SKYSURF VIII -- Modeling SKYSURF Completeness Data for Comparison to the Hubble Space Telescope Exposure Time Calculator

arXiv:2508.08484 · astro-ph.IM, astro-ph.CO · Submitted 2025-08-11 · Read on arXiv

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Introduction to the show: ident: Astrophysics. The day in astrophysics: observations, models and what the data forces.

Vera: We're looking at the paper: "SKYSURF VIII -- Modeling SKYSURF Completeness Data for Comparison to the Hubble Space Telescope Exposure Time Calculator".

Jocelyn: Here's the gist of the paper. Accurately assessing image source completeness is critical for interpreting measurements on telescope data <ref:2508.08484#pg2> Using the Wide Field Camera 3 (WFC3) and Advanced Camera for Surveys (ACS) data from the Hubble Space Telescope (HST) archival project “SKYSURF”, we model galaxy completeness as a function of the exposure time and background of an image <ref:2508.08484#pg2> Ultimately, we find that, for extended galaxies, the ETC predicts a 1-2 magnitudes fainter completeness limit than our data <ref:2508.08484#pg7>.

Vera: Modeling Completeness Simulation The authors model galaxy completeness by adding simulated objects of varying magnitudes and sizes into the images to determine the detection rate for each set of parameters <ref:2508.08484#pg2> In order to simulate data analogous to the ETC data, they use the GalSim Python package from Rowe et al.

Jocelyn: (2015) <ref:2508.08484#pg2> The inserted objects have a Sersic index of 1 and an inclination of 0° <ref:2508.08484#pg7>.

Vera: This process is done 200 pixels from the image edges to avoid drizzling artifacts, and repeated 100 times for each image, to decrease the effect of potential overlap with image sources <ref:2508.08484#pg7>.

Title and authors: Vera: So we're looking at "SKYSURF VIII -- Modeling SKYSURF Completeness Data for Comparison to the Hubble Space Telescope Exposure Time Calculator." The title itself is pretty direct about what they're doing here, trying to model completeness based on exposure time and background.

Jocelyn: Yeah, it’s about taking those real-world images from SKYSURF and seeing how their completeness measurements compare against the existing Exposure Time Calculator. It’s essentially testing a prediction against actual data from the Hubble Space Telescope project.

Subrahmanyan: So, what's the main goal here? Are they trying to find a flaw in the ETC, or are they just building a new way to calculate these detection limits?

Vera: They are specifically testing if their model can explain why the ETC gives fainter completeness limits than what they actually observe for extended galaxies. They want to see if their method captures that difference.

Jocelyn: To do this, the authors model galaxy completeness by adding simulated objects of different magnitudes and sizes into these actual images to find out how often each set of parameters gets detected.

Subrahmanyan: So, the methodology involves creating a synthetic population within the real data set for testing purposes, which is a standard approach in observational astronomy.

Vera: They use the GalSim Python package from Rowe et al. two thousand fifteen to simulate this data, inserting objects with a Sersic index of one and an inclination of zero degrees into those images <ref:2508.08484#pg7>.

Jocelyn: And they have to be careful about where they insert these objects; they do it two hundred pixels from the image edges to avoid drizzling artifacts, which is important for consistency <ref:2508.08484#pg7>.

Subrahmanyan: That careful placement is necessary because if you insert them too close to the edge, you risk artifacts from the image processing steps like drizzling.

Vera: They repeat this insertion process one hundred times for each image, and they do it to decrease the effect of potential overlap with sources already in the images <ref:2508.08484#pg7>.

Jocelyn: That repetition is a way to try and minimize double-counting or confusion when checking if an object is detected by Source Extractor <ref:2508.08484#pg7>.

Subrahmanyan: It sounds like they are building a robust simulation pipeline, trying to get as close to reality as possible given the constraints of their archival data.

The paper's summary: Jocelyn: So putting all that simulation work together, the summary says they model galaxy completeness as a function of exposure time and background for images using WFC3 and ACS data from SKYSURF <ref:2508.08484#pg2>.

Vera: The key result is that they find the fifty percent completeness results can be modeled for different object sizes and magnitudes in different filters <ref:2508.08484#pg3>.

Jocelyn: They then model the fifty percent completeness limit specifically in terms of object size, exposure time, and background conditions for each filter <ref:2508.08484#pg3>.

Subrahmanyan: It's like they are creating a comprehensive predictive function that takes those three variables as inputs to tell you what the detection probability is.

