Axion Superradiance: Black Hole Evolution & Constraints

A computational framework for modeling axion superradiance in rotating black holes and constraining axion physics using multi-messenger astrophysical observations.

Key Physics

Superradiance is an instability where bosonic fields (like axions) extract rotational energy from spinning black holes, causing the black hole to spin down while the axion cloud grows exponentially. This project:

• Computes the eigenvalues of quasi-bound states, and the rate of energy transfer induced by self-interactions
• Simulates black hole mass and spin evolution
• Compares predictions against observed black hole populations (stellar binaries, AGN, gravitational wave sources)
• Derives constraints on axion mass and coupling strength

Project Structure

src/
├── Core Physics Computation
│   ├── solve_sr_rates.jl          # Primary rate calculation engine
│   ├── heunc.jl                   # Heun equation solver (used in radial wave function solutions)
│   ├── super_rad.jl               # Black hole evolution dynamics
│   └── Constants.jl               # Physical constants & utilities
│
├── Rate Computation & Storage
│   ├── Compute_all_rates.jl       # CLI for computing transition rates
│   ├── load_rates.jl              # Load pre-computed rate tables for evaluation during evolution
│   └── rate_sve/                  # Pre-computed rate files [must be pre-computed!]
│
├── Statistical Analysis & Inference
│   ├── MCMC.jl                    # Affine-invariant MCMC sampler
│   ├── stat_analysis.jl           # Likelihood & statistical functions
│   ├── stat_1dL.jl                # 1D likelihood analysis
│   └── output_mcmc/               # MCMC chains and posterior output
│
├── Gravitational Wave Analysis
│   ├── Ligo_limit.jl              # GW event constraint derivation
│   ├── Ligo_1dL.jl                # 1D GW likelihood analysis
│   └── Ligo_1dL_cosma.jl          # HPC-optimized version
│
├── Auxiliary Computation
│   ├── grid_sr_growth.jl          # Superradiance growth grids
│   ├── spin_down_plot_files.jl    # Spin evolution visualization data
│   ├── Make_Regge_Plt_data.jl     # Regge diagram generation
│   ├── binary_mixing_test.jl      # Quantum level mixing validation
│   └── tde_input.jl               # Tidal disruption event modeling
│
├── Utilities & Testing
│   ├── install_pkgs.jl            # Dependency installation
│   ├── test_sr_rates.jl           # Unit tests
│   └── estimate_lim.jl            # Quick limit estimation
│
├── Data & Results
│   ├── BH_data/                   # Astrophysical black hole parameters
│   ├── stored_limits/             # Compiled constraint results
│   └── plts/                      # Jupyter notebooks & visualizations
│
└── Python Utilities
    ├── Print_all_levels.py        # Generate valid quantum transitions [useful for identifying relevant scattering permutations]
    ├── latex_line_gen.py          # LaTeX output generation [for writing papers]
    ├── Run_Ligo.py                # GW data processing
    └── Combine_data.py            # Data combination utilities

Main Components

1. Quantum Superradiance Physics (solve_sr_rates.jl, heunc.jl)

Computes superradiant transition rates for axion-black hole systems:

• Quantum states: |nlm⟩ representation (principal, orbital, azimuthal quantum numbers)
• Transition modes: Spontaneous emission to lower quantum levels
• Three-body processes: Axion-axion scattering enabling higher-level excitations
• Numerical solvers: Leaver eigenvalue method + Heun ODE solver for solving Teukolsky equations in Kerr spacetime
• Supported regime: Up to Nmax=8 principal quantum levels, axion coupling α from 10⁻⁴ to 10⁻¹

2. Black Hole Evolution Dynamics (super_rad.jl)

Models coupled evolution of black hole properties under axion extraction:

• Coupled ODE system: Tracks M(t), a(t), and axion cloud populations simultaneously
• Physical processes:
  • Superradiant growth (exponential amplification phase)
  • Nonlinear saturation via level mixing
  • Angular momentum extraction (spin-down)
  • Mass loss via gravitational wave emission
• Time integration: Adaptive Runge-Kutta with automatic differentiation support
• Evolution scales: up to 10⁸ years of black hole lifetime

3. Statistical Inference (MCMC.jl, stat_analysis.jl)

Bayesian parameter estimation to constrain axion properties:

• Observable constraints:
  • LIGO gravitational wave spin measurements
  • Stellar binary black hole mass/spin (Cygnus X-1, GRS 1915+105, etc.)
  • AGN supermassive black hole spins
  • Tidal disruption event timescales
• MCMC method: Affine-invariant ensemble sampler with 10+ parallel chains
• Parameters: Axion mass (m_a), axion decay constant (f_a)
• Output: Posterior distributions, 95% confidence intervals, exclusion regions

4. Pre-Computed Rate Tables (rate_sve/)

Extensive database of pre-calculated transition rates:

• 740+ rate files spanning parameter space (axion coupling, black hole spin)
• File format: n1l1m1_n2l2m2_n3l3m3_Destination.dat (nlm indices + GW destination)
• Companion data: Imaginary eigenfrequency data (.npz format) for growth rate calculations
• Destinations: "BH" (energy stays near black hole) or "Inf" (radiates to infinity)

5. Astrophysical Data (BH_data/)

Real black hole observations:

• Stellar-mass: Cygnus X-1, GRS 1915+105, M33 X-7, LMC X-3
• Gravitational waves: GW231123, LIGO test events
• Tidal disruption events: Star-black hole encounters
• Parameters: Mass, spin, age, chirp mass, orbital period

Core Workflow

Input: Black hole parameters (M, a, age)
   ↓
Compute transition rates (or load from pre-computed tables)
   ↓
Simulate BH + axion cloud evolution over time
   ↓
Compare final predicted spin vs. observed spin
   ↓
MCMC: Sample (m_a, f_a) parameter space
   ↓
Derive posterior distributions & exclusion limits

Usage

Dependencies

• Julia (v1.7+)

  • DifferentialEquations.jl (ODE solving)
  • SpecialFunctions.jl (Hypergeometric, spheroidal functions)
  • Distributions.jl (Statistical distributions)
  • StatsBase.jl (MCMC diagnostics)
  • ForwardDiff.jl (Automatic differentiation)
  • HDF5.jl, NPZ.jl (Data I/O)

• Python (v3.7+)

  • numpy, scipy (numerical computation)
  • matplotlib, seaborn (visualization)

Install Julia dependencies:

julia install_pkgs.jl

Output & Results

MCMC Results (output_mcmc/)

• MCMC chains (samples from posterior distribution)
• KDE probability density estimates
• Marginalized 1D/2D posterior distributions
• Constraint contours for publication

Computed Rates (rate_sve/)

• Precomputed transition rate databases
• Eigenfrequency tables
• Interpolation data for efficient simulation

Constraints (stored_limits/)

• Compiled axion mass limits
• 95% confidence intervals
• Multi-messenger constraint compilation

Last Updated: November 2025