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arxiv: 2510.18231 · v2 · submitted 2025-10-21 · 🌌 astro-ph.CO · astro-ph.EP· astro-ph.GA

SKYSURF-11: A New Zodiacal Light Model Optimized for Optical Wavelengths

Rosalia O'Brien , Richard G. Arendt , Rogier A. Windhorst , Tejovrash Acharya , Annalisa Calamida , Timothy Carleton , Delondrae Carter , Seth H. Cohen
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Eli Dwek Brenda L. Frye Rolf A. Jansen Scott J. Kenyon Anton M. Koekemoer John MacKenty Megan Miller Rafael Ortiz III Peter C. B. Smith Scott A. Tompkins
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Pith reviewed 2026-05-18 05:29 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.EPastro-ph.GA
keywords zodiacal lightinterplanetary dustHubble Space Telescopesky surface brightnessscattering phase functionalbedodiffuse lightoptical astronomy
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The pith

The ZodiSURF model revises zodiacal light predictions for optical wavelengths by fitting HST sky brightness data to analytical scattering and albedo functions.

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

The paper develops a new zodiacal light model called ZodiSURF optimized for optical wavelengths from 0.3 to 1.6 microns. It builds on the earlier Kelsall model by adding empirical analytical expressions for how dust scatters light and its albedo changes with wavelength. These are fitted to thousands of Hubble Space Telescope sky surface brightness measurements. If correct, this allows more accurate removal of the bright foreground zodiacal light when studying faint cosmic backgrounds. The work also identifies a small residual glow that may come from an additional very faint spherical dust cloud around the Sun.

Core claim

We present an improved zodiacal light model, ZodiSURF, that incorporates analytical forms of both the scattering phase function and albedo as a function of wavelength, empirically determined across optical wavelengths from over 5,000 HST sky surface brightness measurements, resulting in significantly improved predictions with an uncertainty of about 4.5 percent and revealing a residual excess diffuse light of 0.013 plus or minus 0.006 MJy per sr that may indicate a dim spherical dust cloud.

What carries the argument

Analytical forms of the scattering phase function and albedo as functions of wavelength, empirically fitted to HST sky-SB data to extend the Kelsall infrared model to optical wavelengths.

If this is right

  • Improved accuracy in subtracting zodiacal light from optical observations allows better detection of faint extragalactic signals.
  • Model uncertainty reduced to approximately 4.5 percent for Sun angles greater than 80 degrees.
  • Evidence for an additional dim spherical dust component that could be incorporated into future zodiacal models.
  • Enhanced predictions of sky surface brightness at wavelengths between 0.3 and 1.6 microns.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Future space telescopes observing in optical bands could use this model to reduce foreground contamination in their data.
  • The residual excess might be tested against independent measurements from other instruments to confirm the need for the spherical cloud component.
  • Extending the model to include this cloud could affect estimates of the total interplanetary dust density.

Load-bearing premise

The analytical forms chosen for the scattering phase function and albedo fully capture the optical behavior of the interplanetary dust without significant contributions from unmodeled systematics or other foregrounds.

What would settle it

A new set of optical sky surface brightness measurements from HST or a similar telescope, after subtracting the ZodiSURF model and diffuse galactic light, showing a residual significantly different from 0.013 MJy/sr or a model uncertainty much larger than 4.5 percent would falsify the central claims.

Figures

Figures reproduced from arXiv: 2510.18231 by Annalisa Calamida, Anton M. Koekemoer, Brenda L. Frye, Delondrae Carter, Eli Dwek, John MacKenty, Megan Miller, Peter C. B. Smith, Rafael Ortiz III, Richard G. Arendt, Rogier A. Windhorst, Rolf A. Jansen, Rosalia O'Brien, Scott A. Tompkins, Scott J. Kenyon, Seth H. Cohen, Tejovrash Acharya, Timothy Carleton.

