  We report angle-resolved photoemission spectroscopy measurements of the
excitation gap in underdoped superconducting thin films of
Bi_2Sr_2Ca_{1-x}Dy_xCu_2O_{8+d}. As Tc is reduced by a factor of 2 by
underdoping, the superconducting state gap \Delta does not fall proportionally,
but instead stays constant or increases slightly, in violation of the BCS
mean-field theory result. The different doping dependences of \Delta and kT_c
indicate that they represent different energy scales. The measurements also
show that \Delta is highly anisotropic and consistent with a d_{x^2-y^2} order
parameter, as in previous studies of samples with higher dopings. However, in
these underdoped samples, the anisotropic gap persists well above T_c. The
existence of a normal state gap is related to the failure of \Delta to scale
with T_c in theoretical models that predict pairing without phase coherence
above T_c.
