Linear temporal model

This model parametrises a linear time model.

\[F(t) = alpha + beta * (t - t_{ref})\]

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 (
    LinearTemporalModel,
    Models,
    PowerLawSpectralModel,
    SkyModel,
)

time_range = [Time.now(), Time.now() + 2 * u.d]
linear_model = LinearTemporalModel(
    alpha=1, beta=0.5 / u.d, t_ref=(time_range[0].mjd - 0.1) * u.d
)
linear_model.plot(time_range)
plt.grid(which="both")

YAML representation

Here is an example YAML file using the model:

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

print(models.to_yaml())

Out:

components:
-   name: linear-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
            frozen: true
    temporal:
        type: LinearTemporalModel
        parameters:
        -   name: alpha
            value: 1.0
        -   name: beta
            value: 0.5
            unit: d-1
        -   name: t_ref
            value: 59540.78239966044
            unit: d
            frozen: true