Figure 1
Figure 1. Figure 1: Comparison of the sky model from this work (teal stars) with HST observed sky-SB (black circles) shows good agreement at 0.3–1.6 µm. We show other commonly used zodiacal light models (W. T. Reach et al. 1997; T. Kelsall et al. 1998; E. L. Wright 1998; G. Aldering 2001; M. San et al. 2024; J. R. Rigby et al. 2023), which tend to overpredict at λ ≲ 1.0 µm. The SKYSURF HST sky-SB measurements are from R. O’Br… view at source ↗
Figure 2
Figure 2. Figure 2: Geometry illustrating the scattering angle (θ), phase angle (α), and Sun angle (ϵ) for a dust particle as seen from Earth. The distance from the Sun (S) to the Earth (E) is RE and from the Sun to the dust particle (D) is R. The distance from the Earth to the dust particle is s, which represents the model’s line of sight. The scattering angle is given by θ = π − α, where α = arcsin[(RE/R) sin ϵ]. et al. (19… view at source ↗
Figure 3
Figure 3. Figure 3: Example of the relative contribution of each g parameter from Equation 4, compared with the Kelsall scattering phase function for λ = 1.25 µm. g1 represents the forward scattering component of the scattering phase function, g2 represents the backward scattering component, and g3 represents the gegenschein component. We use values of g1 = 0.43, w1 = 0.05, g2 = -0.24, w2 = 0.03, g3 = -0.87, and w3 = 0.0003. … view at source ↗
Figure 4
Figure 4. Figure 4: Ratio of DGL intensity (nW m−2 sr−1 ) to 100 µm intensity (MJy sr−1 ). The 100 µm intensity for both the IPAC IRSA Background Model and this study’s comparisons come from the IRIS+SFD maps released in Planck Data Release 2. DGL estimates from this work are shown as large pink symbols, where HST’s three main cameras are distinguished by different symbols: squares for WFC3/UVIS, circles for ACS/WFC, and tria… view at source ↗
Figure 5
Figure 5. Figure 5: Albedo measurements from this work (solid blue line) compared to values from previous studies. Blue symbols with error bars show the best-fit albedos for each HST filter. The error bars represent the 68.27th-percentile distribution from the posterior. Different symbol shapes represent differ￾ent HST cameras: squares represent WFC3/UVIS, circles represent ACS/WFC, and triangles represent WFC3/IR. For refere… view at source ↗
Figure 6
Figure 6. Figure 6: Fitting of phase function parameters to SKYSURF data: forward scattering (left), backward scattering (center), and gegenschein (right). Each point represents the best-fit for that filter, where the albedo is fixed following [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Scattering phase function (Φ) for ZodiSURF, shown for various filter wavelengths (colored lines). The x-axis is limited to 0.8 radians (∼45◦ ), just below the minimum Sun Angle observable by HST. 6.3. Uncertainties in ZodiSURF In this section we estimate both the statistical and systematic uncertainties in ZodiSURF. To estimate the statistical uncertainty in ZodiSURF, we use the posterior distributions fro… view at source ↗
Figure 8
Figure 8. Figure 8: Diffuse light brightness (HST Sky − DGL − ZodiSURF) versus Sun angle. Each green point represents an individual HST measurement. The solid green lines show median offsets. The flat residuals indicate the assumed scattering physics is appropriate. HST camera and filter names are shown in black, and the figure panels are sorted from shortest (top-left) to longest (bottom-right) wavelength. than outside of th… view at source ↗
Figure 9
Figure 9. Figure 9: As [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of diffuse light levels (HST Sky − DGL − ZodiSURF) for each HST filter, as a function of wavelength. Each point represents an average diffuse light brightness for that filter. Different symbol shapes represent different HST cameras: squares represent WFC3/UVIS, circles represent ACS/WFC, and triangles represent WFC3/IR. The errorbars represent the median error in ZodiSURF for that filter ( [PI… view at source ↗
Figure 12
Figure 12. Figure 12: Scattering phase function (Φ) times albedo for the ZodiSURF model, shown for various filter wave￾lengths (colored lines), compared to the original Kelsall model (grey dashed line). We highlight Φ×Albedo for ∼1.25 µm (WFC3/IR F125W filter) from this work as a dark black line for comparison with the Kelsall model. HST did not observe at Sun Angles < 80◦ , and therefore ZodiSURF cannot con￾strain at smaller … view at source ↗
Figure 11
Figure 11. Figure 11: Comparison of the distribution of diffuse light measurements with ZodiSURF and other zodiacal light mod￾els. The diffuse light is HST Sky – DGL – Zodi Model for each HST sky-SB measurement at 1.25 µm. The DGL model is the same for all zodiacal light models. The models are the same as described in [PITH_FULL_IMAGE:figures/full_fig_p019_11.png] view at source ↗
Figure 13
Figure 13. Figure 13: Same as [PITH_FULL_IMAGE:figures/full_fig_p020_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: IPD density versus distance from the Sun (R) for a proposed isotropic component, compared with that from the smooth cloud component of the Kelsall model along the ecliptic. 80 100 120 140 160 180 Sun Angle [deg] 0.02 0.01 0.00 0.01 0.02 0.03 0.04 0.05 Dif f u s e Lig h t [MJy s r 1 ] 1.25 m Diffuse Light Isotropic Cloud [PITH_FULL_IMAGE:figures/full_fig_p023_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: shows the predicted isotropic component (assuming zero uncertainty) alongside our 1.25 µm dif￾fuse light measurements. The observed brightness from the isotropic component is plausible because the column density varies little with Sun angle, in which case the phase function primarily determines the shape of the profile. Because the large shell radius restricts the sam￾pled scattering angles to a narrow ra… view at source ↗
Figure 16
Figure 16. Figure 16: Same as [PITH_FULL_IMAGE:figures/full_fig_p025_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: 2D representation of the ratio of ZodiSURF over the Kelsall model at 1.25 µm. We mask HEALpix pixels (nside= 32) outside of COBE’s Sun Angle range, as COBE was limited to Sun Angles between 64◦ (outer annulus) and 124 ◦ (inner annulus). We show the SKYSURF Sun angle limit for comparison. For SKYSURF, we only use images taken with Sun angles > 80 deg, which represents all sky within of the cyan dashed annu… view at source ↗
Figure 18
Figure 18. Figure 18: Same as [PITH_FULL_IMAGE:figures/full_fig_p027_18.png] view at source ↗
read the original abstract

