Fe XXV Doppler Shifts Cen X-3

Doppler Shifts in Cen X-3 Chandra Observation¶

Within a Cen X-3 Chandra observation, some very prominent Doppler shifts in the Fe xxv central energy were observed in phase resolved analysis.

In this example, we will explore how these shifts are compatible with the emitting plasma's ballistic movement around the orbit.

In [1]:

Copied!

import xraybinaryorbit
from xraybinaryorbit import *
import xraybinaryorbit
from xraybinaryorbit import *


HELLO, nice to see you! :)

PLEASE READ THIS, IT'S VERY IMPORTANT:

These are the units that must be used within this package:

- Rstar: Solar radius
- Mstar: Solar masses
- Inclination: Sexagesimal degrees
- Periapsis: Sexagesimal degrees
- Semimajor: Stellar radius
- Periods: Days (Periods in the case of the period_sliding_window function will support any units)
- Iphase: Radians

A list of the functions contained in this package will be displayed by runing the function list_functions().

As these functions use a lot of parameters, which can sometimes be difficult to handle, we have implemented a user-friendly method for parameter input:
A form will be displayed, and the parameters will be saved in the directory for further interactions. These saved parameters will be used if new parameters are not provided.
For the function to work, the submit button must be pressed.
If the parameters are already saved within the working directory, setting "load_directly=True" no form will be displayed and that parameters will be used within the function.
Alternatively, the parameters can be provided as lists in the following format: parameter_list=[parameters] for the theoretical functions or as bound_list = [lower_bounds], [upper_bounds] for the fitting functions.

Please, take into account that fits in general will take A LOT of time to complete.

If you need help, contact graciela.sanjurjo@ua.es.

In [2]:

Copied!





# REAL DATA

# Known orbital phases for each time bin
phase_array = np.array([0.21901885, 0.24120082, 0.2522918 , 0.26338279, 0.27447377,
       0.28556475, 0.29665574, 0.30774672, 0.31883771, 0.32715595,
       0.33270144, 0.33824693, 0.35488341, 0.3604289 , 0.36597439,
       0.37706538, 0.38815636, 0.40479284, 0.41033833])

# Time bins: The beguining and end are provided. 
x = np.array([[7.97000557e+08, 7.97002557e+08],
       [7.97004557e+08, 7.97006557e+08],
       [7.97006557e+08, 7.97008557e+08],
       [7.97008557e+08, 7.97010557e+08],
       [7.97010557e+08, 7.97012557e+08],
       [7.97012557e+08, 7.97014557e+08],
       [7.97014557e+08, 7.97016557e+08],
       [7.97016557e+08, 7.97018557e+08],
       [7.97018557e+08, 7.97020557e+08],
       [7.97020557e+08, 7.97021557e+08],
       [7.97021557e+08, 7.97022557e+08],
       [7.97022557e+08, 7.97023557e+08],
       [7.97025557e+08, 7.97026557e+08],
       [7.97026557e+08, 7.97027557e+08],
       [7.97027557e+08, 7.97028557e+08],
       [7.97029557e+08, 7.97030557e+08],
       [7.97031557e+08, 7.97032557e+08],
       [7.97034557e+08, 7.97035557e+08],
       [7.97035557e+08, 7.97036557e+08]])

# Emission line evolution
y = np.array([6.68379, 6.80991, 6.67892, 6.70604, 6.59522, 6.69305, 6.78357,
       6.7602 , 6.71054, 6.59051, 6.58941, 6.6197 , 6.6798 , 6.73628,
       6.72427, 6.70338, 6.81985, 6.60144, 6.60003])



# Emission line evolution positive and negative errors
y_err = np.array([[0.01962, 0.01599, 0.0353 , 0.02163, 0.01522, 0.02066, 0.01784,
        0.0408 , 0.09066, 0.01051, 0.00941, 0.0344 , 0.0998 , 0.02562,
        0.02753, 0.03273, 0.08475, 0.02144, 0.02003],
       [0.09961, 0.01009, 0.04271, 0.02659, 0.12467, 0.01667, 0.03643,
        0.03073, 0.03159, 0.02861, 0.01781, 0.04638, 0.09535, 0.0397 ,
        0.03344, 0.10163, 0.00015, 0.06801, 0.04635]])
# REAL DATA

