the SPARC/MITgcm thermal structure from Adams et al. (2022), modeling three cloud compositions (MgSiO3-only, Mg2SiO4-only, and Mg2SiO4+Al2O3+TiO2) at fsed = 0.03, 0.1, 0.3, and 1.0, and compare KRF-weighted phase curves to the Demory et al. (2013) Kepler data. The models reproduce the general westward cloud asymmetry but under-predict the observed 50 ± 2 ppm amplitude by roughly a factor of three; the lowest reduced chi-square is 1.94 for the three-cloud, fsed = 0.03 model. The paper concludes that Al2O3 and TiO2 contribute substantially to the albedo and that better treatments of zonal transport, cloud radiative feedback, and particle shape are needed.

Significance. If the code is correct, this is a useful contribution: PICASO and Virga are open source, the authors provide a public tutorial, and the comparison to Kepler-7b is transparent, including the factor-of-three amplitude deficit. The use of a standard Toon et al. (1989) radiative-transfer core and the explicit resolution-convergence test in the Appendix are strengths. The paper also makes falsifiable predictions for future reflected-light observations of hot Jupiters. However, the central new routine is not tested against any known solution, and the only benchmark under-predicts the observed amplitude by a factor of three. The scientific conclusions about Kepler-7b's clouds are therefore conditional; the main value of the paper is the tool description and the transparent case study.

major comments (3)

[Section 2.2.1 and Appendix] The new reflected-light phase-curve mode is the central deliverable, yet no known-answer test of its absolute normalization or geometry is provided. The Appendix compares 10×10, 20×20, and 30×30 grids and demonstrates self-convergence, but a grid-convergence test cannot catch a global factor error in the flux normalization of Eq. (5) or in the Chebyshev–Gauss weights of Eq. (6). The factor-of-three amplitude deficit against Kepler-7b (Section 3.2.1) is exactly the symptom such an error would produce, so the current paper cannot distinguish an implementation error from the physical explanations offered. Please add a benchmark against an analytic Lambert-sphere phase curve (with a known full-phase flux) or a fixed-phase comparison against the existing 1D reflected-light mode of PICASO, and verify Eq. (5) with the time-dependent planet–star distance and phase-angle convention.
[Section 3.2.1] The claim that the three-cloud, low-fsed models “match best” is based on reduced chi-square values of 1.94–2.75, all well above unity, with every model under-predicting the observed amplitude by roughly a factor of three. Since no model is an acceptable absolute fit, the ranking may reflect the phase-curve shape and the chosen exclusion of 0° ± 9° rather than a robust amplitude constraint. Please report the number of independent data points used, the number of fitted parameters, and ideally confidence intervals on fsed, and state more explicitly that the preference for fsed = 0.03–0.1 is conditional on the assumed GCM and cloud physics.
[Section 3.2.1] The two dominant explanations for the amplitude deficit—missing zonal transport and missing cloud radiative feedback—are not tested in this paper. In particular, the SPARC/MITgcm thermal structure (Section 2.2, Figure 1) does not include cloud radiative feedback, and Virga cloud locations and optical depths depend on that temperature structure. A GCM with radiative feedback could change the dayside temperature field, the cloud map, and the phase curve. Please either quantify the sensitivity of the phase curve to the temperature structure or clearly label the Kepler-7b conclusions as dependent on this no-feedback assumption.

minor comments (5)

[Equation (5) and surrounding text] “RP is the stellar radius” should read “planetary radius”; the equation and Table 1 otherwise imply R_P is the planet radius.
[Section 4] “N. J. Kasdin (Kasdin et al. 2020; S. R. Vaughan et al. 2023)” should be “N. J. Kasdin et al. (2020)”.
[Section 2.1 and Figure 1 caption] Clarify how negative Kzz values are treated; the text says the minimum is set to 10^5 cm2 s−1, and the caption says “Low/negative Kzz values at pressures >0.1 bar are set to the Kzz minimum”, which should be stated in the main text.
[Section 2.2.1] The sentence describing the 20×20 grid (“grid resolution fluctuates... spans around 167° of longitude for a phase of 0°”) is confusing; it would help to state explicitly that the number of grid points is fixed while the longitudinal extent of the visible dayside shrinks with phase.
[Abstract and Section 3.2.1] “All our Virga models reproduce the cloudy region west of the substellar point expected from previous studies” should be “produce” or “recover”, since the models are not fitting those previous results.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: new phase-curve mode is an externally benchmarked forward model; the low-fsed 'best match' is an explicit model-selection fit, not a prediction.

