A lower limit on the magnitude of the companion to HDE 226868 /Cygnus X-1

High-precision digital spectra of the HDE 226868/Cygnus X-1 system have been obtained at a variety of orbital phases, using a Digicon photon counting array at the coude focus of the Lick Shane reflector. The spectra have been cross-correlated to search for evidence for the existence of a luminous stellar companion to HDE 226868, as has been suggested by several models where the secondary star is not a black hole. We find no evidence for such a star and place a lower limit on the difference between HDE 226868 and its companion of 4 magnitudes. This limit rules out all of the models for the Cygnus X-1 system calculated by Avni and Bahcall which include main-sequence stars as secondaries rather than black holes. A merit function generally useful for cross-correlation of digital spectra is described.