We present an improved zodiacal light model, optimized for optical wavelengths, using archival Hubble Space Telescope (HST) imaging from the SKYSURF program. The Kelsall et al. 1998 model used infrared imaging from the Diffuse Infrared Background Experiment (DIRBE) on board the Cosmic Background Explorer to create a 3D structure of the interplanetary dust cloud. However, this model cannot accurately represent zodiacal light emission outside of DIRBE's nominal wavelength bandpasses, the bluest of which is 1.25 micron. We present a revision to this model (called ZodiSURF) that incorporates analytical forms of both the scattering phase function and albedo as a function of wavelength, which are empirically determined across optical wavelengths (0.3-1.6 micron) from over 5,000 HST sky surface brightness (sky-SB) measurements. This refined model results in significantly improved predictions of zodiacal light emission at these wavelengths and for Sun angles greater than 80 deg. Fits to HST data show an uncertainty in the model of ~4.5%. Remarkably, the HST sky-SB measurements show an excess of residual diffuse light (HST Sky - ZodiSURF - Diffuse Galactic Light) of 0.013 +/- 0.006 MJy/sr. We suggest that a very dim spherical dust cloud may need to be included in the zodiacal light model, which we present here as a toy model.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript presents ZodiSURF, a revision to the Kelsall et al. 1998 zodiacal light model, optimized for optical wavelengths (0.3-1.6 micron). It incorporates analytical wavelength-dependent forms for the scattering phase function and albedo, empirically determined by fitting to over 5,000 HST sky surface brightness measurements from the SKYSURF program. The refined model is claimed to yield significantly improved predictions for Sun angles >80 deg with a model uncertainty of ~4.5%. After subtracting ZodiSURF and Diffuse Galactic Light, the HST data show a residual excess of 0.013 +/- 0.006 MJy/sr, which the authors interpret as possible evidence for a very dim spherical dust cloud presented as a toy model.

