Mode search

Computing eigenfunctions

mascaret.mode_search(model, l_m=None, omega_0=100, omega_1=500, n_grid=300, rot_solar_rate=0, method='inverse', x_span=None, parallelise=False, nodes=2, nchunk=None, verbose=True, double_shooting=False, vanishing_rotation=True, xf=None, formalism='fully_compressible', outer_condition='vacuum', reference_frame='corotation', max_iter=100, tol_delta_grid=1e-12, tol_delta=1e-09, tol_delta_grid_ratio=1e-06, output_dir='.', template_filename=None, maxtasksperchild=5, save_adimensioned=True, profile_to_save=None, start_full_span='stitch', summary_filename=None, format_summary='ascii')

For a given stellar model, search for mode frequencies and eigenfunctions matching the input parameters provided.

This function is a wrapper of scan_frequency_grid and compute_eigenfunction_parallel.

Parameters:

• l_m (dict) – A dictionary specifying the angular degree l and azimuthal numbers m of mode to compute. Each entry of the dictionary must correspond to an l value, with corresponding field given as a list of m. Optional, default None.

• omega_0 (float) – Lower bound of the grid, in muHz. Optional, default 100.

• omega_1 (float) – Upper bound of the grid, in muHz Optional, default 500.

• n_grid (int) – Number of points to consider on the grid

• method (str) – Method to subdivise and scan the frequency grid, can be inverse or linear. Optional, default inverse.

• max_iter (int) – Maximum number of iteration. Optional, default 100.

• tol_delta_grid (float) – Tolerance of interval size between the two points of the grid within which the searched solution is contained. If the interval becomes smaller than tol_delta_grid, the iteration will stop. Optional, default 1e-12.

• tol_delta (float) – If the discriminant becomes smaller than tol_delta, the iteration will stop. Optional, default 1e-9.

• tol_delta_grid_ratio – The iteration will stop if the relative difference in size between the current grid interval size and the previous grid interval size becomes smaller than tol_delta_grid_ratio. Optional, default 1e-6.

• x_span (tuple) – The adimensioned radial span on which to compute the solution. Optional, default None.

• rot_solar_rate (float) – The stellar rotatinal frequency, in solar unit. Optional, default 0.

• verbose (bool) – Output verbosity. Optional, default False.

• nodes (float) – Number of computing nodes to use if parallel is True, optional, default 2.

• maxtaskperchild (int) – Number of task that a child process will execute before re-initialising (allowing to free used memory, in particular from created numpy arrays). Optional, default 5.

• output_dir (str or Path object) – Directory to write the output files. Optional, default ".".

• template_filename (str) – Filename template to use in order to name the output files containing the mode eigenfunctions. Optional, default None.

• double_shooting (bool) – Whether to use double shooting method rather than a simple shooting scheme. Optional, default False.

• start_full_span (str) – Whether to start drawing the full-span solution from the external (surface) or internal (core) boundary, or to stitch ("stitch") the two solutions. Optional, default core.

• summary_filename (str or Path object) – Summary filename. Optional, default None.

• format_summary (str) – Format to use to write the summary, either "ascii" or "hdf5". Optional, default "ascii".

• save_adimensioned (bool) – Whether to save or not adimensioned variables computed by the solver. y1 and y2 must be provided in this case. Optional, default False.

• profile_to_save (list or array-like) – List of profile to interpolate and save from the stellar model. Optional, default None.

• formalism (str) – Formalism to consider when solving the equations. Can be fully compressible "fully_compressible", anelastic "anelastic", LBR anelastic "lbr", or “gamma” (gamma-modes formalism from Ong & Basu 2020). Optional, default "fully_compressible".

• reference_frame (str) – The reference frame considered to look for and compute eigenfrequencies. Can be "corotation" or "inertial". Optional, default "corotation".

Returns:

The table containing the summary properties of the computed modes.

