pint.models.stand_alone_psr_binaries.BT_model.BTmodel
- class pint.models.stand_alone_psr_binaries.BT_model.BTmodel(t=None, input_params=None)[source]
Bases:
PSR_BINARY
This is a class independent from PINT platform for pulsar BT binary model. It is a subclass of PSR_BINARY class defined in file binary_generic.py in the same dierectory. This class is desined for PINT platform but can be used as an independent module for binary delay calculation. To interact with PINT platform, a pulsar_binary wrapper is needed. See the source file pint/models/binary_bt.py Refence ——— The ‘BT’ binary model for the pulse period. Model as in: W.M. Smart, (1962), “Spherical Astronomy”, p35 Blandford & Teukolsky (1976), ApJ, 205, 580-591
- Return type:
A bt binary model class with paramters, delay calculations and derivatives.
Example
>>> import numpy >>> t = numpy.linspace(54200.0,55000.0,800) >>> binary_model = BTmodel() >>> paramters_dict = {'A0':0.5,'ECC':0.01} >>> binary_model.update_input(t, paramters_dict) Here the binary has time input and parameters input, the delay can be calculated.
@param PB: Binary period [days] @param ECC: Eccentricity @param A1: Projected semi-major axis (lt-sec) @param A1DOT: Time-derivative of A1 (lt-sec/sec) @param T0: Time of periastron passage (barycentric MJD) @param OM: Omega (longitude of periastron) [deg] @param EDOT: Time-derivative of ECC [0.0] @param PBDOT: Time-derivative of PB [0.0] @param OMDOT: Time-derivative of OMEGA [0.0]
Methods
BTdelay
()Full BT model delay
Doppler
()E
()Eccentric Anomaly
M
()Orbit phase.
P
()Pobs_designmatrix
(params)TM2
()a1
()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_BTdelay_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.
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_delayL1_d_A1
()d_delayL1_d_A1DOT
()d_delayL1_d_E
()d_delayL1_d_ECC
()d_delayL1_d_EDOT
()d_delayL1_d_GAMMA
()d_delayL1_d_OM
()d_delayL1_d_OMDOT
()d_delayL1_d_T0
()d_delayL1_d_par
(par)d_delayL2_d_A1
()d_delayL2_d_A1DOT
()d_delayL2_d_E
()d_delayL2_d_ECC
()d_delayL2_d_EDOT
()d_delayL2_d_GAMMA
()d_delayL2_d_OM
()d_delayL2_d_OMDOT
()d_delayL2_d_T0
()d_delayL2_d_par
(par)d_ecc_d_ECC
()d_ecc_d_EDOT
()d_ecc_d_T0
()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.
delayL1
()First term of Blandford & Teukolsky (1976), ApJ, 205, 580-591, eq 2.33/ First left-hand term of W.M.
delayL2
()Second term of Blandford & Teukolsky (1976), ApJ, 205, 580-591, eq 2.33/ / Second left-hand term of W.M.
delayR
()Third term of Blandford & Teukolsky (1976), ApJ, 205, 580-591, eq 2.33 / Right-hand term of W.M.
delay_designmatrix
(params)ecc
()Calculate eccentricity with EDOT
get_tt0
(barycentricTOA)tt0 = barycentricTOA - T0
nu
()True anomaly (Ae)
omega
()orbits
()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
()update_input
(**updates)Update the toas and parameters.
Attributes
T0
t
tt0
- delayL1()[source]
First term of Blandford & Teukolsky (1976), ApJ, 205, 580-591, eq 2.33/ First left-hand term of W.M. Smart, (1962), “Spherical Astronomy”, p35 delay equation.
alpha * (cosE-e) alpha = a1*sin(omega) Here a1 is in the unit of light second as distance
- delayL2()[source]
Second term of Blandford & Teukolsky (1976), ApJ, 205, 580-591, eq 2.33/ / Second left-hand term of W.M. Smart, (1962), “Spherical Astronomy”, p35 delay equation.
(beta + gamma) * sinE beta = (1-e^2)*a1*cos(omega) Here a1 is in the unit of light second as distance
- delayR()[source]
Third term of Blandford & Teukolsky (1976), ApJ, 205, 580-591, eq 2.33 / Right-hand term of W.M. Smart, (1962), “Spherical Astronomy”, p35 delay equation.
(alpha*(cosE-e)+(beta+gamma)*sinE)*(1-alpha*sinE - beta*sinE)/ (pb*(1-e*coeE)) (alpha*(cosE-e)+(beta+gamma)*sinE) is define in delayL1 and delayL2
- E()
Eccentric Anomaly
- M()
Orbit phase.
- 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_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_binarydelay_d_par(par)
Get the binary delay derivatives respect to parameters.
- Parameters:
par (str) – Parameter name.
- 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
- 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
- update_input(**updates)
Update the toas and parameters.