Simple Harmonic Oscillator Celerite Kernels for Stellar Granulation and Oscillations

This is the documentation for shocksgo. The goal of shocksgo is to generate light curves of stars accounting for the effects of granulation, super-granulation and p-mode oscillations.

You can view the source code and/or contribute to shocksgo via GitHub.



We compute these light curves efficiently by taking advantage of celerite, a fast Gaussian process regression package, which we use to approximate solar and stellar power spectrum densities with sums of simple harmonic oscillator (SHO) kernels of the form:

\[S(\omega) = \sqrt{\frac{2}{\pi}} \frac{S_0\,\omega_0^4} {(\omega^2-{\omega_0}^2)^2 + {\omega_0}^2\,\omega^2/Q^2}\]

where \(\omega = 2\pi f\) is the angular frequency. We use one SHO kernel term for super/meso-granulation, another for ordinary granulation, and about 50 terms for the comb of p-mode peaks.

Scaling relations for p-modes

For computation of stellar p-mode oscillation frequencies, we use the scaling relations found in Huber et al. (2012) and references therein (e.g. Kjeldsen & Bedding 1995 ), namely Equation 4:

\[\nu_\textrm{max} \propto M R^{-2} T_{\rm eff}^{-1/2},\]

and Equation 3

\[\Delta \nu_\textrm{max} \propto M^{1/2} R^{-3/2}.\]

The amplitude scaling of the p-mode oscillations is given by Equation 9 of Huber et al. (2011):

\[A \propto \frac{L^s}{M^t T_\textrm{eff}^{r-1} c(T_\textrm{eff})}\]

where \(r = 2\), \(s = 0.886\), \(t = 1.89\) and

\[c(T_\textrm{eff}) = \left( \frac{T_\textrm{eff}}{5934 \textrm{K}} \right)^{0.8}.\]

Scaling relations for granulation

For computation of large and small scale stellar surface granulation frequencies, we use the scaling relation found in Kallinger et al. (2014):

\[\tau_\textrm{eff} \propto \nu^{-0.89}_\textrm{max},\]

where \(\tau_\textrm{eff}\) is the characteristic granulation timescale. The amplitudes of granulation scale as

\[a \propto \nu^{-2}_\textrm{max}.\]

(Kjeldsen & Bedding, 2011).