be obtained from basic assumption on the host galaxy luminosity . Alternatively, an upper limit on the distance can instead be estimated by studying the deformation induced by the EBL on the VHE gamma-ray spectrum.

### Host galaxy {#sec3-5-1}

We use the deep I-band image (see \[HGIMAGE\]) to search for the host galaxy emission. Two-dimensional surface brightness models were fitted to the light distribution of S2 0109+22 in order to study its host galaxy. Prior to the fitting, the background level was measured and subtracted, removing also a small tilt in the background. Two models were considered: 1) a point source (jet) model and 2) a point source + elliptical galaxy model. Both models had three free parameters, point source x-y position plus flux in the first model, and point source flux, host galaxy flux and host galaxy effective radius in the second model. The first model was used to fix the position of the nucleus, i.e. the second model was fit using the position from the first model to fix the point source and the host galaxy into the same position. Moreover, the ellipticity of the host galaxy was fixed to $\varepsilon = 0$ and the Sersić index to 