Hydrangea Cosmological Hydrodynamic Simulations

• Hydrangea simulations are high-resolution zoom-in hydrodynamic models that capture galaxy formation and environmental impacts in massive clusters.
• They employ state-of-the-art subgrid physics including radiative cooling, star formation, and AGN feedback to reproduce observed galaxy and halo scaling relations.
• Key results indicate overmassive BCGs, enhanced satellite quenching, and measurable intra-cluster light fractions that act as dynamical clocks for cluster evolution.

The Hydrangea cosmological hydrodynamic simulations are a suite of high-resolution, large-volume “zoom-in” simulations targeting the physics of galaxy formation in and around massive galaxy clusters (halo masses $M_{200c} \sim 10^{14} - 10^{15}~M_\odot$), forming a key component of the Cluster-EAGLE (C-EAGLE) project. Hydrangea is specifically designed to quantify the environmental impact on galaxy populations, baryonic mass assembly, and the structural evolution of (sub-)haloes within dense cluster ecosystems. The simulations exploit advanced subgrid models for baryonic processes and achieve sufficient spatial and mass resolution to resolve galaxies down to $M_\star \sim 10^9~M_\odot$ within cluster and surrounding volumes extending out to $5-10~r_{200c}$.

1. Simulation Design and Physical Modeling

The Hydrangea simulations employ a modified version of the EAGLE (Evolution and Assembly of GaLaxies and their Environments) codebase, upgraded with the “Anarchy” hydrodynamics module, which implements modern SPH improvements, and state-of-the-art subgrid physics. Each of the 24 canonical zoom-in volumes tracks a galaxy cluster and its environment, with a baryonic (gas) particle mass of $m_b \approx 1.81 \times 10^6~M_\odot$, allowing robust sampling of the cluster satellite galaxy population and their progenitors out to at least $10~r_{200c}$ (with some auxiliary runs out to $5~r_{200c}$).

Subgrid Physics

• Radiative Cooling and Photoheating: Employed on an element-by-element basis, including photoionization/heating from a UV/X-ray background.
• Star Formation Prescription: Gas particles above a metallicity-dependent density threshold follow a pressure law,

$$\dot{m}_\mathrm{star} = m_g A \left(1\,M_\odot\,\mathrm{pc}^{-2}\right)^{-n} \left( \frac{\gamma}{G} P \right)^{\frac{n-1}{2}},$$

where $m_g$ is the gas mass, $A$ and $n$ are parameters calibrated to observations, $P$ is the pressure, $\gamma=5/3$, and $G$ is the gravitational constant. The threshold is

$$n_\mathrm{H}^*(Z) = 10^{-1}\,\mathrm{cm}^{-3} \left(\frac{Z}{0.002}\right)^{-0.64},$$

accounting for the transition from atomic to molecular gas.

• Stellar Evolution/Enrichment: Modeled with mass- and metallicity-dependent yields, enriching the surrounding ISM.
• Feedback: Energy and momentum feedback from SN and supermassive black holes (SMBHs) are included.
• SMBH Accretion and AGN Feedback: Bondi-Hoyle accretion with an angular momentum limiter,

$$\dot{m}_\mathrm{accr} = \dot{m}_\mathrm{Bondi} \times \min\left(C_\mathrm{visc}^{-1} \left(\frac{c_s}{V_\phi}\right)^3, 1 \right),$$

with $c_s$ the sound speed and $V_\phi$ the rotational velocity of the gas.

2. Environmental Effects on Galaxy and Sub-Halo Populations

Hydrangea is designed to capture the distinct environmental influences of galaxy clusters on the galaxy population. Several key findings emerge from comparison with observations and field-only simulations:

• Total Stellar Mass of clusters is reproduced within observed scaling relations; normalization and slope agree within $1\,\sigma$ uncertainties across $0 < z < 1.5$ (Ahad et al., 2020).
• Brightest Cluster Galaxies (BCGs) are systematically overmassive, by 0.2–0.6 dex, compared to observed BCGs measured within 50 pkpc (Bahé et al., 2017, Ahad et al., 2020).
• Passive Fraction among satellite galaxies is higher than in the field (especially for $M_\star > 10^{10}~M_\odot$), broadly consistent with observations, but at low masses ($M_\star \lesssim 10^{10}~M_\odot$), satellites may be over-quenched (Bahé et al., 2017).
• Stellar Mass Function (SMF): Satellites’ SMF in clusters matches local surveys down to $M_\star \sim 10^{10.5}~M_\odot$; at $z \gtrsim 1$, an overabundance (up to factor two) of low-mass satellites is noted (Ahad et al., 2020).
• Radial Distribution: Simulated satellite NFW concentrations increase with redshift, in contrast to decreasing dark matter (DM) concentrations. At low $z$, satellite concentrations are %%%%24$5-10~r_{200c}$25%%%% higher than observed, with clusters often showing excess satellites in the inner regions and a deficit in the outskirts (Ahad et al., 2020).

3. Galaxy–Halo Connection and Assembly Bias

Hydrangea directly explores how the cluster environment modifies the relationship between galaxies and their DM haloes:

• Halo Concentration and Stellar Mass: Cluster-associated haloes are more concentrated (up to 15% at small cluster-centric radii) relative to counterparts in the field. However, when matching on both halo mass and concentration, cluster galaxies still exhibit an elevated stellar mass fraction by up to $\sim$0.3 dex (Bahé et al., 2017).
• Environmental Assembly Bias: The excess of stellar mass (especially in massive galaxies and halo outskirts) reflects an enhanced conversion of baryons into stars in high-density environments (e.g., cosmic web filaments feeding clusters) during epochs such as $z\sim2$.

4. Dynamical Indicators: Intra-Cluster Light as a Clock

The Hydrangea suite, in conjunction with other simulation projects (Kimmig et al., 26 Mar 2025), demonstrates that the fraction of stellar mass found in the BCG and intra-cluster light (ICL),

$f_{ICL+BCG} = \frac{M_{*,ICL+BCG}}{M_{*,tot}},$

is an effective quantitative “dynamical clock” for cluster evolution. Clusters with early mass assembly histories (a higher formation redshift, $z_f$) display $f_{ICL+BCG}$ values reaching $90\%$, indicative of extensive dynamical processing via mergers and satellite disruption; recently assembling or disturbed clusters can have values as low as $20\%$. The rate of increase in $f_{ICL+BCG}$ is robust, at $3$–$4\%$ per Gyr, and independent of subgrid physics variations. Tight correlations between $f_{ICL+BCG}$ and stellar mass ratios (such as BCG to second- or fourth-most massive galaxy, $M_{12}$, $M_{14}$) provide practical proxies for observers to estimate dynamical state (Kimmig et al., 26 Mar 2025).

Cluster State	$f_{ICL+BCG}$ (typical)	Evolutionary Implication
Relaxed, old clusters	up to 90%	Early formation, stripped satellites
Disturbed, recent accretion	$\sim$20%	Recent mergers, many bound satellites

5. Structural and Stellar Population Properties

Hydrangea reproduces many observed scaling relations but exhibits systematic discrepancies:

• Size–Mass Relation: Simulated galaxies, including those in Hydrangea, are $42\%$ larger in $R_e$ than observed (SAMI, CALIFA, ATLAS$^{3D}$ samples) (Sande et al., 2018).
• Ellipticity and Disk Structure: Simulated galaxies are systematically rounder (lower median ellipticity) and rarely match the highest-ellipticity class (i.e., very thin disks), attributed in part to the ISM temperature floor ($\sim8,000$~K), which prevents formation of thin disks (Sande et al., 2018).
• Velocity Dispersion: Aperture velocity dispersions ($\sigma_e$) are lower than observed, but this is partly mitigated in dynamical mass estimates when combined with larger $R_e$ (Sande et al., 2018).
• Stellar Ages: Mean luminosity-weighted stellar ages are systematically older than observed, suggesting differences in the simulated star formation history or over-quenching in dense environments (Sande et al., 2018).

6. Model Calibration, Limitations, and Future Directions

The Hydrangea simulations use subgrid models calibrated primarily on field galaxy observations (EAGLE), with cluster applications revealing both successes and limitations:

• Over-massive BCGs and Satellite Excess in Cluster Centers: Point to a possible need for more effective AGN and/or SN feedback, or more realistic descriptions of tidal stripping and satellite disruption at the cluster core.
• Over-abundance of Low-mass Satellites at $z\gtrsim1$: Suggests that the modeling of feedback or satellite destroying processes may be too weak for faint galaxies, possibly requiring adjustments to feedback efficiency, tidal stripping implementation, or star formation thresholds.
• Satellites’ Radial Density Profile: The excess of satellites in cluster cores at $z<0.3$ implies further improvement is needed in satellite disruption modeling or perhaps selection biases in the sample (Ahad et al., 2020).
• Comparison to Other Suites: Key trends—including $f_{ICL+BCG}$ behavior and satellite assembly—are robust against the choice of simulation code or details of baryonic physics when compared to Magneticum, IllustrisTNG, and Horizon-AGN (Kimmig et al., 26 Mar 2025).

7. Broader Impact and Observational Applications

Hydrangea provides benchmark predictions for cluster environments that inform the interpretation of current and upcoming deep surveys (e.g., Euclid, LSST, Roman Space Telescope):

• Cluster Stellar Content and Scaling Relations: The ability to match observed total stellar masses and morphological trends validates Hydrangea’s use for calibrating stellar mass–halo mass scaling relations in clusters.
• Dynamical State Determinations: The predictive power of $f_{ICL+BCG}$ (and its proxies, like $M_{12}$ and $M_{14}$) offers a route for surveys to statistically dissect cluster assembly histories even as direct measurements of the faint ICL remain observationally expensive.
• Testing Subgrid Physics: The discrepancies at low masses or cluster centers provide constraints for improving subgrid models (star formation, feedback, stripping, quenching) in future simulation efforts.

In summary, the Hydrangea cosmological hydrodynamic simulations constitute a reference dataset for understanding galaxy and cluster evolution in dense environments. They combine high-resolution baryonic modeling with large cosmic volumes, directly confronting a wide array of observations. Key successes include realistic total stellar content, environmental differentiation of galaxy properties and mass functions, and the demonstration that diffuse stellar mass fractions—such as $f_{ICL+BCG}$—serve as sensitive, physically interpretable tracers of cluster assembly. Remaining challenges, specifically in satellite abundance and structure within cluster centers, motivate future improvements in cluster-centric feedback and satellite-processing physics. These results are robustly supported by cross-comparisons with other major hydrodynamic simulation projects (Bahé et al., 2017, Sande et al., 2018, Ahad et al., 2020, Kimmig et al., 26 Mar 2025).