# Known orbital phases for each time bin
phase_array = np.array([0.21901885, 0.24120082, 0.2522918 , 0.26338279, 0.27447377,
       0.28556475, 0.29665574, 0.30774672, 0.31883771, 0.32715595,
       0.33270144, 0.33824693, 0.35488341, 0.3604289 , 0.36597439,
       0.37706538, 0.38815636, 0.40479284, 0.41033833])

# Time bins: The beguining and end are provided. 
x = np.array([[7.97000557e+08, 7.97002557e+08],
       [7.97004557e+08, 7.97006557e+08],
       [7.97006557e+08, 7.97008557e+08],
       [7.97008557e+08, 7.97010557e+08],
       [7.97010557e+08, 7.97012557e+08],
       [7.97012557e+08, 7.97014557e+08],
       [7.97014557e+08, 7.97016557e+08],
       [7.97016557e+08, 7.97018557e+08],
       [7.97018557e+08, 7.97020557e+08],
       [7.97020557e+08, 7.97021557e+08],
       [7.97021557e+08, 7.97022557e+08],
       [7.97022557e+08, 7.97023557e+08],
       [7.97025557e+08, 7.97026557e+08],
       [7.97026557e+08, 7.97027557e+08],
       [7.97027557e+08, 7.97028557e+08],
       [7.97029557e+08, 7.97030557e+08],
       [7.97031557e+08, 7.97032557e+08],
       [7.97034557e+08, 7.97035557e+08],
       [7.97035557e+08, 7.97036557e+08]])

# Emission line evolution
y = np.array([6.68379, 6.80991, 6.67892, 6.70604, 6.59522, 6.69305, 6.78357,
       6.7602 , 6.71054, 6.59051, 6.58941, 6.6197 , 6.6798 , 6.73628,
       6.72427, 6.70338, 6.81985, 6.60144, 6.60003])



# Emission line evolution positive and negative errors
y_err = np.array([[0.01962, 0.01599, 0.0353 , 0.02163, 0.01522, 0.02066, 0.01784,
        0.0408 , 0.09066, 0.01051, 0.00941, 0.0344 , 0.0998 , 0.02562,
        0.02753, 0.03273, 0.08475, 0.02144, 0.02003],
       [0.09961, 0.01009, 0.04271, 0.02659, 0.12467, 0.01667, 0.03643,
        0.03073, 0.03159, 0.02861, 0.01781, 0.04638, 0.09535, 0.0397 ,
        0.03344, 0.10163, 0.00015, 0.06801, 0.04635]])

In this observation, the Fe xxvi emission line energy exhibited remarkable Doppler shifts. In this example, we will utilize the fitting functions from the xraybinaryorb package to disentangle this intriguing behavior.

The best model (phisical interpretation + results) was achieved with the fit_disc_ps function, i.e, this emitting plasma is likely orbiting around the compact object, traveling in its orbit.

In [3]:

Copied!





plt.errorbar(phase_array,y, yerr =y_err,fmt="k", alpha=0.5)
plt.errorbar(phase_array,y,fmt="k")
plt.xlabel("Orbital phase")
plt.ylabel("Fe xxi energy evolution")
plt.errorbar(phase_array,y, yerr =y_err,fmt="k", alpha=0.5)
plt.errorbar(phase_array,y,fmt="k")
plt.xlabel("Orbital phase")
plt.ylabel("Fe xxi energy evolution")

Out[3]:

Text(0, 0.5, 'Fe xxi energy evolution')

No description has been provided for this image

DISC IN ORBIT¶

In [4]:

Copied!





lower_bound = [0.18,1.5,2.087,0.0,  0.0,   67.0,11.8,18.7, 1.33, 0.0,0.5,0.14,0.0, 0.0,  67.0,1e-60,6.63,0.0]
upper_bound = [0.25,1.7,2.09, 1e-05,1e-70,76.7, 12.2,22.77,1.45,0.99,1.0,0.16,0.46,360.0,76.7,1e-22,6.7,1e-70]

bound_disc= lower_bound, upper_bound

result, phase, dphase, predicted_data, r_squared = fit_disc_ps(x, y, y_err=y_err, 
                                                               num_iterations=3, maxiter = 1000, swarmsize = 100, 
                                                               units="keV",method_="extended",
                                                               extended_binsize=0.01,bound_list = bound_disc)

plt.plot(phase_array,  predicted_data,"o:")
plt.errorbar(phase_array, y, yerr=y_err)
plt.xlabel("Orbital phase")
plt.ylabel("Fe xvv Doppler shifts")

