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arXiv 1907.08342astro-ph.HE
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完整长伽马射线暴样本的光度函数和形成率

The Luminosity Function and Formation Rate of A Complete Sample of Long Gamma-Ray Bursts

Guang-Xuan Lan, Hou-Dun Zeng, Jun-Jie Wei, Xue-Feng Wu

摘要:

用极大似然法研究了长伽马射线暴的光度函数和形成率。这是第一次这种方法被应用到一个定义明确的样本的伽玛暴是完全的红移。该样本由$Swift$卫星探测到的99个爆发组成,其中81个具有测量的红移和光度,达到了$Swift$的完整性水平。我们证实,一个强大的红移演化的亮度(与演化指数$δ=2.22^{+0.32}_{-0.31}$)或密度($δ=1.92^{+0.20}_{-0.21}$)是需要的,以便重现的观察。但是由于在这两种情况下预测的红移和光度分布非常相似,仅根据当前样本很难区分这两种演化。此外,我们还考虑了一个经验密度的情况下,伽玛暴率密度直接描述为一个破碎的幂律函数和光度函数被视为是非进化的。在这种情况下,我们发现GRB的形成率像$z\leq2$的$(1+z)^{3.85^{+0.48}_{-0.45}}$一样上升,并且与$z\geq2$的$(1+z)^{-1.07^{+0.98}_{-1.12}}$成正比。当地伽玛射线暴率为$1.49^{+0.63}_{-0.64}$ Gpc $^{-3}$ yr $^{-1}$。伽玛射线暴速率可能与$z\leq2$的宇宙恒星形成速率(SFR)一致,但与$z\geq2$的SFR相比有所增强。

英文摘要:

We study the luminosity function and formation rate of long gamma-ray bursts (GRBs) by using a maximum likelihood method. This is the first time this method is applied to a well-defined sample of GRBs that is complete in redshift. The sample is composed of 99 bursts detected by the $Swift$ satellite, 81 of them with measured redshift and luminosity for a completeness level of $82\%$. We confirm that a strong redshift evolution in luminosity (with an evolution index of $δ=2.22^{+0.32}_{-0.31}$) or in density ($δ=1.92^{+0.20}_{-0.21}$) is needed in order to reproduce the observations well. But since the predicted redshift and luminosity distributions in the two scenarios are very similar, it is difficult to distinguish between these two kinds of evolutions only on the basis of the current sample. Furthermore, we also consider an empirical density case in which the GRB rate density is directly described as a broken power-law function and the luminosity function is taken to be non-evolving. In this case, we find that the GRB formation rate rises like $(1+z)^{3.85^{+0.48}_{-0.45}}$ for $z\leq2$ and is proportional to $(1+z)^{-1.07^{+0.98}_{-1.12}}$ for $z\geq2$. The local GRB rate is $1.49^{+0.63}_{-0.64}$ Gpc$^{-3}$ yr$^{-1}$. The GRB rate may be consistent with the cosmic star formation rate (SFR) at $z\leq2$, but shows an enhancement compared to the SFR at $z\geq2$.

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