Return type:

astropy.Table

mascaret.compute_eigenfunction_parallel(list_intervals, model, l=1, m=0, method='inverse', max_iter=100, tol_delta_grid=1e-12, tol_delta=1e-09, tol_delta_grid_ratio=1e-06, x_span=None, rot_solar_rate=0, output_dir='.', template_filename=None, nodes=2, maxtasksperchild=5, double_shooting=True, start_full_span='stitch', vanishing_rotation=True, xf=None, summary_filename=None, format_summary='ascii', save_adimensioned=False, profile_to_save=None, formalism='fully_compressible', outer_condition='vacuum', reference_frame='corotation')

Compute eigenfunctions in parallels using a list of interval obtained from scan_frequency_grid.

Parameters:

• list_intervals (list of tuple) – List of frequency intervals obtained from scan_frequency_grid.

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

• m (int) – Azimuthal number. Optional, default 0.

• method (str) – Method to subdivise and scan the frequency grid, can be inverse or linear. Optional, default inverse.

• max_iter (int) – Maximum number of iteration. Optional, default 100.

• tol_delta_grid (float) – Tolerance of interval size between the two points of the grid within which the searched solution is contained. If the interval becomes smaller than tol_delta_grid, the iteration will stop. Optional, default 1e-12.

• tol_delta (float) – If the discriminant becomes smaller than tol_delta, the iteration will stop. Optional, default 1e-12.

• tol_delta_grid_ratio – The iteration will stop if the relative difference in size between the current grid interval size and the previous grid interval size becomes smaller than tol_delta_grid_ratio. Optional, default 1e-6.

• x_span (tuple) – The adimensioned radial span on which to compute the solution. Optional, default None.

• rot_solar_rate (float) – The stellar rotatinal frequency, in solar unit. Optional, default 0.

• nodes (float) – Number of computing nodes to use if parallel is True, optional, default 2.

• maxtaskperchild (int) – Number of task that a child process will execute before re-initialising (allowing to free used memory, in particular from created numpy arrays). Optional, default 5.

• output_dir (str or Path object) – Directory to write the output files. Optional, default ".".

• template_filename (str) – Filename template to use in order to name the output files containing the mode eigenfunctions. Optional, default None.

• double_shooting (bool) – Whether to use double shooting method rather than a simple shooting scheme. Optional, default False.

• start_full_span (str) – Whether to start drawing the full-span solution from the external (surface) or internal (core) boundary, or to stitch ("stitch") the two solutions. Optional, default core.

• summary_filename (str or Path object) – Summary filename. Optional, default None.

• format_summary (str) – Format to use to write the summary, either "ascii" or "hdf5". Optional, default "ascii".

• save_adimensioned (bool) – Whether to save or not adimensioned variables computed by the solver. y1 and y2`` must be provided in this case. Optional, default False.

• profile_to_save (list or array-like) – List of profile to interpolate and save from the stellar model. Optional, default None.

• formalism (str) – Formalism to consider when solving the equations. Can be fully compressible "fully_compressible", anelastic "anelastic", LBR anelastic "lbr", or “gamma” (gamma-modes formalism from Ong & Basu 2020). Optional, default "fully_compressible".

• reference_frame (str) – The reference frame considered to look for and compute eigenfrequencies. Can be "corotation" or "inertial". Optional, default "corotation".

Returns:

The table containing the summary properties of the computed modes.

Return type:

astropy.Table

mascaret.scan_frequency_grid(model, omega_0=100, omega_1=500, n_grid=300, rot_solar_rate=0, l=1, m=0, method='inverse', x_span=None, parallelise=False, nodes=2, nchunk=None, verbose=False, double_shooting=False, vanishing_rotation=True, xf=None, formalism='fully_compressible', outer_condition='vacuum', reference_frame='corotation')

Scan frequency grid to look for intervals with eigenmodes.

Parameters:

• omega_0 (float) – Lower bound of the grid, in muHz. Optional, default 100.

• omega_1 (float) – Upper bound of the grid, in muHz Optional, default 500.

• n_grid (int) – Number of points to consider on the grid

• rot_solar_rate (float) – The stellar rotatinal frequency, in solar unit. Optional, default 0.

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

• m (int) – Azimuthal number. Optional, default 0.

• method (str) – Method to subdivise and scan the frequency grid, can be inverse or linear. Optional, default inverse.