Vera: And they fit an exponential function y equals v plus w log10(x) minus xzero minus one one plus e minus z (log10(x) minus xzero). The parameters v, w, xzero and z are averaged from all images for a given filter <ref:2508.08484#pg3>.

Jocelyn: This function gives them the fit lines for the fifty percent ninety percent and ninety five percent completeness values shown in Figure three <ref:2508.08484#pg3>.

Subrahmanyan: So they use that fitted curve to show how completeness percentage decreases when the magnitude gets fainter, which you can see in Figure two <ref:2508.08484#pg3>.

Vera: And they specifically look at the effect of confusion limits for brighter inserted objects on these plots, where the number of matches decreases slightly due to occasional overlap <ref:2508.08484#pg3>.

Jocelyn: The main takeaway is that for larger sizes in these figures, they see this effect of confusion limit where brighter inserted objects cause a slight decrease in matches due to occasional overlap <ref:2508.08484#pg3>.

Subrahmanyan: That’s a direct result of the confusion limit kicking in when you have bigger sources, which connects the simulation back to real detection limitations <ref:2508.08484#pg7>.

Vera: The paper essentially shows how image depth and sky conditions interact to determine whether an object gets detected or not <ref:2508.08484#pg2>.

The paper's improvements: Jocelyn: Now let's look at what the authors suggest is improved in this work compared to previous versions of the Exposure Time Calculator.

Vera: One big suggestion is that instead of relying on purely flat surface brightness profiles like the ETC does, they should use a model that accounts for realistic source profiles <ref:2508.08484#pg3>.

Jocelyn: They want an AI system to generate more accurate completeness predictions by incorporating galaxy structure instead of using idealized assumptions about the sources <ref:2508.08484#pg3>.

Subrahmanyan: That makes sense because real galaxies aren't just simple flat surfaces; they have varying structures, and a model that acknowledges that would be much better for cosmological modeling.

Vera: They also suggest training the AI to recognize the impact of image background by isolating it through equation three <ref:2508.08484#pg3>.

Jocelyn: This allows the system to adjust its predictions based on specific filter backgrounds, using equation three which shows "the impact of the image background on the completeness is isolated" <ref:2508.08484#pg3>.

Subrahmanyan: So they are explicitly incorporating sky conditions into their model, not just treating them as a variable to be plugged in later.

Vera: And finally, they propose integrating exposure time and background models into a single predictive framework using equation four <ref:2508.08484#pg4>.

Jocelyn: This creates their own completeness model where exposure time and background are combined into one prediction for the fifty percent completeness magnitude p based on both image depth and sky conditions simultaneously <ref:2508.08484#pg3>.

Subrahmanyan: That's a much more complete framework for predicting detection limits, moving from separate models to a unified one that incorporates both depth and sky conditions <ref:2508.08484#pg3>.

Conclusion: Vera: So, wrapping up the paper "SKYSURF VIII -- Modeling SKYSURF Completeness Data for Comparison to the Hubble Space Telescope Exposure Time Calculator." They found that the ETC predicts fainter completeness magnitudes for all objects, especially the larger ones <ref:2508.08484#pg7>.

Jocelyn: The slope of completeness magnitude as a function of exposure time remains largely identical across their different analyses <ref:2508.08484#pg7>. This leads them to believe that the ETC’s flat surface brightness approximation of the sources is likely causing this discrepancy.

Subrahmanyan: So if you look at that vertical y-intercept shift, it's a major indicator that their model needs to account for how extended these sources actually are when we talk about those completeness limits <ref:2508.08484#pg3>.

Vera: That means the ETC’s flat surface brightness assumption is what makes the difference between their simulation and reality <ref:2508.08484#pg3>.

Jocelyn: Overall, they think this work provides a solid empirical framework for how to handle these kinds of completeness calculations in future observations <ref:2508.08484#pg2>.

Subrahmanyan: They plan on using these methods on the James Webb Space Telescope to model its exposure time calculator and support other future works using the telescope data <ref:2508.08484#pg7>.

