LAT IRFs (Instrument Response Functions)

The Instrument Response Function (IRF) is the mapping between the incoming photon flux and the detected events. 'Detection' depends not only on the LAT hardware but also on the processing that calculates the event parameters from the observables and assigns probabilities that an event is a photon. Indeed, different event cuts are planned based on tradeoffs between the non-photon background, the effective area and the spatial and energy resolution; these cuts result in analysis classes (see the section on LAT Data Products).

The IRF can be framed as an area times the probability that a photon with a given set of input parameters is detected as an event with a set of observables. For the LAT, the photon parameters are the energy E and the inclination angle φ (the angle between the LAT normal and the true source position) and the event is characterized by the apparent energy E' and the apparent source position φ'. Note that φ is an angle while φ' is a vector. Each analysis class has its own IRF. Our current formulation of the IRF is:

R(E',φ' ; E,φ)=A_eff(E,φ)p_PSF(φ' ;E,φ) p_E(E' ;E)
where A_eff is the effective area (with units of area), p_PSF is the PSF and p_E is the energy redistribution function. Again, φ is the inclination angle for the photon's actual direction while φ' is the vector for the photon's apparent direction. A number of assumptions are embedded in this formulation. The energy redistribution function is assumed to have no dependence on the actual or apparent inclination angles while the PSF has no dependence on the apparent energy. In addition, we assume that p_PSF is actually p_PSF(θ ;E,φ), where θ is the angle between the true and apparent source positions; thus we assume that the PSF is circular around the true source position.

The LAT IRF is determined by Monte Carlo simulations of the response of the LAT to a photon of energy E and inclination angle φ, and then reconstructing the resulting event. The comparison between the calculated properties of the event and the incoming photon gives the IRF. The three IRF functions – the Effective Area, Point Spread Function, and Energy Redistribution – are presented in the subsequent sections.

The IRFs shown here represent the current prelaunch analysis. Undoubtedly the analysis classes and their IRFs will be optimized during after science operations begin. The latest plots of the IRF can be found on the GLAST LAT Performance page.