full rationale

The paper's central deliverable is a forward-modeling capability: it takes GCM pressure/temperature and Kzz fields from Adams et al. (2022), computes Virga cloud properties, and integrates reflected intensities with PICASO's Chebyshev-Gauss quadrature. The resulting phase curves are compared to Kepler-7b observations from Demory et al. (2013), an external dataset not used to construct the model. The only tuned parameter, fsed, is scanned over a prechosen grid, and the paper explicitly labels the comparison a 'best-fit' (Section 3.2.1) rather than an independent prediction; moreover, even the lowest fsed under-predicts the observed amplitude by about a factor of three, so the amplitude is not forced by the fit. The acknowledged limitations (no cloud radiative feedback, no zonal transport, spherical particles) and the absence of a known-answer test for the new geometry are validation and correctness risks, not circular reductions: no equation in the paper is defined in terms of the target output, and no conclusion relies on a self-citation to forbid alternatives. Self-citations to Adams et al. (2022) supply the GCM input and a previously noted albedo deficit, but both are independent prior results and are not used to define the new phase-curve routine.

Assumptions & free parameters 2 free parameters · 7 assumptions · 0 invented entities

The central claim rests on the equilibrium cloud model, the GCM input, and the standard RT scheme. The only numeric parameter tuned against the target data is fsed, selected by chi-square; the global-mean Kzz profile is a modeling choice. No new physical entities are introduced.

free parameters (2)

fsed (sedimentation efficiency) = 0.03 (best fit; grid 0.03, 0.1, 0.3, 1.0)
Tunable Virga parameter controlling cloud vertical extent and particle sizes; the best value is chosen by reduced chi-square fit to Kepler data in Section 3.2.1.
Global-mean Kzz profile with a minimum floor = computed from GCM; floor set to 1e5 cm2/s
Virga uses a single globally averaged Kzz profile at every grid point to avoid numerical instability with GCM downward mixing; the floor is the Virga default and affects cloud lofting.

assumptions (7)

standard math The Toon et al. 1989 plane-parallel two-stream radiative transfer scheme computes reflected intensities correctly for each facet.
PICASO's default RT scheme, previously validated in multiple exoplanet studies; Section 2.2.
domain assumption The Ackerman and Marley 2001 equilibrium cloud condensation model as implemented in Virga governs cloud vertical structure and particle sizes.
Equation (1) balances sedimentation against eddy lofting with no microphysical nucleation or horizontal transport; Section 2.1.
domain assumption Thermochemical equilibrium composition applies at every GCM grid point.
PICASO post-processes chemistry using Gordon and McBride 1994 and Visscher et al. 2010; the paper notes 3D disequilibrium chemistry is not yet supported.
domain assumption The Adams et al. 2022 SPARC/MITgcm thermal structure accurately represents Kepler-7b.
The GCM lacks cloud radiative feedback, which the paper itself lists as a missing process in Section 3.2.1.
domain assumption Cloud particles are spherical Mie scatterers.
Virga uses Mie theory with spherical particles; the paper cites nonsphericity as a candidate cause of the amplitude discrepancy.
domain assumption Clouds form independently at each grid point with no zonal transport of condensate.
Virga computes columns independently; the paper states zonal transport could brighten the dayside and increase the phase offset.
domain assumption The phase-curve integration treats each atmosphere column as an independent plane-parallel facet with no horizontal photon transport.
Section 2.2.1: Chebyshev-Gauss integration over 20x20 facets with bilinear interpolation; horizontal scattering between facets is ignored.

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Cite this review

Pith. "Pith review of Reflected-light Phase Curves with PICASO: A Kepler-7b Case Study." pith.science (2026). https://pith.science/paper/JMJ6WJXH

@misc{pith2026241114225,
  author       = {Pith},
  title        = {Pith review of: Reflected-light Phase Curves with PICASO: A Kepler-7b Case Study},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JMJ6WJXH}},
  note         = {Machine review of arXiv:2411.14225}
}

read the original abstract

Examining reflected light from exoplanets aids in our understanding of the scattering properties of their atmospheres and will be a primary task of future flagship space- and ground-based telescopes. We introduce an enhanced capability of Planetary Intensity Code for Atmospheric Scattering Observations (PICASO), an open-source radiative transfer model used for exoplanet and brown dwarf atmospheres, to produce reflected light phase curves from three-dimensional atmospheric models. Since PICASO is coupled to the cloud code Virga, we produce phase curves for different cloud condensate species and varying sedimentation efficiencies (fsed) and apply this new functionality to Kepler-7b, a hot Jupiter with phase curve measurements dominated by reflected starlight. We model three different cloud scenarios for Kepler-7b: MgSiO3 clouds only, Mg2SiO4 clouds only, and Mg2SiO4, Al2O3, and TiO2 clouds. All our Virga models reproduce the cloudy region west of the substellar point expected from previous studies, as well as clouds at high latitudes and near the eastern limb, which are primarily composed of magnesium silicates. Al2O3 and TiO2 clouds dominate near the substellar point. We then compare our modeled reflected light phase curves to Kepler observations and find that models with all three cloud condensate species and low sedimentation efficiencies (0.03 - 0.1) match best, though our reflected light phase curves show intensities approximately one-third of those observed by Kepler. We conclude that a better understanding of zonal transport, cloud radiative feedback, and particle scattering properties is needed to further explain the differences between the modeled and observed reflected light fluxes.

