Morphologies for DECaLS Galaxies through a combination of non-parametric indices and machine learning methods: A comprehensive catalog using the Galaxy Morphology Extractor (galmex) code

This paper introduces the galmex Python package to generate a comprehensive catalog of non-parametric morphological indices for DECaLS galaxies, demonstrating their effectiveness—particularly when combined with LightGBM machine learning—in reliably classifying spiral and elliptical galaxies for future southern hemisphere surveys.

The Gist

Imagine the universe as a giant, bustling city. In this city, galaxies are the buildings. Some are sleek, modern skyscrapers with smooth glass facades (elliptical galaxies), while others are sprawling, complex neighborhoods with winding streets, parks, and distinct districts (spiral galaxies).

For decades, astronomers have tried to map this city. They used to do it by looking at photos and guessing, "That looks like a spiral!" or "That looks like a blob." But with millions of new photos coming in from powerful telescopes, human eyes just can't keep up. We need a robot to do the sorting.

This paper is about building that robot and teaching it how to tell the difference between a "skyscraper" and a "neighborhood" without ever needing to see the whole building clearly.

Here is the story of how they did it, broken down into simple steps:

1. The Problem: Too Many Galaxies, Too Little Time

The researchers are using data from the DECaLS survey, which is like a massive, high-resolution photo album of the southern sky. It contains millions of galaxies.

• The Challenge: If you try to measure a galaxy by fitting a mathematical curve to its shape (like trying to force a square peg into a round hole), it often fails because galaxies are messy. They have bars, spirals, and weird bumps.
• The Solution: Instead of guessing the shape, they decided to measure how the light is distributed. Think of it like judging a cake not by its shape, but by how the sugar is sprinkled on top. Is the sugar concentrated in the middle? Is it spread out evenly? Is it clumpy?

2. The Tool: "Galmex" (The Digital Chef)

The team built a new software package called galmex (Galaxy Morphology Extractor). You can think of this as a super-precise kitchen robot.

• Preparation: Before measuring, the robot has to clean the image. It removes the "sky" (the background noise), cuts out the specific galaxy, and paints over any neighboring stars or galaxies that might be getting in the way.
• The Measurements: Once the image is clean, galmex calculates a set of "fingerprints" for each galaxy. These are called non-parametric indices.
  • Concentration: How much of the light is in the center? (Like how much frosting is in the middle of a cupcake).
  • Asymmetry: Is the galaxy lopsided? (Like a crooked tower).
  • Smoothness: Is the surface bumpy or smooth?
  • Gini & Entropy: These are fancy math ways of asking, "Is the light spread out evenly, or is it clumped up in a few bright spots?"

3. The Training: Teaching the Robot with "Control Samples"

To teach the robot what a "spiral" and an "elliptical" look like, they didn't just guess. They used a "Gold Standard" dataset from a project called Galaxy Zoo, where thousands of real humans looked at galaxies and voted on what they were.

• They took the human-voted "Spirals" and "Ellipticals" and fed them into their robot.
• They asked the robot: "Look at the fingerprints (the measurements) of these human-confirmed spirals. What do they have in common? Now look at the ellipticals. How are they different?"

4. The Brain: Machine Learning (The Detective)

They didn't just look at the measurements; they used a powerful AI tool called LightGBM (a type of machine learning).

• Think of this AI as a master detective. It looks at all the fingerprints (Concentration, Gini, Entropy, etc.) at once.
• It learned that Entropy (how spread out the light is) and Gini (how unequal the light distribution is) were the biggest clues.
• The Result: The AI became incredibly good at guessing. It could look at a galaxy it had never seen before and say, "I am 98% sure this is a spiral," or "I am 99% sure this is an elliptical."

5. The Big Discovery: What Works Best?

The paper found some interesting things about which "fingerprints" are the most reliable:

• The "Concentration" metric is great for telling the difference between a smooth blob (elliptical) and a disk (spiral).
• The "Asymmetry" metrics are actually terrible at telling spirals from ellipticals (because both can be symmetrical), but they are amazing at spotting messy galaxies, like those that are crashing into each other.
• The "MEGG" metrics (a fancy name for a group of measurements including Gini and Entropy) were the real stars of the show. They provided the clearest separation between the two types.

