2009A&A...508..141F

We predict the abundance of giant gravitational arcs produced by submillimeter galaxies (SMGs) lensed by foreground galaxy clusters, both at radio and submm wavelengths. The galaxy cluster population is modeled in a realistic way with the use of semi-analytic merger trees, while the density profiles of individual deflectors take into account ellipticity and substructures. The adopted typical size of the radio and submm emitting regions of SMGs is based on current radio/CO observations and the FIR-radio correlation. The source redshift distribution has been modeled using three different functions (based on spectroscopic/photometric redshift measurements and a simple evolutionary model) to quantify the effect of a high redshift tail on the number of arcs. The source number counts are compatible with currently available observations, and were suitably distorted to take into account the lensing magnification bias. We present tables and plots for the numbers of radio and submm arcs produced by SMGs as a function of surface brightness, useful for the planning of future surveys aimed at arc statistics studies. They show that e.g., the detection of several hundred submm arcs on the whole sky with a signal-to-noise ratio of at least 5 requires a sensitivity of 1mJy/arcsec2 at 850µm. Approximately the same number of radio arcs should be detected with the same signal-to-noise ratio with a surface brightness threshold of 20µJy/arcsec² at 1.4GHz. Comparisons of these results with previous work found in the literature are also discussed.