Joint fitting XRT and GBM data with XSPEC models

Goals

3ML is designed to properly joint fit data from different instruments with thier instrument dependent likelihoods. We demostrate this with joint fitting data from GBM and XRT while simultaneously showing hwo to use the XSPEC models form astromodels

Setup

You must have you HEASARC initiated so that astromodels can find the XSPEC libraries.

[2]:
%%capture
import matplotlib.pyplot as plt
from pathlib import Path
from threeML import *
from threeML.io.package_data import get_path_of_data_file

# we will need XPSEC models for extinction
from astromodels.xspec import *
from astromodels.xspec.xspec_settings import *

Load XRT data

Make a likelihood for the XRT including all the appropriate files

[4]:
trigger = "GRB110731A"
dec = -28.546
ra = 280.52

p = Path("datasets/xrt")

xrt = OGIPLike(
    "XRT",
    observation=get_path_of_data_file(p / "xrt_src.pha"),
    background=get_path_of_data_file(p / "xrt_bkg.pha"),
    response=get_path_of_data_file(p / "xrt.rmf"),
    arf_file=get_path_of_data_file(p / "xrt.arf"),
)


fig = xrt.view_count_spectrum()
ax = fig.get_axes()[0]
_ = ax.set_xlim(1e-1)
../_images/notebooks_joint_fitting_xrt_and_gbm_xspec_models_5_0.png
[5]:
fit = xrt.view_count_spectrum(scale_background=False)
../_images/notebooks_joint_fitting_xrt_and_gbm_xspec_models_6_0.png

Load GBM data

Load all the GBM data you need and make appropriate background, source time, and energy selections. Make sure to check the light curves!

[6]:
trigger_number = "bn110731465"
gbm_data = download_GBM_trigger_data(trigger_number, detectors=["n3"])
[7]:
# Select the time interval
src_selection = "100.169342-150.169342"
bkg_selection = ["-25.0--10.0", "300-400"]
ts = TimeSeriesBuilder.from_gbm_cspec_or_ctime(
    name="gbm_n3",
    cspec_or_ctime_file=gbm_data["n3"]["cspec"],
    rsp_file=gbm_data["n3"]["rsp"],
)


ts.set_background_interval(*bkg_selection)
ts.save_background("n3_bkg.h5", overwrite=True)
fig = ts.view_lightcurve(-50, 450)
../_images/notebooks_joint_fitting_xrt_and_gbm_xspec_models_9_3.png
[8]:
ts = TimeSeriesBuilder.from_gbm_tte(
    "gbm_n3",
    tte_file=gbm_data["n3"]["tte"],
    rsp_file=gbm_data["n3"]["rsp"],
    restore_background="n3_bkg.h5",
)


ts.set_active_time_interval(src_selection)

fig = ts.view_lightcurve(90, 160)
../_images/notebooks_joint_fitting_xrt_and_gbm_xspec_models_10_0.png
[9]:
nai3 = ts.to_spectrumlike()

Make energy selections and check them out

[10]:
nai3.set_active_measurements("8-900")
fig = nai3.view_count_spectrum()
../_images/notebooks_joint_fitting_xrt_and_gbm_xspec_models_13_0.png

Setup the model

astromodels allows you to use XSPEC models if you have XSPEC installed. Set all the normal parameters you would in XSPEC and build a model the normal 3ML/astromodels way! Here we will use the phabs model from XSPEC and mix it with powerlaw model in astromodels.

With XSPEC

[11]:
xspec_abund("angr")

spectral_model = XS_phabs() * XS_zphabs() * Powerlaw()


spectral_model.nh_1 = 0.101
spectral_model.nh_1.bounds = (None, None)
spectral_model.nh_1.fix = True

spectral_model.nh_2 = 0.1114424
spectral_model.nh_2.fix = True
spectral_model.nh_2.bounds = (None, None)
spectral_model.redshift_2 = 0.618
spectral_model.redshift_2.fix = True
 Solar Abundance Vector set to angr:  Anders E. & Grevesse N. Geochimica et Cosmochimica Acta 53, 197 (1989)

With astromodels PHABS

We can build the exact same models in native astromodels thanks to Dominique Eckert. Here, there is no extra function for redshifting the absorption model, just pass a redshift.

