We have argued ( e.g . ( ( 1 ) ) ) that the well-known ‘ ankle ’ in the cosmic ray energy spectrum , at logE ( eV ) \sim 18.7-19.0 , marks the transition from mainly Galactic sources at lower energies to mainly extragalactic above .
Recently , however , there have been claims for lower transitional energies , specifically from logE ( eV ) \sim 17.0 ( ( 2 ) ) via 17.2 - 17.8 ( ( 3 ) ) to 18.0 ( ( 4 ) ) .
In our model the ankle arises naturally from the sum of simple power law-spectra with slopes differing by \Delta \gamma \sim 1.8 ; from differential slope \gamma = -3.8 for Galactic particles ( near logE = 19 ) to \gamma \sim - 2.0 for extragalactic sources .
In the other models , on the other hand , the ankle is intrinsic to the extragalactic component alone , and arises from the shape of the rate of energy loss versus energy for the ( assumed ) protons interacting with the cosmic microwave background ( CMB ) . Our detailed analysis of the world ’ s data on the ultra-high energy spectrum shows that taken together , or separately , the resulting mean sharpness of the ankle ( second difference of the log ( intensity \times E ^ { 3 } ) with respect to logE ) is consistent with our ‘ mixed ’ model .
For explanation in terms of extragalactic particles alone , however , the ankle will be at the wrong energy – for reasonable production models and of insufficient magnitude if , as seems likely , there is still a significant fraction of heavy nuclei at the ankle energy .