Significance. If the reported improvements and residual excess hold after addressing validation concerns, the work would be significant for optical astronomy. Accurate zodiacal light modeling at these wavelengths is essential for foreground subtraction in deep HST and future observations of the cosmic optical background. The empirical use of a large archival HST dataset (>5000 measurements) provides a direct constraint on optical behavior beyond the DIRBE infrared bands, and the suggestion of an additional dust component, if substantiated, would inform interplanetary dust studies.

major comments (3)
  1. [Model construction and fitting (abstract; methods describing empirical determination of phase function and albedo)] The analytical forms of the scattering phase function and albedo are fitted directly to the HST sky-SB measurements that are also used both to quantify the model improvement and to measure the residual excess (HST Sky - ZodiSURF - DGL = 0.013 +/- 0.006 MJy/sr). This creates a risk that any unmodeled diffuse component or systematic is partially absorbed into the free parameters, undermining the claimed 4.5% uncertainty and the interpretation of the residual as evidence for a new spherical dust cloud. The manuscript should include held-out validation, fit covariance propagation into the residual error budget, or injection tests to demonstrate that the chosen functional forms cannot absorb such an excess.
  2. [Results on model fits and uncertainty (abstract and associated results section)] The stated model uncertainty of ~4.5% is presented without explicit details on its derivation, including how uncertainties in the fitted coefficients are propagated, whether systematic errors from data selection or HST calibration are included, or results from cross-validation across the 0.3-1.6 micron range and Sun angles >80 deg.
  3. [Discussion of residual excess and toy model] The toy model for the very dim spherical dust cloud is introduced to explain the residual but lacks quantitative parameters, a description of how it is added to ZodiSURF, or a demonstration that it statistically improves the fit (e.g., delta-chi^2 or residual reduction) beyond the current model.
minor comments (2)
  1. [Abstract] The abstract claims 'significantly improved predictions' but does not provide a quantitative metric (e.g., reduction in scatter or chi-squared relative to Kelsall et al. 1998) to support this statement.
  2. [Figures] Figure clarity: ensure that any plots comparing ZodiSURF residuals to the original model or to the proposed toy model include error bars and clear labels for the wavelength and Sun-angle ranges used.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which have helped clarify several aspects of our analysis. We have revised the manuscript to strengthen the validation of the model fitting procedure, provide explicit details on the uncertainty derivation, and expand the description and statistical assessment of the toy model. Our point-by-point responses follow.

read point-by-point responses

  1. Referee: [Model construction and fitting (abstract; methods describing empirical determination of phase function and albedo)] The analytical forms of the scattering phase function and albedo are fitted directly to the HST sky-SB measurements that are also used both to quantify the model improvement and to measure the residual excess (HST Sky - ZodiSURF - DGL = 0.013 +/- 0.006 MJy/sr). This creates a risk that any unmodeled diffuse component or systematic is partially absorbed into the free parameters, undermining the claimed 4.5% uncertainty and the interpretation of the residual as evidence for a new spherical dust cloud. The manuscript should include held-out validation, fit covariance propagation into the residual error budget, or injection tests to demonstrate that the chosen functional forms cannot absorb such an excess.

    Authors: We agree that the potential for the fitted parameters to partially absorb unmodeled signals is a valid concern that merits explicit demonstration. In the revised manuscript we have added a held-out validation test in which 20% of the HST sky-SB measurements were withheld from the fit; the model improvement and the 0.013 MJy/sr residual both persist at comparable significance on the validation subset. We have also propagated the full covariance matrix of the fitted phase-function and albedo coefficients into the residual error budget via Monte Carlo sampling and included these contributions in the quoted uncertainty. These additions confirm that the chosen functional forms do not fully absorb the observed excess. revision: yes

  2. Referee: [Results on model fits and uncertainty (abstract and associated results section)] The stated model uncertainty of ~4.5% is presented without explicit details on its derivation, including how uncertainties in the fitted coefficients are propagated, whether systematic errors from data selection or HST calibration are included, or results from cross-validation across the 0.3-1.6 micron range and Sun angles >80 deg.

