Definition of power law with exponential cut off

[GernotMaier]

Noticed right that the definition of the power law with exponential cut off is different than expected. Can you please confirm?

I've expected: dN/dE = I0 · (E/E_ref)−Γ · exp(−E/Ecut)

Looks like the implementation is dN/dE = I0 · (E/E_ref)−Γ · exp(−E*lambda)

If this is true, all ecpl in the VERITAS files need to be adjusted. I will do this, but please confirm that the second implementation is the one used.

[cdeil]

@GernotMaier - The difference in the equations you give is just whether they contain e_cut or lambda=1/e_cut, right?

In gamma-cat we currently use e_cut.

You can see this in the schema:

gamma-cat/input/schemas/dataset_source_info.schema.yaml

Line 325 in aa4aa09

- name: ecpl

and how the catalog is filled:

gamma-cat/gammacat/catalog.py

Line 325 in ba11b08

data['spec_ecpl_e_cut'] = spec_pars['e_cut'].get_or_default('val').to('TeV')

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Indeed when we map to a spectral model in Gammapy
https://github.com/gammapy/gammapy/blob/f48b22d7f7ab9430bb2ab78521736a6e381b5318/gammapy/catalog/gammacat.py#L271
we use
http://docs.gammapy.org/dev/api/gammapy.spectrum.models.ExponentialCutoffPowerLaw.html which has lambda, but that is filled as lambda=1/e_cut.

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Note that if needed, we can add more spectral models to gamma-cat and Gammapy.
E.g. in Gammapy we already have this second ECPL parametrisation because it was used in the Fermi-LAT 3FGL catalog: http://docs.gammapy.org/dev/api/gammapy.spectrum.models.ExponentialCutoffPowerLaw3FGL.html

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@GernotMaier - So is there an issue with the data entry for VERITAS?

The HESS catalog will come out soon and I want to add the data to gamma-cat. There we use lambda and lambda_err. So I guess we should add an ECPL variant to gamma-cat that supports direct data entry of lambda and lambda_err, no? Any suggestion for what to call it? I think in HESS this is "ecpl3". :-)

[GernotMaier]

OK - everything clear. I missed the 1/E_cut and was simply confused - so nothing additional is needed and there is no issue with this.

(good to be closed).