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The influence of the matter along the line of sight and in the lens environment on the strong gravitational lensing

We investigate the influence of the matter along the line of sight and in the lens environment on the image configurations, relative time delays, and the resulting models of strong gravitational lensing. The distribution of matter in space and properties of gravitationally bound haloes are based on the Millennium Simulation. In our numerical experiments we consider isolated lens in a uniform universe model and the same lens surrounded by close neighbours and/or objects close to the line of sight which gives four different descriptions of the light propagation. We compare the results of the lens modeling which neglects effects of the environment and line of sight, when applied to image configurations resulting from approaches partially or fully taking into account these effects. We show that for a source at the redshift z=2 the effects are indeed important and may prevent successful fitting of lens models in a substantial part of simulated image configurations, especially when the relative time delays are taken into account. To have good constraints on the models we limit ourselves to configurations of four images. We consider eighty lenses and large number of source positions in each case. The influence of the lens neighbourhood and the line of sight introduces the spread into the fitted values of the deflection angles which translates into the spread in the lens velocity dispersion of 4 per cent. Similarly for the lens axis ratio we get the spread of 10 per cent and for the Hubble's constant of 6 per cent. When averaged over all lenses and all image configurations considered, the median fitted values of the parameters (including the Hubble's constant) do not differ more than 1 per cent from their values used in simulations.