BRAHMA: Cosmological Hydrodynamic Simulations

• BRAHMA is a cosmological hydrodynamic simulation suite that employs advanced moving-mesh techniques to study black hole seeding, growth, and feedback across cosmic time.
• It features dual seeding models—light direct gas-based and heavy DCBH paradigms—that enable systematic comparisons of black hole formation pathways and their observable signatures.
• Leveraging the AREPO code with full MHD and sophisticated subgrid physics, BRAHMA generates predictions for AGN luminosity functions, gravitational wave merger rates, and local dwarf galaxy black hole populations.

The BRAHMA (Black hole seeding, Reionization And Hydrodynamics with MAchiNa) cosmological hydrodynamic simulation suite is a set of advanced moving-mesh simulations designed to probe the formation, early growth, and long-term legacy of black hole (BH) seeds across cosmic time. BRAHMA addresses principal uncertainties in massive black hole assembly by implementing physically motivated, high-resolution seeding schemes and tracking the influence of seed formation physics on black hole demographics from the epoch of reionization to the present day. Its unique two-tiered seeding approach enables systematic comparison of low-mass and heavy-seed channels, allowing robust predictions for observables tied to early BH populations, AGN luminosity functions, gravitational-wave merger rates, and signatures in local dwarf galaxies. The suite adopts the AREPO code with full magnetohydrodynamics (MHD), consistent IllustrisTNG subgrid physics, and a battery of novel treatments for BH dynamics and feedback.

1. Simulation Framework and Subgrid Physics

BRAHMA employs the moving-mesh MHD code AREPO, leveraging TreePM gravity and an unstructured Voronoi mesh for hydrodynamics. The default cosmology matches Planck 2015/2016 parameters (Ωm=0.3089, ΩΛ=0.6911, Ω_b=0.0486, H_0=67.74 km s^−1 Mpc^−1, σ_8=0.8159, n_s=0.9667).

Key simulation box configurations span a dynamic range from (4.5 Mpc)^3 to (36 Mpc)^3, with DM particle masses from 2.4×10^4 M_⊙ (high resolution) to 1.5×10^6 M_⊙ (large volume), and adaptive gas cell masses from ~10^3 M_⊙ to ~10^5 M_⊙. Gravitational softening scales as ε=0.09–0.72 kpc. Initial conditions are generated with MUSIC at z=127. Star formation follows an effective-equation-of-state multiphase ISM model with a threshold n_H > 0.1–0.15 cm^−3 and t_sf ≈ 2.2 Gyr. Stellar evolution tracks enrichment of H, He, and seven heavy elements, with feedback implemented as hydrodynamically decoupled galactic winds, tied to the local DM velocity dispersion.

AGN feedback is modeled via the IllustrisTNG two-mode prescription, distinguishing between high Eddington-ratio (thermal) and low Eddington-ratio (kinetic) modes. Radiative efficiency is set to ε_r = 0.2 with efficiency parameters ε_f,high=0.02 for thermal and ε_f,low≈0.2 for kinetic modes (Bhowmick et al., 2024, Bhowmick et al., 2024, LaChance et al., 15 Dec 2025).

2. Black Hole Seeding Models

BRAHMA implements two principal classes of seed formation:

• Direct Gas-Based Seeding (Low-Mass/Light Seeds): In high-resolution boxes (e.g., BRAHMA-9-D3), seeds of mass M_seed ≈ 2.2–2.3×10^3 M_⊙ are placed within halos when two criteria are met: (1) a threshold of dense, metal-poor gas (n_H > 0.13 cm^−3, Z<10^−4 Z_⊙, M_gas > 5–150 M_seed) and (2) a halo mass exceeding 10^3–10^4 M_seed (Bhowmick et al., 10 Jun 2025).
• Heavy Seed / Direct Collapse Black Hole (DCBH) Paradigm: In larger or lower-resolution boxes (e.g., BRAHMA-18, BRAHMA-36), M_seed~1.5×10^5 M_⊙ are planted under more restrictive criteria, successively adding:
  • presence of sufficient dense, metal-poor gas,
  • a local Lyman–Werner flux J_LW ≥ 10 J_21,
  • low gas spin (λ < λ_max, set by Toomre instability),
  • environmental richness (neighbor halo within 5 R_vir).
• Stochastic Extrapolated Seed Descendants (ESDs): To bridge resolution gaps, ESDs model higher-mass seeds (~10^4-10^5 M_⊙) as statistical descendants of calibrated low-mass seed populations, factoring in galaxy mass and local environment (Bhowmick et al., 2024, Bhowmick et al., 2024).

The ESD criterion samples galaxy masses from a redshift-dependent lognormal distribution determined by high-resolution runs and applies a seeding probability tied to neighboring galaxy properties.

3. Black Hole Growth, Dynamics, and Mergers

Black holes grow via Eddington-limited Bondi–Hoyle (or Bondi–Hoyle–Lyttleton) accretion:

$$\dot{M}_\mathrm{Bondi} = \alpha\,\frac{4\pi G^2 M_\mathrm{BH}^2 \rho}{(c_s^2 + v^2)^{3/2}},$$

with $\alpha = 1$ and capped at the Eddington rate ($$\dot{M}_\mathrm{Edd} = 4\pi G M_\mathrm{BH} m_p / (\epsilon_r \sigma_T c)$$).

AGN feedback is triggered according to the instantaneous Eddington ratio $\dot m = \dot M_\mathrm{BH} / \dot M_\mathrm{Edd}$, with the mode switching between thermal and kinetic injection. Repositioning ("pinning") places BHs near the local potential minimum of their gas cell kernel, ensuring centering but potentially overestimating merger efficiency.