6. The Gift to the World

The team didn't just keep this to themselves. They released:

1. The Code (galmex): A free, open-source tool that anyone can use to measure galaxies. It's modular, meaning you can tweak every step of the process, like adjusting the focus on a camera.
2. The Catalog: A massive list of over 1.7 million galaxies with their "fingerprints" and a probability score telling you how likely they are to be a spiral or an elliptical.

Why Does This Matter?

Imagine you are studying how cities evolve. You need to know which buildings are old and which are new, and how they change over time.

• By having a reliable, automated way to sort millions of galaxies, astronomers can now study how galaxies grow, how they crash into each other, and how they change from "messy" to "smooth" over billions of years.
• This is especially important for the southern hemisphere, where fewer surveys exist. This paper fills in the missing pieces of the cosmic map.

In a nutshell: The authors built a smart, automated system that measures the "texture" of galaxy light. By teaching it with human-voted examples, they created a highly accurate tool that can sort millions of galaxies into spirals and ellipticals, helping us understand the life story of the universe's most beautiful structures.

Technical Summary

Here is a detailed technical summary of the paper "Morphologies for DECaLS Galaxies through a combination of non-parametric indices and machine learning methods":

1. Problem Statement

Galaxy morphology is a critical tracer of formation and evolutionary history. However, classifying millions of galaxies in modern large-scale imaging surveys (like DECaLS) via visual inspection is impossible due to subjectivity and scalability issues. While parametric methods (e.g., Sérsic profile fitting) exist, they often fail for irregular, clumpy, or merging systems due to degeneracies in fitted parameters. Non-parametric indices (such as Concentration, Asymmetry, and Smoothness) offer a model-independent alternative, but their reliability depends heavily on image pre-processing and the specific definitions used. Furthermore, existing machine learning classifiers often rely on training sets with subjective labels (e.g., "smooth" vs. "disk") that do not perfectly map to classical morphological types (Elliptical vs. Spiral).

The authors aim to:

1. Create a homogeneous catalog of non-parametric morphological indices for DECaLS galaxies.
2. Develop a robust, modular software package to measure these indices.
3. Quantify the discriminatory power of these indices in separating spirals from ellipticals.
4. Train a machine learning model to provide probabilistic morphological classifications for the entire DECaLS sample.

2. Methodology

Data Selection

• Survey: Dark Energy Camera Legacy Survey (DECaLS), Data Release 10 (DR10), $r$-band.
• Sample Constraints:
  • Effective radius ($R_e$) > 2 arcsec (to ensure resolution).
  • Apparent magnitude $m_r \le 21$ (ensuring high Signal-to-Noise ratio).
  • Surface brightness limit $\langle \mu_{2R_e} \rangle < 26$ mag arcsec$^{-2}$.
  • Redshift $z \le 0.15$ (limited by the availability of visual labels in Galaxy Zoo 1).
• Final Sample: ~1.74 million galaxies, with a control sample of ~80,500 labeled spirals and ellipticals.

Software Development: galmex

The authors developed galmex (Galaxy Morphology Extractor), a modular Python package designed to address the lack of flexibility in existing codes.

• Key Features: Modular architecture allowing independent customization of pre-processing steps (cutout creation, background subtraction, object detection, cleaning, and metric definition).
• Pre-processing Pipeline:
  1. Cutout: Extracts $20 \times R_e$ regions.
  2. Background Subtraction: Uses sigma-clipping on image borders.
  3. Detection: Uses SEP (Source Extractor in Python) with matched filters.
  4. Cleaning: "Painting" procedure to remove neighbors/stars via elliptical isophote interpolation.
  5. Radii Estimation: Computes Petrosian ($R_P$), Kron, and half-light radii using elliptical apertures (crucial for avoiding bias in flattened galaxies).
• Metrics Measured:
  • CA[AS]S System: Concentration ($C$), Asymmetry ($A$), Shape Asymmetry ($AS$), Smoothness ($S$).
  • MEGG System: $M_{20}$, Entropy ($E$), Gini ($G$), Gradient Pattern Asymmetry ($G_2$).

