pint.models.stand_alone_psr_binaries.ELL1_model.ELL1model
- class pint.models.stand_alone_psr_binaries.ELL1_model.ELL1model[source]
Bases:
ELL1BaseModelThis is a ELL1 model using M2 and SINI as the Shapiro delay parameters.
References
Lange et al. (2001), MNRAS, 326 (1), 274–282 [1]
Methods
Doppler()Drep()dDre/dPhi
Drepp()d^2Dre/dPhi^2
E()Eccentric Anomaly
ELL1_T0()ELL1_ecc()ELL1_om()ELL1delay()M()Orbit phase.
P()Phi()Orbit phase in ELL1 model.
Pobs_designmatrix(params)TM2()a1()ELL1 model a1 calculation.
add_binary_params(parameter, defaultValue[, ...])Add one parameter to the binary class.
add_inter_vars(interVars)Returns total pulsar binary delay.
compute_eccentric_anomaly(eccentricity, ...)Solve the Kepler Equation, E - e * sin(E) = M
d_Dre_d_par(par)Derivative computation.
d_Drep_d_par(par)Derivative computation.
d_Drepp_d_par(par)Derivative computation
d_ELL1delay_d_par(par)d_E_d_ECC()d_E_d_EDOT()d_E_d_T0()Analytic derivative
d_E_d_par(par)derivative for E respect to binary parameter.
d_M_d_par(par)derivative for M respect to binary parameter.
dPhi/dTASC
d_Phi_d_par(par)The derivative of Phi with respect to parameter
d_Pobs_d_A1()d_Pobs_d_A1DOT()d_Pobs_d_ECC()d_Pobs_d_EDOT()d_Pobs_d_OM()d_Pobs_d_OMDOT()d_Pobs_d_P0()d_Pobs_d_P1()d_Pobs_d_PB()d_Pobs_d_PBDOT()d_Pobs_d_T0()d_TM2_d_M2()d_a1_d_A1()d_a1_d_A1DOT()d_a1_d_T0()d_a1_d_par(par)d_binarydelay_d_par(par)Get the binary delay derivatives respect to parameters.
d (ELL1 Roemer delay)/dPhi in proper time divided by a1/c
d^2 (ELL1 Roemer delay)/dPhi^2 in proper time divided by a1/c
d_delayI_d_par(par)Delay derivative.
ELL1 Roemer delay in proper time divided by a1/c, including third order corrections
d_delayS_d_par(par)Derivative for binary Shapiro delay.
d_ecc_d_ECC()d_ecc_d_EDOT()d_ecc_d_T0()d_eps1_d_EPS1()d_eps1_d_EPS1DOT()d_eps1_d_TASC()d_eps2_d_EPS2()d_eps2_d_EPS2DOT()d_eps2_d_TASC()d_nhat_d_par(par)d_nu_d_E()Analytic calculation.
d_nu_d_EDOT()Analytic calculation.
d_nu_d_ecc()d_nu_d_par(par)derivative for nu respect to binary parameter.
dOmega/dOM = 1
dOmega/dOMDOT = tt0
dOmega/dPB = dnu/dPB*k+dk/dPB*nu
d_omega_d_par(par)derivative for omega respect to user input Parameter.
d_pb_d_par(par)derivative for pbprime respect to binary parameter.
delayI()Inverse time delay formula.
delayR()ELL1 Roemer delay in proper time.
delayS()ELL1 Shapiro delay.
delay_designmatrix(params)ecc()Calculate eccentricity with EDOT
eps1()eps2()get_tt0(barycentricTOA)tt0 = barycentricTOA - T0
nhat()nu()True anomaly (Ae)
omega()orbits()orbits_ELL1()pb()pbdot()pbprime()prtl_der(y, x)Find the partial derivatives in binary model pdy/pdx
search_alias(parname)set_param_values([valDict])Set the parameters and assign values,
t0()ttasc()ttasc = t - TASC
update_input(**updates)Update the toas and parameters.
Attributes
T0ttt0- d_delayS_d_par(par)[source]
Derivative for binary Shapiro delay.
Computes:
delayS = -2 * TM2 * np.log(1 - self.SINI * np.sin(Phi)) d_delayS_d_par = d_delayS_d_TM2 * d_TM2_d_par + d_delayS_d_SINI*d_SINI_d_par + d_delayS_d_Phi * d_Phi_d_par
- Drep()
dDre/dPhi
- Drepp()
d^2Dre/dPhi^2
- E()
Eccentric Anomaly
- M()
Orbit phase.
- Phi()
Orbit phase in ELL1 model. Using TASC
- a1()
ELL1 model a1 calculation.
This method overrides the a1() method in pulsar_binary.py. Instead of tt0, it uses ttasc.
- add_binary_params(parameter, defaultValue, unit=False)
Add one parameter to the binary class.
- binary_delay()
Returns total pulsar binary delay.
- Returns:
Pulsar binary delay in the units of second
- Return type:
- compute_eccentric_anomaly(eccentricity, mean_anomaly)
Solve the Kepler Equation, E - e * sin(E) = M
- Parameters:
eccentricity (array_like) – Eccentricity of binary system
mean_anomaly (array_like) – Mean anomaly of the binary system
- Returns:
The eccentric anomaly in radians, given a set of mean_anomalies in radians.
- Return type:
array_like
- d_Dre_d_par(par)
Derivative computation.