[12]:
phabs_local = PhAbs(NH=0.101)
phabs_local.NH.fix = True
phabs_local.redshift.fix = True
phabs_src = PhAbs(NH=0.1114424, redshift=0.618)
phabs_src.NH.fix = True
phabs_src.redshift.fix = True
pl = Powerlaw()
spectral_model_native = phabs_local * phabs_src * pl

Setup the joint likelihood

Create a point source object and model.

Load the data into a data list and create the joint likelihood

With XSPEC models

First we will fit with the XSPEC model

[13]:
ptsrc = PointSource(trigger, ra, dec, spectral_shape=spectral_model)
model = Model(ptsrc)
[14]:
data = DataList(xrt, nai3)

jl = JointLikelihood(model, data, verbose=False)
model.display()
Model summary:

N
Point sources 1
Extended sources 0
Particle sources 0


Free parameters (2):

value min_value max_value unit
GRB110731A.spectrum.main.composite.K_3 1.0 0.0 1000.0 keV-1 s-1 cm-2
GRB110731A.spectrum.main.composite.index_3 -2.0 -10.0 10.0


Fixed parameters (8):
(abridged. Use complete=True to see all fixed parameters)


Linked parameters (0):

(none)

Independent variables:

(none)
[15]:
res = jl.fit()
fig = display_spectrum_model_counts(jl, min_rate=[0.5, 0.1])
Best fit values:

result unit
parameter
GRB110731A.spectrum.main.composite.K_3 (1.83 +/- 0.07) x 10^-1 1 / (cm2 keV s)
GRB110731A.spectrum.main.composite.index_3 -1.93 +/- 0.05

Correlation matrix:

1.00-0.57
-0.571.00

Values of -log(likelihood) at the minimum:

-log(likelihood)
XRT 2064.144639
gbm_n3 984.434512
total 3048.579151

Values of statistical measures:

statistical measures
AIC 6101.173191
BIC 6110.549900
../_images/notebooks_joint_fitting_xrt_and_gbm_xspec_models_24_8.png
[16]:
res = jl.get_contours(spectral_model.index_3, -2.5, -1.5, 50)
../_images/notebooks_joint_fitting_xrt_and_gbm_xspec_models_25_1.png
[17]:
_ = jl.get_contours(
    spectral_model.K_3, 0.1, 0.3, 25, spectral_model.index_3, -2.5, -1.5, 50
)
../_images/notebooks_joint_fitting_xrt_and_gbm_xspec_models_26_1.png
[18]:
fig = plot_spectra(jl.results, show_legend=False, emin=0.01 * u.keV)
../_images/notebooks_joint_fitting_xrt_and_gbm_xspec_models_27_3.png

Fit with astromodels PhAbs

Now lets repeat the fit in pure astromodels.

[19]:
ptsrc_native = PointSource(trigger, ra, dec, spectral_shape=spectral_model_native)
model_native = Model(ptsrc_native)
[20]:
data = DataList(xrt, nai3)

jl_native = JointLikelihood(model_native, data, verbose=False)
model.display()
Model summary:

N
Point sources 1
Extended sources 0
Particle sources 0


Free parameters (2):

value min_value max_value unit
GRB110731A.spectrum.main.composite.K_3 0.3 0.0 1000.0 keV-1 s-1 cm-2
GRB110731A.spectrum.main.composite.index_3 -1.5 -10.0 10.0


Fixed parameters (8):
(abridged. Use complete=True to see all fixed parameters)


Linked parameters (0):

(none)

Independent variables:

(none)
[21]:
res = jl_native.fit()
fig = display_spectrum_model_counts(jl_native, min_rate=[0.5, 0.1])
Best fit values:

result unit
parameter
GRB110731A.spectrum.main.composite.K_3 (1.83 +/- 0.07) x 10^-1 1 / (cm2 keV s)
GRB110731A.spectrum.main.composite.index_3 -1.93 +/- 0.05

Correlation matrix:

1.00-0.57
-0.571.00

Values of -log(likelihood) at the minimum:

-log(likelihood)
XRT 2064.134895
gbm_n3 984.434410
total 3048.569305

Values of statistical measures:

statistical measures
AIC 6101.153498
BIC 6110.530208
../_images/notebooks_joint_fitting_xrt_and_gbm_xspec_models_32_8.png
[22]:
fig = plot_spectra(jl.results, jl_native.results, show_legend=False, emin=0.01 * u.keV)
../_images/notebooks_joint_fitting_xrt_and_gbm_xspec_models_33_4.png

Both approaches give the same answer as they should.

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