In this paper, we study the evolution of the ionization fraction x _e(z) during the epoch of reionization by using the dispersion measurements (DMs) of fast radio bursts (FRBs). Different from the previous studies, here we turn to consider the large-scale clustering information of observed DMs of FRB catalog, which only needs the rough redshift distribution, instead of the exact redshift information of each FRB. Firstly, we consider the instantaneous “tanh” model for x _e(z) and find that including the auto-correlation information of the mock catalog, about 10⁴ FRBs with the intrinsic DM scatter of 100 pc/cm³ spanning 20% of all sky, could significantly improve the constraint on the width Δ_z of the model, when comparing with that from the CMB data alone. The evolution shape of the ionization fraction will be tightly narrowed, namely the duration of the epoch of reionization has been shrunk, z _dur < 2.24 (95% C.L.). Furthermore, we also use another redshift-asymmetric reionization model and obtain that the FRB mock catalog could measure the ionization fraction at z = 6 precisely with the 1σ error Δ x _e (z = 6) = 0.012, which means that the large-scale clustering information of observed DMs of FRB catalog is very sensitive to the ionization fraction of the end of reionization epoch. We conclude that the observation of high-redshift FRBs could be a complementary probe to study the reionization history in the future.

在本文中，我们利用快速射电暴 (FRB) 的色散测量 (DM) 研究了再电离时期电离分数x _e ( z ) 的演变。与以往的研究不同，这里我们转向考虑FRB目录中观测到的DM的大规模聚类信息，它只需要粗略的红移分布，而不是每个FRB的精确红移信息。首先，我们考虑x _e ( z )的瞬时“ tanh ”模型，发现包括模拟目录的自相关信息在内，大约有10 ^{4 个}FRB，其固有DM 散射为100 pc/cm ³ 与单独的 CMB 数据相比，跨越 20% 的天空，可以显着改善对模型宽度 Δz 的约束_。电离部分的演化形状将被紧紧地收窄，即再电离时期的持续时间已经缩短，z _dur < 2.24 (95% CL)。此外，我们还使用了另一个红移非对称再电离模型，得到 FRB 模拟目录可以精确测量z = 6 处的电离分数，误差为 1σ Δ x _e ( z= 6) = 0.012，表示观测到的快速射电暴目录的大尺度聚类信息对再电离期末的电离分数非常敏感。我们得出结论，对高红移 FRB 的观察可以作为研究未来再电离历史的补充探针。