On the abundance of gravitational arcs produced by submillimeter
  galaxies at radio and submm wavelengths
  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 1 mJy
arcsec$^{-2}$ at $850 \mu$m. Approximately the same number of radio arcs should
be detected with the same signal-to-noise ratio with a surface brightness
threshold of $20 \mu$Jy arcsec$^{-2}$ at 1.4 GHz. Comparisons of these results
with previous work found in the literature are also discussed.
