This is the first paper in a series that present a multi-wavelength analysis of the archetype Ultra-Luminous InfraRed Galaxy ( ULIRG ) IRAS FSC10214+47 , a gravitationally lensed , starburst/AGN at z = 2.3 .
Here we present a new lens model and spatially-resolved radio data , as well as a deep HST F160W map .
The lens modelling employs a Bayesian Markov Chain Monte Carlo algorithm with extended-source , forward ray-tracing .
Using these high resolution HST , MERLIN and VLA maps , the algorithm allows us to constrain the level of distortion to the continuum spectral energy distribution resulting from emission components with differing magnification factors , due to their size and proximity to the caustic .
Our lens model finds the narrow line region ( NLR ) , and by proxy the active nucleus , is preferentially magnified .
This supports previous claims that preferential magnification could mask the expected polycyclic aromatic hydrocarbon spectral features in the Spitzer mid-infrared spectrum which roughly trace the star-forming regions .
Furthermore , we show the arc-to-counter-image flux ratio is not a good estimate of the magnification in this system , despite its common use in the IRAS FSC10214+47 literature .
Our lens modelling suggests magnifications of \mu \sim 15 - 20 \pm 2 for the HST F814W , MERLIN 1.7 GHz and VLA 8 GHz maps , significantly lower than the canonical values of \mu = 50 - 100 often used for this system .
Systematic errors such as the dark matter density slope and co-location of stellar and dark matter centroids dominate the uncertainties in the lens model at the 40 percent level .