result
lower_bound = [0.18,1.5,2.087,0.0,  0.0,   67.0,11.8,18.7, 1.33, 0.0,0.5,0.14,0.0, 0.0,  67.0,1e-60,6.63,0.0]
upper_bound = [0.25,1.7,2.09, 1e-05,1e-70,76.7, 12.2,22.77,1.45,0.99,1.0,0.16,0.46,360.0,76.7,1e-22,6.7,1e-70]

bound_disc= lower_bound, upper_bound

result, phase, dphase, predicted_data, r_squared = fit_disc_ps(x, y, y_err=y_err, 
                                                               num_iterations=3, maxiter = 1000, swarmsize = 100, 
                                                               units="keV",method_="extended",
                                                               extended_binsize=0.01,bound_list = bound_disc)

plt.plot(phase_array,  predicted_data,"o:")
plt.errorbar(phase_array, y, yerr=y_err)
plt.xlabel("Orbital phase")
plt.ylabel("Fe xvv Doppler shifts")

result

Loaded bounds from the provided array:
iphase  0.18 - 0.25
semimajor  1.5 - 1.7
orbitalperiod  2.087 - 2.09
eccentricity  0.0 - 1e-05
periapsis  0.0 - 1e-70
inclination  67.0 - 76.7
Rstar  11.8 - 12.2
Mstar1  18.7 - 22.77
Mstar2  1.33 - 1.45
iphase2  0.0 - 0.99
semimajor2  0.5 - 1.0
orbitalperiod2  0.14 - 0.16
eccentricity2  0.0 - 0.46
periapsis2  0.0 - 360.0
inclination2  67.0 - 76.7
Mass3  1e-60 - 1e-22
feature  6.63 - 6.7
wind_vel  0.0 - 1e-70

Stopping search: Swarm best objective change less than 1e-08
Stopping search: Swarm best objective change less than 1e-08
Stopping search: Swarm best objective change less than 1e-08

Out[4]:

Name of the parameter	iphase	semimajor	orbitalperiod	eccentricity	periapsis	inclination	Rstar	Mstar1	Mstar2	iphase2	semimajor2	orbitalperiod2	eccentricity2	periapsis2	inclination2	Mass3	feature	wind_vel
Value	0.182875	1.672746	2.088299	0.000004	6.688620e-71	68.926749	11.959089	20.052763	1.363479	0.990000	1.0	0.148633	0.460000	173.982326	75.687856	3.630221e-23	6.700000e+00	4.089993e-72
Std	0.021976	0.051049	0.000436	0.000003	2.586819e-71	1.744880	0.071862	1.167779	0.006301	0.465039	0.0	0.000472	0.000002	2.216911	3.188393	2.430893e-23	1.657071e-09	4.492871e-71

In [5]:

Copied!





result, phase, dphase, predicted_data, r_squared = fit_disc_ls(x, y, y_err=y_err,  
                                                               units="keV",method_="discrete",
                                                               extended_binsize=0.01, 
                                                               bound_list = bound_disc)


plt.plot(phase_array,  predicted_data,"o:")
plt.errorbar(phase_array, y, yerr=y_err)
plt.xlabel("Orbital phase")
plt.ylabel("Fe xvv Doppler shifts")

result
result, phase, dphase, predicted_data, r_squared = fit_disc_ls(x, y, y_err=y_err,  
                                                               units="keV",method_="discrete",
                                                               extended_binsize=0.01, 
                                                               bound_list = bound_disc)


plt.plot(phase_array,  predicted_data,"o:")
plt.errorbar(phase_array, y, yerr=y_err)
plt.xlabel("Orbital phase")
plt.ylabel("Fe xvv Doppler shifts")

result

Loaded bounds from the provided array:
iphase  0.18 - 0.25
semimajor  1.5 - 1.7
orbitalperiod  2.087 - 2.09
eccentricity  0.0 - 1e-05
periapsis  0.0 - 1e-70
inclination  67.0 - 76.7
Rstar  11.8 - 12.2
Mstar1  18.7 - 22.77
Mstar2  1.33 - 1.45
iphase2  0.0 - 0.99
semimajor2  0.5 - 1.0
orbitalperiod2  0.14 - 0.16
eccentricity2  0.0 - 0.46
periapsis2  0.0 - 360.0
inclination2  67.0 - 76.7
Mass3  1e-60 - 1e-22
feature  6.63 - 6.7
wind_vel  0.0 - 1e-70

Out[5]:

