The process by which the mass density profile of certain galaxy clusters becomes centrally concentrated enough to produce high strong lensing (SL) cross-sections is not well understood. It has been suggested that the baryonic condensation of the intra-cluster medium (ICM) due to cooling may drag dark matter to the cores and thus steepen the profile. In this work, we search for evidence of ongoing ICM cooling in the first large, well-defined sample of strong lensing selected galaxy clusters in the range 0.1 < z < 0.6. Based on known correlations between the ICM cooling rate and both optical emission line luminosity and star formation, we measure, for a sample of 89 strong lensing clusters, the fraction of clusters that have [OII]3727 emission in their brightest cluster galaxy (BCG). We find that the fraction of line-emitting BCGs is constant as a function of redshift for z > 0.2 and shows no statistically significant deviation from the total cluster population. Specific star formation rates, as traced by the strength of the 4000 angstrom break, D_4000, are also consistent with the general cluster population. Finally, we use optical imaging of the SL clusters to measure the angular separation, R_arc, between the arc and the center of mass of each lensing cluster in our sample and test for evidence of changing [OII] emission and D_4000 as a function of R_arc, a proxy observable for SL cross-sections. D_4000 is constant with all values of R_arc, and the [OII] emission fractions show no dependence on R_arc for R_arc > 10 and only very marginal evidence of increased weak [OII] emission for systems with R_arc < 10. These results argue against the ability of baryonic cooling associated with cool core activity in the cores of galaxy clusters to strongly modify the underlying dark matter potential, leading to an increase in strong lensing cross-sections.
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