伽马射线暴亮度函数基于峰值能谱与V/V_max的新相关性
Gamma-Ray Burst Luminosity Functions Based On a Newly Discovered Correlation Between Peak Spectral Energy and V/V_max
摘要：
我们发现，观测到的伽马射线暴（GRB）的峰值谱能量E_pk，obs与V/V_max的平均欧几里德值之间存在相关性。我们在GUSBAD星表中给出了相关性的证据，并利用它在不使用任何红移的情况下导出了伽玛暴的光度函数。该过程涉及到划分GUSBAD伽玛暴在五个光谱类的基础上，他们的E_pk，obs。总的光度函数推导出假设每个光谱类贡献一个高斯光度函数。它们的中心光度是由观测到的平均欧几里德V/V_max导出的。我们探讨了不同形式的伽玛暴率函数GR（z）在预测红移分布的伽玛暴雨燕检测。我们发现GR（z）的峰值比文献中目前支持的典型恒星形成历史的红移更高。我们考虑两个GR（z）的例子，成功地预测了观测到的雨燕伽玛暴的红移分布。利用光度函数，我们将E_pk，obs-V/V_max关联转换为E_pk，obs-L_iso关联和静止帧E_pk-L_iso关联。在比较E_pk-L_iso关联与已知E_pk、obs和红移的伽玛暴关联时，我们讨论了Malmquist偏差的影响。
英文摘要：
We have discovered a correlation between the observed peak spectral energy E_pk,obs and the average Euclidean value of V/V_max of gamma-ray bursts (GRBs). We present the evidence for the correlation in the GUSBAD catalog and use it to derive the luminosity function of GRBs without using any redshifts. The procedure involves dividing GUSBAD GRBs in five spectral classes based on their E_pk,obs. The overall luminosity function is derived assuming that each of the spectral classes contributes a gaussian luminosity function. Their central luminosity is derived from the average observed Euclidean V/V_max. We explore various forms for the GRB rate function GR(z) in predicting redshift distributions of GRBs detected by Swift. We find that GR(z) peaks at a higher redshift than the typical star formation history currently favored in the literature. We consider two examples of GR(z) that successfully predict the observed redshift distribution of Swift GRBs. With the luminosity functions in hand, we convert the E_pk,obs-V/V_max correlation into an E_pk,obs-L_iso correlation and a rest frame E_pk-L_iso correlation. In comparing the E_pk-L_iso correlation with a published correlation based on GRBs with known E_pk,obs and redshifts, we discuss the effect of Malmquist bias.
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