Revisiting the Long/Soft-Short/Hard Classification of Gamma-Ray Bursts in the Fermi Era

We perform a statistical analysis of the temporal and spectral properties of the latest Fermi gamma-ray bursts (GRBs) to revisit the classification of GRBs. We find that the bimodalities of duration and the energy ratio ($E_{\mathrm{peak}}$/Fluence) and the anti-correlation between spectral hardness (hardness ratio ($HR$), peak energy and spectral index) and duration ($T_{90}$) support the long/soft $-$ short/hard classification scheme for Fermi GRBs. The $HR - T_{90}$ anti-correlation strongly depends upon the spectral shape of GRBs and energy bands, and the bursts with the curved spectra in the typical BATSE energy bands show a tighter anti-correlation than those with the power-law spectra in the typical BAT energy bands. This might explain why the $HR - T_{90}$ correlation is not evident for those GRB samples detected by instruments like {\it Swift} with a narrower/softer energy bandpass. We also analyze the intrinsic energy correlation for the GRBs with measured redshifts and well defined peak energies. The current sample suggests $E_{\mathrm{p,rest}}=2455\times (E_{\mathrm{iso}}/10^{52})^{0.59}$ for short GRBs, significantly different from that for long GRBs. However, both the long and short GRBs comply with the same $E_{\mathrm{p,rest}}-L_{\mathrm{iso}}$ correlation.