This is a fixed-text formatted version of a Jupyter notebook

Flux point fitting in Gammapy

Introduction

In this tutorial we’re going to learn how to fit spectral models to combined Fermi-LAT and IACT flux points.

The central class we’re going to use for this example analysis is:

In addition we will work with the following data classes:

And the following spectral model classes:

Setup

Let us start with the usual IPython notebook and Python imports:

[1]:

%matplotlib inline

[2]:

import numpy as np
from astropy import units as u
from gammapy.modeling.models import (
    PowerLawSpectralModel,
    ExpCutoffPowerLawSpectralModel,
    LogParabolaSpectralModel,
    SkyModel,
)
from gammapy.spectrum import FluxPointsDataset, FluxPoints
from gammapy.catalog import SOURCE_CATALOGS
from gammapy.modeling import Fit

Load spectral points

For this analysis we choose to work with the source ‘HESS J1507-622’ and the associated Fermi-LAT sources ‘3FGL J1506.6-6219’ and ‘3FHL J1507.9-6228e’. We load the source catalogs, and then access source of interest by name:

[3]:

catalog_3fgl = SOURCE_CATALOGS["3fgl"]()
catalog_3fhl = SOURCE_CATALOGS["3fhl"]()
catalog_gammacat = SOURCE_CATALOGS["gamma-cat"]()

[4]:

source_fermi_3fgl = catalog_3fgl["3FGL J1506.6-6219"]
source_fermi_3fhl = catalog_3fhl["3FHL J1507.9-6228e"]
source_gammacat = catalog_gammacat["HESS J1507-622"]

The corresponding flux points data can be accessed with .flux_points attribute:

[5]:

flux_points_gammacat = source_gammacat.flux_points
flux_points_gammacat.table

[5]:
Table length=6
e_refdndednde_errndnde_errp
TeV1 / (cm2 s TeV)1 / (cm2 s TeV)1 / (cm2 s TeV)
float32float32float32float32
0.86092.29119e-128.70543e-138.95502e-13
1.561516.98172e-132.20354e-132.30407e-13
2.763751.69062e-136.7587e-147.18838e-14
4.89167.72925e-142.40132e-142.60749e-14
9.988581.03253e-145.06315e-155.64195e-15
27.04037.44987e-165.72089e-167.25999e-16

In the Fermi-LAT catalogs, integral flux points are given. Currently the flux point fitter only works with differential flux points, so we apply the conversion here.

[6]:

flux_points_3fgl = source_fermi_3fgl.flux_points.to_sed_type(
    sed_type="dnde", model=source_fermi_3fgl.spectral_model()
)
flux_points_3fhl = source_fermi_3fhl.flux_points.to_sed_type(
    sed_type="dnde", model=source_fermi_3fhl.spectral_model()
)

Finally we stack the flux points into a single gammapy.spectrum.FluxPoints object and drop the upper limit values, because currently we can’t handle them in the fit:

[7]:

# Stack flux point tables
flux_points = FluxPoints.stack(
    [flux_points_gammacat, flux_points_3fhl, flux_points_3fgl]
)

t = flux_points.table
t["dnde_err"] = 0.5 * (t["dnde_errn"] + t["dnde_errp"])

# Remove upper limit points, where `dnde_errn = nan`
is_ul = np.isfinite(t["dnde_err"])
flux_points = FluxPoints(t[is_ul])
flux_points

[7]:

FluxPoints(sed_type='dnde', n_points=14)

Power Law Fit

First we start with fitting a simple gammapy.modeling.models.PowerLawSpectralModel.

[8]:

pwl = PowerLawSpectralModel(
    index=2, amplitude="1e-12 cm-2 s-1 TeV-1", reference="1 TeV"
)
model = SkyModel(spectral_model=pwl)

After creating the model we run the fit by passing the 'flux_points' and 'model' objects:

[9]:

dataset_pwl = FluxPointsDataset(model, flux_points)
fitter = Fit([dataset_pwl])
result_pwl = fitter.run()

And print the result:

[10]:

print(result_pwl)

OptimizeResult

        backend    : minuit
        method     : minuit
        success    : True
        message    : Optimization terminated successfully.
        nfev       : 40
        total stat : 28.29


[11]:

print(pwl)

