Fast radio bursts (FRBs) are mysterious extragalactic radio signals. Revealing their origin is one of the central foci in modern astronomy. Previous studies suggest that occurrence rates of non-repeating and repeating FRBs could be controlled by the cosmic stellar-mass density (CSMD) and star formation-rate density (CSFRD), respectively. The Square Kilometre Array (SKA) is one of the best future instruments to address this subject due to its high sensitivity and high-angular resolution. Here, we predict the number of FRBs to be detected with the SKA. In contrast to previous predictions, we estimate the detections of non-repeating and repeating FRBs separately, based on latest observational constraints on their physical properties including the spectral indices, FRB luminosity functions, and their redshift evolutions. We consider two cases of redshift evolution of FRB luminosity functions following either the CSMD or CSFRD. At $z\gtrsim2$, $z\gtrsim6$ and $z\gtrsim10$, non-repeating FRBs will be detected with the SKA at a rate of $\sim10^{4}$, $\sim10^{2}$, and $\sim10$ (sky$^{-1}$ day$^{-1}$), respectively, if their luminosity function follows the CSMD evolution. At $z\gtrsim1$, $z\gtrsim2$, and $z\gtrsim4$, sources of repeating FRBs will be detected at a rate of $\sim10^{3}$, $\sim10^{2}$, and $\lesssim10$ (sky$^{-1}$ day$^{-1}$), respectively, assuming that the redshift evolution of their luminosity function is scaled with the CSFRD. These numbers could change by about one order of magnitude depending on the assumptions on the CSMD and CSFRD. In all cases, abundant FRBs will be detected by the SKA, which will further constrain the luminosity functions and number density evolutions.

中文翻译：

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用平方公里阵列检测快速射电暴

快速射电暴 (FRB) 是神秘的河外射电信号。揭示它们的起源是现代天文学的中心焦点之一。先前的研究表明，非重复和重复 FRB 的发生率可以分别受宇宙恒星质量密度 (CSMD) 和恒星形成率密度 (CSFRD) 的控制。由于其高灵敏度和高角分辨率，平方公里阵列 (SKA) 是解决这一问题的最佳未来仪器之一。在这里，我们预测要使用 SKA 检测到的 FRB 的数量。与之前的预测相反，我们根据对其物理特性（包括光谱指数、FRB 光度函数及其红移演化）的最新观测限制，分别估计对非重复和重复 FRB 的检测。我们考虑了在 CSMD 或 CSFRD 之后 FRB 光度函数红移演化的两种情况。在 $z\gtrsim2$、$z\gtrsim6$ 和 $z\gtrsim10$ 处，SKA 将以 $\sim10^{4}$、$\sim10^{2}$ 的速率检测到非重复 FRB和 $\sim10$ (sky$^{-1}$ day$^{-1}$)，如果它们的光度函数遵循 CSMD 演化。在 $z\gtrsim1$、$z\gtrsim2$ 和 $z\gtrsim4$ 处，重复 FRB 的来源将以 $\sim10^{3}$、$\sim10^{2}$ 和$\lesssim10$ (sky$^{-1}$ day$^{-1}$)，假设它们的光度函数的红移演化与 CSFRD 成比例。根据对 CSMD 和 CSFRD 的假设，这些数字可能会发生大约一个数量级的变化。在所有情况下，SKA 都会检测到大量的 FRB，