🔭 astrophysics

The Impact of Galaxy Formation on Galaxy Biasing, and Implications for Primordial non-Gaussianity Constraints

This paper utilizes the CAMELS-SAM pipeline and separate-universe simulations to demonstrate how variations in galaxy formation parameters affect galaxy biasing ( $b_1$ and $b_\phi$ ), revealing that specific star formation rate selections are robust against modeling uncertainties and thus critical for improving constraints on primordial non-Gaussianity ( $f_{\textrm{NL}}$ ).

Original authors: Lucia A. Perez, Shy Genel, Elisabeth Krause, Rachel S. Somerville

Published 2026-02-06

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CC BY 4.0

Original authors: Lucia A. Perez, Shy Genel, Elisabeth Krause, Rachel S. Somerville

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 the universe as a giant, cosmic ocean. A long time ago, right after the Big Bang, this ocean was mostly calm, but it had tiny ripples. Scientists call these ripples "primordial fluctuations." Most of these ripples were perfectly smooth and predictable, like gentle waves on a pond. However, some theories suggest that a few of these ripples were a bit "bumpy" or "lumpy" in a specific way. This bumpiness is called non-Gaussianity.

The paper you are reading is a detective story about how to find these ancient bumps. The main character in this story is a number called $f_{NL}$ . If scientists can measure this number accurately, it will tell us exactly how the universe began (a process called "inflation").

The Problem: The "Translator" is Confused

To find these ancient bumps, astronomers look at how galaxies are clustered together in the sky. It's like looking at a crowd of people at a concert to guess where the music is loudest.

However, there is a major problem. The galaxies aren't just sitting there; they are formed by complex physics involving gas, stars, and black holes. This process is called galaxy formation.

Think of the universe's dark matter (the invisible scaffolding) as the terrain (hills and valleys). Galaxies are like houses built on that terrain.

The Goal: We want to measure the shape of the terrain to find the ancient bumps ( $f_{NL}$ ).
The Obstacle: The way we build the houses (galaxy formation) changes how they are distributed. If we don't understand the "construction rules" perfectly, we can't tell if a cluster of houses is there because of the terrain's shape or because the builders (physics) just liked building houses there.

In scientific terms, this confusion is called bias. The paper focuses on a specific type of bias called $b_\phi$ . It's like a "translation error" between the map of the terrain and the actual location of the houses. If we get this translation wrong, our measurement of the ancient bumps ( $f_{NL}$ ) will be wrong.

The Experiment: The "What-If" Factory

The authors used a powerful computer tool called the Santa Cruz Semi-Analytic Model (SC-SAM). Instead of simulating every single drop of water in the ocean (which is too slow and expensive), this tool uses a set of "recipes" to build galaxies on top of a simulated universe.

They ran 56 different versions of this recipe. Imagine you are baking a cake, and you want to see how the taste changes if you tweak the ingredients:

Recipe A: Change how much "stellar feedback" (stars blowing gas away) happens.
Recipe B: Change how much "AGN feedback" (supermassive black holes blowing gas away) happens.
Recipe C: Change the combination of both.

They ran these 56 different "batches" of the universe to see how the "translation error" ( $b_\phi$ ) changed when the construction rules changed.

The Key Findings: Which Galaxies are the Best Messengers?

The team looked at galaxies in three different ways to see which group gave the most reliable "translation" of the ancient terrain:

By Mass (How heavy the galaxy is):
- Result: This was messy. Depending on which "recipe" (model) you used, the translation error changed wildly. It's like trying to guess the terrain shape by looking at houses of different sizes; the builders' preferences made the data too noisy.
By Star Formation Rate (How fast the galaxy is making new stars):
- Result: This was chaotic. The translation error jumped around unpredictably. It's like trying to guess the terrain by looking at how fast the houses are being painted; the painters' moods (the model parameters) made it impossible to find a pattern.
By Specific Star Formation Rate (sSFR):
- Result: This was the winner. This is a measure of how efficiently a galaxy is making stars relative to its size.
- The Analogy: Imagine that no matter how the builders tweaked their recipes (adding more gas, changing the black hole power), the efficiency of the construction remained surprisingly consistent. The "translation error" ( $b_\phi$ ) for these galaxies followed a single, predictable path regardless of the model used.
- Why it matters: This suggests that if astronomers want to measure the ancient bumps ( $f_{NL}$ ) in the future, they should pick galaxies based on this specific efficiency metric. It is "robust," meaning it doesn't get confused by the uncertainties in how galaxies are built.

The "Assembly Bias" Twist

The paper also checked something called assembly bias. This is like asking: "Does the history of the hill matter, or just the current height?"

They found that for some galaxy types, the history of how the galaxy formed did change the "translation."
However, for the sSFR (efficiency) galaxies, this history didn't mess up the results. They remained reliable messengers.

The Bottom Line

The universe is trying to tell us a secret about its birth through the pattern of galaxies. But the "construction crew" (galaxy formation physics) is messy and introduces noise.

This paper tested 56 different ways the construction crew could work. They found that while many ways of picking galaxies lead to confusion, picking galaxies based on their star-forming efficiency (sSFR) cuts through the noise. It provides a clear, consistent signal that allows scientists to finally measure the ancient bumps ( $f_{NL}$ ) and understand how our universe began.

In short: To hear the universe's birth cry clearly, don't just listen to the loudest or the biggest galaxies. Listen to the ones that are most efficient at making stars; they are the ones that won't lie to you about the terrain.

Technical Summary: The Impact of Galaxy Formation on Galaxy Biasing, and Implications for Primordial non-Gaussianity Constraints

Problem Statement
The parameter $f_{\text{NL}}$ quantifies local primordial non-Gaussianity (PNG) in the Universe's initial energy fluctuations. A non-zero detection would distinguish between single-field and multi-field inflation models. While next-generation galaxy surveys aim to constrain $f_{\text{NL}}$ with statistical errors of $\sigma_{f_{\text{NL}}} \sim 1$ , systematic errors currently dominate these constraints. Specifically, the measurement of $f_{\text{NL}}$ via galaxy clustering is degenerate with the galaxy bias parameters $b_1$ (response to mass density) and $b_\phi$ (response to primordial potential perturbations).

Current constraints often rely on the "universality relation," which assumes a fixed scaling between $b_\phi$ and $b_1$ (e.g., $b_\phi = 2\delta_c(b_1 - 1)$ ) derived from dark matter halos. However, recent work (e.g., Barreira et al. 2020) indicates this relation fails for galaxies, as $b_\phi$ depends on galaxy selection and the specific physics of galaxy formation. The complexity of modeling galaxy formation introduces significant uncertainty into $b_\phi$ , threatening the precision of future $f_{\text{NL}}$ constraints.

Methodology
To address the uncertainty in $b_\phi$ arising from galaxy formation modeling, the authors utilize the Santa Cruz Semi-Analytic Model (SC-SAM) embedded within separate-universe N-body simulations.

Simulations: Three AREPO N-body simulations were run with box size $L = 205 h^{-1}$ cMpc and $N = 1280^3$ particles. These simulations share identical Gaussian initial conditions but differ in the amplitude of the primordial power spectrum ( $\sigma_8$ ), utilizing the separate-universe technique to efficiently measure the response of galaxy formation to long-wavelength perturbations.
Model Variations: The authors ran 56 unique instances of the SC-SAM. These variations involve modifying three key feedback parameters:
1. $\epsilon_{\text{SN}}$ (stellar-driven mass outflow amplitude, varied via factor $A_{\text{SN1}}$ ).
2. $\alpha_{\text{rh}}$ (exponent of the mass outflow relation, varied via factor $A_{\text{SN2}}$ ).
3. $\kappa_{\text{radio}}$ (AGN radio-mode feedback amplitude, varied via factor $A_{\text{AGN}}$ ).
Measurements:
- $b_\phi$ is calculated via finite differencing of galaxy number counts between high- $\sigma_8$ , fiducial, and low- $\sigma_8$ simulations.
- $b_1$ is derived from the galaxy-matter cross-power spectrum.
- Galaxies were selected based on Stellar Mass ( $M_*$ ), Star Formation Rate (SFR), and specific SFR (sSFR) across redshifts $z=0, 1, 2$ .
- A "realism" metric ( $\chi^2$ ) was assigned to each model based on its agreement with observed $z=0$ stellar mass functions (Bernardi et al. 2018).
- The study also assessed the impact of galaxy assembly bias by shuffling galaxies into halos of similar mass but different formation histories.