Figures

Figures reproduced from arXiv: 2411.14225 by the authors.

**Figure 1.** Left: temperature map of Kepler-7b’s dayside hemisphere at 1 mbar. Middle: averaged temperature profiles of Kepler-7b for the western limb (blue) and hot dayside (red) regions, with the condensation curves (gray dashed) of the clouds (MgSiO3, Mg2SiO4, Al2O3, and TiO2) modeled in this study. Right: globally averaged Kzz profile of the atmosphere. Low/negative Kzz values at pressures >0.1 bar are set to the Kzz minimu… view at source ↗

**Figure 2.** Temperature maps of the dayside hemisphere at 1 mbar illustrating how PICASO regrids and rotates the GCM for eight discrete planetary phases with 20 × 20 spatial grid resolution. The substellar point is located at the center of each map (0° latitude, 0° longitude), meaning these maps show the dayside hemisphere of Kepler-7b. Only colored regions contribute to reflected-light intensity. A phase angle of 0° correspond… view at source ↗

**Figure 3.** Left: full-resolution optical depth map of the dayside hemisphere at 1 mbar and a wavelength of 604 nm. Right: eight corresponding 20 × 20 grid phase maps used to compute reflected-light spectra. The optical depth maps here are generated with Virga considering Mg2SiO4, Al2O3, and TiO2 as cloud condensates with fsed = 0.03. The substellar point is located at the center of each map (0° latitude, 0° longitude). 6 The A… view at source ↗

Figures from the paper (8 more)

**Figure 4.** Figure 4: Cloud optical depth per layer for all cloudy scenarios as a function of longitude and pressure for the dayside hemisphere, at a latitude of 1°. 4N and a wavelength of 604 nm. The columns represent the three cloud scenarios: MgSiO3 only, Mg2SiO4 only, and Mg2SiO4, Al2O3…

**Figure 5.** Figure 5: Wavelength-independent column optical depths for Mg2SiO4, Al2O3, and TiO2, as a function of pressure, assuming geometric scatterers (see Equation (16) of A. S. Ackerman & M. S. Marley 2001). Blue corresponds to a western grid point centered at (1°. 4N, −68°. 9W), while…

**Figure 6.** Figure 6: The planet-to-star flux ratio in parts per million (ppm) at phase 0° (secondary eclipse) for Kepler-7b for the cloudless case (black solid), and the MgSiO3- only (green dashed–dotted lines), Mg2SiO4-only (orange dashed lines), and Mg2SiO4, TiO2, and Al2O3 (blue solid l…

**Figure 7.** Figure 7: shows the relative flux changes for the cloudless scenario (left) and a cloudy scenario (right) with seven unique phase angles ranging from 0° to ±168°. The cloudy scenario is again showing the three-cloud regime (Mg2SiO4, Al2O3, and TiO2) with fsed = 0.03. As phase in…

**Figure 8.** Figure 8: Reflected-light phase curves of Kepler-7b showing the planet-to-star flux ratio in parts per million (ppm) as a function of phase angle (−168° to 168°) for cloudless (gray solid), and MgSiO3-only (green dashed–dotted), Mg2SiO4-only (orange dashed), and Mg2SiO4, Al2O3, …

**Figure 9.** Figure 9: Same as [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]

**Figure 10.** Figure 10: Same as [PITH_FULL_IMAGE:figures/full_fig_p010_10.png]

**Figure 11.** Figure 11: Top: comparison of the phase curves for the three-cloud scenario that considers Mg2SiO4, Al2O3, and TiO2 as cloud condensates with fsed = 0.03 for three different Chebyshev–Gauss spatial resolutions: 10 × 10 (blue), 20 × 20 (green), and 30 × 30 (orange). Bottom: absol…

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Works this paper leans on

2 extracted references · 1 canonical work pages

[1]

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

Abramowitz, M., & Stegun, I. A. 1972, Handbook of Mathematical Functions (New York: Dover ) Ackerman, A. S., & Marley, M. S. 2001, ApJ, 556, 872 Adams, D. J., Kataria, T., Batalha, N. E., Gao, P., & Knutson, H. A. 2022, ApJ, 926, 157 Albert, L., Lafrenière, D., Doyon, R., et al. 2023, PASP, 135, 075001 Allard, F., Allard, N. F., Homeier, D., et al. 2007, ...

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arXiv 2020