Name of the parameter	iphase	semimajor	orbitalperiod	eccentricity	periapsis	inclination	Rstar	Mstar1	Mstar2	iphase2	semimajor2	orbitalperiod2	eccentricity2	periapsis2	inclination2	Mass3	feature	wind_vel
Value	0.250000	1.694740e+00	2.087018	2.259942e-07	5.000000e-71	7.198385e+01	1.220000e+01	2.032715e+01	1.447569e+00	0.050640	1.000000	0.151972	0.46000	180.583401	7.640269e+01	5.000000e-23	6.700000	5.000000e-71
Std	164.126605	1.854087e+06	24133.338396	4.939998e+03	8.027963e+00	1.482286e+08	1.077802e+07	3.601628e+07	1.032793e+06	0.161378	981028.811535	0.024955	0.71266	38.957554	1.562515e+08	0.000000e+00	21.285067	0.000000e+00

SIMPLE ORBIT¶

In [6]:

Copied!





result, phase,  predicted_data, r_squared = fit_orbit_ps(x, y, y_err=y_err, 
                                                         units="keV",method_="extended",
                                                         num_iterations=3, maxiter = 1000, swarmsize = 100, 
                                                         extended_binsize=0.01, load_directly=False)

plt.plot(phase_array,  predicted_data,"o:")
plt.errorbar(phase_array, y, yerr=y_err)
plt.xlabel("Orbital phase")
plt.ylabel("Fe xvv Doppler shifts")

result
result, phase,  predicted_data, r_squared = fit_orbit_ps(x, y, y_err=y_err, 
                                                         units="keV",method_="extended",
                                                         num_iterations=3, maxiter = 1000, swarmsize = 100, 
                                                         extended_binsize=0.01, load_directly=False)

plt.plot(phase_array,  predicted_data,"o:")
plt.errorbar(phase_array, y, yerr=y_err)
plt.xlabel("Orbital phase")
plt.ylabel("Fe xvv Doppler shifts")

result

2026-07-10 16:33:59.351 python[24526:7652270] +[IMKClient subclass]: chose IMKClient_Modern
2026-07-10 16:33:59.351 python[24526:7652270] +[IMKInputSession subclass]: chose IMKInputSession_Modern

Bounds after modification or user input:
iphase  0.18 - 0.25
semimajor  0.5 - 1.0
orbitalperiod  0.1 - 0.25
eccentricity  0.0 - 0.3
periapsis  0.0 - 360.0
inclination  67.0 - 76.7
Rstar  11.8 - 12.2
Mstar1  18.7 - 22.77
Mstar2  1.33 - 1.45
wind_vel  0.0 - 0.99
feature  6.63 - 6.67

Stopping search: Swarm best objective change less than 1e-08
Stopping search: Swarm best objective change less than 1e-08
Stopping search: Swarm best objective change less than 1e-08

Out[6]:

Name of the parameter	iphase	semimajor	orbitalperiod	eccentricity	periapsis	inclination	Rstar	Mstar1	Mstar2	wind_vel	feature
Value	1.800000e-01	1.0	0.150667	0.3	276.805627	74.435504	12.200000	18.700000	1.450000	0.000000	6.670000e+00
Std	2.775558e-17	0.0	0.001011	0.0	130.306809	2.432374	0.063113	0.000007	0.045652	0.444778	8.881784e-16

In [7]:

Copied!





result, phase, predicted_data, r_squared = fit_orbit_ls(x, y, y_err=y_err, 
                                                        units="keV",method_="discrete",
                                                        extended_binsize=0.01, load_directly=False)

plt.plot(phase_array,  predicted_data,"o:")
plt.errorbar(phase_array, y, yerr=y_err)
plt.xlabel("Orbital phase")
plt.ylabel("Fe xvv Doppler shifts")

result
result, phase, predicted_data, r_squared = fit_orbit_ls(x, y, y_err=y_err, 
                                                        units="keV",method_="discrete",
                                                        extended_binsize=0.01, load_directly=False)

plt.plot(phase_array,  predicted_data,"o:")
plt.errorbar(phase_array, y, yerr=y_err)
plt.xlabel("Orbital phase")
plt.ylabel("Fe xvv Doppler shifts")

result

Bounds after modification or user input:
iphase  0.18 - 0.25
semimajor  0.5 - 1.0
orbitalperiod  0.1 - 0.25
eccentricity  0.0 - 0.3
periapsis  0.0 - 360.0
inclination  67.0 - 76.7
Rstar  11.8 - 12.2
Mstar1  18.7 - 22.77
Mstar2  1.33 - 1.45
wind_vel  0.0 - 0.99
feature  6.63 - 6.67

Out[7]:

Name of the parameter	iphase	semimajor	orbitalperiod	eccentricity	periapsis	inclination	Rstar	Mstar1	Mstar2	wind_vel	feature
Value	0.180000	0.500000	0.105937	0.300000	292.260655	6.986850e+01	1.180464e+01	2.263201e+01	1.330000e+00	9.214084e-01	6.670000
Std	795.825826	781584.201408	0.290567	10.940606	286936.086377	1.645053e+08	1.462678e+07	2.571824e+07	1.163928e+06	1.401576e+06	1.974792

SIMPLE SPIRAL¶

In [8]:

Copied!





result, phase, predicted_data, r_squared = fit_spiral_ps(x, y, y_err=y_err, 
                                                         num_iterations=3, maxiter = 1000, swarmsize = 100, 
                                                         units="keV",method_="extended",
                                                         extended_binsize=0.01, load_directly=False)

plt.plot(phase_array,  predicted_data,"o:")
plt.errorbar(phase_array, y, yerr=y_err)
plt.xlabel("Orbital phase")
plt.ylabel("Fe xvv Doppler shifts")

result
result, phase, predicted_data, r_squared = fit_spiral_ps(x, y, y_err=y_err, 
                                                         num_iterations=3, maxiter = 1000, swarmsize = 100, 
                                                         units="keV",method_="extended",
                                                         extended_binsize=0.01, load_directly=False)

plt.plot(phase_array,  predicted_data,"o:")
plt.errorbar(phase_array, y, yerr=y_err)
plt.xlabel("Orbital phase")
plt.ylabel("Fe xvv Doppler shifts")

result

Bounds after modification or user input:
iphase_spiral  0.0 - 1.0
semimajor_spiral  1.0 - 20.0
b  -1.0 - -0.001
omega  0.0 - 0.0001
inclination_spiral  67.0 - 77.0
feature  6.63 - 6.7

Stopping search: Swarm best objective change less than 1e-08
Stopping search: Swarm best objective change less than 1e-08
Stopping search: Swarm best objective change less than 1e-08

Out[8]:

Name of the parameter	iphase_spiral	semimajor_spiral	b	omega	inclination_spiral	feature
Value	0.898103	15.423805	-0.007317	0.000082	71.091282	6.696234
Std	0.423216	0.934388	0.002459	0.000003	2.521821	0.001618

In [14]:

Copied!





result, phase, predicted_data, r_squared = fit_spiral_ls(x, y, y_err=y_err, 
                                                         units="keV",method_="discrete",
                                                         extended_binsize=0.01, load_directly=True)

plt.plot(phase_array,  predicted_data,"o:")
plt.errorbar(phase_array, y, yerr=y_err)
plt.xlabel("Orbital phase")
plt.ylabel("Fe xvv Doppler shifts")

result
result, phase, predicted_data, r_squared = fit_spiral_ls(x, y, y_err=y_err, 
                                                         units="keV",method_="discrete",
                                                         extended_binsize=0.01, load_directly=True)

plt.plot(phase_array,  predicted_data,"o:")
plt.errorbar(phase_array, y, yerr=y_err)
plt.xlabel("Orbital phase")
plt.ylabel("Fe xvv Doppler shifts")

result

Loaded bounds from file:
iphase_spiral 0.0 - 1.0
semimajor_spiral 1.0 - 20.0
b -1.0 - -0.001
omega 0.0 - 0.0001
inclination_spiral 67.0 - 77.0
feature 6.63 - 6.7

Out[14]:

Name of the parameter	iphase_spiral	semimajor_spiral	b	omega	inclination_spiral	feature
Value	1.208116e-24	1.455126e+01	-0.006969	0.000081	7.227472e+01	6.696275
Std	6.678903e-02	2.476164e+06	0.038106	0.000004	3.050408e+07	0.016871

SPIRAL IN ORBIT¶

In [13]:

Copied!





