Contents

persephone.kernels

The kernels submodule provides a set of function dedicated to compute 1- and 2D seismic kernels.

persephone.kernels.rotation

persephone.kernels.rotation.compute_general_kernel(r, rho, xi_r, xi_h, l=1, m=1, theta_res=90, unimodular=True, theta_0=0, theta_1=180)

Compute general 2D kernel term after Christensen-Dalsgaard’s Lecture Notes on Stellar Oscillations Eq. (8.31), (8.33), and (8.35).

Note that by default the kernel is normalised to be unimodular.

Parameters

  • r (ndarray) – Radial coordinates of the eigenfunctions.

  • rho (ndarray) – Radial density profile.

  • xi_r (ndarray) – Mode radial eigenfuction.

  • xi_h (ndarray) – Mode horizontal eigenfuction.

  • l (int) – Mode spherical degree. Optional, default 1.

  • m (int) – Mode azimuthal degree. Optional, default 1.

  • theta_res (int) – Number of grid point in the latitudinal direction.

  • unimodular (bool) – Whether to compute a unimodular kernel or not. Optional, default True.

  • theta_0 (float) – Minimal co-latitude on which to compute the kernel.

  • theta_1 (float) – Maximal co-latitude on which to compute the kernel.

Returns

A tuple of arrays with the 2D-radial grid coordinates, r, the 2D-latitudinal grid coordinates, theta, the beta_nlm coefficient and the 2D-kernel, K_nlm.

Return type

tuple

persephone.kernels.rotation.compute_shellular_kernel(r, rho, xi_r, xi_h, l=1)

Compute beta_nl and K_nl 1D shellular kernels terms after Christensen-Dalsgaard’s Lecture Notes on Stellar Oscillations Eq. (8.42) and Eq. (8.43).

Parameters

  • r (ndarray) – Radial coordinates of the eigenfunctions.

  • rho (ndarray) – Radial density profile.

  • xi_r (ndarray) – Mode radial eigenfuction.

  • xi_h (ndarray) – Mode horizontal eigenfuction.

  • l (int) – Mode spherical degree. Optional, default 1.

Returns

A tuple of arrays with the``beta_nl`` coefficient and the shellular kernel, K_nl.

Return type

tuple

persephone.kernels.rotation.compute_splittings(r, theta, K_nlm, Omega, beta_nlm, m=1)

Compute rotational splittings in the general perturbative case, after Christensen-Dalsgaard’s Lecture Notes on Stellar Oscillations Eq. (8.35).

Parameters

  • r (ndarray) – Radial coordinates.

  • K_nlm (ndarray) – 2D radial/latitudinal kernel.

  • Omega (ndarray) – 2D radial/latitudinal rotation profile.

  • beta_nlm (ndarray) – Prefactor.

  • m (int) – Azimuthal number. Optional, default 1.

Returns

The rotational splitting.

Return type

float

persephone.kernels.rotation.compute_shellular_splittings(r, K_nl, Omega, beta_nl, m=1)

Compute rotational splittings in the case of a shellular perturbative rotation, after Christensen-Dalsgaard’s Lecture Notes on Stellar Oscillations Eq. (8.41).

Parameters

  • r (ndarray) – Radial coordinates.

  • K_nl (ndarray) – Radial kernel.

  • Omega (ndarray) – Radial rotation profile.

  • beta_nl (ndarray) – Prefactor.

  • m (int) – Azimuthal number. Optional, default 1.

Returns

The shellular rotational splitting.

Return type

float

persephone.kernels.rotation.plot_2D_kernel(r, theta, K_nlm, cmap='cividis', figsize=(3, 6), levels=None, contour_colors='black', contour_ls='--', contour_lw=1, vmin=None, vmax=None, shading='nearest', colorbar=False, colorbar_label=None, title=None)

Plot 2D kernel.

Parameters

  • r (ndarrray) – 2D grid with radial coordinates.

  • theta (ndarrray) – 2D grid with latitudinal coordinates.

  • K_nlm (ndarray) – 2D radial/latitudinal kernel.

  • cmap (str or Colormap instance) – Color map to use for the kernel. Optional, default cividis.

  • figsize (tuple) – Figure size. Optional, default (3,6).

  • levels (array-like) – Contour levels. Optional, default None.

  • contour_colors (str or Color instance) – Contour color. Optional, default black.

  • contour_ls (str) – Contour linestyle. Optional, default "--".

  • contour_lw (str) – Contour linewidth. Optional, default 1.

  • vmin (float) – Minimal value for the colormap. Optional, default None.

  • vmax (float) – Maximal value for the colormap. Optional, default None.

  • shading (str) – Shading type. Optional, default nearest.

  • colorbar (bool) – Whether to show the colorbar or not. Optional, default False.

  • colorbar_label (str) – Color bar label. Optional, default None.

  • title (str) – The axes title. Optional, default None.

Returns

The generated figure.

Return type

matplotlib.pyplot.figure

persephone.kernels.rotation.plot_shellular_kernel(r, K_nl, figsize=(6, 6), xlabel=None, ylabel=None, title=None, **kwargs)

Plot shellular kernel.

Parameters

  • r (ndarray) – Radial coordinates.

  • K_nl (ndarray) – Radial kernel.

  • figsize (tuple) – Figure size. Optional, default (6,6).

  • xlabel (str) – x-axis label. Optional, default None.

  • ylabel (str) – y-axis label. Optional, default None.

  • title (str) – The axes title. Optional, default None.

Returns

The generated figure.

Return type

matplotlib.pyplot.figure