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We predict the abundance of giant gravitational arcs produced bysubmillimeter galaxies (SMGs) lensed by foreground galaxy clusters, both atradio and submm wavelengths. The galaxy cluster population is modeled in arealistic way with the use of semi-analytic merger trees, while the densityprofiles of individual deflectors take into account ellipticity andsubstructures. The adopted typical size of the radio and submm emitting regionsof SMGs is based on current radio/CO observations and the FIR-radiocorrelation. The source redshift distribution has been modeled using threedifferent functions (based on spectroscopic/photometric redshift measurementsand a simple evolutionary model) to quantify the effect of a high redshift tailon the number of arcs. The source number counts are compatible with currentlyavailable observations, and were suitably distorted to take into account thelensing magnification bias. We present tables and plots for the numbers ofradio and submm arcs produced by SMGs as a function of surface brightness,useful for the planning of future surveys aimed at arc statistics studies. Theyshow that e.g., the detection of several hundred submm arcs on the whole skywith a signal-to-noise ratio of at least 5 requires a sensitivity of 1 mJyarcsec$^{-2}$ at $850 \mu$m. Approximately the same number of radio arcs shouldbe detected with the same signal-to-noise ratio with a surface brightnessthreshold of $20 \mu$Jy arcsec$^{-2}$ at 1.4 GHz. Comparisons of these resultswith previous work found in the literature are also discussed.

On the abundance of gravitational arcs produced by submillimeter galaxies at radio and submm wavelengths