PowerLaw temporal model

This model parametrises a power-law time model.

\[F(t) = \left( \frac{t - t_{\rm{ref}}}{t_0} \right)^\alpha\]

Example plot

Here is an example plot of the model:

from astropy import units as u
from astropy.time import Time
import matplotlib.pyplot as plt
from gammapy.modeling.models import (
    Models,
    PowerLawSpectralModel,
    PowerLawTemporalModel,
    SkyModel,
)

time_range = [Time.now(), Time.now() + 2 * u.d]
pl_model = PowerLawTemporalModel(alpha=-2.0, t_ref=(time_range[0].mjd - 0.1) * u.d)
pl_model.plot(time_range)
plt.grid(which="both")
plt.yscale("log")

YAML representation

Here is an example YAML file using the model:

model = SkyModel(
    spectral_model=PowerLawSpectralModel(),
    temporal_model=pl_model,
    name="powerlaw-model",
)
models = Models([model])

print(models.to_yaml())

components:
-   name: powerlaw-model
    type: SkyModel
    spectral:
        type: PowerLawSpectralModel
        parameters:
        -   name: index
            value: 2.0
        -   name: amplitude
            value: 1.0e-12
            unit: cm-2 s-1 TeV-1
        -   name: reference
            value: 1.0
            unit: TeV
    temporal:
        type: PowerLawTemporalModel
        parameters:
        -   name: alpha
            value: -2.0
        -   name: t_ref
            value: 60662.576732046284
            unit: d
        -   name: t0
            value: 1.0
            unit: d
        scale: utc
metadata:
    creator: Gammapy 2.0.dev155+g9309a089d
    date: '2024-12-18T16:14:29.845084'
    origin: null