Data-driven analysis for understanding ultrahigh energy cosmic ray source spectra

One of the most challenging open questions regarding the origin of ultrahigh energy cosmic rays (UHECRs) deals with the shape of the source emission spectra. A commonly-used simplifying assumption is that the source spectra of the highest energy cosmic rays trace a Peters cycle, in which the maximum cosmic-ray energy scales linearly with $Z$, i.e., with the charge of the UHECR in units of the proton charge. However, this would only be a natural assumption for models in which UHECRs escape the acceleration region without suffering significant energy losses. In most cases, however, UHECRs interact in the acceleration region and/or in the source environment changing the shape of the source emission spectra. Energy losses are typically parameterized in terms of $Z$ and the UHECR baryon number $A$, and therefore one would expect the source emission spectra to be a function of both $Z$ and $A$. Taking a pragmatic approach, we investigate whether existing data favor any region of the $(Z,A)$ parameter space. Using data from the Pierre Auger Observatory, we carry out a maximum likelihood analysis of the observed spectrum and nuclear composition to shape the source emission spectra for the various particle species. We also study the impact of possible systematic uncertainties driven by hadronic models describing interactions in the atmosphere.