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Table 7:

Predicted number of radio (1.4 GHz) arcs produced by SMGs for an all-sky survey, using only clusters with $M \ge 5$ $\times $ $10^{14}~M_\odot~h^{-1}$ to compute the optical depths (see Fig. 10).
$B_{1.4~{\rm GHz}}^{~(1)}$ $\rm 500~\mu Jy~arcsec^{-2}$ $\rm 100~\mu Jy~arcsec^{-2}$ $\rm 50~\mu Jy~arcsec^{-2}$ $\rm 10~\mu Jy~arcsec^{-2}$ $\rm 5~\mu Jy~arcsec^{-2}$ $\rm 1~\mu Jy~arcsec^{-2}$
d0 (2) 7.5 10 7.5 10 7.5 10 7.5 10 7.5 10 7.5 10
SPZ DB (3) 0 (0) 0 (0) 17 (8) 8 (0) 42 (17) 17 (8) 267 (125) 92 (42) 592 (267) 200 (92) 3542 (1633) 1192 (550)
PHZ DB (3) 0 (0) 0 (0) 17 (8) 8 (0) 42 (17) 17 (8) 283 (133) 92 (42) 625 (283) 208 (92) 3758 (1733) 1267 (583)
CHM DB (3) 0 (0) 0 (0) 25 (8) 8 (0) 50 (25) 17 (8) 325 (150) 108 (50) 725 (325) 242 (108) 4350 (2008) 1475 (683)
SPZ SM (3) 0 (0) 0 (0) 17 (8) 8 (0) 33 (17) 8 (8) 117 (75) 42 (25) 183 (117) 58 (42) 458 (308) 158 (108)
PHZ SM (3) 0 (0) 0 (0) 17 (8) 8 (0) 33 (17) 8 (8) 125 (75) 42 (25) 192 (125) 67 (42) 492 (333) 167 (108)
CHM SM (3) 0 (0) 0 (0) 25 (8) 8 (0) 42 (25) 17 (8) 142 (83) 50 (33) 225 (142) 75 (50) 567 (383) 192 (133)

(1) Surface brightness limit used to determine the number of arcs; (2) arc length-to-width ratio thresholds; (3) redshift distribution and number count function, as introduced in Figs. 3 and 6.
Values with and without brackets correspond to $S_{850~\mu{\rm m}} /S_{1.4~{\rm GHz}}=100$ and 50, respectively.


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