statmorph-lsst: Quantifying and correcting morphological biases in galaxy surveys

This paper investigates and quantifies the morphological biases introduced by varying imaging quality in galaxy surveys, offering empirical corrections, new measurement metrics, and a dedicated Python package to ensure robust analysis of galaxy evolution for upcoming Rubin LSST and JWST data.

The Gist

Imagine you are trying to describe the architecture of a city to a friend, but you can only see it through different windows: sometimes the glass is crystal clear, sometimes it's foggy, and sometimes you are looking from a very far distance where the buildings look like tiny dots.

This is exactly the problem astronomers face when studying galaxies. They want to understand how galaxies change over billions of years, but their "windows" (telescopes) have different levels of clarity (resolution) and sensitivity (depth).

This paper, STATMORPH-LSST, is essentially a user manual for the "foggy windows" of the universe. The authors are preparing for the upcoming Rubin LSST, a massive telescope survey that will take pictures of billions of galaxies. They realized that if they don't correct for how the "glass" distorts the view, they might think a galaxy is changing shape when it's actually just the telescope's fault.

Here is a breakdown of their findings using simple analogies:

1. The "Pixelated Photo" Problem

Think of a galaxy like a high-resolution digital photo.

• High Resolution (Clear Glass): You can see individual stars, spiral arms, and dust lanes.
• Low Resolution (Blurry/Foggy Glass): The photo gets pixelated. The sharp edges of a spiral arm blur together. A distinct "bulge" in the center might look like a smooth, round blob.

The authors took 190 nearby, high-quality photos of galaxies (their "perfect reference") and then deliberately degraded them to simulate looking at them through foggy glass or from a great distance. They then ran a computer program called statmorph to measure the shape of these "blurred" galaxies and compared the results to the "perfect" ones.

2. What Survives the Blur? (The Robust Measurements)

Some measurements are like the outline of a building. Even if the photo is blurry, you can still tell if the building is tall and thin or short and wide.

• Centroid (Center): Where the galaxy is located is very hard to mess up.
• Ellipticity (Shape): Whether a galaxy is round or oval is generally reliable, unless the blur is extreme.
• Petrosian Radius (Size): The overall size of the galaxy is surprisingly stable, even in low-quality images.

The Takeaway: If you just want to know "how big is it?" or "is it round?", you can trust the data even from lower-quality telescopes.

3. What Gets Distorted? (The Biased Measurements)

Other measurements are like counting the number of windows on a building. If the photo is blurry, you can't see the small windows anymore.

• Concentration (How "bulgy" it is): This is the biggest victim. When a galaxy gets blurry, the bright center spreads out. A galaxy that looks like a dense, bulging ball (an "early-type" galaxy) starts to look like a flat, spread-out disk.
  • The Analogy: Imagine a drop of ink in water. If the water is still (high res), the drop is tight. If you stir the water (blur), the ink spreads out. The computer thinks the ink was never a tight drop to begin with.
  • The Consequence: Astronomers might look at distant galaxies and think, "Wow, there are no bulging galaxies in the early universe!" But the paper says, "No, they are there; they just look blurry."
• Gini and M20: These are complex math tricks to measure how "clumpy" a galaxy is. Blurring smears out the clumps, making a chaotic, messy galaxy look smooth and peaceful.

4. The "Noise" Problem (Disturbance Measurements)

Some measurements try to detect messiness, like a tidal tail (a stream of stars ripped off during a collision).

• Asymmetry (A): This tries to see if the left side of the galaxy looks different from the right side.
• The Issue: If the image is noisy (grainy), the computer mistakes random static for a "tail." If the image is too shallow (not deep enough), the faint tails disappear into the background.
• The Fix: The authors propose a new way to measure this called Isophotal Asymmetry ($A_X$). Instead of looking at the whole image, they look at specific "brightness levels." It's like saying, "I only care about the parts of the galaxy that are as bright as a full moon," ignoring the faint, noisy background. This makes the measurement much more reliable.

5. The "Fitting" Trap (Sérsic Index)

Astronomers often try to fit a mathematical curve (a "Sérsic profile") to a galaxy to describe its shape.