• x_span (tuple) – The adimensioned radial span on which to compute the solution. Optional, default None (in this case the solution will be computed considering the model boundaries).

• parallelise (bool) – Run in parallel if set to True. Optional, default False.

• nodes (float) – Number of computing nodes to use if parallel is True, optional, default 2.

• nchunk (int) – Number of chunks to subdivise the grid in. Optional, default None.

• verbose (bool) – Output verbosity. Optional, default False.

• formalism (str) – Formalism to consider when solving the equations. Can be fully compressible "fully_compressible", anelastic "anelastic", LBR anelastic "lbr", or “gamma” (gamma-modes formalism from Ong & Basu 2020). Optional, default "fully_compressible".

• reference_frame (str) – The reference frame considered to look for and compute eigenfrequencies. Can be "corotation" or "inertial". Optional, default "corotation".

Returns:

A list of restricted intervals to look for eigenmodes by dichotomy

Return type:

list of tuples

mascaret.search_eigenfunction_dichotomy(model, omega_0, omega_1, l=1, m=0, method='inverse', max_iter=100, tol_delta_grid=1e-12, tol_delta=1e-09, tol_delta_grid_ratio=1e-06, x_span=(0, 1), verbose=False, rot_solar_rate=0, double_shooting=True, xf=None, start_full_span='stitch', vanishing_rotation=True, formalism='fully_compressible', outer_condition='vacuum', reference_frame='corotation')

Newton procedure to look for eigenfunction.

Parameters:

• model (object) – Stellar model.

• omega_0 (float) – Lower bound for the dichotomy search, in muHz

• omega_1 (float) – Upper bound for the dichotomy search, in muHz

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

• m (int) – Azimuthal number. Optional, default 0.

• method (str) – Method to subdivise and scan the frequency grid, can be inverse or linear. Optional, default inverse.

• max_iter (int) – Maximum number of iteration. Optional, default 100.

• tol_delta_grid (float) – Tolerance of interval size between the two points of the grid within which the searched solution is contained. If the interval becomes smaller than tol_delta_grid, the iteration will stop. Optional, default 1e-12.

• tol_delta (float) – If the discriminant becomes smaller than tol_delta, the iteration will stop. Optional, default 1e-12.

• tol_delta_grid_ratio – The iteration will stop if the relative difference in size between the current grid interval size and the previous grid interval size becomes smaller than tol_delta_grid_ratio. Optional, default 1e-6.

• x_span (tuple) – The adimensioned radial span on which to compute the solution. Optional, default (0,1).

• verbose (bool) – Output verbosity. Optional, default False.

• rot_solar_rate (float) – The stellar rotatinal frequency, in solar unit. Optional, default 0.

• double_shooting (bool) – Whether to use double shooting method rather than a simple shooting scheme. Optional, default False.

• xf (float) – The position of the boundary point between the external and internal solution if double_shooting is True. If not provided, it will be taken as the radius where the Brunt-Väisälä frequency is maximum. Optional, default None.

• start_full_span (str) – Whether to start drawing the full-span solution from the external (surface) or internal (core) boundary, or to stitch ("stitch") the two solutions. Optional, default core.

• formalism (str) – Formalism to consider when solving the equations. Can be fully compressible "fully_compressible", anelastic "anelastic", LBR anelastic "lbr", or “gamma” (gamma-modes formalism from Ong & Basu 2020). Optional, default "fully_compressible".

• reference_frame (str) – The reference frame considered to look for and compute eigenfrequencies. Can be "corotation" or "inertial". Optional, default "corotation".

Returns:

The eigenfrequency omega, the adimensioned radial coordinate x, the radial displacement xi_r, the reduced pressure perturbation W, the adimensioned variables y1 and y2, the discriminant value of the computed solution, and the scipy.integrate.solve_ivp result object.

Return type:

tuple

mascaret.shooting_method_solve_ivp(model, omega=None, omega_ad=None, m=0, l=1, x_span=(0, 1), rot_solar_rate=0, double_shooting=False, xf=None, compute_full_span=False, start_full_span='stitch', vanishing_rotation=True, formalism='fully_compressible', outer_condition='vacuum', reference_frame='corotation')

Solve the second order problem with a shooting method (see e.g. Numerical Recipes, Press 1992).

