Background modelling in very-high-energy gamma-ray astronomy

Context.Ground based Cherenkov telescope systems measure astrophysical $\gamma$-ray emission against a background of cosmic-ray induced air showers. The subtraction of this background is a major challenge for the extraction of spectra and morphology of $\gamma$-ray sources. Aims.The unprecedented sensitivity of the new generation of ground based very-high-energy $\gamma$-ray experiments such as HESS has lead to the discovery of many previously unknown extended sources. The analysis of such sources requires a range of different background modelling techniques. Here we describe some of the techniques that have been applied to data from the HESS instrument and compare their performance. Methods.Each background model is introduced and discussed in terms of suitability for image generation or spectral analysis and possible caveats are mentioned. Results.We show that there is not a single multi-purpose model, different models are appropriate for different tasks. To keep systematic uncertainties under control it is important to apply several models to the same data set and compare the results.