IRF TheoryΒΆ

TODO: do a detailed writeup of how IRFs are implemented and used in Gammapy.

For high-level gamma-ray data analysis (measuring morphology and spectra of sources) a canonical detector model is used, where the gamma-ray detection process is simplified as being fully characterized by the following three “instrument response functions”:

  • Effective area \(A(p, E)\) (unit: \(m^2\))
  • Point spread function \(PSF(p'|p, E)\) (unit: \(sr^{-1}\))
  • Energy dispersion \(D(E'|p, E)\) (unit: \(TeV^{-1}\))

The effective area represents the gamma-ray detection efficiency, the PSF the angular resolution and the energy dispersion the energy resolution of the instrument.

The full instrument response is given by

\[R(p', E'|p, E) = A(p, E) \times PSF(p'|p, E) \times D(E'|p, E),\]

where \(p\) and \(E\) are the true gamma-ray position and energy and \(p'\) and \(E'\) are the reconstructed gamma-ray position and energy.

The instrument function relates sky flux models to expected observed counts distributions via

\[N(p', E') = t_{obs} \int_E \int_\Omega R(p', E'|p, E) \times F(p, E) dp dE,\]

where \(F\), \(R\), \(t_{obs}\) and \(N\) are the following quantities:

  • Sky flux model \(F(p, E)\) (unit: \(m^{-2} s^{-1} TeV^{-1} sr^{-1}\))
  • Instrument response \(R(p', E'|p, E)\) (unit: \(m^2 TeV^{-1} sr^{-1}\))
  • Observation time: \(t_{obs}\) (unit: \(s\))
  • Expected observed counts model \(N(p', E')\) (unit: \(sr^{-1} TeV^{-1}\))

If you’d like to learn more about instrument response functions, have a look at the descriptions for Fermi, for TeV data analysis and for GammaLib.

TODO: add an overview of what is / isn’t available in Gammapy.