Computes:
Dre = delayR = a1/c.c*(sin(phi) - 0.5* eps1*cos(2*phi) + 0.5* eps2*sin(2*phi) + ...) d_Dre_d_par = d_a1_d_par /c.c*(sin(phi) - 0.5* eps1*cos(2*phi) + 0.5* eps2*sin(2*phi)) + d_Dre_d_Phi * d_Phi_d_par + d_Dre_d_eps1*d_eps1_d_par + d_Dre_d_eps2*d_eps2_d_par
- d_Drep_d_par(par)
Derivative computation.
Computes:
Drep = d_Dre_d_Phi = a1/c.c*(cos(Phi) + eps1 * sin(Phi) + eps2 * cos(Phi) + ...) d_Drep_d_par = ...
- d_Drepp_d_par(par)
Derivative computation
Computes:
Drepp = d_Drep_d_Phi = ... d_Drepp_d_par = ...
- d_E_d_T0()
Analytic derivative
d(E-e*sinE)/dT0 = dM/dT0 dE/dT0(1-cosE*e)-de/dT0*sinE = dM/dT0 dE/dT0(1-cosE*e)+eDot*sinE = dM/dT0
- d_E_d_par(par)
derivative for E respect to binary parameter.
- Parameters:
par (string) – parameter name
- Return type:
Derivative of E respect to par
- d_M_d_par(par)
derivative for M respect to binary parameter.
- Parameters:
par (string) – parameter name
- Return type:
Derivative of M respect to par
- d_Phi_d_TASC()
dPhi/dTASC
- d_Phi_d_par(par)
The derivative of Phi with respect to parameter
- Parameters:
par (string) – parameter name
- Return type:
Derivative of Phi respect to par
- d_binarydelay_d_par(par)
Get the binary delay derivatives respect to parameters.
- Parameters:
par (str) – Parameter name.
- d_d_delayR_dPhi_da1()
d (ELL1 Roemer delay)/dPhi in proper time divided by a1/c
- d_dd_delayR_dPhi_da1()
d^2 (ELL1 Roemer delay)/dPhi^2 in proper time divided by a1/c
- d_delayI_d_par(par)
Delay derivative.
Computes:
delayI = Dre*(1 - nhat*Drep + (nhat*Drep)**2 + 1.0/2*nhat**2*Dre*Drepp) d_delayI_d_par = d_delayI_d_Dre * d_Dre_d_par + d_delayI_d_Drep * d_Drep_d_par + d_delayI_d_Drepp * d_Drepp_d_par + d_delayI_d_nhat * d_nhat_d_par
- d_delayR_da1()
ELL1 Roemer delay in proper time divided by a1/c, including third order corrections
typo corrected from Zhu et al., following: https://github.com/nanograv/tempo/blob/master/src/bnryell1.f
- d_nu_d_ECC()
Analytic calculation.
dnu(e,E)/dECC = dnu/de*de/dECC+dnu/dE*dE/dECC de/dECC = 1 dnu/dPBDOT = dnu/dE*dE/dECC+dnu/de
- d_nu_d_T0()
Analytic calculation.
dnu/dT0 = dnu/de*de/dT0+dnu/dE*dE/dT0 de/dT0 = -EDOT
- d_nu_d_par(par)
derivative for nu respect to binary parameter.
- Parameters:
par (string) – parameter name
- Return type:
Derivative of nu respect to par
- d_omega_d_OM()
dOmega/dOM = 1
- d_omega_d_OMDOT()
dOmega/dOMDOT = tt0
- d_omega_d_T0()
dOmega/dPB = dnu/dPB*k+dk/dPB*nu
- d_omega_d_par(par)
derivative for omega respect to user input Parameter.
- Parameters:
par (string) – parameter name
- Return type:
Derivative of omega respect to par
- d_pb_d_par(par)
derivative for pbprime respect to binary parameter.
- Parameters:
par (string) – parameter name
- Return type:
Derivative of M respect to par
- delayI()
Inverse time delay formula.
The treatment is similar to the one in DD model (T. Damour & N. Deruelle (1986) equation [46-52]):
Dre = a1*(sin(Phi)+eps1/2*sin(2*Phi)+eps1/2*cos(2*Phi)) Drep = dDre/dt Drepp = d^2 Dre/dt^2 nhat = dPhi/dt = 2pi/pb nhatp = d^2Phi/dt^2 = 0 Dre(t-Dre(t-Dre(t))) = Dre(Phi) - Drep(Phi)*nhat*Dre(t-Dre(t)) = Dre(Phi) - Drep(Phi)*nhat*(Dre(Phi)-Drep(Phi)*nhat*Dre(t)) + 1/2 (Drepp(u)*nhat^2 + Drep(u) * nhat * nhatp) * (Dre(t)-...)^2 = Dre(Phi)(1 - nhat*Drep(Phi) + (nhat*Drep(Phi))^2 + 1/2*nhat^2* Dre*Drepp)
- delayR()
ELL1 Roemer delay in proper time. Include terms up to third order in eccentricity Zhu et al. (2019), Eqn. 1 Fiore et al. (2023), Eqn. 4
- ecc()
Calculate eccentricity with EDOT
- get_tt0(barycentricTOA)
tt0 = barycentricTOA - T0
- nu()
True anomaly (Ae)
- prtl_der(y, x)
Find the partial derivatives in binary model pdy/pdx
- set_param_values(valDict=None)
Set the parameters and assign values,
If the valDict is not provided, it will set parameter as default value
- ttasc()
ttasc = t - TASC
- update_input(**updates)
Update the toas and parameters.