result, phase,predicted_data, r_squared = fit_spiral_in_orbit_ps(x, y, y_err=y_err, 
                                                                          num_iterations=3, maxiter = 1000, swarmsize = 100,  
                                                                          units="keV",method_="extended",
                                                                          extended_binsize=0.01, load_directly=False)

plt.plot(phase_array,  predicted_data,"o:")
plt.errorbar(phase_array, y, yerr=y_err)
plt.xlabel("Orbital phase")
plt.ylabel("Fe xvv Doppler shifts")

result
result, phase,predicted_data, r_squared = fit_spiral_in_orbit_ps(x, y, y_err=y_err, 
                                                                          num_iterations=3, maxiter = 1000, swarmsize = 100,  
                                                                          units="keV",method_="extended",
                                                                          extended_binsize=0.01, load_directly=False)

plt.plot(phase_array,  predicted_data,"o:")
plt.errorbar(phase_array, y, yerr=y_err)
plt.xlabel("Orbital phase")
plt.ylabel("Fe xvv Doppler shifts")

result

Bounds after modification or user input:
iphase_orbit  0.18 - 0.25
semimajor_orbit  1.56 - 1.6
orbitalperiod  2.08 - 2.1
eccentricity  0.0 - 1e-05
periapsis  0.0 - 1e-05
inclination  67.0 - 77.0
Rstar  11.8 - 12.2
Mstar1  18.7 - 22.77
Mstar2  1.33 - 1.45
iphase_spiral  0.0 - 1.0
semimajor_spiral  0.01 - 100.0
b  -0.006969 - -0.0006969
omega  8.1e-05 - 8.2e-05
inclination_spiral  67.0 - 77.0
feature  6.63 - 6.7

Stopping search: Swarm best objective change less than 1e-08
Stopping search: Swarm best objective change less than 1e-08
Stopping search: Swarm best objective change less than 1e-08

Out[13]:

Name of the parameter	iphase_orbit	semimajor_orbit	orbitalperiod	eccentricity	periapsis	inclination	Rstar	Mstar1	Mstar2	iphase_spiral	semimajor_spiral	b	omega	inclination_spiral	feature
Value	0.234229	1.598999	2.093790	0.000008	3.637154e-06	72.877011	12.026251	18.762555	1.447588	0.906157	1.230532	-0.002198	8.197541e-05	68.340892	6.696535
Std	0.011636	0.006809	0.000701	0.000001	6.424740e-07	3.262074	0.022349	1.064923	0.039922	0.006704	0.010484	0.000522	4.272031e-07	2.882683	0.000161

In [15]:

Copied!





result, phase, predicted_data, r_squared = fit_spiral_in_orbit_ls(x, y, y_err=y_err, 
                                                                          units="keV",method_="discrete",
                                                                          extended_binsize=0.01, load_directly=True)


plt.plot(phase_array,  predicted_data,"o:")
plt.errorbar(phase_array, y, yerr=y_err)
plt.xlabel("Orbital phase")
plt.ylabel("Fe xvv Doppler shifts")

result
result, phase, predicted_data, r_squared = fit_spiral_in_orbit_ls(x, y, y_err=y_err, 
                                                                          units="keV",method_="discrete",
                                                                          extended_binsize=0.01, load_directly=True)


plt.plot(phase_array,  predicted_data,"o:")
plt.errorbar(phase_array, y, yerr=y_err)
plt.xlabel("Orbital phase")
plt.ylabel("Fe xvv Doppler shifts")

result

Loaded bounds from file:
iphase_orbit 0.18 - 0.25
semimajor_orbit 1.56 - 1.6
orbitalperiod 2.08 - 2.1
eccentricity 0.0 - 1e-05
periapsis 0.0 - 1e-05
inclination 67.0 - 77.0
Rstar 11.8 - 12.2
Mstar1 18.7 - 22.77
Mstar2 1.33 - 1.45
iphase_spiral 0.0 - 1.0
semimajor_spiral 0.01 - 100.0
b -0.006969 - -0.0006969
omega 8.1e-05 - 8.2e-05
inclination_spiral 67.0 - 77.0
feature 6.63 - 6.7

Out[15]:

Name of the parameter	iphase_orbit	semimajor_orbit	orbitalperiod	eccentricity	periapsis	inclination	Rstar	Mstar1	Mstar2	iphase_spiral	semimajor_spiral	b	omega	inclination_spiral	feature
Value	0.250000	1.600000e+00	2.080001	8.467492e-11	0.000010	7.699999e+01	1.206760e+01	1.870000e+01	1.450000	0.008802	1.250501	-0.005635	0.000081	6.706118e+01	6.696298
Std	165.586271	1.741014e+06	32553.676233	6.741066e+03	0.870268	3.950366e+07	1.054803e+07	1.083641e+07	941411.577794	0.117017	809059.676331	0.170112	0.000006	7.562214e+07	30.842994

In [ ]: