Assembly bias and the redshift evolution of intrinsic alignments for LRGs

Technical Summary: Assembly bias and the redshift evolution of intrinsic alignments for LRGs

Problem Statement
Intrinsic alignments (IA) of galaxies constitute a primary astrophysical systematic contaminant in weak gravitational lensing surveys, capable of biasing cosmological parameter inference if not correctly modeled. Current modeling efforts, such as the Non-Linear Alignment (NLA) model, often assume that the alignment amplitude depends solely on halo mass. However, with the advent of high-statistics surveys like Euclid and LSST, secondary dependencies previously hidden by observational uncertainties may become significant. Specifically, the impact of assembly bias—the dependence of halo properties on formation history beyond mass—and the redshift evolution of the alignment signal require investigation using large-scale hydrodynamic simulations to ensure robust modeling for future cosmic shear analyses.

Methodology
The authors utilize the 2.8 Gpc box-size run of the FLAMINGO suite of cosmological hydrodynamic simulations (Schaye et al. 2023), which includes baryonic physics and a fiducial feedback variation. The study focuses on a sample of Luminous Red Galaxy (LRG)-like central galaxies, defined by haloes with a bound dark matter mass $M_h > 10^{12} M_\odot$ and galaxies with more than 300 stellar particles ($\sim 2.22 \times 10^{11} M_\odot$).

Key methodological steps include:

1. Formation Redshift Definition: The formation redshift ($z_f$) is defined as the redshift at which a halo contained half of its present-day mass ($0.5 M_{200\text{mean}}$). This definition is validated by its strong correlation with halo concentration ($c_{200\text{crit}}$).
2. Correlation Estimation: Position-position ($gg$) and position-shape ($g+$) correlation functions are computed using generalized Landy-Szalay estimators and modeled using the IATheory code with the NLA framework.
3. Assembly Bias Analysis: The sample is binned by halo mass and formation redshift to isolate the dependence of the alignment amplitude ($A_1$) on $z_f$ at fixed mass.
4. Redshift Evolution Modeling: The authors fit a power-law relation between alignment amplitude and halo mass ($A_1 \propto M^{\beta_M}$) across different simulation snapshots ($z=0$ to $z=1.5$).
5. Galaxy Tracking: To disentangle redshift evolution from simple mass growth, central galaxies are tracked across snapshots using the Track_id from the HBT-HERONS subhalo finder. The sample is selected at an initial redshift ($z_i$) and followed to $z=0$, with objects removed if they merge or fall below the stellar particle threshold.

Key Results

• Assembly Bias Dependence: The alignment amplitude depends not only on halo mass but also on formation redshift. At a fixed halo mass, haloes and their central galaxies that formed earlier (higher $z_f$) exhibit a systematically higher alignment amplitude. This effect manifests as a vertical shift in the $A_1$–mass relation, while the power-law slope remains largely unchanged.
• Redshift Evolution of Parameters: The amplitude of the mass-alignment power-law ($\alpha_M$) increases steadily with redshift. The slope ($\beta_M$) decreases with redshift until $z \sim 1$ and then flattens. The authors provide empirical quadratic fits for $\alpha_M(z)$ and $\beta_M(z)$ (Eqs. 13 and 14).
• Mass-Redshift Model: A combined mass-redshift model is proposed (Eqs. 12–14) to predict alignment amplitudes for LRG samples given their redshift and mean halo mass.
• Tracking Analysis: When tracking galaxies from high initial redshifts ($z_i$), the alignment amplitude increases as redshift decreases, consistent with mass accretion. However, even after normalizing by the mass-redshift model prediction, a systematic offset remains: galaxies tracked from higher $z_i$ retain a higher alignment amplitude than those tracked from lower $z_i$. This confirms that assembly bias introduces an irreducible scatter in the alignment amplitude at a given mass and redshift.
• Power-Law Deviations: The power-law fit deviates at low masses ($< 10^{13} M_\odot$) and high masses ($> 3 \times 10^{14} M_\odot$). At low masses, the authors observe a decrease relative to the power-law (contrasting with some gravity-only results), while at high masses, a decrease is observed, attributed to ongoing halo formation.

Significance and Claims
The paper claims that IA modeling in weak lensing surveys cannot rely on arbitrarily small prior ranges for the alignment amplitude, as assembly bias introduces a fundamental spread in amplitude at fixed halo mass. While the functional form of existing models (like NLA) may not require modification to account for assembly bias, the prior constraints on the amplitude parameter must be widened to accommodate this secondary dependence.

Furthermore, the results complicate the implementation of Halo Occupation Distribution (HOD) based alignment models for gravity-only simulations. Since HOD models typically assign properties based solely on mass, they fail to capture the formation-time dependence unless explicitly incorporated. The study provides simulation-based guidelines for a redshift evolution model of IA, offering empirical fits for the mass-redshift dependence of the alignment amplitude for LRG-like samples.

Limitations
The authors note that the resolution of the FLAMINGO simulation is insufficient to resolve the evolution of galaxy disks (the disk fraction remains $<1\%$ out to $z \sim 1.5$). Consequently, the results strictly apply to pure LRG samples (ellipticals) and do not account for the evolution of ellipticals into disks or the alignment signals of disk galaxies. The mass-redshift model is valid for halo masses between $10^{13}$ and $10^{14.5} M_\odot$ and redshifts up to $z \sim 1.5$.