The Highest-Energy Cosmic Rays Cannot be Dominantly Protons from Steady Sources

The bulk of observed ultrahigh energy cosmic rays could be light or heavier elements, and originate from an either steady or transient population of sources. This leaves us with four general categories of sources. Energetic requirements set a lower limit on single source luminosities, while the distribution of particle arrival directions in the sky sets a lower limit on the source number density. The latter constraint depends on the angular smearing in the skymap due to the magnetic deflections of the charged particles during their propagation from the source to the Earth. We contrast these limits with the luminosity functions from surveys of existing luminous steady objects in the nearby universe, and strongly constrain one of the four categories of source models, namely, steady proton sources. The possibility that cosmic rays with energy $> 8\times 10^{19}\,$eV are dominantly pure protons coming from steady sources is excluded at 95\% confidence level, under the safe assumption that protons experience less than $30^\circ$ magnetic deflection on flight.