pygwtf.models.taylort3spin.common
=================================

.. py:module:: pygwtf.models.taylort3spin.common


Functions
---------

.. autoapisummary::

   pygwtf.models.taylort3spin.common.phase
   pygwtf.models.taylort3spin.common.frequency
   pygwtf.models.taylort3spin.common.frequency_derivative
   pygwtf.models.taylort3spin.common.time_to_merger
   pygwtf.models.taylort3spin.common.tau_to_x


Module Contents
---------------

.. py:function:: phase(x, sigma, delta, eta, s)

   '
   3.5PN in aligned spin effects. Circular.

   Link to PNpedia for the expression:
   https://github.com/davidtrestini/PNpedia/blob/275c95c8f6765d5628eeb2549d17250cd16e6617/Core%20post-Newtonian%20quantities/Circular%20orbits/Spinning/Nonprecessing/Without%20tidal%20effects/Waveform/phase.txt

   Parameters:
   ----------
       x (float): The PN expansion parameter, defined as (pi*M*f)^(2/3), where M is the total mass of the binary and f is the GW frequency.
       sigma (float): Reduced spin parameter (m2 * s2 - m1 * s1) / M
       delta (float): Mass difference parameter (m1 - m2) / M
       eta (float): Symmetric mass ratio m1 * m2 / M^2
       s (float): Spin parameter (m1**2 * s1 + m2**2 * s2) / (M**2)

   Returns:
   -------
       Phi_0_minus_phi (float): The value of Phi_0 - phi at the given x, sigma, delta, eta, and s.


.. py:function:: frequency(tau, sigma, delta, eta, s)

   3.5PN in aligned spin effects. Circular.

   Obtained from x(tau) = F(tau).

   Link to PNpedia for the expression:
   https://github.com/davidtrestini/PNpedia/blob/275c95c8f6765d5628eeb2549d17250cd16e6617/Core%20post-Newtonian%20quantities/Circular%20orbits/Spinning/Nonprecessing/Without%20tidal%20effects/Waveform/chirp.txt


   Parameters:
   ----------
       tau (float): Defined as tau = (eta / 5) * (t-t_0), where t_0 is the initial time and t is the time variable. It is a dimensionless time parameter that measures the time to coalescence in units of the symmetric mass ratio eta.
       sigma (float): Reduced spin parameter (m2 * s2 - m1 * s1) / M
       delta (float): Mass difference parameter (m1 - m2) / M
       eta (float): Symmetric mass ratio m1 * m2 / M^2
       s (float): Spin parameter (m1**2 * s1 + m2**2 * s2) / (M**2)

   Returns:
   -------
       F (float): The value of frequency at the given tau, sigma, delta, eta, and s.


.. py:function:: frequency_derivative(tau, sigma, delta, eta, s)

   '
   Differentiated form of frequency above.

   With respect to t not tau. (Uses Chain rule to get dF/dt from dF/dtau, where tau is a function of t, using dTau/dt = -eta/5).

   Parameters:
   ----------
       tau (float): Defined as tau = (eta / 5) * (t-t_0), where t_0 is the initial time and t is the time variable. It is a dimensionless time parameter that measures the time to coalescence in units of the symmetric mass ratio eta.
       sigma (float): Reduced spin parameter (m2 * s2 - m1 * s1) / M
       delta (float): Mass difference parameter (m1 - m2) / M
       eta (float): Symmetric mass ratio m1 * m2 / M^2
       s (float): Spin parameter (m1**2 * s1 + m2**2 * s2) / (M**2)

   Returns:
   -------
       dFdt (float): The value of the derivative of frequency with respect to time at the given tau, sigma, delta, eta, and s.


.. py:function:: time_to_merger(x, sigma, delta, eta, s)

   Series inverstion of x(tau) (used for frequency) to get t(x) in the form (NOTE: not tau, t):

   tc(x) = t_0 - t(x) (I think should be the other way around(?))

   Parameters:
   ---------
       x (float): The PN expansion parameter, defined as (pi*M*f)^(2/3), where M is the total mass of the binary and f is the GW frequency.
       sigma (float): Reduced spin parameter (m2 * s2 - m1 * s1) / M
       delta (float): Mass difference parameter (m1 - m2) / M
       eta (float): Symmetric mass ratio m1 * m2 / M^2
       s (float): Spin parameter (m1**2 * s1 + m2**2 * s2) / (M**2)

   Returns:
   -------
       tc (float): The value of time to merger at the given x, sigma, delta, eta, and s.


.. py:function:: tau_to_x(tau, sigma, delta, eta, s)

   Directly using x(tau) used for the frequency function

   PNpedia link:
   https://github.com/davidtrestini/PNpedia/blob/275c95c8f6765d5628eeb2549d17250cd16e6617/Core%20post-Newtonian%20quantities/Circular%20orbits/Spinning/Nonprecessing/Without%20tidal%20effects/Waveform/chirp.txt

   Parameters:
   ----------
       tau (float): Defined as tau = (eta / 5) * (t-t_0), where t_0 is the initial time and t is the time variable. It is a dimensionless time parameter that measures the time to coalescence in units of the symmetric mass ratio eta.
       sigma (float): Reduced spin parameter (m2 * s2 - m1 * s1) / M
       delta (float): Mass difference parameter (m1 - m2) / M
       eta (float): Symmetric mass ratio m1 * m2 / M^2
       s (float): Spin parameter (m1**2 * s1 + m2**2 * s2) / (M**2)

   Returns:
   -------
       x (float): The value of the dimensionless frequency at the given tau, sigma, delta, eta, and s.