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GalSBI: Forward Modelling Galaxy Clustering and Population

This paper presents an extension of the GalSBI framework that jointly models galaxy populations and clustering using optimal transport-based subhalo abundance matching and simulation-based inference, successfully validating the approach against DES and HSC data to produce realistic image simulations for analyzing current and next-generation cosmological surveys.

Original authors: Silvan Fischbacher, Luca Tortorelli, Tomasz Kacprzak, Alexandre Refregier

Published 2026-06-24

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CC BY 4.0

Original authors: Silvan Fischbacher, Luca Tortorelli, Tomasz Kacprzak, Alexandre Refregier

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine trying to understand the entire history of a bustling city just by looking at a single, blurry photograph taken from a drone. You can see the buildings (galaxies), but you don't know exactly how tall they are, what they're made of, or how they are grouped together in neighborhoods. This is the challenge astronomers face when studying the universe. They have massive surveys of the sky, but to make sense of them, they need to know if the patterns they see are real or just tricks of the camera.

This paper introduces an upgrade to a powerful tool called GalSBI. Think of GalSBI as a "cosmic video game engine." Instead of just looking at real photos, scientists use this engine to build a fake, synthetic universe that looks and behaves exactly like the real one. They then compare their fake universe to the real data to see if their rules of physics and galaxy formation are correct.

Here is a simple breakdown of what this paper does:

1. The Old Problem: Randomly Scattered Galaxies

In previous versions of this tool, the scientists could simulate what galaxies looked like (their color, brightness, and shape) very well. However, when it came to placing them on the map, they did it randomly. It was like populating a city map by dropping people at random coordinates, ignoring that people actually live in neighborhoods, suburbs, and downtown areas.

In the real universe, galaxies aren't scattered randomly; they cluster together in groups and filaments, much like cities are clustered along rivers or coastlines. The old tool missed this "neighborhood effect," which is crucial for understanding how the universe is structured.

2. The New Solution: The "Galaxy-Halo" Connection

The authors upgraded GalSBI to fix this. They introduced a new method called SHAM-OT (Subhalo Abundance Matching with Optimal Transport).

The Analogy: Imagine you have a list of all the houses in a city (dark matter "halos") and a list of all the families (galaxies). You want to assign families to houses.
The Old Way: You might just guess or sort them one by one, which is slow and clunky.
The New Way (SHAM-OT): The authors use a mathematical trick called "Optimal Transport." Think of this as a super-efficient logistics company. Instead of moving one family at a time, they calculate the most efficient way to move all families to houses at once, ensuring the biggest families get the biggest mansions and the smaller families get the cozy cottages, while respecting the "neighborhood" rules.

This allows them to place galaxies in the simulation exactly where they should be, creating realistic "galaxy neighborhoods" that match the real universe.

3. Testing the Engine

To prove their new engine works, they ran a massive test using real data from two major sky surveys:

DES (Dark Energy Survey): A wide view of the sky.
HSC (Hyper Suprime-Cam): A very deep, detailed view of a small patch of sky.

They generated thousands of fake sky patches and compared them to the real photos. They checked:

Photometry: Do the fake galaxies have the right colors and brightness? (Yes, they match perfectly).
Morphology: Do the fake galaxies look like the right shapes (spirals, blobs)? (Yes).
Clustering: Do the fake galaxies group together in the same way real galaxies do? (Yes, the "neighborhoods" look real).
Redshift: Do the fake galaxies appear at the correct distances? (Yes, the distribution of distances matches high-precision measurements).

4. Why This Matters (According to the Paper)

The paper claims that by adding these realistic "neighborhoods" (clustering), the tool becomes much more powerful for two main reasons:

Better Error Checking: In the real world, if you look at a small patch of sky, you might just happen to see a lucky (or unlucky) cluster of galaxies. This is called "sample variance." The new tool can simulate this effect, helping scientists understand how much their measurements might be skewed just by looking at a small area.
Blending: In crowded neighborhoods, galaxies often overlap in photos, making them look like one big blob. The new tool simulates these crowded areas, allowing scientists to better understand and fix errors caused by overlapping galaxies.

Summary

The authors have taken a cosmic simulation tool and taught it how to build realistic "galaxy neighborhoods." By using a smart mathematical method to place galaxies where they belong, they created a tool that can generate fake universe images that are indistinguishable from the real thing in terms of color, shape, and grouping. This tool is now ready to help astronomers analyze current and future massive sky surveys with greater accuracy, ensuring that when they measure the universe, they aren't being fooled by the camera or the randomness of the sky.

Note: The paper focuses strictly on improving the simulation and validation against existing data (DES and HSC). It does not claim to have discovered new physical laws or applied this to medical or clinical fields. Its primary goal is to make the "cosmic video game" more realistic so scientists can play with it to understand the real universe better.

Technical Summary of "GalSBI: Forward Modelling Galaxy Clustering and Population"

Problem Statement
Forward modelling has emerged as a powerful approach for analyzing large-scale structure surveys, aiming to generate synthetic observations subject to the same systematic effects and selections as real data. While previous implementations of the GalSBI framework successfully modelled galaxy photometry and morphology using parametric population models and image simulations (UFig), they assigned galaxy positions uniformly at random. This neglect of spatial clustering limits the framework's ability to accurately quantify sample variance, model source blending in overdense regions, and perform fully self-consistent $3\times2$ pt (weak lensing and galaxy clustering) analyses. Furthermore, existing Subhalo Abundance Matching (SHAM) techniques, which link galaxies to dark matter halos, were computationally prohibitive for on-the-fly image simulation pipelines due to the need for sampling and sorting massive catalogs.

Methodology
The authors extend the GalSBI framework to jointly model the galaxy population and their spatial clustering. The methodology integrates three primary components:

Halo and Subhalo Simulation: The authors utilize PINOCCHIO to generate a halo lightcone catalog and merger history using Lagrangian Perturbation Theory. Subhalos are extracted from the merger history, with their survival times modelled via a fitting function dependent on host-to-subhalo mass ratios and orbital circularity. Subhalo positions are drawn from an isothermal profile within their host halos.
Galaxy-Halo Connection via SHAM-OT: To populate the halo catalog with galaxies, the authors employ Subhalo Abundance Matching (SHAM). To overcome computational bottlenecks, they utilize SHAM-OT, which reformulates SHAM as an Optimal Transport (OT) problem. Instead of sorting large catalogs, the method matches the halo mass function with the galaxy luminosity function using normalized histograms. Entropic regularization is applied to the OT solution to incorporate scatter in the galaxy-halo connection, emulating lognormal scatter in luminosity without requiring deconvolution.
- The model distinguishes between red (quenched) and blue (star-forming) populations. Quenching is modelled via smooth transitions (error functions) dependent on halo mass for central galaxies and time since merger for satellite galaxies.
Simulation-Based Inference (SBI): The model parameters are constrained using an iterative Approximate Bayesian Computation (ABC) approach.
- Data: The framework is validated against Dark Energy Survey Year 3 (DES Y3) imaging and Hyper Suprime-Cam (HSC) deep/ultra-deep fields.
- Emulator Adaptation: Recognizing that clustered positions make blending a local environmental effect rather than a global nuisance, the authors replaced the previous detection classifier with actual image simulations for the detection step (specifically the $i$ -band). Photometry in other bands is emulated using a normalizing flow. This preserves clustering statistics while maintaining computational efficiency.
- Distance Measures: The inference minimizes a weighted distance metric combining fractional galaxy counts, a Wasserstein distance for photometric/morphological properties, and a distance based on the angular power spectrum ( $C_\ell$ ) computed across 12 magnitude and color sub-samples.

Key Contributions

Extension of GalSBI: The first implementation of GalSBI that jointly models galaxy photometry, morphology, and spatial clustering.
Efficient SHAM-OT: The application of optimal transport to SHAM allows for the on-the-fly computation of galaxy-halo connections, reducing computational costs by orders of magnitude compared to traditional SHAM.
Realistic Clustering in Simulations: The generation of image simulations where galaxy positions are physically correlated with dark matter halos, enabling the study of sample variance and blending in overdense regions.
Updated Inference Pipeline: A modified SBI pipeline that uses image-based detection to avoid biases in clustering statistics introduced by uniform position assumptions.

Results

Galaxy Population Constraints: The inferred galaxy population parameters (luminosity functions, size-luminosity relations) are consistent with previous GalSBI results and external literature. The quenching parameters (mass limit and time scales) are consistent with prior work but show reduced degeneracy due to the relaxed assumption of sharp transitions.
Galaxy-Halo Connection: The measured galaxy-halo connection, including scatter, aligns well with local measurements (e.g., Milky Way, Andromeda) and the Tully-Fisher relation. The model finds significantly larger scatter for red galaxies compared to blue ones, attributed to the dominance of satellite galaxies in the red population.
Validation against DES and HSC:
- Photometry and Morphology: Simulated magnitude, color, and size distributions agree well with DES Y3 and HSC deep field data.
- Clustering: The angular power spectra ( $C_\ell$ ) of simulated galaxy positions match data across various magnitude and color cuts.
- Redshift Distributions: The simulated redshift distributions ( $n(z)$ ) for HSC deep fields show "spiky" features similar to real data (unlike the smoother distributions of previous non-clustered models). The mean redshifts agree with high-precision photometric redshifts (LePhare, EAZY) within $0.2\sigma$ to $1.6\sigma$ across magnitude cuts.
Uncertainty Quantification: The study quantifies the impact of sample variance on redshift distributions. For the COSMOS field size, sample variance is the dominant uncertainty source for bright samples ( $<24$ mag), while galaxy population model uncertainty dominates for fainter samples.

Significance
The paper claims that the updated GalSBI framework enables accurate, forward-modelled image simulations with realistic clustering. This capability is significant for:

Sample Variance: Quantifying the impact of sample variance when calibrating on small fields like COSMOS.
Blending Calibration: Improving blending calibration for deep surveys (e.g., HSC deep fields show a $\sim7\%$ reduction in detected galaxies due to clustering, compared to negligible effects in DES), which is crucial for Stage-IV surveys.
Systematic Control: Providing a self-consistent tool for $3\times2$ pt analyses by jointly modelling photometry, morphology, and spatial positions.
Future Surveys: Serving as a powerful tool for current and next-generation cosmological surveys (e.g., Rubin-LSST, Euclid, Roman) by providing realistic simulations that include source clustering and sample variance effects.

The authors note that while the current scatter model is symmetric and constant, future work may adapt the cost matrix to account for mass-dependent scatter variations. Additionally, the framework is designed to be extensible to spectroscopic data and other surveys with broader wavelength coverage.