Redshift degeneracy in the E-iso-E-peak relation of gamma-ray bursts

In this Letter we show that there is a redshift degeneracy in the E-iso-E-peak relation of gammaray bursts (GRBs). If a GRB has a redshift solved from the E-iso-E-peak relation that lies in the range of 0.9 < z < 20, a GRB that has the same observed fluence and peak spectral energy but is at a different redshift in that range also satisfies the E-iso-E-peak relation within a 1 sigma error, implying an extremely large error in the calculated redshift. Even if the data scatter in the E-iso-E-peak relation is reduced by a factor of 2, the error in the predicted redshift is still large enough to prevent one from constraining the redshift meaningfully. Hence, the E-iso-E-peak relation is not useful for determining the GRB distance.