Log parabola 2 spectral model

This model parametrises a log parabola spectrum, where the energy scale of the exponente, \(E_s\), and the reference energy, \(E_0\), can be different. It is defined by the following equation:

\[\phi(E) = \phi_0 \left( \frac{E}{E_0} \right) ^ { - \alpha - \beta \log{ \left( \frac{E}{E_s} \right) } }\]

Note that \(log\) refers to the natural logarithm. 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 LogParabola2SpectralModel, Models, SkyModel

energy_bounds = [0.1, 100] * u.TeV
model = LogParabola2SpectralModel(
    alpha=2.3,
    amplitude="1e-12 cm-2 s-1 TeV-1",
    reference=10 * u.TeV,
    beta=0.5,
    escale=1 * u.TeV,
)
model.plot(energy_bounds)
plt.grid(which="both")

YAML representation

Here is an example YAML file using the model:

model = SkyModel(spectral_model=model, name="log-parabola2-model")
models = Models([model])

print(models.to_yaml())

components:
-   name: log-parabola2-model
    type: SkyModel
    spectral:
        type: LogParabola2SpectralModel
        parameters:
        -   name: amplitude
            value: 1.0e-12
            unit: TeV-1 s-1 cm-2
        -   name: reference
            value: 10.0
            unit: TeV
        -   name: alpha
            value: 2.3
        -   name: beta
            value: 0.5
        -   name: escale
            value: 1.0
            unit: TeV
metadata:
    creator: Gammapy 2.0.dev2512+g0733504a8
    date: '2025-11-30T05:22:18.018928'
    origin: null