Possible existence of Ep-Lp and Ep-Eiso correlations for Short Gamma-Ray Bursts with a factor 5 to 100 dimmer than those for Long Gamma-Ray Bursts

Abstract

We analyzed correlations among the rest frame spectral peak energy $E_{\mathrm{p}}$, the observed frame 64ms peak isotropic luminosity $L_{\mathrm{p}}$ and the isotropic energy $E_{\mathrm{iso}}$ for 13 Short Gamma Ray Burst (SGRB) candidates having the measured redshift $z$, $T_{90}^{\mathrm{obs}}/(1+z)<2$ sec and well determined spectral parameters. A SGRB candidate is regarded as a misguided SGRB if it is located in the 3-${\sigma }_{\mathrm{int}}$ dispersion region from the best-fit function of the $E_{\mathrm{p}}$--$E_{\mathrm{iso}}$ correlation for Long GRBs (LGRBs) while the others are regarded as secure SGRBs possibly from compact star mergers. Using 8 secure SGRBs out of 13 SGRB candidates, we tested whether $E_{\mathrm{p}}$--$E_{\mathrm{iso}}$ and $E_{\mathrm{p}}$--$L_{\mathrm{p}}$ correlations exist for SGRBs. We found that $E_{\mathrm{p}}$--$E_{\mathrm{iso}}$ correlation for SGRBs($E_{\mathrm{iso}}=10^{51.42\pm 0.15}\mathrm{erg}{\mathrm{s}}^{-1}(E_{\mathrm{p}}/774.5keV{)}^{1.58\pm 0.28}$) seems to exist with the correlation coefficeint $r=0.91$ and chance probability $p=1.5\times 10^{-3}$. We found also that the $E_{\mathrm{p}}$--$L_{\mathrm{p}}$ correlation for SGRBs($L_{\mathrm{p}}=10^{52.29\pm 0.066}\mathrm{erg}{\mathrm{s}}^{-1}(E_{\mathrm{p}}/774.5keV{)}^{1.59\pm 0.11}$) is tighter than $E_{\mathrm{p}}$--$E_{\mathrm{iso}}$ correlation since $r=0.98$ and $p=1.5\times 10^{-5}$. Both correlations for SGRBs are dimmer than those of LGRBs for the same $E_{\mathrm{p}}$ by factors $\sim$100 ($E_{\mathrm{p}}$--$E_{\mathrm{iso}}$) and $\sim$ 5($E_{\mathrm{p}}$--$L_{\mathrm{p}}$). Applying the tighter $E_{\mathrm{p}}$--$L_{\mathrm{p}}$ correlation for SGRBs to 71 bright BATSE SGRBs, we found that pseudo redshift $z$ ranges from 0.097 to 2.258 with the mean $<z>$ of 1.05. The redshifts of SGRBs apparently cluster at lower redshift than those of LGRBs ($<z>\sim 2.2$), which supports the merger scenario of SGRBs.

8 pages, 6 figures, Accepted for publication in MNRAS