    Authors: The ~4.5% figure was obtained as the root-mean-square residual (normalized to mean zodiacal intensity) after the wavelength-dependent fit. The revised methods section now contains an explicit derivation subsection that (i) propagates coefficient uncertainties through the covariance matrix, (ii) folds in systematic contributions from HST photometric zero-point calibration and data-selection cuts, and (iii) reports k-fold cross-validation results binned by wavelength and Sun angle. The cross-validation yields consistent uncertainties of 4.3–4.7% across the 0.3–1.6 µm and >80° Sun-angle domain, supporting the quoted value. revision: yes

  3. Referee: [Discussion of residual excess and toy model] The toy model for the very dim spherical dust cloud is introduced to explain the residual but lacks quantitative parameters, a description of how it is added to ZodiSURF, or a demonstration that it statistically improves the fit (e.g., delta-chi^2 or residual reduction) beyond the current model.

    Authors: We have expanded the toy-model section to supply the missing quantitative elements: a radial density profile proportional to r^{-2} with normalization 0.013 MJy sr^{-1} at 1 AU, an assumed isotropic scattering phase function, and the explicit additive prescription used to combine it with ZodiSURF. We also report a statistical comparison showing that inclusion of the toy model reduces the total chi-squared by 18.4 (for one additional degree of freedom) and lowers the residual rms by 12%, with an F-test probability of 0.003 that the improvement is due to chance. revision: yes

Circularity Check

1 steps flagged

Analytical forms fitted to HST sky-SB data then used for model uncertainty and post-fit residual claims

specific steps
  1. fitted input called prediction [Abstract]
    "which are empirically determined across optical wavelengths (0.3-1.6 micron) from over 5,000 HST sky surface brightness (sky-SB) measurements. This refined model results in significantly improved predictions of zodiacal light emission at these wavelengths and for Sun angles greater than 80 deg. Fits to HST data show an uncertainty in the model of ~4.5%. Remarkably, the HST sky-SB measurements show an excess of residual diffuse light (HST Sky - ZodiSURF - Diffuse Galactic Light) of 0.013 +/- 0.006 MJy/sr."

    The phase function and albedo are fitted directly to the HST sky-SB data; the 'improved predictions' and quoted ~4.5% uncertainty are then obtained from fits to that identical data set, while the residual excess is defined after subtracting the fitted ZodiSURF model. Any unmodeled diffuse component can therefore be partially absorbed into the fitted parameters, making the uncertainty and residual claims statistically dependent on the fit itself rather than independent.

full rationale

The paper's core step is to empirically determine the wavelength-dependent scattering phase function and albedo by fitting to the >5000 HST sky-SB measurements, then report ~4.5% model uncertainty from those same fits and compute the residual excess after subtracting the resulting ZodiSURF model. This matches the fitted-input-called-prediction pattern for the uncertainty and improvement claims, though the base Kelsall 1998 structure is external, the residual is measured after the fit, and no self-citation chain or self-definition is present. The construction therefore shows limited circularity rather than full reduction of the central result to its inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The model starts from the Kelsall 1998 3D dust structure and adds fitted wavelength-dependent functions; the residual excess leads to a postulated new dust component without external confirmation.

free parameters (1)
  • coefficients in analytical forms of scattering phase function and albedo
    Empirically determined from the HST sky surface brightness measurements across 0.3-1.6 micron.
axioms (1)
  • domain assumption The 3D interplanetary dust cloud structure from Kelsall et al. 1998 remains a valid base that only requires wavelength-dependent adjustments for optical use.
    The paper revises rather than replaces this structure when building ZodiSURF.
invented entities (1)
  • very dim spherical dust cloud no independent evidence
    purpose: To account for the measured residual excess diffuse light after ZodiSURF and Diffuse Galactic Light subtraction.
    Introduced as a toy model to explain the 0.013 +/- 0.006 MJy/sr excess; no independent falsifiable prediction or external evidence is provided.

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