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  • Time Phase Relation Theoretical
  • Doppler Theoretical in four scenarios
  • Density Through the Orbit and Absorption Column
  • Density and Ionization Parameter in the Orbital Path of Radiation
  • Ionization Map of 4U0114+65
  • Ns pulse shape in Vela X-1
  • Fe XXV Doppler Shifts Cen X-3
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    • SIMPLE ORBIT
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    • SPIRAL IN ORBIT
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xraybinaryorbit
  • EXAMPLES
  • Fe XXV Doppler Shifts Cen X-3

Doppler Shifts in Cen X-3 Chandra ObservationĀ¶

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.

InĀ [1]:
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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.

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.
InĀ [3]:
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# 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.

InĀ [4]:
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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 ORBITĀ¶

InĀ [4]:
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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, 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, 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, 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
Stopping search: Swarm best objective change less than 1e-08
Stopping search: maximum iterations reached --> 100
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 0.199140 1.589276 2.087822 2.533493e-06 9.943691e-71 68.621156 11.800649 21.335643 1.405025 0.002423 1.00000 0.148397 0.419432 178.353129 71.852455 9.003696e-23 6.697133 1.000000e-70
Std 0.015315 0.024253 0.000174 5.184498e-07 4.034923e-71 3.297979 0.023713 1.298307 0.020059 0.455633 0.05892 0.001728 0.047004 19.276144 0.956224 1.764827e-23 0.005342 2.214635e-71
No description has been provided for this image
InĀ [5]:
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result, phase, dphase, predicted_data, r_squared = fit_disc_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, dphase, predicted_data, r_squared = fit_disc_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
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 0.229421 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
No description has been provided for this image

SIMPLE ORBITĀ¶

InĀ [13]:
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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
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 semimajor orbitalperiod eccentricity periapsis inclination Rstar Mstar1 Mstar2 wind_vel feature
Value 0.877626 0.953377 0.136915 0.000001 0.000003 71.100357 12.153615 22.598133 1.359200 0.259007 6.681255
Std 0.438781 0.502451 0.075085 0.000004 0.000002 1.420469 0.172452 0.473675 0.002993 0.113941 0.001278
No description has been provided for this image
InĀ [7]:
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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=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_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
Out[7]:
Name of the parameter iphase semimajor orbitalperiod eccentricity periapsis inclination Rstar Mstar1 Mstar2 wind_vel feature
Value 0.346083 3.000000e+00 1.413539 0.00001 2.588310e-07 7.600000e+01 1.220000e+01 22.770000 1.330000 0.968640 6.68708
Std 94.048495 2.070051e+06 532.634043 98.38035 5.926204e-05 7.721913e+07 8.800959e+06 48832.976952 836035.252628 567833.929341 0.40136
No description has been provided for this image

SIMPLE SPIRALĀ¶

InĀ [8]:
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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=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_ps(x, y, y_err=y_err, num_iterations=2, maxiter = 100, swarmsize = 10, units="keV",method_="extended", 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
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 0.914062 6.775387 -0.953417 0.911496 21.639983 6.693066
Std 0.393342 4.181845 0.347828 0.161760 34.180008 0.000001
No description has been provided for this image
InĀ [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_="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_ps(x, y, y_err=y_err, num_iterations=2, maxiter = 100, swarmsize = 10, 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
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 0.00000 1.000000 -0.193534 0.110914 90.0 6.693068
Std 0.30383 41.613181 0.085854 0.004413 45.0 0.000003
No description has been provided for this image

SPIRAL IN ORBITĀ¶

InĀ [10]:
Copied! 
result, phase,predicted_data, r_squared = fit_spiral_in_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=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_ps(x, y, y_err=y_err, num_iterations=2, maxiter = 100, swarmsize = 10, units="keV",method_="extended", 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
Stopping search: Swarm best objective change less than 1e-08
Stopping search: Swarm best position change less than 1e-08
Out[10]:
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 0.193541 1.599911 2.092679 0.000009 9.043930e-06 68.408215 12.000956 22.605434 1.422866 0.035448 32.299697 -0.078057 0.000458 71.420973 6.668666
Std 0.024344 0.011176 0.002397 0.000004 5.012522e-07 1.907146 0.083272 0.857287 0.029576 0.062191 33.850152 0.023385 0.001986 2.789513 0.014301
No description has been provided for this image
InĀ [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
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
No description has been provided for this image
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