Key Contributions

Systematic Exploration of Feedback: Unlike previous studies that often used a single hydrodynamical simulation or a fixed SAM, this work systematically varies stellar and AGN feedback parameters to map the resulting landscape of $b_\phi$ and $b_1$ .
Separate-Universe SAM Application: The authors apply the separate-universe technique to a semi-analytic model, allowing for the efficient measurement of $b_\phi$ across a wide parameter space that would be computationally prohibitive with full hydrodynamical simulations.
Selection Dependence Analysis: The paper explicitly compares how different galaxy selection criteria ( $M_*$ , SFR, sSFR) respond to variations in galaxy formation physics, identifying which selections are most robust to modeling uncertainties.
Cross-Model Validation: The results are compared against previous findings from the IllustrisTNG hydrodynamical simulation, the Munich SAM, and the Galacticus SAM to determine if the SC-SAM parameter space encompasses the behavior of other galaxy formation models.

Results

Deviation from Universality: The SC-SAM models confirm that the universality relation ( $b_\phi = 2\delta_c(b_1 - 1)$ ) is not accurate for galaxies. The $b_\phi(b_1)$ relationship varies significantly depending on the galaxy selection and the specific feedback parameters.
Stellar Mass Selections: $b_\phi$ generally increases with stellar mass. However, the $b_\phi(b_1)$ relationship is steeper than that found in IllustrisTNG (Barreira et al. 2020), particularly for low-mass selections. The relationship is sensitive to the stellar feedback parameters ( $A_{\text{SN1}}, A_{\text{SN2}}$ ).
SFR Selections: $b_\phi$ values for SFR-selected galaxies are chaotic and often close to zero. The relationship is highly sensitive to feedback parameters because different parameters shift the SFR–halo mass relation in complex ways.
sSFR Selections (Key Finding): Selections based on specific SFR (sSFR) are remarkably robust to variations in galaxy formation modeling. Across all 56 models, the $b_\phi$ vs. sSFR and $b_\phi(b_1)$ relationships follow a tight, consistent path. This is attributed to the self-regulating nature of the SC-SAM, which maintains a consistent sSFR–halo mass relationship regardless of feedback parameter variations.
Assembly Bias: The study finds that galaxy assembly bias affects $b_1$ measurements (reducing clustering for stellar mass selections, increasing it for SFR/sSFR selections when formation history is shuffled). However, these assembly bias signals have minimal impact on the measured $b_\phi(b_1)$ relationships.
Comparison to Other Models: The SC-SAM variations encompass the $b_\phi$ behaviors measured in the Munich SAM and Galacticus. While there are tensions with IllustrisTNG results (likely due to baryonic effects absent in SAMs or differences in merger tree construction), the SC-SAM variations cover a broad range of $b_\phi$ values consistent with other models.

Significance and Claims
The paper claims that uncertainties in galaxy formation modeling are a critical systematic for future $f_{\text{NL}}$ constraints. By demonstrating that $b_\phi$ is not universal and depends heavily on selection and modeling, the authors argue that assuming a fixed universality relation risks biased constraints.

The primary significance of this work lies in identifying sSFR as a robust galaxy selection for $f_{\text{NL}}$ studies. Because sSFR selections yield consistent $b_\phi$ values across a wide range of galaxy formation physics, they offer a pathway to reduce systematic errors in future surveys. The authors conclude that while no single model can perfectly describe the universe, selecting galaxies by sSFR minimizes the sensitivity of $f_{\text{NL}}$ constraints to the specific details of galaxy formation physics. Furthermore, the work provides a framework for building informative priors for $b_\phi$ based on observational data, moving toward physically motivated constraints on primordial non-Gaussianity.

The Problem: The "Translator" is Confused

The Experiment: The "What-If" Factory

The Key Findings: Which Galaxies are the Best Messengers?

The "Assembly Bias" Twist

The Bottom Line

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