Parameters:

• model (StellarModel) – The model object with stellar structure informations.

• omega (float) – The dimension frequency of the solution to compute. Optional, default None.

• omega_ad (float) – The adimensioned frequency of the solution to compute. The value of omega will be ignored if provided. Optional, default None.

• m (int) – Azimuthal number. Optional, default 0.

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

• x_span (tuple) – The adimensioned radial span on which to compute the solution. Optional, default (0,1).

• rot_solar_rate (float) – The stellar rotational frequency, in solar unit. Optional, default 0.

• double_shooting (bool) – Whether to use double shooting method rather than a simple shooting scheme. Optional, default False.

• xf (float) – The position of the boundary point between the external and internal solution if double_shooting is True. If not provided, it will be taken as the radius where the Brunt-Väisälä frequency is maximum. Optional, default None.

• compute_full_span (bool) – If set to True and double_shooting is used, a full span solution will be computed and returned to the user. Otherwise the internal solution spanning from x_span[0] to xf will be returned. Optional, default False.

• start_full_span (str) – If compute_full_span is True, whether to start drawing the full-span solution from the external boundary (surface), the internal boundary (core) or stitch ("stitch") the two solutions. Optional, default core.

• formalism (str) – Formalism to consider when solving the equations. Can be fully compressible "fully_compressible", anelastic "anelastic", LBR anelastic "lbr", or “gamma” (gamma-modes formalism from Ong & Basu 2020). Optional, default "fully_compressible".

• outer_condition (str) – Outer boundary condition, can be "vacuum" or "zero_r". Optional, default "vacuum".

• reference_frame (str) – The reference frame considered to look for and compute eigenfrequencies. Can be "corotation" or "inertial". Optional, default "corotation".

Returns:

The adimensioned radial coordinate x, the radial displacement xi_r, the reduced pressure perturbation W, the discriminant value of the computed solution, and the scipy.integrate.solve_ivp result object.

Return type:

tuple

Plotting functions

mascaret.plot_eigenfunction(x, xi_r, W, axs=None, model=None, omega=None, rot_solar_rate=None, c1='darkorange', c2='blue', xlabel=None, ylabels=None, **kwargs)

Plot eigenfunctions computed by shooting method

Parameters:

• x (ndarray) – Radial coordinate.

• xi_r (ndarray) – Radial displacement.

• W (ndarray) – Reduced pressure perturbation

• axs (list of matplotlib.Axes) – The axes to use for the plot. A new figure will be created if not provided. Optional, default None.

• model (StellarModel) – The model object with stellar structure informations. Optional, default None.

• omega (float) – The mode frequency in muHz. Optional, default None.

• rot_solar_rate (float) – The stellar rotation frequency in solar unit. Optional, default None.

• c1 (str) – Color to use for the radial displacement. Optional, default "darkorange".

• c1 – Color to use for the reduced pressure. Optional, default "blue".

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

• ylabels (tuple of str) – Labels for y-axis. Must be given as tuple with the label for the first panel and the label for the second panel (either can be set to None to use default label). Optional, default None.

• **kwargs – Keyword arguments to be passed to matplotlib.pyplot.plot.

Returns:

The created figure.

Return type:

matplotlib.Figure

Auxiliary functions

mascaret.compute_physical_quantities(result, model, l=1)

Compute physical quantities from the adimensioned solutions of the IVP.

Parameters:

• result (object) – The scipy.integrate.solve_ivp result object.

• model (StellarModel) – The model object with stellar structure informations.

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

Returns:

The adimensioned radial coordinate x, the radial displacement xi_r and the reduced pressure perturbation W.

Return type:

tuple of arrays

mascaret.compute_radial_order(x, xi_r, W, scheme='eckart_1960')

Compute radial order of the eigenmode.

Returns:

A tuple of integers with the global radial order n, the number of gravity nodes n_g and the number of acoustic nodes n_p.

Return type:

tuple