Red Giant Power Spectra

Implements helper methods to generate synthetic power spectrum envelopes without white noise or activity similar to de Assis Peralta et al. 2018 Equation (9).

\[\mathrm{PSD}(\nu) = \eta^2(\nu) \left[ \frac{P}{1 + \left(2 \pi \tau \nu \right)^\alpha} + H \exp \left( \frac{-(\nu - \nu_\mathrm{max})^2} {0.66 \nu_\mathrm{max}^{0.88} /4 \ln 2} \right) \right]\]

The whole equation is implemented in PSD(), and individual components are implemented as follows:

• The damping factor, \(\eta^2(\nu)\) is implemented in damping()

• The granulation background, the first term in the brackets, is implemented in granulation()

• The signal excess envelope, the second term in the brackets, is implemented in excess().

This submodule also implements simple scaling relations for \(\nu_\mathrm{max}\), the frequency at maximum power, and \(\Delta \nu\), the large frequency separation in nu_max() and delta_nu() respectively.

grannules.utils.psd.PSD(nu, nu_max, H, P, tau, alpha, reshape=True)

Parameters:

reshape (bool) – Reshapes nu into a “row” array of shape (1, len(nu)) and the other input parameters into “column” arrays of shape (len(arg), 1) such that the output is a 2D array where the ijth element corresponds to power of the ith star at the jth frequency. Defaults to True.

grannules.utils.psd.damping(nu)

grannules.utils.psd.granulation(nu, P, tau, alpha)

grannules.utils.psd.excess(nu, nu_max, H)

grannules.utils.psd.nu_max(M, R, Teff, nu_max_solar=3090, Teff_solar=5777)

grannules.utils.psd.delta_nu(M, R, delta_nu_solar=135.1)