School of Earth and Space Exploration, Arizona State University · School of Electrical and Computer Engineering, Arizona State University

astro-ph.IM, astro-ph.CO

Submitted: 2025-08-11

Updated: 2025-08-11

Comments: 7 pages, 6 figures. This paper has been accepted by the Publications of the Astronomical Society of the Pacific, though is not published at this moment

Journal ref: Publ. Astron. Soc. Pac. 137(9), 094501 (2025)

DOI: 10.1088/1538-3873/adfab0

Project page: https://galsimdevelopers.github.io/GalSim

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 79/100

The gist: Accurately assessing image source completeness is critical for interpreting measurements on telescope data <ref:2508.08484#pg2> Using the Wide Field Camera 3 (WFC3) and Advanced Camera for Surveys

Key concepts

Galaxy Completeness Modeling
This involves simulating various sized and bright objects into telescope images to determine the rate at which they are successfully detected. The researchers used simulated objects with a Sersic index of 1 to mimic real galaxy structures.
Source Extractor Program
This software was used to identify detected sources in the HST images. It matched inserted objects if they were within three pixels of an actual source, using specific thresholds and filters to define what counts as a detection.
Exposure Time and Background Modeling
The study developed mathematical equations to link image depth (exposure time) and sky brightness (background) to detection limits. These models combine to create a single predictive formula for completeness.
ETC Comparison
They compared their derived completeness limits against the Exposure Time Calculator (ETC). The main finding was a vertical shift in the intercept, suggesting the ETC's flat surface brightness assumption is inaccurate for extended sources.

Terminology

Summary

Accurately assessing image source completeness is critical for interpreting measurements on telescope data <ref:2508.08484#pg2> Using the Wide Field Camera 3 (WFC3) and Advanced Camera for Surveys (ACS) data from the Hubble Space Telescope (HST) archival project “SKYSURF”, we model galaxy completeness as a function of the exposure time and background of an image <ref:2508.08484#pg2> Ultimately, we find that, for extended galaxies, the ETC predicts a 1-2 magnitudes fainter completeness limit than our data <ref:2508.08484#pg7>.

Modeling Completeness Simulation

The authors model galaxy completeness by adding simulated objects of varying magnitudes and sizes into the images to determine the detection rate for each set of parameters <ref:2508.08484#pg2> In order to simulate data analogous to the ETC data, they use the GalSim Python package from Rowe et al. (2015) <ref:2508.08484#pg2> The inserted objects have a Sersic index of 1 and an inclination of 0° <ref:2508.08484#pg7>. This process is done 200 pixels from the image edges to avoid drizzling artifacts, and repeated 100 times for each image, to decrease the effect of potential overlap with image sources <ref:2508.08484#pg7>.

Source Detection Methodology

To check whether the sources were detected, they use the Source Extractor program from Bertin & Arnouts (1996) <ref:2508.08484#pg2> An object is matched if it is within three pixels of one of their inserted object’s locations <ref:2508.08484#pg7>. The Source Extractor parameters include a minimum detection area of 5.0, a detection threshold of 1, an analysis threshold of 1, and a 3-sigma Gaussian 5x5 convolution filter <ref:2508.08484#pg7>. Because the used HST images have few sources (under 15000 sources), the impact from overlapping objects, i.e. the confusion limit, is negligible most of the time <ref:2508.08484#pg7>.

Completeness Curve Fitting

Using the number of object matches from Source Extractor for each size and magnitude, they construct a set of completeness curves, fit with the complementary error function for each size in every image They create a box plot with a color gradient representing the various number of matches and fit an exponential function to certain completeness levels shown in Figure 3. The exponential function used is y = v + w log10(x) − x0 − 1 + e−z(log10(x)−x0). The parameters v, w, x0, and z are taken from all analyzed images for a given filter and were averaged.

Exposure Time and Background Modeling

They model the relationship between exposure time and completeness using Equation 2: p = a(log10(e) − ⟨e⟩) + c. The impact of the image background on the completeness is isolated through Equation 3: R = b(log10(g) − ⟨g⟩) + f. The exposure time and background models are combined to create their completeness model in Equation 4: p = a(log10(e) − ⟨e⟩) + b(log10(g) − ⟨g⟩) + c.

Comparison with ETC

They compare their results to the Exposure Time Calculator (ETC) by fitting the 50% completeness points for each image at various inserted object sizes to determine the significance of the dependence on each. The main difference they find, shown by the comparison plot in Figure 6, is a vertical y-intercept shift, particularly for the larger sizes. This large discrepancy in magnitude intercept is likely due to the ETC’s flat surface brightness model being not good at estimating for their extended sources.

Conclusion and Future Work

Generally, they find that the ETC predicts fainter completeness magnitudes for all objects, especially the larger ones. The slope of completeness magnitude as a function of the exposure time remains largely identical. They plan on using these methods on the James Webb Space Telescope to model its ETC and to support other future works using the telescope.

