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spotgp: Gaussian Process kernels for stellar starspot variability implemented in JAX.

Installation

git clone https://github.com/jbirky/spotgp.git
cd spotgp
pip install -e .

For JAX acceleration:

pip install -e ".[jax]"

Development

This project is build and maintained by Jess Birky–keep an eye out for the paper (coming soon). If you are interested in contributing, feel free to reach out or make a pull request!

Documentation Contents

Basics

• Home
• Time Domain
  • 1. Envelope Model \(\Gamma(t)\): spot growth and decay
  • 2. Visibility Function \(\Pi(t)\): rotational modulation
  • 3. Putting the Envelope and Visibility Components Together
• Fourier Domain
  • 1. Envelope Spectrum \(|\hat{\Gamma}(\omega)|\): spot lifetime sets the peak width
  • 2. Rotation Harmonics \(c_n^2\): inclination shapes the harmonic amplitudes
  • 3. Full Analytic PSD: combining envelope spectrum and rotation harmonics
• Code Overview
  • Module architecture
  • Module descriptions
  • Data flow: fitting a lightcurve
  • Extending the library
• Lightcurve Animations
  • Build a SpotEvolutionModel
  • Simulate a lightcurve
  • Create an animation of the star rotation and lightcurve
• JAX JIT Compilation
  • 1. Inspect the envelope
  • 2. Build a SpotEvolutionModel
  • 3. Simulate a stellar lightcurve
  • 4. Warm up JAX with build_jax()
• GP Solver
  • 1. Model setup and lightcurve simulation
  • 2. Warm up JAX with build_jax()
  • 3. GP hyperparameter fit — MAP solution
  • 4. Multi-start MAP (optional)

Advanced

• Custom Envelope Functions
  • 1. Analytic equations for the Gaussian envelope
  • 2. Minimal implementation — Gamma(t) only
  • 3. Add analytic Gamma_hat(omega)
  • 4. Add analytic R_Gamma(tlag)
  • 5. Build a SpotEvolutionModel with the Gaussian envelope
• Custom Visibility Functions
  • 1. The exact projected area
  • 2. Implementing a custom VisibilityFunction
  • 3. Visualize the projected area
  • 4. Compare Fourier coefficients \(|c_n|^2\)
  • 5. Divergence threshold: where does the approximation break down?
  • 6. Compare GP kernels
  • 7. Computation speed comparison
  • Summary
• Custom Latitude Distributions
  • 1. Default uniform distribution
  • 2. Equatorial band
  • 3. Gaussian-weighted distribution
  • 4. Polar band
  • 5. Kernel and lightcurve comparison
• MCMC Sampling with BlackJAX
  • 1. Build the spot model and simulate a lightcurve
  • 2. Find the MAP estimate
  • 3. Run NUTS warmup and sampling
  • 4. Diagnostics and posterior summary
  • 5. Resume sampling in batches
  • 6. Visualize the posterior
• Cramér-Rao Bound
  • 1. Simulate a Synthetic Lightcurve
  • 2. Compute the Fisher Information Matrix
  • 3. Visualizing the CRB
  • 4. Dependence on Noise Level and Observation Baseline
  • Summary

API Reference

• API Reference (src)
  • Lightcurve Model
  • Analytic Kernel
  • Numerical Kernel
  • GP Solver
  • Power Spectral Density
  • MCMC Sampler