On the dependence of galaxy assembly bias on the selection criteria, number density, and redshift of galaxy samples

Using the IllustrisTNG hydrodynamical simulation, this study demonstrates that galaxy assembly bias varies significantly with selection criteria, number density, and redshift, cannot be fully captured by a single secondary halo property, and arises from the interplay between halo assembly bias and occupancy variation, for which the authors propose a fast analytical prediction method.

The Gist

Imagine the universe as a giant, invisible scaffolding made of dark matter. Think of these dark matter structures as houses (called "halos"). Galaxies, which are the cities of stars we can actually see, form inside these houses.

For a long time, astronomers thought that the only thing that mattered for how these "cities" clumped together was the size of the house (the mass of the dark matter halo). If you had two houses of the same size, you'd expect the cities inside them to behave the same way.

But this paper argues that's not the whole story. It's like saying two houses of the same size will always have the same neighborhood vibe. In reality, one house might be brand new, another might be old and creaky, one might be spinning fast, and another might be very dense. These extra details matter. This phenomenon is called Galaxy Assembly Bias.

Here is a breakdown of what the researchers found, using simple analogies:

1. The "House Features" Matter

The researchers looked at a massive computer simulation of the universe (called IllustrisTNG). They treated galaxies like people moving into houses. They wanted to see if the "personality" of the house affected how the people clustered together.

They looked at three specific "house features":

• Concentration: How packed the furniture is in the house.
• Spin: How fast the house is spinning.
• Formation Time: How old the house is (when it was built).

The Finding: They found that these features do change how galaxies cluster. But here's the twist: It depends entirely on who you are asking.

2. The "Selection Bias" (Who are you looking at?)

The paper shows that the answer changes based on which group of galaxies you pick, similar to how a survey about "happiness" gives different results if you ask teenagers, retirees, or athletes.

• If you look at massive, bright galaxies (like Red Giants): They tend to live in older, denser houses. These galaxies cluster more tightly than expected.
• If you look at blue, star-forming galaxies: They tend to live in younger, less dense houses. Surprisingly, these galaxies actually cluster less tightly than expected (a "negative" bias).

The Analogy: Imagine a high school dance.

• If you only look at the popular kids (Red galaxies), they all stick together in a tight circle.
• If you look at the quiet kids in the corner (Blue galaxies), they might actually spread out more than you'd expect for their group size.
• The "bias" isn't just about the room size (mass); it's about the type of kid and the type of room they are in.

3. The "One-Size-Fits-All" Trap

The authors discovered that you cannot use a single rule to predict this behavior.

• You can't just say, "Older houses always make galaxies cluster more."
• You can't just say, "Spinning houses always make them cluster less."

For some galaxy groups, the "age" of the house is the most important factor. For others, the "spin" is what matters. Trying to use a simple formula based on just one feature is like trying to predict the weather in New York, London, and Tokyo using only one thermometer. It won't work.

4. The "Recipe" for Prediction

The most exciting part of the paper is that the authors didn't just find a problem; they cooked up a new recipe to solve it.

Previously, to figure out how much these "house features" mattered, scientists had to run incredibly slow, expensive computer simulations where they would literally shuffle the galaxies around like cards in a deck to see what happened. It was like trying to learn how a cake tastes by baking 100 different versions and swapping the eggs and flour randomly.

The authors created a fast mathematical shortcut.

• The Shortcut: Instead of shuffling cards, you just need to know two things:
  1. How much the "houses" themselves like to cluster based on their features (Halo Assembly Bias).
  2. Which "houses" the "galaxies" prefer to live in (Occupancy Variation).

By multiplying these two factors, they can predict the result instantly without running the heavy computer simulations. It's like having a master chef's formula that tells you exactly how the cake will taste just by looking at the ingredients, without needing to bake it first.

Why Does This Matter?

We are currently building huge maps of the universe to understand Dark Energy (the force pushing the universe apart). To do this, we need to know exactly how galaxies are moving and clustering.

If we ignore this "Assembly Bias" (the extra personality of the houses), our maps will be slightly off. It's like trying to navigate a city using a map that only shows street names but ignores traffic lights and one-way streets. You might get there, but you'll take the wrong turn.

In summary:
This paper tells us that the universe is more complex than just "big houses hold big cities." The history and shape of the dark matter houses matter, and it matters differently for different types of galaxies. But don't worry—the authors gave us a new, fast tool to account for this complexity so we can map the universe more accurately.

Technical Summary

Here is a detailed technical summary of the paper "On the dependence of galaxy assembly bias on the selection criteria, number density, and redshift of galaxy samples" by García-Moreno and Chaves-Montero (2026).

1. Problem Statement

Galaxy assembly bias (GAB) refers to the dependence of galaxy clustering on halo properties beyond just halo mass (e.g., concentration, spin, formation time). While hydrodynamical simulations predict this effect, its magnitude is highly variable and depends on the specific galaxy population being observed.

• The Challenge: Observational detection of GAB is difficult because it requires unambiguous association of galaxies with host halos and precise mass estimation. Current empirical models often rely on fitting parameters to clustering data, but there is significant disagreement in the literature regarding the existence and strength of GAB.
• The Gap: There is a lack of systematic quantification of GAB across the diverse galaxy populations targeted by modern large-scale structure surveys (e.g., SDSS, DESI, DES, KiDS) using a single, high-fidelity galaxy formation model. Furthermore, it is unclear if a single secondary halo property can fully explain GAB for all galaxy types.

2. Methodology

The authors utilized the IllustrisTNG suite, specifically the TNG300-1 hydrodynamical simulation, which employs the AREPO code and accurately reproduces observed galaxy clustering.

• Galaxy Samples: They extracted four distinct galaxy populations based on observational selection criteria:
  1. Stellar Mass ($M_*$)
  2. $r$-band Magnitude (Luminosity)
  3. Blue (Star-forming)
  4. Red (Quenched)
  • Samples were generated at four redshifts ($z = 0, 0.5, 1, 2$) and four number densities ($n = 0.01, 0.003, 0.001, 0.0003 \, h^3 \text{Mpc}^{-3}$).
• Halo Properties: The study focused on three secondary halo properties:
  1. Concentration ($c$)
  2. Spin ($\lambda$)
  3. Formation time ($t_f$)
• Measurement Technique (Shuffling): To quantify GAB, the authors employed a "shuffling" technique:
  • Galaxies were shuffled among halos of similar mass bins to remove any dependence on secondary properties while preserving the 1-halo term (satellite distances).
  • The level of GAB was measured as the ratio of the two-point correlation function of the original sample ($\xi$) to the shuffled sample ($\xi_{\text{fix } M_h}$) on scales $r = 8–25 \, h^{-1}\text{Mpc}$.
  • A ratio $>1$ indicates positive bias (clustering enhanced), $<1$ indicates negative bias, and $=1$ indicates no bias.
• Analytical Modeling: The authors decomposed GAB into two components:
  1. Halo Assembly Bias (HAB): The clustering dependence of halos on secondary properties.
  2. Occupancy Variation (OV): The correlation between galaxy occupation and secondary halo properties.
  • They derived an analytical expression to predict GAB based on the median secondary property of host halos and the known HAB, avoiding expensive shuffling.

3. Key Results

A. Dependence on Selection Criteria and Redshift

• Strong Variability: The strength of GAB varies significantly depending on the selection criteria, number density, and redshift. The effect can increase or decrease galaxy clustering by up to 25%.
• Redshift Evolution Trends:
  • Stellar Mass & Red Samples: Generally show a steady increase in positive assembly bias as redshift decreases (e.g., from 1% at $z=2$ to 17% at $z=0$ for a specific stellar mass sample).
  • Blue Samples: Exhibit a decline in assembly bias from $z=1$ to $z=0$, resulting in negative assembly bias at $z=0$ (reaching -24% for low number densities). This is driven by the correlation between blue galaxies and halo formation time.
• No Single Proxy: No single secondary halo property (concentration, spin, or formation time) fully captures the total GAB for any galaxy population. For instance, concentration and spin generally yield positive bias, while formation time drives the negative bias in blue samples.

B. Mechanism: Interplay of HAB and OV

• Halo Assembly Bias (HAB): Low-mass, high-concentration halos are more clustered; high-mass halos show a reversal. High-spin and early-forming halos are generally more clustered.
• Occupancy Variation: The authors found that the sign of GAB is determined by which halos host the galaxies.
  • Positive GAB: Samples (Stellar Mass, Red) preferentially occupy halos with positive HAB (e.g., high-concentration low-mass halos).
  • Negative GAB: Blue galaxies preferentially occupy halos with negative HAB (e.g., specific mass ranges where high concentration correlates with lower clustering), leading to an overall suppression of clustering.

C. Analytical Prediction Model

• The authors derived a fast analytical expression (Eq. 5) to predict GAB:
  $$GAB(x) = \frac{b_{\text{gal}}^{\text{w/ HAB}}(\tilde{x})}{b_{\text{gal}}^{\text{w/o HAB}}}$$
  where the numerator accounts for the modified halo bias due to the secondary property $x$.
• Validation: This model accurately reproduces the results of the computationally expensive shuffling technique, achieving a Pearson correlation coefficient of $r_p = 0.8$. It requires only the median secondary property of host halos and the HAB curve, making it efficient for cosmological modeling.

4. Significance and Implications

• Cosmological Inference: The study demonstrates that GAB cannot be neglected for any galaxy sample in large-scale structure surveys. Ignoring it or modeling it with a single parameter (e.g., only concentration) introduces biases in cosmological parameter estimation.
• Model Limitations: Empirical models that attempt to predict GAB as a function of a single halo property are insufficient to reproduce hydrodynamical simulation predictions.
• Practical Tool: The provided analytical expression offers a computationally efficient method for cosmologists to incorporate GAB into their models without running expensive shuffling simulations. This allows for rapid assessment of whether empirical models are consistent with physical simulations.
• Observational Strategy: The results suggest that the detectability of GAB in future surveys (like DESI or Euclid) will vary drastically depending on the target galaxy population (e.g., blue vs. red) and redshift, necessitating tailored modeling approaches for different samples.

Conclusion

García-Moreno and Chaves-Montero provide the first systematic quantification of galaxy assembly bias across the primary galaxy populations relevant to modern cosmology using the IllustrisTNG simulation. They establish that GAB is a complex, multi-factor phenomenon driven by the interplay of halo assembly bias and occupancy variation, capable of altering clustering measurements by up to 25%. They conclude that robust cosmological inference requires models that account for this complexity, for which they provide a validated, fast analytical framework.