Distortion of the SED of High-z Luminous Infrared Galaxies by Strong Lensing

We present a model to estimate the effect of differential magnification on the SED of high-z ULIRGs. It is found that the ratio of the high temperature component to the low temperature component can vary with up to a factor of ten with source position on very small angular scales (∼ 0.01). This means that a correction for differential magnification is needed when deriving dust properties from strongly lensed sources. This work was inspired by the discovery of high redshift galaxies with a very high IR luminosity emanating from dust grains (Hughes 1998). It is expected that the thermal dust emission has a temperature gradient over a fairly large spatial region spanning from a temperature near the dust evaporation temperature (Tev ≃ 1500K) to a much lower background temperature of about 30 K in a cautious analogy to the nearby ultraluminous infrared galaxies (ULIRGs). Partly because of selection effects a large percentage of the sources in the current sample are strongly lensed. In the strong lensing region, there is a large spatial variation of the magnification parameter, especially near caustics. It is therefore conceivable that thermal emission from a region in the source with a specific temperature is enhanced in comparison with thermal emission with different temperatures from other regions (Blain 1999). The following presents a model which quantitatively tries to determine the importance of this effect. The model consists of a gravitational potential modeling a single lens galaxy and a face-on disc-shaped source with a Gaussian temperature distribution modeling a dusty torus surrounding an AGN. The lens is modeled by an elliptical potential. In the more realistic case of a number of compact starbursts embedded in a clumpy torus, the temperature structure will be more complicated. For simplicity only the first case is studied. It is not difficult to include the second case in the model using a phenomenological approach to the temperature structure, but the qualitative conclusions will be the same. The dust emission is modeled in each point in the source by a modified blackbody spectrum, where the power of the dust emissivity function, β, may vary between 1.5 and 2.0. The calculation of the magnification is done with a straight forward rayshooting algorithm, which simply maps every point in the lens plane to the source plane and sums the number of hits in each source pixel. For the chosen temperature distribution the distortion appears as either an enhancement of a low temperature component compared to a high temperature Astronomical Observatory, University of Copenhagen, Copenhagen, Denmark Onsala Space Observatory, Sweden