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We have published the energy spectrum of ultra-high energy cosmic rays(UHECRs) for E > 10^18.2 eV from our first 5-year observation with the surfacedetectors of Telescope Array. We found two breaking points in the power-lawspectrum, a flattening known as the "ankle" or "dip" at E = 10^18.66 eV, and asteepening at E = 10^19.72 eV. The spectral features must be related todistribution of cosmic ray sources, injection spectrum, and energy lossprocesses during propagation in inter-galactic space. We constructed a model ofsource distribution of UHECRs and energy loss processes in the CMB photon fieldto calculate energy spectrum to be observed at the Earth. The model includesinjection energy spectra at the sources, energy loss processes, and evolutionof cosmic ray fluxes with red shift. We consider two cases that the UHECRsources are distributed uniformly, or same as galaxies in the local universe.We found that the spectrum can be well fitted with the model. We discuss togive a constraint to the model parameters, e.g. the injection power indices andcosmological evolution from the observed data.

Constraining UHECR source models by the TA SD energy spectrum