SIMBAD references

Using 148 out-axis gamma-ray bursts (GRBs), we build their spectrum-energy relations of peak energy versus isotropic energy, peak energy versus peak luminosity, and peak energy versus jet-calibrated energy, which are corrected for a structured jet model. These relations are found to depend on the observer's viewing angle as long as the observer is within the jet cone. After converting the out-axis energy relations to the in-axis situations, we find that the corresponding in-axis energy relations are universally steeper, of which all of them can be roughly interpreted by the synchrotron radiation mechanism as shown in Xu et al. Meanwhile, we notice that the in-axis means of isotropic energies are about 1 order of magnitude larger than the out-axis means for both short and long bursts except the supernova-associated GRBs. Furthermore, we apply all the newly found energy relations to construct the Hubble diagrams of out/in-axis bursts. It is found that the in-axis Hubble diagrams are better cosmological indicators.