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 input parameters or bounds can be provided as lists, by providing a "parameter_list" or "bound_list" as imputs.

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 [3]:

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 [4]:

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[4]:

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

No description has been provided for this image

DISC IN ORBIT¶

In [5]:

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=2, maxiter = 100, swarmsize = 10, 
                                                               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=2, maxiter = 100, swarmsize = 10, 
                                                               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

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	0.25	1.500000	2.090000	0.000000	9.208236e-72	67.577456	12.170968	22.613230	1.364358	0.0	0.918103	0.143691	0.216322	202.394165	72.606602	3.964419e-23	6.687392	1.195249e-71
Std	0.00	0.050169	0.001172	0.000004	4.600157e-72	3.994346	0.168759	1.208276	0.013431	0.0	0.034347	0.000094	0.066788	6.900522	1.484255	4.377393e-24	0.006667	2.620325e-71

In [6]:

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

The number of time points does not allow an extended approach. Changing to discrete
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[6]:

Name of the parameter	iphase	semimajor	orbitalperiod	eccentricity	periapsis	inclination	Rstar	Mstar1	Mstar2	iphase2	semimajor2	orbitalperiod2	eccentricity2	periapsis2	inclination2	Mass3	feature	wind_vel
Value	0.229421	1.602705e+00	2.088416	0.000005	5.000000e-71	7.185122e+01	1.202115e+01	2.073527e+01	1.389881e+00	0.051058	9.478598e-01	0.149553	0.309786	179.230921	7.188573e+01	5.000000e-23	6.687091	5.000000e-71
Std	95.773487	3.305021e+06	17491.780267	1018.059231	1.510464e+01	3.136903e+08	2.269546e+07	3.994571e+07	1.581843e+06	0.605037	2.592831e+06	0.000017	1.071481	141.799174	1.839176e+08	0.000000e+00	163.553841	0.000000e+00

SIMPLE ORBIT¶

In [9]:

Copied!





result, phase,  predicted_data, r_squared = fit_orbit_ps(x, y, y_err=y_err, 
                                                         num_iterations=2, maxiter = 100, swarmsize = 10, 
                                                         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_orbit_ps(x, y, y_err=y_err, 
                                                         num_iterations=2, maxiter = 100, swarmsize = 10, 
                                                         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  0.18 - 0.25
semimajor  0.1 - 0.7
orbitalperiod  0.1 - 0.3
eccentricity  0.0 - 0.9
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
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

Out[9]:

Name of the parameter	iphase	semimajor	orbitalperiod	eccentricity	periapsis	inclination	Rstar	Mstar1	Mstar2	wind_vel	feature
Value	0.214426	0.607301	0.155116	0.254905	3.553538e-71	73.573204	11.961102	21.042315	1.404470	0.310709	6.67
Std	0.011215	0.072998	0.006641	0.151526	2.439175e-71	0.679432	0.054641	0.355267	0.001021	0.102472	0.00

In [11]:

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

The number of time points does not allow an extended approach. Changing to discrete
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[11]:

Name of the parameter	iphase	semimajor	orbitalperiod	eccentricity	periapsis	inclination	Rstar	Mstar1	Mstar2	wind_vel	feature
Value	0.180000	0.908372	0.156026	0.300000	234.106099	7.468590e+01	1.211418e+01	2.143424e+01	1.430856	1.603272e-39	6.670000
Std	2.567568	459909.501250	0.021669	0.390541	1034.799705	4.495860e+07	6.987350e+06	8.941463e+06	774536.971182	4.583158e+04	0.059582

$No description has been provided for this image$

SIMPLE SPIRAL¶

In [9]:

Copied!





result, phase, predicted_data, r_squared = fit_spiral_ps(x, y, y_err=y_err, 
                                                         num_iterations=2, maxiter = 100, swarmsize = 10, 
                                                         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=2, maxiter = 100, swarmsize = 10, 
                                                         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 - 0.01
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

Out[9]:

Name of the parameter	iphase_spiral	semimajor_spiral	b	omega	inclination_spiral	feature
Value	0.831337	13.049990	-0.00100	0.004289	69.090425	6.700000
Std	0.029064	0.103194	0.28238	0.001722	0.497996	0.003441

In [13]:

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

The number of time points does not allow an extended approach. Changing to discrete
Loaded bounds from file:
iphase_spiral 0.0 - 1.0
semimajor_spiral 1.0 - 100.0
b -1.0 - 0.0
omega 0.0 - 1.0
inclination_spiral 0.0 - 90.0
feature 6.63 - 6.7

Coefficient of Determination (R-squared): 0.0003
Name of the parameter  iphase_spiral  semimajor_spiral             b         omega  inclination_spiral   feature
Value                       0.500014      5.049513e+01 -5.000492e-01  4.999508e-01        4.499557e+01  6.689007
Std                         0.000248      7.086160e-11  1.124131e-08  7.156945e-09        6.245946e-11  0.020589

Out[13]:

Name of the parameter	iphase_spiral	semimajor_spiral	b	omega	inclination_spiral	feature
Value	0.500014	5.049513e+01	-5.000492e-01	4.999508e-01	4.499557e+01	6.689007
Std	0.000248	7.086160e-11	1.124131e-08	7.156945e-09	6.245946e-11	0.020589

SPIRAL IN ORBIT¶

In [14]:

Copied!





result, phase,predicted_data, r_squared = fit_spiral_in_orbit_ps(x, y, y_err=y_err, 
                                                                          num_iterations=2, maxiter = 100, swarmsize = 30,  
                                                                          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=2, maxiter = 100, swarmsize = 30,  
                                                                          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  -0.1 - 0.0
omega  1e-07 - 0.1
inclination_spiral  67.0 - 77.0
feature  6.63 - 6.7

Stopping search: maximum iterations reached --> 100
Stopping search: Swarm best objective change less than 1e-08

Out[14]:

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	0.197037	1.587306	2.084676	0.000004	0.000008	73.143157	11.861213	22.244802	1.336289	0.645055	14.172908	-0.071236	0.000099	68.071782	6.679339
Std	0.005283	0.003933	0.004866	0.000002	0.000002	1.195020	0.031785	0.999569	0.034654	0.172345	0.543587	0.028510	0.001052	0.117379	0.009189

In [11]:

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

The number of time points does not allow an extended approach. Changing to discrete
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 -0.1 - 0.0
omega 1e-07 - 0.1
inclination_spiral 67.0 - 77.0

Out[11]:

Name of the parameter	iphase_orbit	semimajor_orbit	orbitalperiod	eccentricity	periapsis	inclination	Rstar	Mstar1	Mstar2	iphase_spiral	semimajor_spiral	b	omega	inclination_spiral
Value	2.150000e-01	1.580000e+00	2.090000e+00	0.000005	5.000000e-06	72.000000	12.000000	20.735000	1.39	0.499992	5.000500e+01	-0.050000	0.050000	7.200000e+01
Std	1.196357e+06	4.569182e+06	3.836764e+06	0.000105	1.305855e-09	7.368156	601608.972213	348170.132775	0.00	0.394674	5.964791e-07	0.000022	0.001275	2.582047e-07

In [ ]: