Fermi-LAT via FermiPyLike

In this Example we show how to use the fermipy plugin in threeML. We perform a Binned likelihood analysis and a Bayesian analysis of the Crab, optimizing the parameters of the Crab Pulsar (PSR J0534+2200) keeping fixed the parameters of the Crab Nebula. In the model, the nebula is described by two sources, one representing the synchrotron spectrum, the othet the Inverse Compton emission. In this example we show how to download Fermi-LAT data, how to build a model starting from the 4FGL, how to free and fix parameters of the sources in the model, and how to perform a spectral analysis using the fermipy plugin.

[1]:

import warnings

warnings.simplefilter("ignore")
import numpy as np

np.seterr(all="ignore")
import shutil
from IPython.display import Image, display
import glob
from pathlib import Path
import matplotlib as mpl
from matplotlib import pyplot as plt
from astropy.io import fits as pyfits
import scipy as sp

[2]:

%%capture
from threeML import *

[3]:

from jupyterthemes import jtplot

%matplotlib inline
jtplot.style(context="talk", fscale=1, ticks=True, grid=False)
set_threeML_style()
silence_warnings()

The Fermi 4FGL catalog

Let’s interrogate the 4FGL to get the sources in a radius of 20.0 deg around the Crab

[4]:

lat_catalog = FermiLATSourceCatalog()

ra, dec, table = lat_catalog.search_around_source("Crab", radius=20.0)

table

23:17:17 INFO      The cache for fermilpsc does not yet exist. We will try to     get_heasarc_table_as_pandas.py:64
                  build it                                                                                         
                                                                                                                   

         INFO      Building cache for fermilpsc                                  get_heasarc_table_as_pandas.py:112

Trying https://heasarc.gsfc.nasa.gov/cgi-bin/vo/cone/coneGet.pl?table=fermilpsc&

[4]:
Table length=196
namesource_typeshort_source_typeradecassoc_nametevcat_assocSearch_Offset
degdeg
objectstr52objectfloat64float64objectobjectfloat64
4FGL J0534.5+2201spulsar wind nebulaPWN83.633122.0199Crab NebulaCrab0.3965
4FGL J0534.5+2201ipulsar wind nebulaPWN83.633022.0200Crab NebulaCrab0.3979
4FGL J0534.5+2200pulsar, identified by pulsationsPSR83.636722.0149PSR J0534+2200Crab pulsar0.4447
4FGL J0526.3+2246active galaxy of uncertain typebcu81.590822.7778NVSS J052622+224801121.9694
4FGL J0544.4+2238unknown86.109322.6418142.7227
4FGL J0521.7+2112BL Lac type of blazarbll80.444521.2131TXS 0518+211VER J0521+211184.0105
4FGL J0528.3+1817unknownunk82.094618.29431RXS J052829.6+181657239.3570
4FGL J0519.7+1939unknown79.945719.6646250.0485
4FGL J0536.2+1733BL Lac type of blazarbll84.071917.5534TXS 0533+175268.8438
........................
4FGL J0552.8+0313active galaxy of uncertain typebcu88.21803.2322PKS 0550+0321158.2177
4FGL J0431.0+3529cunknown67.765035.49491159.0130
4FGL J0653.6+1636active galaxy of uncertain typebcu103.410516.61062MASX J06533986+16364321164.9659
4FGL J0658.7+2318unknown104.680823.30271167.1721
4FGL J0552.0+0256cunknown88.01402.94171172.5618
4FGL J0555.1+0304active galaxy of uncertain typebcu88.77763.0710GB6 J0555+03041175.5384
4FGL J0658.2+2709active galaxy of uncertain typebcu104.573527.1501B2 0655+27A1181.9183
4FGL J0642.4+1048unknown100.608110.81351184.1778
4FGL J0506.9+0323BL Lac type of blazarbll76.73143.3917NVSS J050650+0324011187.3710
4FGL J0409.2+2542unknown62.314425.70221188.9075

This gets a 3ML model (a Model instance) from the table above, where every source in the 4FGL becomes a Source instance. Note that by default all parameters of all sources are fixed.

[5]:

model = lat_catalog.get_model()

Let’s free all the normalizations within 3 deg from the center.

[6]:

model.free_point_sources_within_radius(3.0, normalization_only=True)

model.display()
Model summary:

N
Point sources 196
Extended sources 0
Particle sources 0


Free parameters (5):

value min_value max_value unit
Crab_synch.spectrum.main.Log_parabola.K 0.0 0.0 0.0 keV-1 s-1 cm-2
Crab_IC.spectrum.main.Log_parabola.K 0.0 0.0 0.0 keV-1 s-1 cm-2
PSR_J0534p2200.spectrum.main.Super_cutoff_powerlaw.K 0.0 0.0 0.0 keV-1 s-1 cm-2
NVSS_J052622p224801.spectrum.main.Powerlaw.K 0.0 0.0 0.0 keV-1 s-1 cm-2
x4FGL_J0544d4p2238.spectrum.main.Powerlaw.K 0.0 0.0 0.0 keV-1 s-1 cm-2


Fixed parameters (1089):
(abridged. Use complete=True to see all fixed parameters)


Properties (0):

(none)


Linked parameters (0):

(none)

Independent variables:

(none)

Linked functions (0):

(none)

but then let’s fix the sync and the IC components of the Crab nebula (cannot fit them with just one month of data) (these two methods are equivalent)

[7]:

model["Crab_IC.spectrum.main.Log_parabola.K"].fix = True
model.Crab_synch.spectrum.main.Log_parabola.K.fix = True

However, let’s free the index of the Crab Pulsar

[8]:

model.PSR_J0534p2200.spectrum.main.Super_cutoff_powerlaw.index.free = True

model.display()
Model summary:

N
Point sources 196
Extended sources 0
Particle sources 0


Free parameters (4):

value min_value max_value unit
PSR_J0534p2200.spectrum.main.Super_cutoff_powerlaw.K 0.0 0.0 0.0 keV-1 s-1 cm-2
PSR_J0534p2200.spectrum.main.Super_cutoff_powerlaw.index -1.826553 -10.0 10.0
NVSS_J052622p224801.spectrum.main.Powerlaw.K 0.0 0.0 0.0 keV-1 s-1 cm-2
x4FGL_J0544d4p2238.spectrum.main.Powerlaw.K 0.0 0.0 0.0 keV-1 s-1 cm-2


Fixed parameters (1090):
(abridged. Use complete=True to see all fixed parameters)


Properties (0):

(none)


Linked parameters (0):

(none)

Independent variables:

(none)

Linked functions (0):

(none)
[9]:

# Download data from Jan 01 2010 to February 1 2010

tstart = "2010-01-01 00:00:00"
tstop = "2010-02-01 00:00:00"

# Note that this will understand if you already download these files, and will
# not do it twice unless you change your selection or the outdir

evfile, scfile = download_LAT_data(
    ra,
    dec,
    20.0,
    tstart,
    tstop,
    time_type="Gregorian",
    destination_directory="Crab_data",
)

23:17:33 INFO      Query parameters:                                                       download_LAT_data.py:262

         INFO                          coordfield = 83.6287,22.0147                        download_LAT_data.py:266

         INFO                         coordsystem = J2000                                  download_LAT_data.py:266

         INFO                          shapefield = 20.0                                   download_LAT_data.py:266

         INFO                           timefield = 2010-01-01 00:00:00,2010-02-01         download_LAT_data.py:266
                  00:00:00                                                                                         

         INFO                            timetype = Gregorian                              download_LAT_data.py:266

         INFO                         energyfield = 30.000,1000000.000                     download_LAT_data.py:266

         INFO              photonOrExtendedOrNone = Photon                                 download_LAT_data.py:266

         INFO                         destination = query                                  download_LAT_data.py:266

         INFO                          spacecraft = checked                                download_LAT_data.py:266

         INFO      Query ID: b7ba925258c89244b49cc1889e66d453                              download_LAT_data.py:271

23:17:34 INFO      Estimated complete time for your query: 13 seconds                      download_LAT_data.py:428

         INFO      If this download fails, you can find your data at                       download_LAT_data.py:437
                  https://fermi.gsfc.nasa.gov/cgi-bin/ssc/LAT/QueryResults.cgi?id=L2402071                         
                  81735E696CEF296 (when ready)                                                                     

23:17:47 INFO      Downloading FT1 and FT2 files...                                        download_LAT_data.py:527

Configuration for Fermipy

3ML provides and intreface into Fermipy via the FermipyLike plugin. We can use it to generate basic configuration files.

Note

Currently, the FermipyLike plugin does not provide an interface to handle extended sources. This will change

[10]:

config = FermipyLike.get_basic_config(
    evfile=evfile,
    scfile=scfile,
    ra=ra,
    dec=dec,
    fermipy_verbosity=1,
    fermitools_chatter=0,
)

# See what we just got

config.display()

binning:
  binsperdec: 8
  binsz: 0.1
  roiwidth: 10.0
data:
  evfile: /Users/runner/work/threeML/threeML/docs/md_docs/slow_execute/Crab_data/Lb7ba925258c89244b49cc1889e66d453_FT1.fits
  scfile: /Users/runner/work/threeML/threeML/docs/md_docs/slow_execute/Crab_data/L240207181735E696CEF296_SC00.fits
logging:
  chatter: 0
  verbosity: 1
selection:
  dec: 22.014694786873797
  emax: 100000.0
  emin: 100.0
  evclass: 128
  evtype: 3
  filter: DATA_QUAL>0 && LAT_CONFIG==1
  ra: 83.62870762486367
  tmax: 286675202.0
  tmin: 283996802.0
  zmax: 100.0


binning:
  binsperdec: 8
  binsz: 0.1
  roiwidth: 10.0
data:
  evfile: /Users/runner/work/threeML/threeML/docs/md_docs/slow_execute/Crab_data/Lb7ba925258c89244b49cc1889e66d453_FT1.fits
  scfile: /Users/runner/work/threeML/threeML/docs/md_docs/slow_execute/Crab_data/L240207181735E696CEF296_SC00.fits
logging:
  chatter: 0
  verbosity: 1
selection:
  dec: 22.014694786873797
  emax: 100000.0
  emin: 100.0
  evclass: 128
  evtype: 3
  filter: DATA_QUAL>0 && LAT_CONFIG==1
  ra: 83.62870762486367
  tmax: 286675202.0
  tmin: 283996802.0
  zmax: 100.0

You can of course modify the configuration as a dictionary

[11]:

config["selection"]["emax"] = 300000.0

and even add sections

[12]:

config["gtlike"] = {"edisp": False}

config.display()

binning:
  binsperdec: 8
  binsz: 0.1
  roiwidth: 10.0
data:
  evfile: /Users/runner/work/threeML/threeML/docs/md_docs/slow_execute/Crab_data/Lb7ba925258c89244b49cc1889e66d453_FT1.fits
  scfile: /Users/runner/work/threeML/threeML/docs/md_docs/slow_execute/Crab_data/L240207181735E696CEF296_SC00.fits
gtlike:
  edisp: false
logging:
  chatter: 0
  verbosity: 1
selection:
  dec: 22.014694786873797
  emax: 300000.0
  emin: 100.0
  evclass: 128
  evtype: 3
  filter: DATA_QUAL>0 && LAT_CONFIG==1
  ra: 83.62870762486367
  tmax: 286675202.0
  tmin: 283996802.0
  zmax: 100.0


binning:
  binsperdec: 8
  binsz: 0.1
  roiwidth: 10.0
data:
  evfile: /Users/runner/work/threeML/threeML/docs/md_docs/slow_execute/Crab_data/Lb7ba925258c89244b49cc1889e66d453_FT1.fits
  scfile: /Users/runner/work/threeML/threeML/docs/md_docs/slow_execute/Crab_data/L240207181735E696CEF296_SC00.fits
gtlike:
  edisp: false
logging:
  chatter: 0
  verbosity: 1
selection:
  dec: 22.014694786873797
  emax: 300000.0
  emin: 100.0
  evclass: 128
  evtype: 3
  filter: DATA_QUAL>0 && LAT_CONFIG==1
  ra: 83.62870762486367
  tmax: 286675202.0
  tmin: 283996802.0
  zmax: 100.0

FermipyLike

Let’s create an instance of the plugin/ Note that here no processing is made, because fermipy still doesn’t know about the model you want to use.

[13]:

LAT = FermipyLike("LAT", config)

The plugin modifies the configuration as needed to get the output files in a unique place, which will stay the same as long as your selection does not change.

[14]:

config.display()

binning:
  binsperdec: 8
  binsz: 0.1
  roiwidth: 10.0
data:
  evfile: /Users/runner/work/threeML/threeML/docs/md_docs/slow_execute/Crab_data/Lb7ba925258c89244b49cc1889e66d453_FT1.fits
  scfile: /Users/runner/work/threeML/threeML/docs/md_docs/slow_execute/Crab_data/L240207181735E696CEF296_SC00.fits
fileio:
  outdir: __eaf75afb6de1afbb594846503fe66a3e
gtlike:
  edisp: false
logging:
  chatter: 0
  verbosity: 1
selection:
  dec: 22.014694786873797
  emax: 300000.0
  emin: 100.0
  evclass: 128
  evtype: 3
  filter: DATA_QUAL>0 && LAT_CONFIG==1
  ra: 83.62870762486367
  tmax: 286675202.0
  tmin: 283996802.0
  zmax: 100.0


binning:
  binsperdec: 8
  binsz: 0.1
  roiwidth: 10.0
data:
  evfile: /Users/runner/work/threeML/threeML/docs/md_docs/slow_execute/Crab_data/Lb7ba925258c89244b49cc1889e66d453_FT1.fits
  scfile: /Users/runner/work/threeML/threeML/docs/md_docs/slow_execute/Crab_data/L240207181735E696CEF296_SC00.fits
fileio:
  outdir: __eaf75afb6de1afbb594846503fe66a3e
gtlike:
  edisp: false
logging:
  chatter: 0
  verbosity: 1
selection:
  dec: 22.014694786873797
  emax: 300000.0
  emin: 100.0
  evclass: 128
  evtype: 3
  filter: DATA_QUAL>0 && LAT_CONFIG==1
  ra: 83.62870762486367
  tmax: 286675202.0
  tmin: 283996802.0
  zmax: 100.0

Here is where the fermipy processing happens (the .setup method)

[15]:

fermipy_output_directory = Path(config["fileio"]["outdir"])
print("Fermipy Output directoty: %s" % fermipy_output_directory)

# This remove the output directory, to start a fresh analysis...

if fermipy_output_directory.exists():
    shutil.rmtree(fermipy_output_directory)

# Here is where the fermipy processing happens (the .setup method)

data = DataList(LAT)

jl = JointLikelihood(model, data)

Fermipy Output directoty: __eaf75afb6de1afbb594846503fe66a3e

23:18:16 INFO      Using IRFs P8R3_SOURCE_V3                                                     FermipyLike.py:126


Found Galactic template for IRF. P8R3_SOURCE_V3: /usr/local/miniconda/envs/test_env/share/fermitools/refdata/fermi/galdiffuse/gll_iem_v07.fits

Cutting the template around the ROI:



Found Isotropic template for irf P8R3_SOURCE_V3: /usr/local/miniconda/envs/test_env/share/fermitools/refdata/fermi/galdiffuse/iso_P8R3_SOURCE_V3_v1.txt

WARNING: Point source PKS_0459p060 lies 17.6405 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0610d7p3752 lies 17.6676 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0624d0p0855 lies 17.6938 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4C_p06d21 lies 17.7181 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x1ES_0647p250 lies 17.73 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source NVSS_J065035p205556 lies 17.7308 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0551d7p0446 lies 17.737 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source GB6_J0454p3724 lies 17.7478 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source PSR_J0631p1036 lies 17.7855 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source GB6_J0648p1749 lies 17.8446 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0600d8p0509c lies 18.0094 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0537d6p0400 lies 18.0282 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0442d8p3609 lies 18.0627 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0424d8p3117 lies 18.084 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0450d7p0715 lies 18.14 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0640d4p3307 lies 18.3188 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source B2_0552p39A lies 18.3305 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x1RXS_J064814d1p160708 lies 18.3652 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0634d7p1036 lies 18.3827 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source MG2_J065230p1934 lies 18.3991 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source PKS_0502p049 lies 18.4192 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source RX_J0648d7p1516 lies 18.8123 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source GB6_J0620p3806 lies 18.8411 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source PSR_J0622p3749 lies 18.8574 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0641d4p3349 lies 18.8694 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source B2_0654p24 lies 18.8719 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x1RXS_J065331d8p181448 lies 18.8996 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0412d6p2253c lies 18.9275 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source GB6_J0653p2816 lies 18.9534 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source PMN_J0444p0717 lies 18.9966 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source MG1_J050533p0415 lies 19.08 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source TXS_0431p092 lies 19.116 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0559d3p0352 lies 19.1165 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source B3_0509p406 lies 19.2321 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source B2_0635p35 lies 19.3015 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source PKS_0550p032 lies 19.3036 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0431d0p3529c lies 19.3169 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x2MASX_J06533986p1636432 lies 19.4161 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0658d7p2318 lies 19.4529 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0552d0p0256c lies 19.5427 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source GB6_J0555p0304 lies 19.5923 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source B2_0655p27A lies 19.6986 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0642d4p1048 lies 19.7363 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source NVSS_J050650p032401 lies 19.7895 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0409d2p2542 lies 19.8151 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107

23:32:48 INFO      set the minimizer to minuit                                             joint_likelihood.py:1045

The normalization factors of the LAT background components are included in the models as nuisance parameters. They are only added during the previous step (during the model assignment). Let’s display them:

[16]:

for k, v in LAT.nuisance_parameters.items():
    print(k, ":", v)

LAT_isodiff_Normalization : Parameter LAT_isodiff_Normalization = 1.0 []
(min_value = 0.001, max_value = 1000.0, delta = 0.01, free = True)
LAT_galdiff_Prefactor : Parameter LAT_galdiff_Prefactor = 1.0 []
(min_value = 0.1, max_value = 10.0, delta = 0.01, free = True)

We will fix the isotropic BG as we are not sensitive to it with this dataset. We will also fix one more weak source.

[17]:

model.LAT_isodiff_Normalization.fix = True
model.x4FGL_J0544d4p2238.spectrum.main.Powerlaw.K.fix = True
model.display()
Model summary:

N
Point sources 196
Extended sources 0
Particle sources 0


Free parameters (4):

value min_value max_value unit
PSR_J0534p2200.spectrum.main.Super_cutoff_powerlaw.K 0.0 0.0 0.0 keV-1 s-1 cm-2
PSR_J0534p2200.spectrum.main.Super_cutoff_powerlaw.index -1.826553 -10.0 10.0
NVSS_J052622p224801.spectrum.main.Powerlaw.K 0.0 0.0 0.0 keV-1 s-1 cm-2
LAT_galdiff_Prefactor 1.0 0.1 10.0


Fixed parameters (1092):
(abridged. Use complete=True to see all fixed parameters)


Properties (0):

(none)


Linked parameters (0):

(none)

Independent variables:

(none)

Linked functions (0):

(none)

Performing the fit

[18]:

jl.set_minimizer("minuit")

res = jl.fit()

         INFO      set the minimizer to MINUIT                                             joint_likelihood.py:1062

Best fit values:
result unit
parameter
PSR_J0534p2200...K (2.46 -0.08 +0.09) x 10^-13 1 / (cm2 keV s)
PSR_J0534p2200...index -1.790 +/- 0.025
NVSS_J052622p224801.spectrum.main.Powerlaw.K (1.0 -0.5 +1.0) x 10^-16 1 / (cm2 keV s)
LAT_galdiff_Prefactor (9.35 +/- 0.08) x 10^-1 
Correlation matrix:
1.000.73-0.05-0.11
0.731.000.100.16
-0.050.101.00-0.14
-0.110.16-0.141.00
Values of -log(likelihood) at the minimum:
-log(likelihood)
LAT 118073.606157
total 118073.606157 
Values of statistical measures:
statistical measures
AIC 236155.212456
BIC 236197.382493

Now let’s compute the errors on the best fit parameters

[19]:

res = jl.get_errors()
result unit
parameter
PSR_J0534p2200...K (2.46 +/- 0.09) x 10^-13 1 / (cm2 keV s)
PSR_J0534p2200...index -1.790 -0.025 +0.024
NVSS_J052622p224801.spectrum.main.Powerlaw.K (10 -6 +7) x 10^-17 1 / (cm2 keV s)
LAT_galdiff_Prefactor (9.35 -0.17 +0.18) x 10^-1

We might also want to look at the profile of the likelihood for each parameter.

[20]:

res = jl.get_contours(
    model.PSR_J0534p2200.spectrum.main.Super_cutoff_powerlaw.index, -2.0, -1.6, 30
)

[21]:

res[-1]

[21]:
../_images/notebooks_Fermipy_LAT_40_0.png

Or we might want to produce a contour plot

[22]:

res = jl.get_contours(
    "PSR_J0534p2200.spectrum.main.Super_cutoff_powerlaw.K",
    2.1e-13,
    2.7e-13,
    20,
    "PSR_J0534p2200.spectrum.main.Super_cutoff_powerlaw.index",
    -2.0,
    -1.7,
    20,
)

[23]:

res[-1]

[23]:
../_images/notebooks_Fermipy_LAT_43_0.png

Pro-trick: We can also axcess the GTAnalysis object of fermipy:

[24]:

# res = jl.fit()
# LAT.gta.write_roi('test',make_plots=True)

All the plots are saved in the output directory as png files:

[25]:

# pngs=Path(f"{fermipy_output_directory}").glob("*png")
# for png in pngs:
#    print(png)
#    my_image=Image(str(png))
#    display(my_image)

We can also plot the resulting model:

[26]:

energies = sp.logspace(1, 6, 100) * u.MeV
fig, ax = plt.subplots()
# we only want to visualize the relevant sources...
src_to_plot = ["Crab", "PSR_J0534p2200"]
# Now loop over all point sources and plot them
for source_name, point_source in model.point_sources.items():
    for src in src_to_plot:
        if src in source_name:
            # Plot the sum of all components for this source

            ax.loglog(energies, point_source(energies), label=source_name)
            # If there is more than one component, plot them also separately

            if len(point_source.components) > 1:
                for component_name, component in point_source.components.items():
                    ax.loglog(
                        energies,
                        component.shape(energies),
                        "--",
                        label=f"{component_name} of {source_name}",
                    )

# Add a legend
ax.legend(loc=0, frameon=False)

ax.set_xlabel("Energy (MeV)")
ax.set_ylabel(r"Flux (ph cm$^{-2}$ s$^{-1}$ keV$^{-1}$")
ax.set_ylim([1e-18, 1e-8])

# show the plot
fig

[26]:
../_images/notebooks_Fermipy_LAT_49_0.png

We can also do a bayesian analysis.

This will set priors based on the current defined min-max (log-uniform or uniform).

[27]:

for param in model.free_parameters.values():
    if param.has_transformation():
        param.set_uninformative_prior(Log_uniform_prior)
    else:
        param.set_uninformative_prior(Uniform_prior)

[28]:

# It's better to remove the output directory,...
shutil.rmtree(fermipy_output_directory)

bayes = BayesianAnalysis(model, data)

00:16:11 INFO      Using IRFs P8R3_SOURCE_V3                                                     FermipyLike.py:126


Found Galactic template for IRF. P8R3_SOURCE_V3: /usr/local/miniconda/envs/test_env/share/fermitools/refdata/fermi/galdiffuse/gll_iem_v07.fits

Cutting the template around the ROI:



Found Isotropic template for irf P8R3_SOURCE_V3: /usr/local/miniconda/envs/test_env/share/fermitools/refdata/fermi/galdiffuse/iso_P8R3_SOURCE_V3_v1.txt

WARNING: Point source PKS_0459p060 lies 17.6405 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0610d7p3752 lies 17.6676 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0624d0p0855 lies 17.6938 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4C_p06d21 lies 17.7181 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x1ES_0647p250 lies 17.73 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source NVSS_J065035p205556 lies 17.7308 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0551d7p0446 lies 17.737 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source GB6_J0454p3724 lies 17.7478 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source PSR_J0631p1036 lies 17.7855 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source GB6_J0648p1749 lies 17.8446 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0600d8p0509c lies 18.0094 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0537d6p0400 lies 18.0282 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0442d8p3609 lies 18.0627 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0424d8p3117 lies 18.084 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0450d7p0715 lies 18.14 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0640d4p3307 lies 18.3188 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source B2_0552p39A lies 18.3305 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x1RXS_J064814d1p160708 lies 18.3652 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0634d7p1036 lies 18.3827 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source MG2_J065230p1934 lies 18.3991 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source PKS_0502p049 lies 18.4192 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source RX_J0648d7p1516 lies 18.8123 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source GB6_J0620p3806 lies 18.8411 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source PSR_J0622p3749 lies 18.8574 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0641d4p3349 lies 18.8694 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source B2_0654p24 lies 18.8719 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x1RXS_J065331d8p181448 lies 18.8996 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0412d6p2253c lies 18.9275 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source GB6_J0653p2816 lies 18.9534 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source PMN_J0444p0717 lies 18.9966 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source MG1_J050533p0415 lies 19.08 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source TXS_0431p092 lies 19.116 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0559d3p0352 lies 19.1165 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source B3_0509p406 lies 19.2321 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source B2_0635p35 lies 19.3015 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source PKS_0550p032 lies 19.3036 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0431d0p3529c lies 19.3169 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x2MASX_J06533986p1636432 lies 19.4161 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0658d7p2318 lies 19.4529 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0552d0p0256c lies 19.5427 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source GB6_J0555p0304 lies 19.5923 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source B2_0655p27A lies 19.6986 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0642d4p1048 lies 19.7363 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source NVSS_J050650p032401 lies 19.7895 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107
WARNING: Point source x4FGL_J0409d2p2542 lies 19.8151 degrees from the ROI center at RA, Dec = 83.6287, 22.0147 7.57107

Take care of the nuisance parameters LAT_isodiff_Normalization and LAT_galdiff_Prefactor, which are only created during the previous step.

[29]:

model.LAT_isodiff_Normalization.fix = True
model.LAT_galdiff_Prefactor.set_uninformative_prior(Log_uniform_prior)

[30]:

bayes.set_sampler("emcee")

n_walkers = 10
burn_in = 10
n_samples = 500

bayes.sampler.setup(n_iterations=n_samples, n_burn_in=burn_in, n_walkers=n_walkers)

res = bayes.sample()

00:29:52 INFO      sampler set to emcee                                                    bayesian_analysis.py:202

00:36:04 INFO      Mean acceptance fraction: 0.4742                                            emcee_sampler.py:157

00:36:05 INFO      fit restored to maximum of posterior                                         sampler_base.py:178

         INFO      fit restored to maximum of posterior                                         sampler_base.py:178

Maximum a posteriori probability (MAP) point:
result unit
parameter
PSR_J0534p2200...K (2.61 -0.22 -0.05) x 10^-13 1 / (cm2 keV s)
PSR_J0534p2200...index -1.767 -0.05 +0.006
NVSS_J052622p224801.spectrum.main.Powerlaw.K (0.000 +0.009 +1.1) x 10^-16 1 / (cm2 keV s)
LAT_galdiff_Prefactor (9.38 -0.18 +0.15) x 10^-1 
Values of -log(posterior) at the minimum:
-log(posterior)
LAT -118001.672064
total -118001.672064 
Values of statistical measures:
statistical measures
AIC 236011.344270
BIC 236053.514307
DIC 236017.451557
PDIC 1.408666

You can access to the parameter range like this (HPD):

[31]:

this_K = bayes.results.get_variates(
    "PSR_J0534p2200.spectrum.main.Super_cutoff_powerlaw.K"
)
this_idx = bayes.results.get_variates(
    "PSR_J0534p2200.spectrum.main.Super_cutoff_powerlaw.index"
)

print("Highest_posterior_density_intervals :")
print(
    "K (68%%):     %10.2e,%10.2e" % this_K.highest_posterior_density_interval(cl=0.68)
)
print(
    "K (95%%):     %10.2e,%10.2e" % this_K.highest_posterior_density_interval(cl=0.95)
)
print(
    "Index (68%%): %10.2e,%10.2e" % this_idx.highest_posterior_density_interval(cl=0.68)
)
print(
    "Index (95%%): %10.2e,%10.2e" % this_idx.highest_posterior_density_interval(cl=0.95)
)

Highest_posterior_density_intervals :
K (68%):       2.39e-13,  2.55e-13
K (95%):       2.31e-13,  2.65e-13
Index (68%):  -1.81e+00, -1.76e+00
Index (95%):  -1.84e+00, -1.75e+00

[32]:

corner_figure = bayes.results.corner_plot()
corner_figure

[32]:
../_images/notebooks_Fermipy_LAT_59_0.png 
[ ]: