ExpDecay temporal model

This model parametrises an ExpDecay time model.

\[F(t) = \exp \left( \frac{t - t_{\rm{ref}}}{t0} \right)\]

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 (
    ExpDecayTemporalModel,
    Models,
    PowerLawSpectralModel,
    SkyModel,
)

t0 = "5 h"
t_ref = Time("2020-10-01")
time_range = [t_ref, t_ref + 1 * u.d]
expdecay_model = ExpDecayTemporalModel(t_ref=t_ref.mjd * u.d, t0=t0)
expdecay_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=expdecay_model,
    name="expdecay_model",
)
models = Models([model])

print(models.to_yaml())

/Users/terrier/Code/anaconda3/envs/gammapy-dev/lib/python3.8/site-packages/astropy/units/quantity.py:611: RuntimeWarning: overflow encountered in exp
  result = super().__array_ufunc__(function, method, *arrays, **kwargs)
/Users/terrier/Code/anaconda3/envs/gammapy-dev/lib/python3.8/site-packages/astropy/units/quantity.py:611: RuntimeWarning: invalid value encountered in subtract
  result = super().__array_ufunc__(function, method, *arrays, **kwargs)
components:
-   name: expdecay_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: ExpDecayTemporalModel
        parameters:
        -   name: t0
            value: 5.0
            unit: h
        -   name: t_ref
            value: 59123.0
            unit: d