• The Problem: When a galaxy is blurry, the math gets confused. It's like trying to guess the shape of a cloud by looking at a single pixel. The computer might guess the cloud is a circle when it's actually a long streak.
• The Result: The "Sérsic index" (a number describing the shape) becomes very uncertain. The authors found that for distant galaxies, this number can be off by 20-40% just because of the blur.

6. The Big Picture: Why This Matters

The authors ran a simulation: "What if we took a galaxy from today and pretended it was 10 billion light-years away?"

• The Result: The galaxy looked less "bulgy," less "disturbed," and more "disk-like."
• The Conclusion: Many recent studies using the James Webb Space Telescope (JWST) have claimed that the early universe was full of smooth, disk-like galaxies and lacked the messy, bulging ones we see today. This paper suggests that might be an illusion. The galaxies might actually be messy and bulgy, but the distance and the telescope's limits are hiding their true nature.

7. The Solution: A New Toolkit

To fix this, the authors are releasing a new version of their software, statmorph-lsst.

• Correction Functions: They provide mathematical formulas (like a "de-blurring" recipe) that astronomers can use to correct their data based on how blurry the image is.
• New Metrics: They introduced two new ways to measure galaxies:
  1. Isophotal Asymmetry: To measure shape without being fooled by noise.
  2. Substructure ($S_t$): To find "clumps" (like star clusters) by ignoring the random noise that usually hides them.

Summary

Think of this paper as a calibration guide for the universe's camera. It tells astronomers: "Don't trust the raw numbers if the picture is blurry or grainy. Use our new tools to correct the data, or you might think the universe is changing when it's just the camera lens."

By doing this, they hope to ensure that when the Rubin Telescope starts taking millions of photos, we get a true picture of how galaxies really evolve, rather than a distorted one caused by the limitations of our eyes (and telescopes).

Technical Summary

1. Problem Statement

Quantitative galaxy morphology is a critical tool for understanding galaxy evolution, star formation, and structural changes across cosmic time. However, morphological metrics are highly sensitive to observational conditions, specifically image resolution (pixel scale and Point Spread Function) and depth (signal-to-noise ratio and surface brightness limits).

As surveys like the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) and deep observations from JWST push to higher redshifts and fainter objects, galaxies appear smaller and dimmer due to cosmological surface brightness dimming. This creates a systematic bias where:

• Low-resolution images blur structural features.
• Low signal-to-noise (SNR) images obscure faint tidal features or low-surface-brightness structures.
• Consequently, metrics may falsely suggest that high-redshift galaxies are less disturbed, less bulge-dominated, or more disk-like than they truly are, confounding physical evolution with observational artifacts.

There is a lack of a unified, open-source framework that quantifies these biases for all standard morphological parameters and provides empirical corrections.

2. Methodology

The authors conducted a systematic investigation using a "data augmentation" approach to simulate varying observational conditions.

• Sample Selection: They utilized a high-quality sample of 189 nearby galaxies (distances < 200 Mpc) observed by the Hubble Space Telescope (HST) in the F814W (I-band). These images offer exquisite resolution (<25 pc/px) and depth (surface brightness limit $\mu_0 \geq 24$ mag/arcsec$^2$).
• Image Augmentation:
  • Resolution Degradation: Original images were convolved with a Moffat PSF and resampled to physical resolutions ranging from 25 to 2,500 pc/px.
  • Depth Degradation: Gaussian white noise was added to simulate shallower surface brightness limits ranging from 20 to 26 mag/arcsec$^2$.
  • Segmentation: New segmentation maps were generated for each degraded image to mimic real-world source detection challenges (e.g., masking foreground stars or merging galaxies).
  • Dataset: This process generated 64,000 augmented images for 189 galaxies.
• Metric Measurement: The authors measured a comprehensive suite of morphological parameters using statmorph (non-parametric), Galfit (parametric Sérsic fitting), and custom algorithms.
• Analysis: They compared measurements from degraded images against a "baseline" (defined as $R=100$ pc/px and $\mu_0=23.5$ mag/arcsec$^2$). They used mutual information regression to determine which variable (resolution $R$, effective resolution $R_{eff}$, SNR, or surface brightness $\mu_0$) drove the bias for each parameter.
• Correction: Using SymbolicRegression.jl, they derived empirical correction functions to map biased measurements back to baseline values.

