Modes Sub-Library #

The modes sub-library provides a collection of predefined modes and user-defined functions for generating gravitational wave signals. These modes can be used to construct custom gravitational wave signals using the Signal class.

Predefined Modes #

The predefined modes available in the modes sub-library are:

• fmode
• p1mode
• p2mode
• p3mode
• g1mode
• g2mode
• g3mode
• gmode_default_func

These modes are those obtained in Universal relations for gravitational-wave asteroseismology of proto-neutron stars by Alejandro Torres-Forné et al. (arXiv:1902.10048). The function gmode_default_func is a toy function for testing purposes.

Each predefined mode is implemented as a function that generates a gravitational wave signal based on the given time array and mode-specific parameters. The parameters of the modes are passed through the Signal.mode_kwargs dict. The dict is the same for every mode, but each mode is free to use the parts it needs and nothing more. This is a practical way of coding the modes, but it might be sub-optimal if Signal.mode_kwargs grows large. In such cases, we recommended running the signal generation using precomputed input arrays for the central frequency. Note that Signal.mode_kwargs must contain elements that are numpy arrays and have the same length as Signal.time.

Any array can be given to these modes, but for them to function as intended, the input must be reasonable and in accordance with the method described in Torres-Forné et al.

p1mode #

p1mode generates a gravitational wave frequency based on the first pressure mode (p1-mode) of a neutron star. The function takes the mass (in solar masses) and radius (in km) as input parameters and returns a frequency array.

Parameters:

• msh: numpy.array - An array containing the mass values (in solar masses)
• rsh: numpy.array - An array containing the radius values (in km)

p2mode #

p2mode generates a gravitational wave frequency based on the second pressure mode (p2-mode) of a neutron star. The function takes the mass (in solar masses) and radius (in km) as input parameters and returns a frequency array.

Parameters:

• msh: numpy.array - An array containing the mass values (in solar masses)
• rsh: numpy.array - An array containing the radius values (in km)

p3mode #

p3mode generates a gravitational wave frequency based on the third pressure mode (p3-mode) of a neutron star. The function takes the mass (in solar masses) and radius (in km) as input parameters and returns a frequency array.

Parameters:

• msh: numpy.array - An array containing the mass values (in solar masses)
• rsh: numpy.array - An array containing the radius values (in km)

g1mode #

g1mode generates a gravitational wave frequency based on the first gravity mode (g1-mode) of a neutron star. The function takes the mass (in solar masses) and radius (in km) as input parameters and returns a frequency array.

Parameters:

• mpns: numpy.array - An array containing the mass values (in solar masses)
• rpns: numpy.array - An array containing the radius values (in km)

g2mode #

g2mode generates a gravitational wave frequency based on the second gravity mode (g2-mode) of a neutron star. The function takes the mass (in solar masses) and radius (in km) as input parameters and returns a frequency array.

Parameters:

• mpns: numpy.array - An array containing the mass values (in solar masses)
• rpns: numpy.array - An array containing the radius values (in km)

g3mode #

g3mode generates a gravitational wave frequency based on the third gravity mode (g3-mode) of a neutron star. The function takes the mass (in solar masses), radius (in km), central pressure, and central density as input parameters and returns a frequency array.

Parameters:

• msh: numpy.array - An array containing the mass values (in solar masses)
• rsh: numpy.array - An array containing the radius values (in km)
• pC: numpy.array - An array containing the central pressure values
• rhoC: numpy.array - An array containing the central density values

gmode_default_func #

gmode_default_func is a simple toy mode function that generates a gravitational wave frequency based on time. It serves as a default function for testing purposes. The function takes time as an input parameter and returns a frequency array.

Parameters:

• time: numpy.array - An array containing the time values

User-Defined Modes #

Users can create custom mode functions to generate gravitational wave signals. To use a custom mode function with the Signal class, pass it as a dictionary value to the modes parameter when initializing the Signal instance. A user-defined mode function must have the following signature:

def custom_mode_function(mode_kwargs):
    '''
    Arguments:
      mode_kwargs: dict. A dictionary containing any additional mode-specific parameters required by the custom mode function.
    Returns:
      central_frequency: numpy.array. An array with the same length as Signal.time describing the time evolution of the mode's central
      frequency
      '''
    return central_frequency

Example #

import numpy as np
def custom_mode_function(**kwargs):
    t = kwargs['time']
    a = kwargs['a']
    b = kwargs['b']
    return a*t+b
  
my_modes = {'custom_mode': custom_mode_function}
my_mode_kwargs = {'time' : np.linspace(0,1,100), 'a' : 150, 'b' : 130 }
signal = Signal(time, my_modes, mode_kwargs=my_mode_kwargs)