Machine Learning Framework

• Training Labels: Used Galaxy Zoo 1 (GZ1) classifications (Spiral vs. Elliptical) as the ground truth, rather than the "Smooth vs. Disk/Feature" labels from Galaxy Zoo DECaLS, to ensure a cleaner separation of classical types.
• Algorithm: LightGBM (Light Gradient Boosted Machine).
• Handling Imbalance: Addressed the class imbalance (spirals vastly outnumber ellipticals) using SMOTE (Synthetic Minority Over-sampling Technique) only on the training set.
• Interpretability: Used SHAP (SHapley Additive exPlanations) values to determine feature importance.

3. Key Contributions

1. The galmex Package: A transparent, modular tool that allows fine-tuning of every step in the morphological measurement process, specifically optimizing for elliptical apertures to reduce bias in characteristic radii.
2. First Public CA[AS]S+MEGG Catalog for DECaLS: A homogeneous catalog of non-parametric indices for ~1.7 million galaxies in the southern hemisphere.
3. Probabilistic Classification: A calibrated machine learning model that outputs the probability of a galaxy being a spiral ($P_{spiral}$) rather than a binary label, trained on the non-parametric parameter space.
4. Validation of Training Labels: A critical analysis showing that GZ DECaLS "Smooth" labels are not equivalent to "Elliptical" labels, leading to degraded classifier performance if used directly. The study advocates for using GZ1 labels for training.

4. Key Results

Performance of Non-Parametric Indices

• CAS System: Concentration ($C$) is the most reliable single parameter for separating early- and late-types. Asymmetry ($A, AS$) and Smoothness ($S$) show significant overlap between spirals and ellipticals; they are better suited for identifying disturbed systems (mergers) rather than standard morphological classification.
• MEGG System: These indices provide superior separation.
  • Entropy ($E$) and Gini ($G$) are the strongest discriminators.
  • $M_{20}$ and $G_2$ trace gradients within the spiral sequence.
  • The overlap coefficient (OVL) for Entropy and Gini is very low (~0.14–0.18), indicating excellent separation.

Machine Learning Performance

• Accuracy: The LightGBM classifier achieved an AUC of 0.996 and an Average Precision (AP) of 0.999.
• Calibration: The model is well-calibrated (Brier score = 0.022), meaning the predicted probabilities accurately reflect the true likelihood of a galaxy being a spiral.
• Feature Importance (SHAP): The most influential features driving the classification are Entropy ($E$), Concentration ($C$), and Gini ($G$).
• Robustness: Performance remains high across different apparent sizes and magnitudes, with only a slight degradation for the faintest/smallest galaxies where resolution limits morphological detection.

Comparison with Visual Classifications

• The non-parametric indices correlate strongly with CNN-based T-Types and Galaxy Zoo visual classifications, confirming that these metrics capture the same physical structural differences perceived by human classifiers.
• However, using "Smooth/Disk" labels from GZ DECaLS as training data resulted in significantly lower accuracy (AUC ~0.91) compared to using GZ1 Spiral/Elliptical labels, highlighting the subjectivity of the "Smooth" category.

5. Significance and Future Work

• Scientific Utility: This work provides a vital resource for studying galaxy evolution in the southern hemisphere, particularly for upcoming spectroscopic surveys like 4MOST/CHANCES and WEAVE, which overlap with the DECaLS footprint.
• Methodological Impact: It demonstrates that combining non-parametric indices with machine learning yields more robust and interpretable classifications than visual inspection or parametric fitting alone.
• Future Directions: The authors plan to extend this methodology to:
  • Higher redshifts ($z > 0.15$).
  • Explicitly classifying disturbed systems (mergers, jellyfish galaxies) and lenticulars (S0), moving beyond the simple Spiral/Elliptical dichotomy.

In summary, this paper establishes a reproducible, high-accuracy framework for automated galaxy morphology classification, releasing both the software (galmex) and a massive, calibrated catalog of morphological probabilities for the astronomical community.