3. Key Contributions

1. Comprehensive Bias Quantification: The paper provides the first systematic quantification of biases for nearly all morphological parameters available in statmorph across a wide range of resolutions and depths.
2. Empirical Correction Functions: They offer mathematical corrections (via symbolic regression) for parameters like Concentration ($C$), Gini ($G$), $M_{20}$, and Asymmetry ($A$) to mitigate observational biases.
3. New Metrics:
   • Isophotal Asymmetry ($A_X$): A new metric measuring asymmetry at a specific surface brightness isophote (e.g., 22 mag/arcsec$^2$) rather than a noise threshold. This allows tracing specific physical structures (e.g., tidal tails vs. star-forming clumps) independent of image depth.
   • Substructure Index ($S_t$): A new metric derived from the smoothness residual but filtered to count only connected regions above the noise. This removes noise-dominated scatter and better identifies physical substructures like clumps, bars, and spiral arms.
4. Open Data and Software:
   • Release of the statmorph-lsst Python package, implementing these corrections and new metrics.
   • Publication of the 64,000-image dataset on Zenodo for training deep learning models or testing custom metrics.

4. Key Results

The authors categorized parameters based on their robustness:

• Robust Parameters:
  • Geometric measurements: Centroid, Ellipticity ($e$), Orientation ($\theta$), and Petrosian Radius ($R_p$) are generally robust (within 10%) at most depths, though $R_p$ can be overestimated at very low resolution.
  • Sérsic Fitting: The Sérsic index ($n$) and effective radius ($R_{0.5}$) from Galfit are largely unbiased by resolution if the PSF is modeled correctly. However, $n$ suffers from a 20–40% intrinsic uncertainty due to parameter degeneracies ($n$ vs. $R_{0.5}$).
• Resolution-Dependent Parameters (Bulge Strength):
  • Concentration ($C$), Gini ($G$), and $M_{20}$: These systematically decrease with lower resolution. Low-mass or high-redshift bulge-dominated galaxies appear indistinguishable from disks because the PSF smears the central light.
  • Bias Magnitude: $C$ can be underestimated by $\sim 1.5$ at low effective resolution ($R_{eff} < 5$).
• Depth/SNR-Dependent Parameters (Disturbance):
  • Asymmetry ($A$) and Smoothness ($S$): These are highly sensitive to SNR. Low SNR leads to underestimation of asymmetry and high scatter in smoothness (often dominated by noise).
  • Shape Asymmetry ($A_S$): Sensitive to surface brightness limits; it measures different physical features depending on the depth of the image.
  • RMS Asymmetry ($A_{RMS}$): More robust to noise than standard asymmetry but sensitive to resolution.
• Unreliable Parameters:
  • Multimode ($M$), Intensity ($I$), and Deviation ($D$): These are highly sensitive to segmentation and watershed algorithms. $M$ and $I$ can produce spurious results in noisy or low-resolution data (e.g., noise spikes mimicking double nuclei).

Implication for High-Redshift Evolution:
The authors simulated shifting local galaxies from $z=0.5$ to $z=3.5$. They found that the observed decline in bulge strength ($C$) and disturbance ($A$) at high redshifts can be entirely explained by observational biases (loss of resolution and depth). The true number of disturbed or bulge-dominated galaxies at high $z$ is likely significantly higher than currently reported.

5. Significance

• Preparation for LSST: This work is essential for the upcoming Rubin LSST data releases. It provides the necessary tools to construct morphological catalogs that are consistent across the survey area and time, correcting for the varying depth of stacked images.
• Re-evaluating Galaxy Evolution: The study suggests that previous conclusions about the "disky" nature of early-universe galaxies or the scarcity of mergers at high $z$ may be artifacts of poor resolution and depth, rather than physical reality.
• Standardization: By providing correction functions and a unified package, the authors enable cross-survey comparisons (e.g., comparing HST, JWST, and LSST data) that were previously unreliable due to inconsistent metric behaviors.
• Machine Learning Readiness: The released dataset of 64,000 augmented images serves as a gold standard for training deep learning models to be invariant to observational biases, a critical step for automated morphology analysis in the era of big data.