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Absorbed Spectral Model

This model evaluates absorbed spectral model.

The spectral model is evaluated, and then multiplied with an EBL absorption factor given by

$$\exp{ \left ( -\alpha \times \tau(E, z) \right )}$$

where $\tau(E, z)$ is the optical depth predicted by the model (Absorption), which depends on the energy of the gamma-rays and the redshift z of the source, and $\alpha$ is a scale factor (default: 1) for the optical depth.

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 (
    AbsorbedSpectralModel,
    Absorption,
    Models,
    PowerLawSpectralModel,
    SkyModel,
)

redshift = 0.117
absorption = Absorption.read_builtin("dominguez")

# Spectral model corresponding to PKS 2155-304 (quiescent state)
index = 3.53
amplitude = 1.81 * 1e-12 * u.Unit("cm-2 s-1 TeV-1")
reference = 1 * u.TeV
pwl = PowerLawSpectralModel(index=index, amplitude=amplitude, reference=reference)

# EBL + PWL model
model = AbsorbedSpectralModel(
    spectral_model=pwl, absorption=absorption, redshift=redshift
)

energy_range = [0.1, 100] * u.TeV
model.plot(energy_range)
plt.grid(which="both")
plt.ylim(1e-24, 1e-8)

YAML representation

Here is an example YAML file using the model:

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

print(models.to_yaml())

Out:

components:
-   name: absorbed-model
    type: SkyModel
    spectral:
        type: AbsorbedSpectralModel
        base_model:
            type: PowerLawSpectralModel
            parameters:
            - {name: index, value: 3.53, unit: '', min: .nan, max: .nan, frozen: false,
                error: 0}
            - {name: amplitude, value: 1.81e-12, unit: cm-2 s-1 TeV-1, min: .nan,
                max: .nan, frozen: false, error: 0}
            - {name: reference, value: 1.0, unit: TeV, min: .nan, max: .nan, frozen: true,
                error: 0}
        absorption:
            type: Absorption
            filename: !!python/object/apply:pathlib.PosixPath [/, Users, terrier,
                Code, gammapy-dev, gammapy-datasets, ebl, ebl_dominguez11.fits.gz]
        absorption_parameter: {name: redshift, value: 0.117}
        parameters:
        - {name: redshift, value: 0.117, unit: '', min: 0.009999999776482582, max: 3.990000009536743,
            frozen: true, error: 0}
        - {name: alpha_norm, value: 1.0, unit: '', min: .nan, max: .nan, frozen: true,
            error: 0}