Subgrid dynamical friction (DF)—following Ma et al. (2023)—applies a velocity-dependent drag, efficiently sinking BHs to the halo center on 50–1000 Myr timescales. Mergers can occur via several prescriptions: instant merging within kernel radii ("repositioning"), or, more realistically, when BH pairs approach within twice the softening length and are gravitationally bound. Under subgrid DF, merger delay times of 100–1000 Myr are typical after the host halos coalesce (Bhowmick et al., 10 Jun 2025).

Gas accretion is subdominant for low/intermediate-mass BHs (≲10^6 M_⊙) to z=0; mergers are overwhelmingly dominant at z>5 (Bhowmick et al., 2024, Bhowmick et al., 2024, Bhowmick et al., 10 Jun 2025).

4. Observable Predictions Across Cosmic Time

High-Redshift (z > 5) BH Demographics

Simulated BHs at z=7–11 are overmassive by factors 10–100 compared to local M_*–M_\mathrm{BH} scaling. Multiple seed models produce AGN luminosity functions varying by ≲2–3× near current/future X-ray detection limits (L_bol≳10^43 erg s^−1), implying that AGN LFs alone offer limited discriminatory power for seeding models (Bhowmick et al., 2024). Merger rates for BHs (M_1, M_2 > 2.3×10^3 M_⊙) peak at ~200–2000 yr^−1 at z ≈ 10–12, decreasing sharply for higher-mass events and stricter seeding criteria.

Heavy-seed prescriptions that impose strong environmental, radiative, and dynamical constraints severely reduce the abundance of overmassive high-z BHs. Only less restrictive (or merger/time-delay-optimized) models match the high-z M_*–M_\mathrm{BH} relation implied by JWST AGN; strict DCBH channels underproduce BH masses unless seed masses are increased beyond 10^5 M_⊙ or alternative formation/growth mechanisms invoke an additional contribution from lighter seeds or super-Eddington accretion is assumed (Bhowmick et al., 2024).

Local Universe Low-Mass Black Holes

Strong signatures of the initial BH seeding prescription persist in z=0 BHs with M_\mathrm{BH} ≈ 10^5–10^6 M_⊙ hosted in M_*≲10^9 M_⊙ galaxies. These include:

• a substantial relic population minimally grown since z≈5–10,
• steep model-dependent differences in low-mass BH mass functions,
• high occupation fractions (20–100%) of 10^6 M_⊙ BHs in dwarfs contingent on seed model.

Signatures of seeding are erased at higher BH masses (≳10^7 M_⊙), where gas accretion and AGN feedback dominate growth by z=0 (Bhowmick et al., 2024).

5. Black Hole Dynamics and Gravitational Wave Events

The mode of BH dynamical evolution—repositioning versus subgrid DF—critically affects predicted merger rates and the persistence of wandering BHs:

• Repositioning yields artificially prompt, high-rate (factor 4–10 higher) mergers, while subgrid DF introduces merger delays and allows realistic inspiral times.
• Under subgrid DF, high-z (z>5) merger rates are 100–1000 yr^−1 for BHs above the seed mass; rates fall off steeply with redshift and mass.
• The dominant mode of growth for 10^3–10^5 M_⊙ BHs at high z is merger-driven; less than 2% of their mass comes from gas accretion at z=5 in the most physically motivated runs.
• These rates imply hundreds of intermediate-mass BH mergers per year could be detectable by LISA, providing robust, model-sensitive gravitational-wave probes of seed physics (Bhowmick et al., 10 Jun 2025).

6. Synthetic Observables and Comparison to JWST Populations

BRAHMA's postprocessed spectral energy distributions, built using BPASS and CLOUDY, predict that overmassive, gas-enshrouded black holes (M_\mathrm{BH}/M_* ≈ 0.1) can account for the "little red dot" (LRD) population observed by JWST at z=5–8. Dense gas clouds create a pronounced Balmer break and suppress X-ray emission, explaining the characteristic near-infrared colors, compactness, and ALMA non-detections.

The simulated BRAHMA LRD number density, n_\mathrm{LRD}=(2.04 ± 0.32) × 10^−4 Mpc^−3, matches current JWST estimates; comparable simulations (e.g., ASTRID) with less efficient or later seeding underproduce this population by >100×. Brightest LRDs (L_bol≥10^45 erg s^−1) are rare in the current volumes, possibly due to cosmic variance or implementation details (LaChance et al., 15 Dec 2025).

7. Legacy, Implications, and Future Prospects

BRAHMA’s flexible approach demonstrates that seed physics imprints persist both in the early AGN population and in local low-mass BHs, especially in dwarf galaxies where occupation fractions and mass functions are sensitive to the underlying seeding channel. This suite establishes that:

• merger-driven growth is an inevitable outcome at high z for light and heavy seeds,
• AGN luminosity functions and scaling relations alone are insufficient to uniquely determine seed models at z>7,
• the redshift and mass evolution of the BH population, the demographics of LISA-detectable mergers, and the census of BH relics in dwarfs provide complementary multi-messenger avenues to constrain seeding physics.

Future extensions of the BRAHMA suite aim to include alternative subgrid accretion models, larger simulation volumes for better cosmic statistics at the massive end, and tighter connections to GW event catalogs as LISA and pulsar timing arrays come online. The combined approach of detailed seeding prescriptions, physically motivated dynamical treatments, and careful observable predictions provides a benchmark for the field and a platform for interpreting upcoming observations of the high-redshift and local black hole populations (Bhowmick et al., 2024, Bhowmick et al., 2024, Bhowmick et al., 10 Jun 2025, Bhowmick et al., 2024, LaChance et al., 15 Dec 2025).