Fitting a model with polarization using ixpeOGIPSpectrumLike
Using ixpeOGIPSpectrumLike, this tutorial will download simulated data and run joint likelihood and Bayesian analyses.
[1]:
import os
import matplotlib.pyplot as plt
import numpy as np
from threeML import *
from astromodels.core.polarization import *
from ixpepy.ixpeOGIPSpectrumLike import ixpeOGIPSpectrumLike
from ixpepy.utils.stokes import get_polarization_angle, get_polarization_degree
17:19:11 WARNING The naima package is not available. Models that depend on it will not be functions.py:45 available
WARNING The GSL library or the pygsl wrapper cannot be loaded. Models that depend on it functions.py:67 will not be available.
WARNING The ebltable package is not available. Models that depend on it will not be absorption.py:34 available
17:19:12 INFO Starting 3ML! __init__.py:44
WARNING WARNINGs here are NOT errors __init__.py:45
WARNING but are inform you about optional packages that can be installed __init__.py:46
WARNING to disable these messages, turn off start_warning in your config file __init__.py:47
WARNING ROOT minimizer not available minimization.py:1208
INFO IXPE plugin found. Enabling Gaussian source with Gaussian background. spectrum_likelihood.py:397
17:19:13 WARNING The cthreeML package is not installed. You will not be able to use plugins which __init__.py:95 require the C/C++ interface (currently HAWC)
WARNING Could not import plugin HAWCLike.py. Do you have the relative instrument __init__.py:136 software installed and configured?
WARNING Env. variable OMP_NUM_THREADS is not set. Please set it to 1 for optimal __init__.py:345 performances in 3ML
WARNING Env. variable MKL_NUM_THREADS is not set. Please set it to 1 for optimal __init__.py:345 performances in 3ML
WARNING Env. variable NUMEXPR_NUM_THREADS is not set. Please set it to 1 for optimal __init__.py:345 performances in 3ML
Downloading the simulated data
[2]:
from io import BytesIO
from urllib.request import urlopen
from zipfile import ZipFile
zipurl = "https://www.dropbox.com/scl/fi/thw3ql0must8vvh34509v/toy_point_source.zip?rlkey=4b9zs2g4ue3u82d7lg2340heq&st=spirza10&dl=1"
with urlopen(zipurl) as zipresp:
with ZipFile(BytesIO(zipresp.read())) as zfile:
zfile.extractall('.')
Creating the model
[3]:
source_name = 'toy_point_source'
RA = 30.
DEC = 40.
spectral_shape = Powerlaw() #Spectral shapes defined by astromodels.functions
spectral_shape.K = 20
spectral_shape.index = -2
polarization = StokesPolarization(Q=Constant(), U=Constant())
polarization.Q.Constant.k.bounds = (-1, 1)
polarization.U.Constant.k.bounds = (-1, 1)
#polarization.Q.Constant.k.prior = Uniform_prior(lower_bound=-1.0, upper_bound=1.0)
#polarization.U.Constant.k.prior = Uniform_prior(lower_bound=-1.0, upper_bound=1.0)
point_source = PointSource( source_name, RA, DEC, spectral_shape = spectral_shape, polarization = polarization)
model = Model(point_source)
model.display(complete = True)
Model summary:
Free parameters (4):
Fixed parameters (3):
Properties (0):
(none)
Linked parameters (0):
(none)
Independent variables:
(none)
Linked functions (0):
(none)
| N | |
|---|---|
| Point sources | 1 |
| Extended sources | 0 |
| Particle sources | 0 |
Free parameters (4):
| value | min_value | max_value | unit | |
|---|---|---|---|---|
| toy_point_source.spectrum.main.Powerlaw.K | 20.0 | 0.0 | 1000.0 | keV-1 s-1 cm-2 |
| toy_point_source.spectrum.main.Powerlaw.index | -2.0 | -10.0 | 10.0 | |
| toy_point_source.spectrum.main.polarization.Q.Constant.k | 0.0 | -1.0 | 1.0 | |
| toy_point_source.spectrum.main.polarization.U.Constant.k | 0.0 | -1.0 | 1.0 |
Fixed parameters (3):
| value | min_value | max_value | unit | |
|---|---|---|---|---|
| toy_point_source.position.ra | 30.0 | 0.0 | 360.0 | deg |
| toy_point_source.position.dec | 40.0 | -90.0 | 90.0 | deg |
| toy_point_source.spectrum.main.Powerlaw.piv | 1.0 | None | None | keV |
Properties (0):
(none)
Linked parameters (0):
(none)
Independent variables:
(none)
Linked functions (0):
(none)
Creating the ixpeOGIPSpectrumLike object and retrieving the datalist
[4]:
emin, emax = 2, 8
obs_list=[]
for du in [1,2,3]:
for stokes in ['', 'q', 'u']:
obs_file = os.path.join('.', '%s_du%s_pha1%s.fits' % (source_name, du, stokes))
obs_list.append(obs_file)
ixpe = ixpeOGIPSpectrumLike(energy_range='%d-%d' % (emin, emax), caldb=None)
ixpe.load_file_list(obs_list)
data = ixpe.get_datalist()
17:19:14 INFO Loading the spectrum file: ./toy_point_source_du1_pha1.fits ixpeOGIPSpectrumLike.py:81
INFO ixpeOGIPSpectrumLike will use Poisson errors for I ixpeOGIPSpectrumLike.py:89
WARNING Found 115 energy channels where STAT_ERR is 0: (array([216, 230, ixpeOGIPSpectrumLike.py:208 242, 244, 250, 253, 257, 259, 260, 264, 266, 268, 269, 270, 271, 274, 275, 276, 277, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374]),)
WARNING Forcing the corresponding RATE channels to 0! ixpeOGIPSpectrumLike.py:209
17:19:14 WARNING Could not find QUALITY in columns or header of PHA file. This is not a valid pha_spectrum.py:201 OGIP file. Assuming QUALITY =0 (good)
WARNING Found TSTOP and TELAPSE. This file is invalid. Using TSTOP. pha_spectrum.py:249
WARNING FILTER is not set. This is not a compliant OGIP file. Assuming no FILTER. pha_spectrum.py:385
WARNING Maximum MC energy (12.0) is smaller than maximum EBOUNDS energy (15.0) response.py:125
WARNING Minimum MC energy (1.0) is larger than minimum EBOUNDS energy (0.0) response.py:133
INFO Auto-probed noise models: SpectrumLike.py:478
INFO - observation: poisson SpectrumLike.py:479
INFO - background: None SpectrumLike.py:480
INFO Plugin assigned to: I ixpeOGIPSpectrumLike.py:151
INFO Range 2-8 translates to channels 49-199 SpectrumLike.py:1229
INFO Loading the spectrum file: ./toy_point_source_du1_pha1q.fits ixpeOGIPSpectrumLike.py:81
WARNING Found 115 energy channels where STAT_ERR is 0: (array([216, 230, ixpeOGIPSpectrumLike.py:208 242, 244, 250, 253, 257, 259, 260, 264, 266, 268, 269, 270, 271, 274, 275, 276, 277, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374]),)
WARNING Forcing the corresponding RATE channels to 0! ixpeOGIPSpectrumLike.py:209
WARNING Could not find QUALITY in columns or header of PHA file. This is not a valid pha_spectrum.py:201 OGIP file. Assuming QUALITY =0 (good)
WARNING Found TSTOP and TELAPSE. This file is invalid. Using TSTOP. pha_spectrum.py:249
WARNING FILTER is not set. This is not a compliant OGIP file. Assuming no FILTER. pha_spectrum.py:385
WARNING Maximum MC energy (12.0) is smaller than maximum EBOUNDS energy (15.0) response.py:125
WARNING Minimum MC energy (1.0) is larger than minimum EBOUNDS energy (0.0) response.py:133
INFO Auto-probed noise models: SpectrumLike.py:478
INFO - observation: gaussian SpectrumLike.py:479
INFO - background: None SpectrumLike.py:480
INFO Plugin assigned to: Q ixpeOGIPSpectrumLike.py:151
INFO Range 2-8 translates to channels 49-199 SpectrumLike.py:1229
INFO Remove channels with 0 counts for spectrum Q ixpeOGIPSpectrumLike.py:154
INFO Loading the spectrum file: ./toy_point_source_du1_pha1u.fits ixpeOGIPSpectrumLike.py:81
WARNING Found 115 energy channels where STAT_ERR is 0: (array([216, 230, ixpeOGIPSpectrumLike.py:208 242, 244, 250, 253, 257, 259, 260, 264, 266, 268, 269, 270, 271, 274, 275, 276, 277, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374]),)
WARNING Forcing the corresponding RATE channels to 0! ixpeOGIPSpectrumLike.py:209
WARNING Could not find QUALITY in columns or header of PHA file. This is not a valid pha_spectrum.py:201 OGIP file. Assuming QUALITY =0 (good)
WARNING Found TSTOP and TELAPSE. This file is invalid. Using TSTOP. pha_spectrum.py:249
WARNING FILTER is not set. This is not a compliant OGIP file. Assuming no FILTER. pha_spectrum.py:385
WARNING Maximum MC energy (12.0) is smaller than maximum EBOUNDS energy (15.0) response.py:125
WARNING Minimum MC energy (1.0) is larger than minimum EBOUNDS energy (0.0) response.py:133
INFO Auto-probed noise models: SpectrumLike.py:478
INFO - observation: gaussian SpectrumLike.py:479
INFO - background: None SpectrumLike.py:480
INFO Plugin assigned to: U ixpeOGIPSpectrumLike.py:151
INFO Range 2-8 translates to channels 49-199 SpectrumLike.py:1229
INFO Remove channels with 0 counts for spectrum U ixpeOGIPSpectrumLike.py:154
INFO Loading the spectrum file: ./toy_point_source_du2_pha1.fits ixpeOGIPSpectrumLike.py:81
INFO ixpeOGIPSpectrumLike will use Poisson errors for I ixpeOGIPSpectrumLike.py:89
WARNING Found 123 energy channels where STAT_ERR is 0: (array([232, 242, ixpeOGIPSpectrumLike.py:208 245, 247, 249, 251, 253, 254, 255, 256, 257, 258, 259, 260, 261, 263, 264, 265, 266, 267, 268, 270, 271, 272, 273, 274, 276, 277, 278, 279, 280, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374]),)
WARNING Forcing the corresponding RATE channels to 0! ixpeOGIPSpectrumLike.py:209
WARNING Could not find QUALITY in columns or header of PHA file. This is not a valid pha_spectrum.py:201 OGIP file. Assuming QUALITY =0 (good)
WARNING Found TSTOP and TELAPSE. This file is invalid. Using TSTOP. pha_spectrum.py:249
WARNING FILTER is not set. This is not a compliant OGIP file. Assuming no FILTER. pha_spectrum.py:385
WARNING Maximum MC energy (12.0) is smaller than maximum EBOUNDS energy (15.0) response.py:125
WARNING Minimum MC energy (1.0) is larger than minimum EBOUNDS energy (0.0) response.py:133
INFO Auto-probed noise models: SpectrumLike.py:478
INFO - observation: poisson SpectrumLike.py:479
INFO - background: None SpectrumLike.py:480
INFO Plugin assigned to: I ixpeOGIPSpectrumLike.py:151
INFO Range 2-8 translates to channels 49-199 SpectrumLike.py:1229
INFO Loading the spectrum file: ./toy_point_source_du2_pha1q.fits ixpeOGIPSpectrumLike.py:81
WARNING Found 123 energy channels where STAT_ERR is 0: (array([232, 242, ixpeOGIPSpectrumLike.py:208 245, 247, 249, 251, 253, 254, 255, 256, 257, 258, 259, 260, 261, 263, 264, 265, 266, 267, 268, 270, 271, 272, 273, 274, 276, 277, 278, 279, 280, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374]),)
WARNING Forcing the corresponding RATE channels to 0! ixpeOGIPSpectrumLike.py:209
WARNING Could not find QUALITY in columns or header of PHA file. This is not a valid pha_spectrum.py:201 OGIP file. Assuming QUALITY =0 (good)
WARNING Found TSTOP and TELAPSE. This file is invalid. Using TSTOP. pha_spectrum.py:249
WARNING FILTER is not set. This is not a compliant OGIP file. Assuming no FILTER. pha_spectrum.py:385
WARNING Maximum MC energy (12.0) is smaller than maximum EBOUNDS energy (15.0) response.py:125
WARNING Minimum MC energy (1.0) is larger than minimum EBOUNDS energy (0.0) response.py:133
INFO Auto-probed noise models: SpectrumLike.py:478
INFO - observation: gaussian SpectrumLike.py:479
INFO - background: None SpectrumLike.py:480
INFO Plugin assigned to: Q ixpeOGIPSpectrumLike.py:151
INFO Range 2-8 translates to channels 49-199 SpectrumLike.py:1229
INFO Remove channels with 0 counts for spectrum Q ixpeOGIPSpectrumLike.py:154
INFO Loading the spectrum file: ./toy_point_source_du2_pha1u.fits ixpeOGIPSpectrumLike.py:81
WARNING Found 123 energy channels where STAT_ERR is 0: (array([232, 242, ixpeOGIPSpectrumLike.py:208 245, 247, 249, 251, 253, 254, 255, 256, 257, 258, 259, 260, 261, 263, 264, 265, 266, 267, 268, 270, 271, 272, 273, 274, 276, 277, 278, 279, 280, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374]),)
WARNING Forcing the corresponding RATE channels to 0! ixpeOGIPSpectrumLike.py:209
17:19:15 WARNING Could not find QUALITY in columns or header of PHA file. This is not a valid pha_spectrum.py:201 OGIP file. Assuming QUALITY =0 (good)
WARNING Found TSTOP and TELAPSE. This file is invalid. Using TSTOP. pha_spectrum.py:249
WARNING FILTER is not set. This is not a compliant OGIP file. Assuming no FILTER. pha_spectrum.py:385
WARNING Maximum MC energy (12.0) is smaller than maximum EBOUNDS energy (15.0) response.py:125
WARNING Minimum MC energy (1.0) is larger than minimum EBOUNDS energy (0.0) response.py:133
INFO Auto-probed noise models: SpectrumLike.py:478
INFO - observation: gaussian SpectrumLike.py:479
INFO - background: None SpectrumLike.py:480
17:19:15 INFO Plugin assigned to: U ixpeOGIPSpectrumLike.py:151
INFO Range 2-8 translates to channels 49-199 SpectrumLike.py:1229
INFO Remove channels with 0 counts for spectrum U ixpeOGIPSpectrumLike.py:154
INFO Loading the spectrum file: ./toy_point_source_du3_pha1.fits ixpeOGIPSpectrumLike.py:81
INFO ixpeOGIPSpectrumLike will use Poisson errors for I ixpeOGIPSpectrumLike.py:89
WARNING Found 116 energy channels where STAT_ERR is 0: (array([238, 241, ixpeOGIPSpectrumLike.py:208 247, 250, 252, 255, 257, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 272, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 287, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374]),)
WARNING Forcing the corresponding RATE channels to 0! ixpeOGIPSpectrumLike.py:209
WARNING Could not find QUALITY in columns or header of PHA file. This is not a valid pha_spectrum.py:201 OGIP file. Assuming QUALITY =0 (good)
WARNING Found TSTOP and TELAPSE. This file is invalid. Using TSTOP. pha_spectrum.py:249
WARNING FILTER is not set. This is not a compliant OGIP file. Assuming no FILTER. pha_spectrum.py:385
WARNING Maximum MC energy (12.0) is smaller than maximum EBOUNDS energy (15.0) response.py:125
WARNING Minimum MC energy (1.0) is larger than minimum EBOUNDS energy (0.0) response.py:133
INFO Auto-probed noise models: SpectrumLike.py:478
INFO - observation: poisson SpectrumLike.py:479
INFO - background: None SpectrumLike.py:480
INFO Plugin assigned to: I ixpeOGIPSpectrumLike.py:151
INFO Range 2-8 translates to channels 49-199 SpectrumLike.py:1229
INFO Loading the spectrum file: ./toy_point_source_du3_pha1q.fits ixpeOGIPSpectrumLike.py:81
WARNING Found 116 energy channels where STAT_ERR is 0: (array([238, 241, ixpeOGIPSpectrumLike.py:208 247, 250, 252, 255, 257, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 272, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 287, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374]),)
WARNING Forcing the corresponding RATE channels to 0! ixpeOGIPSpectrumLike.py:209
WARNING Could not find QUALITY in columns or header of PHA file. This is not a valid pha_spectrum.py:201 OGIP file. Assuming QUALITY =0 (good)
WARNING Found TSTOP and TELAPSE. This file is invalid. Using TSTOP. pha_spectrum.py:249
WARNING FILTER is not set. This is not a compliant OGIP file. Assuming no FILTER. pha_spectrum.py:385
WARNING Maximum MC energy (12.0) is smaller than maximum EBOUNDS energy (15.0) response.py:125
WARNING Minimum MC energy (1.0) is larger than minimum EBOUNDS energy (0.0) response.py:133
INFO Auto-probed noise models: SpectrumLike.py:478
INFO - observation: gaussian SpectrumLike.py:479
INFO - background: None SpectrumLike.py:480
INFO Plugin assigned to: Q ixpeOGIPSpectrumLike.py:151
INFO Range 2-8 translates to channels 49-199 SpectrumLike.py:1229
INFO Remove channels with 0 counts for spectrum Q ixpeOGIPSpectrumLike.py:154
INFO Loading the spectrum file: ./toy_point_source_du3_pha1u.fits ixpeOGIPSpectrumLike.py:81
WARNING Found 116 energy channels where STAT_ERR is 0: (array([238, 241, ixpeOGIPSpectrumLike.py:208 247, 250, 252, 255, 257, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 272, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 287, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374]),)
WARNING Forcing the corresponding RATE channels to 0! ixpeOGIPSpectrumLike.py:209
WARNING Could not find QUALITY in columns or header of PHA file. This is not a valid pha_spectrum.py:201 OGIP file. Assuming QUALITY =0 (good)
WARNING Found TSTOP and TELAPSE. This file is invalid. Using TSTOP. pha_spectrum.py:249
WARNING FILTER is not set. This is not a compliant OGIP file. Assuming no FILTER. pha_spectrum.py:385
WARNING Maximum MC energy (12.0) is smaller than maximum EBOUNDS energy (15.0) response.py:125
WARNING Minimum MC energy (1.0) is larger than minimum EBOUNDS energy (0.0) response.py:133
INFO Auto-probed noise models: SpectrumLike.py:478
INFO - observation: gaussian SpectrumLike.py:479
INFO - background: None SpectrumLike.py:480
INFO Plugin assigned to: U ixpeOGIPSpectrumLike.py:151
INFO Range 2-8 translates to channels 49-199 SpectrumLike.py:1229
INFO Remove channels with 0 counts for spectrum U ixpeOGIPSpectrumLike.py:154
Fitting the data with JointLikelihood
[5]:
jl = JointLikelihood(model, data)
ixpe.fit_area_correction(model)
jl.fit()
results = jl.results
INFO set the minimizer to minuit joint_likelihood.py:994
INFO Fitting an effective area correction for DU1 ixpeOGIPSpectrumLike.py:185
INFO ixpe_DU1_I is using effective area correction (between 0.5 and 1.2) SpectrumLike.py:2216
