Constraints on the ultrahigh-energy photon flux using inclined showers from the Haverah Park array

We describe a method to analyze inclined air showers produced by ultrahigh-energy cosmic rays using an analytical description of the muon densities. We report the results obtained using data from inclined events $(60\mathrm{}°<\theta <80\mathrm{}°)$ recorded by the Haverah Park shower detector for energies above ${10}^{19}\hspace{0.5em}\mathrm{eV}.$ Using mass independent knowledge of the UHECR spectrum obtained from vertical air shower measurements and comparing the expected horizontal shower rate to the reported measurements we show that above ${10}^{19}\hspace{0.5em}\mathrm{eV}$ less than $48\%$ of the primary cosmic rays can be photons at the $95\%$ confidence level and above $4\times {10}^{19}\hspace{0.5em}\mathrm{eV}$ less than $50\%$ of the cosmic rays can be photonic at the same confidence level. These limits place important constraints on some models of the origin of ultrahigh-energy cosmic rays.