Primordial stars are expected to be very massive and hot, producing copious amounts of hard ionizing radiation. The best place to study hard ionizing radiation in the local universe is in very metal-deficient Blue Compact Dwarf (BCD) galaxies. We have carried out a MMT spectroscopic search for [Ne V] 3426 (ionization potential of 7.1 Ryd), [Fe V] 4227 (ionization potential of 4 Ryd) and He II 4686 (ionization potential of 4 Ryd) emission in a sample of 18 BCDs. We have added data from previous work and from the Data Release 3 of the Sloan Digital Sky Survey. In total, we have assembled a BCD high-ionization sample with [Ne V] emission in 4 galaxies, [Fe V] emission in 15 galaxies and He II emission in 465 galaxies. With this large sample, we have reached the following conclusions. There is a general trend of higher [Ne V], [Fe V] and He II emission at lower metallicities. However metallicity is not the only factor which controls the hardness of the radiation. High-mass X-ray binaries and main-sequence stars are probably excluded as the main sources of the very hard ionizing radiation responsible for [Ne V] emission. The most likely source of [Ne V] emission is probably fast radiative shocks moving with velocities > 450 km/s through a dense interstellar medium with an electron number density of several hundreds per cm^-3 and associated with supernova explosions of the most massive stars. These have masses of ~ 50 - 100 Msun and are formed in very compact super-star clusters. The softer ionizing radiation required for He II emission is likely associated with less massive evolved stars and/or radiative shocks moving through a less dense interstellar medium.
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