INFO Fitting an effective area correction for DU1 ixpeOGIPSpectrumLike.py:185
INFO ixpe_DU1_Q is using effective area correction (between 0.5 and 1.2) SpectrumLike.py:2216
INFO Fitting an effective area correction for DU1 ixpeOGIPSpectrumLike.py:185
INFO ixpe_DU1_U is using effective area correction (between 0.5 and 1.2) SpectrumLike.py:2216
INFO Fitting an effective area correction for DU2 ixpeOGIPSpectrumLike.py:185
INFO ixpe_DU2_I is using effective area correction (between 0.5 and 1.2) SpectrumLike.py:2216
INFO Fitting an effective area correction for DU2 ixpeOGIPSpectrumLike.py:185
INFO ixpe_DU2_Q is using effective area correction (between 0.5 and 1.2) SpectrumLike.py:2216
INFO Fitting an effective area correction for DU2 ixpeOGIPSpectrumLike.py:185
INFO ixpe_DU2_U is using effective area correction (between 0.5 and 1.2) SpectrumLike.py:2216
INFO Fitting an effective area correction for DU3 ixpeOGIPSpectrumLike.py:185
INFO ixpe_DU3_I is using effective area correction (between 0.5 and 1.2) SpectrumLike.py:2216
INFO Fitting an effective area correction for DU3 ixpeOGIPSpectrumLike.py:185
INFO ixpe_DU3_Q is using effective area correction (between 0.5 and 1.2) SpectrumLike.py:2216
INFO Fitting an effective area correction for DU3 ixpeOGIPSpectrumLike.py:185
INFO ixpe_DU3_U is using effective area correction (between 0.5 and 1.2) SpectrumLike.py:2216
Best fit values:
| result | unit | |
|---|---|---|
| parameter | ||
| toy_point_source.spectrum.main.Powerlaw.K | 9.84 +/- 0.04 | 1 / (cm2 keV s) |
| toy_point_source.spectrum.main.Powerlaw.index | -1.998 +/- 0.004 | |
| toy_point_source...k | (5.8 +/- 0.5) x 10^-2 | |
| toy_point_source...k | (8.3 +/- 0.5) x 10^-2 | |
| cons_ixpe_DU2_I | 1.0010 +/- 0.0024 | |
| cons_ixpe_DU3_I | 1.0023 +/- 0.0024 |
Correlation matrix:
| 1.00 | -0.92 | 0.00 | 0.01 | -0.28 | -0.27 |
| -0.92 | 1.00 | -0.01 | -0.01 | 0.00 | -0.00 |
| 0.00 | -0.01 | 1.00 | 0.00 | 0.00 | -0.00 |
| 0.01 | -0.01 | 0.00 | 1.00 | -0.00 | 0.00 |
| -0.28 | 0.00 | 0.00 | -0.00 | 1.00 | 0.48 |
| -0.27 | -0.00 | -0.00 | 0.00 | 0.48 | 1.00 |
Values of -log(likelihood) at the minimum:
| -log(likelihood) | |
|---|---|
| ixpe_DU1_I | 694.526948 |
| ixpe_DU1_Q | 87.645864 |
| ixpe_DU1_U | 83.819290 |
| ixpe_DU2_I | 691.749668 |
| ixpe_DU2_Q | 68.628108 |
| ixpe_DU2_U | 88.687331 |
| ixpe_DU3_I | 687.240547 |
| ixpe_DU3_Q | 99.876708 |
| ixpe_DU3_U | 90.165734 |
| total | 2592.340199 |
Values of statistical measures:
| statistical measures | |
|---|---|
| AIC | 5196.742528 |
| BIC | 5227.967425 |
Getting the results
[6]:
u = results.get_variates('toy_point_source.spectrum.main.polarization.U.Constant.k')
q = results.get_variates('toy_point_source.spectrum.main.polarization.Q.Constant.k')
pol_angle = get_polarization_angle(q, u)
pol_degree = get_polarization_degree(q, u)
print("PD: ", pol_degree)
print("PA: ", pol_angle)
PD: equal-tail: (1.01 +/- 0.05) x 10^-1, hpd: (1.01 +/- 0.05) x 10^-1
PA: equal-tail: (2.74 +/- 0.14) x 10, hpd: (2.74 -0.13 +0.15) x 10
Plotting spectrum and polarization
[7]:
%matplotlib inline
from ixpepy.io.plotting import plot_I_spectrum, plot_QU_spectra
figI = plot_I_spectrum(jl, emin, emax)
figQ, figU = plot_QU_spectra(jl, emin, emax, ymin=-3, ymax=3)
[ ]:
from ixpepy.io.plotting import plot_QU_polar
fig = plot_QU_polar(q, u, sigma=True)
[ ]:
from ixpepy.io.plotting import plot_QU
fig = plot_QU(q, u)
