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At higher energies the uncertainty in the estimated cosmic ray masscomposition, extracted from the observed distributions of the depth of showermaximum $X_\text{max}$, is dominated by uncertainties in the hadronicinteraction models. Thus, the estimated composition depends strongly on theparticular model used for its interpretation. To reduce this model dependencyin the interpretation of the mass composition, we have developed a novelapproach which allows the adjustment of the normalisation levels of the proton$<X_\text{max}>$ and $\sigma (X_\text{max})$ guided by real observations of$X_\text{max}$ distributions. In this paper we describe the details of thisapproach and present a study of its performance and its limitations. Using thisapproach we extracted cosmic ray mass composition information from thepublished Pierre Auger $X_\text{max}$ distributions. We have obtained aconsistent mass composition interpretation for Epos-LHC, QGSJetII-04 andSibyll2.3. Our fits suggest a composition consisting of predominantly iron.Below $10^{18.8}$ eV, the small proportions of proton, helium and nitrogenvary. Above $10^{18.8}$ eV, there is little proton or helium, and withincreasing energy the nitrogen component gradually gives way to the growingiron component, which dominates at the highest energies. The fits suggest thatthe normalisation level for proton $<X_\mathrm{max}>$ is much deeper than theinitial predictions of the hadronic interaction models. The fittednormalisation level for proton $\sigma (X_\text{max})$ is also greater than themodel predictions. When fixing the expected normalisation of$\sigma(X_\mathrm{max})$ to that suggested by the QGSJetII-04 model, a slightlylarger fraction of protons is obtained. These results remain sensitive to theother model parameters that we keep fixed, such as the elongation rate and the$<X_\text{max}>$ separation between p and Fe.

Extracting a less model dependent cosmic ray composition from $X_\mathrm{max}$ distributions