AstroTurbulence 🌌

Advanced toolkit for simulating and analyzing turbulent polarization in astrophysical environments

Simulate Kolmogorov turbulence, generate polarization maps, analyze Faraday rotation, and compute structure functions for astrophysical research.

✨ Features

🌪️ Turbulence Simulation

• Kolmogorov Power Spectrum: Generate realistic 3D turbulent velocity fields
• Solenoidal & Compressive: Support for both solenoidal and non-solenoidal turbulence
• Configurable Resolution: From 256³ to 512³ grid points and beyond
• Helmholtz Decomposition: Advanced vector field decomposition

📡 Polarization Analysis

• Stokes Parameters: Full I, Q, U parameter computation
• Synchrotron Emission: Realistic synchrotron polarization modeling
• Dust Polarization: Dust-based polarization prescriptions
• Faraday Rotation: Screen effects and rotation measure analysis

📊 Statistical Tools

• Structure Functions: Angular structure function computation D_φ(R)
• Power Law Analysis: Automated slope fitting and validation
• PDF Analysis: Single-point and two-point probability distributions
• Correlation Analysis: Spatial correlation characterization

🎯 Research Applications

• Interstellar Medium studies
• Magnetohydrodynamic turbulence analysis
• Cosmic ray propagation modeling
• Radio astronomy data interpretation

🚀 Quick Start

Installation

git clone https://github.com/astrosander/AstroTurbulence.git
cd AstroTurbulence
pip install -r requirements.txt

Basic Usage

Generate Turbulent Velocity Field

from turbulence_angles.turbulence_angles_full import generate_velocity_cube

# Generate 256³ solenoidal velocity field
u = generate_velocity_cube(N=256, solenoidal=True, seed=42)
print(f"Generated velocity cube: {u.shape}")

Compute Polarization Maps

# Synchrotron polarization
Q_syn = np.sum(u[:,:,:,0]**2 - u[:,:,:,1]**2, axis=2)
U_syn = np.sum(2 * u[:,:,:,0] * u[:,:,:,1], axis=2)
phi_syn = 0.5 * np.arctan2(U_syn, Q_syn)

Structure Function Analysis

from check_power_law import structure_function_2d

Rs = np.logspace(0, 2, 20).astype(int)
R_vals, D_phi = structure_function_2d(phi_syn, Rs)

# Should recover ~R^(5/3) Kolmogorov scaling

📁 Project Structure

AstroTurbulence/
├── 🌪️ turbulence_angles/          # Core turbulence simulation
│   ├── turbulence_angles_full.py   # Main simulation engine
│   ├── single_PDF_vector.py        # Statistical analysis
│   └── figures/                    # Generated plots
├── 📡 faradays_angles_stats/       # Faraday rotation analysis
│   ├── faraday_screen_demo.py     # Faraday screen modeling
│   └── lp_structure_tests/         # Linear polarization tests
├── 📊 stokesMaps_velocity_kolmogorov_NoNorm/  # Stokes parameter maps
│   ├── read_and_plot.py           # Visualization tools
│   └── check_power_law.py         # Power law validation
├── ⚡ spectrum_generation/         # Power spectrum analysis
└── 🧮 check_integration_factors/  # Numerical validation

📈 Example Results

Polarization Structure Functions

The toolkit reproduces the expected Kolmogorov R^(5/3) scaling for turbulent polarization:

# Expected output:
# Stokes azimuth slope: 1.67 ± 0.05
# Vector azimuth slope: 1.65 ± 0.04

Faraday Rotation Analysis

Analyze how magnetic field turbulence affects polarization:

python faradays_angles_stats/faraday_screen_demo.py

🔬 Scientific Applications

This toolkit has been used for research in:

• Interstellar Turbulence: Characterizing magnetohydrodynamic turbulence in the ISM
• Pulsar Studies: Understanding scintillation and Faraday rotation effects
• Galaxy Formation: Modeling magnetic field evolution in cosmic structure
• Radio Astronomy: Interpreting polarization observations from SKA/LOFAR

📚 Documentation

Core Functions

Function	Description	Key Parameters
generate_velocity_cube()	Generate 3D turbulent velocity field	N, solenoidal, seed
structure_function_2d()	Compute angular structure function	field, Rs, max_pairs
angle_stokes()	Calculate Stokes polarization angle	u (velocity field)
sample_pairs_3d()	Sample vector angle differences	u, R, max_pairs

Mathematical Background

The toolkit implements several key astrophysical relations:

Synchrotron Polarization:

$$Q(x,y) = ∫ dz (v_x² - v_y²) U(x,y) = ∫ dz (2 v_x v_y)$$

Angular Structure Function:

$$D_φ(R) = ⟨[φ(r+R) - φ(r)]²⟩$$

Kolmogorov Spectrum:

$$E(k) ∝ k^{-5/3}$$

🛠️ Requirements

• Python 3.8+
• NumPy (≥1.19)
• SciPy (≥1.6)
• Matplotlib (≥3.3)
• h5py (≥3.0)
• numba (≥0.54) - for performance
• Fortran compiler (for I/O routines)

🤝 Contributing

We welcome contributions! See our Contributing Guide for details.

Development Setup

git clone https://github.com/astrosander/AstroTurbulence.git
cd AstroTurbulence
pip install -e .
pre-commit install

📜 License

This project is licensed under the MIT License - see the LICENSE file for details.

📖 Citation

If you use this toolkit in your research, please cite:

@software{astroturbulence2024,
  title={AstroTurbulence: Advanced Toolkit for Astrophysical Turbulence Analysis},
  author={Aliaksandr Melnichenka},
  year={2024},
  url={https://github.com/astrosander/AstroTurbulence}
}

🌟 Acknowledgments

• Built for the astrophysics and plasma physics communities
• Inspired by modern magnetohydrodynamic turbulence research
• Optimized for high-performance scientific computing

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