Softness Ratio of SWIFT Gamma-Ray Bursts and Relevant Correlations

Abstract The properties of X-ray flashes (XRFs) and X-ray-rich gamma-ray bursts (XRRs) as compared with classical gamma-ray bursts (C-GRBs) have been widely discussed during the SWIFT era. It has been proposed that XRFs and XRRs are low-energy extensions of the gamma-ray burst (GRB) population, and therefore, they should follow similar correlations. To further examine this idea, we collect a sample of 303 GRBs detected by SWIFT over the past two decades, all of which have reliable redshifts and spectral parameters. The bursts are classified into XRFs, XRRs, and C-GRBs based on their softness ratio (SR), which is calculated by dividing the 25–50 keV fluence with the 50–100 keV fluence. A strong correlation is found among the isotropic energy E iso , peak luminosity L p , and rest-frame burst duration T 90,rest , i.e., <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">iso</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∝</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">p</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0.88</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.02</mml:mn> </mml:mrow> </mml:msubsup> <mml:msubsup> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>90</mml:mn> <mml:mo>,</mml:mo> <mml:mi mathvariant="normal">rest</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0.58</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.02</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> . Additionally, two tight three-parameter correlations involving SR and the rest-frame peak energy E p are also derived, i.e., <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">p</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∝</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">iso</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0.20</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.02</mml:mn> </mml:mrow> </mml:msubsup> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">SR</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2.27</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.15</mml:mn> </mml:mrow> </mml:msup> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">p</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∝</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">p</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0.17</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.02</mml:mn> </mml:mrow> </mml:msubsup> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">SR</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>2.33</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.14</mml:mn> </mml:mrow> </mml:msup> </mml:math> . It is interesting to note that XRFs, XRRs, and C-GRBs all follow the above correlations. The implications of these correlations and their potential application in cosmology are discussed.