Note
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Log parabola spectral model#
This model parametrises a log parabola spectrum.
It is defined by the following equation:
\[\phi(E) = \phi_0 \left( \frac{E}{E_0} \right) ^ {
- \alpha - \beta \log{ \left( \frac{E}{E_0} \right) }
}\]
Note that \(log\) refers to the natural logarithm. This is consistent
with the Fermi Science Tools
and ctools.
The Sherpa package, however, uses \(log_{10}\). If you have
parametrization based on \(log_{10}\) you can use the
from_log10()
method.
Example plot#
Here is an example plot of the model:
from astropy import units as u
import matplotlib.pyplot as plt
from gammapy.modeling.models import LogParabolaSpectralModel, Models, SkyModel
energy_bounds = [0.1, 100] * u.TeV
model = LogParabolaSpectralModel(
alpha=2.3,
amplitude="1e-12 cm-2 s-1 TeV-1",
reference=1 * u.TeV,
beta=0.5,
)
model.plot(energy_bounds)
plt.grid(which="both")
YAML representation#
Here is an example YAML file using the model:
components:
- name: log-parabola-model
type: SkyModel
spectral:
type: LogParabolaSpectralModel
parameters:
- name: amplitude
value: 1.0e-12
unit: cm-2 s-1 TeV-1
- name: reference
value: 1.0
unit: TeV
- name: alpha
value: 2.3
- name: beta
value: 0.5