pygwtf.models.taylort3spin.common#
Functions#
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3.5PN in aligned spin effects. Circular. |
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Series inverstion of x(tau) (used for frequency) to get t(x) in the form (NOTE: not tau, t): |
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Directly using x(tau) used for the frequency function |
Module Contents#
- pygwtf.models.taylort3spin.common.phase(x, sigma, delta, eta, s)#
‘ 3.5PN in aligned spin effects. Circular.
Link to PNpedia for the expression: davidtrestini/PNpedia
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.
- pygwtf.models.taylort3spin.common.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: davidtrestini/PNpedia
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.
- pygwtf.models.taylort3spin.common.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.
- pygwtf.models.taylort3spin.common.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.
- pygwtf.models.taylort3spin.common.tau_to_x(tau, sigma, delta, eta, s)#
Directly using x(tau) used for the frequency function
PNpedia link: davidtrestini/PNpedia
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.