Polarization Selection Rules and Superconducting Gap Anisotropy in $Bi_2Sr_2CaCu_2O_8$

We discuss polarization selection rules for angle-resolved photoemission spectroscopy in Bi2212. Using these we show that the ``hump'' in the superconducting gap observed in the $X$ quadrant in our earlier work is not on the main $CuO_2$ band, but rather on an umklapp band arising from the structural superlattice. The intrinsic gap is most likely quite small over a range of $\pm 10^\circ$ about the diagonal directions.