Summary

In this paper, they measure the completeness limits for a representative set of images from each filter. The 50%, 90%, and 95% magnitude points can be modeled for different object sizes and magnitudes in the different filters. The 50% completeness limit, in particular, is then modeled for each filter in terms of object size, exposure and background of the images. Ultimately, they find that the ETC predicts fainter completeness magnitudes for all objects, especially the larger ones. The slope of completeness magnitude as a function of the exposure time remains largely identical leading them to believe that the ETC’s flat surface brightness approximation of the sources is the cause of this discrepancy.

Acknowledgments

Support for program HST AR-15810 was provided by NASA through a grant from the Space Telescope Science Institute. The project SKYSURF is based on observations made with the NASA/ESA Hubble Space Telescope obtained from the Data Archive at the Space Telescope Science Institute. They thank Dr. Windhorst also acknowledges support from NASA JWST Interdisciplinary Scientist grants NAG5-12460, NNX14AN10G and 80NSSC18K0200 from GSFC. All of the data presented in this paper were obtained from the Mikulski Archive for Space Telescopes. They also acknowledge the indigenous peoples of Arizona, including the Akimel O’odham (Pima) and Pee Posh (Maricopa) Indian Communities whose care and keeping of the land has enabled them to ASU’s Tempe campus in the Salt River Valley where this work was conducted.

Software Used

The software used includes Astropy http://www.astropy.org (Astropy Collaboration et al. 2013, 2018), SourceExtractor https://www.astromatic.net/software/sextractor/ or https://sextractor.readthedocs.io/en/latest/ (Bertin & Arnouts 1996), and GalSim: https://galsimdevelopers.github.io/GalSim/ build/html/index.html (Rowe et al. 2015).

References

The references listed include Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33 doi: 10.1051/0004-6361/201322068, Astropy Collaboration, Price-Whelan, A. M., Sip˝ocz, B. M., et al. 2018, AJ, 156, 123 doi: 10.3847/1538-3881/aabc4f, Beckwith, S. V. W., Stiavelli, M., Koekemoer, A. M., et al. 2006, AJ, 132, 1729 doi: 10.1086/507302 <ref:2508.08484#pg7>, Bertin, E., & Arnouts, S. 1996, A&AS, 117, 393 doi: 10.1051/aas:1996164 <ref:

Improvements for AI systems

  1. Automated completeness modeling for HST data can be improved by using a model that accounts for realistic source profiles instead of purely flat surface brightness profiles that the ETC uses, as noted in the introduction. This allows AI systems to generate more accurate completeness predictions by incorporating galaxy structure rather than relying on idealized assumptions.

  2. The AI system can be enhanced to compare its derived completeness limits directly against the Exposure Time Calculator (ETC) results, specifically identifying discrepancies such as the ETC predicts a 1-2 magnitudes fainter completeness limit than our data for extended galaxies. This capability allows the system to quantify and pinpoint where idealized models fail when applied to real archival data.

  3. The AI can be trained to recognize the impact of image background on completeness by isolating it through Equation 3, which shows the impact of the image background on the completeness is isolated. This enables the system to adjust its predictions based on specific filter backgrounds (g), as demonstrated in Figure 5 showing a slight negative influence of background on our completeness.

  4. The AI can be developed to integrate exposure time and background models into a single predictive framework using Equation 4, which combines them into our completeness model. This allows the system to predict the 50% completeness magnitude (p) based on both image depth and sky conditions simultaneously.

  5. The AI can utilize the fitted parameters from Table 1 through Table 3 to create filter-specific predictive functions for source detection limits. This provides a comprehensive tool where, given an exposure time and background, the system can output the expected completeness magnitude (p) for any given object size (0.1'', 0.5'', or 1.0'').

Abstract

Accurately assessing image source completeness is critical for interpreting measurements on telescope data. Using the Wide Field Camera 3 (WFC3) and Advanced Camera for Surveys (ACS) data from the Hubble Space Telescope (HST) archival project "SKYSURF", we model galaxy completeness as a function of the exposure time and background of an image. This is accomplished by adding simulated objects with varying magnitudes and sizes into these images, and determining the detection rate for each set of parameters. The fifty percent completeness results are then compared to the Exposure Time Calculator (ETC), in order to assess the differences between the STSCI ETC and our analysis of the archival data. Ultimately, we find that, for extended galaxies, the ETC predicts a 1-2 magnitudes fainter completeness limit than our data. We believe the difference is due to the ETC's flat surface brightness profiles being less accurate at predicting for extended sources compared to our more realistic profiles.

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