# 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.

## Documentation¶

## Overview¶

### Methods¶

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:

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:

and Equation 3

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

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

#### 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):

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