PowerLawSpectralModel

   name     value   error      unit      min max frozen
--------- --------- ----- -------------- --- --- ------
    index 1.985e+00   nan                nan nan  False
amplitude 1.283e-12   nan cm-2 s-1 TeV-1 nan nan  False
reference 1.000e+00   nan            TeV nan nan   True

Finally we plot the data points and the best fit model:

[12]:

ax = flux_points.plot(energy_power=2)
pwl.plot(energy_range=[1e-4, 1e2] * u.TeV, ax=ax, energy_power=2)

# assign covariance for plotting
pwl.parameters.covariance = result_pwl.parameters.covariance

pwl.plot_error(energy_range=[1e-4, 1e2] * u.TeV, ax=ax, energy_power=2)
ax.set_ylim(1e-13, 1e-11);
../_images/notebooks_sed_fitting_22_0.png

Exponential Cut-Off Powerlaw Fit

Next we fit an gammapy.modeling.models.ExpCutoffPowerLawSpectralModel law to the data.

[13]:

ecpl = ExpCutoffPowerLawSpectralModel(
    index=1.8,
    amplitude="2e-12 cm-2 s-1 TeV-1",
    reference="1 TeV",
    lambda_="0.1 TeV-1",
)
model = SkyModel(spectral_model=ecpl)

We run the fitter again by passing the flux points and the model instance:

[14]:

dataset_ecpl = FluxPointsDataset(model, flux_points)
fitter = Fit([dataset_ecpl])
result_ecpl = fitter.run()
print(ecpl)

ExpCutoffPowerLawSpectralModel

   name     value   error      unit      min max frozen
--------- --------- ----- -------------- --- --- ------
    index 1.894e+00   nan                nan nan  False
amplitude 1.962e-12   nan cm-2 s-1 TeV-1 nan nan  False
reference 1.000e+00   nan            TeV nan nan   True
  lambda_ 7.766e-02   nan          TeV-1 nan nan  False
    alpha 1.000e+00   nan                nan nan   True

We plot the data and best fit model:

[15]:

ax = flux_points.plot(energy_power=2)
ecpl.plot(energy_range=[1e-4, 1e2] * u.TeV, ax=ax, energy_power=2)

# assign covariance for plotting
ecpl.parameters.covariance = result_ecpl.parameters.covariance

ecpl.plot_error(energy_range=[1e-4, 1e2] * u.TeV, ax=ax, energy_power=2)
ax.set_ylim(1e-13, 1e-11)

[15]:

(1e-13, 1e-11)
../_images/notebooks_sed_fitting_28_1.png

Log-Parabola Fit

Finally we try to fit a gammapy.modeling.models.LogParabolaSpectralModel model:

[16]:

log_parabola = LogParabolaSpectralModel(
    alpha=2, amplitude="1e-12 cm-2 s-1 TeV-1", reference="1 TeV", beta=0.1
)
model = SkyModel(spectral_model=log_parabola)

[17]:

dataset_log_parabola = FluxPointsDataset(model, flux_points)
fitter = Fit([dataset_log_parabola])
result_log_parabola = fitter.run()
print(log_parabola)

LogParabolaSpectralModel

   name     value   error      unit      min max frozen
--------- --------- ----- -------------- --- --- ------
amplitude 1.877e-12   nan cm-2 s-1 TeV-1 nan nan  False
reference 1.000e+00   nan            TeV nan nan   True
    alpha 2.144e+00   nan                nan nan  False
     beta 4.936e-02   nan                nan nan  False

[18]:

ax = flux_points.plot(energy_power=2)
log_parabola.plot(energy_range=[1e-4, 1e2] * u.TeV, ax=ax, energy_power=2)

# assign covariance for plotting
log_parabola.parameters.covariance = result_log_parabola.parameters.covariance

log_parabola.plot_error(
    energy_range=[1e-4, 1e2] * u.TeV, ax=ax, energy_power=2
)
ax.set_ylim(1e-13, 1e-11);
../_images/notebooks_sed_fitting_32_0.png

Exercises

What next?

This was an introduction to SED fitting in Gammapy.

  • If you would like to learn how to perform a full Poisson maximum likelihood spectral fit, please check out the spectrum analysis tutorial.

  • To learn more about other parts of Gammapy (e.g. Fermi-LAT and TeV data analysis), check out the other tutorial notebooks.

  • To see what’s available in Gammapy, browse the Gammapy docs or use the full-text search.

  • If you have any questions, ask on the mailing list .

[ ]: