MGDStars

A Python package for Minimal Geometrical Deformation (MGD) compact star calculations in modified gravity theories.

🌟 Features

• Multiple seed models: TolmanIV, HeintzmannIIa, WymanIIa
• Robust numerical solver with adaptive initial guess strategies
• Comprehensive physical property evaluation: density, pressure, anisotropy profiles
• Model performance comparison and convergence diagnostics
• Professional visualization tools for stellar structure analysis

🚀 Quick Start

Installation

pip install mgdstars

Basic Usage

from mgdstars import MGDStars
import numpy as np

# Create MGD star solver
star = MGDStars(alpha=0.1, seed_model='TolmanIV')

# Solve for a neutron star configuration
result = star.solve_star_configuration(M_val=1.4, R_val=12.0)

if result['success']:
    print(f"Solution found!")
    print(f"A0 = {result['A0']:.4f}")
    print(f"B0 = {result['B0']:.6f}")
    print(f"C0 = {result['C0']:.4f}")
    
    # Evaluate physical properties
    r_range = np.linspace(0.1, 11.9, 100)
    properties = star.evaluate_at_radius(r_range)
    
    print(f"Central density: {properties['rho'][0]:.4f}")
    print(f"Central pressure: {properties['pr'][0]:.4f}")

Advanced: Model Comparison

# Compare different seed models
models = ['TolmanIV', 'HeintzmannIIa', 'WymanIIa']
results = {}

for model in models:
    star = MGDStars(alpha=0.01, seed_model=model)  # Note: smaller alpha for some models
    result = star.solve_star_configuration(M_val=1.4, R_val=12.0)
    results[model] = result
    
    if result['success']:
        print(f"{model}: SUCCESS (residual: {result['residual']:.2e})")
    else:
        print(f"{model}: FAILED")

📊 Seed Models

Model	Metric Structure	Recommended α Range	Best For
TolmanIV	e^ν = B₀²(r²/A₀² + 1)	0.005 - 0.15	General use, robust convergence
HeintzmannIIa	e^ν = A₀²(B₀r² + 1)³	0.001 - 0.02	Alternative parameterization
WymanIIa	e^ν = (A₀ - B₀r²)²	0.001 - 0.008	Specialized applications

🔬 Examples

Check the examples/ directory for comprehensive notebooks:

• mgd_seed_models_comparison.ipynb: Systematic comparison of all seed models
• neutron_star_mgd_analysis_tolmaniv.ipynb: Detailed TolmanIV analysis

📖 API Reference

MGDStars Class

Constructor

MGDStars(alpha=0.1, k2_factor=8*np.pi, seed_model='TolmanIV')

Key Methods

• solve_star_configuration(M_val, R_val, **kwargs): Solve for stellar configuration
• evaluate_at_radius(r_vals): Calculate physical properties at given radii
• diagnose_convergence_failure(M_val, R_val): Debug convergence issues

🤝 Contributing

1. Fork the repository
2. Create a feature branch
3. Add tests for new functionality
4. Submit a pull request

📄 License

MIT License - see LICENSE file for details.

📧 Contact

Mariannly Marquez
📧 mariannly.marquez@yachaytech.edu.ec
🏫 Yachay Tech University

🙏 Citation

If you use MGDStars in your research, please cite:

@software{mgdstars2024,
  author = {Marquez, Mariannly},
  title = {MGDStars: Minimal Geometrical Deformation compact star calculations},
  year = {2024},
  url = {https://github.com/mariannly/mgdstars}
}