标题： 以秒为单位计算第一个十亿年：第三族恒星21厘米信号的有效模型 显示英文标题

标题： The First Billion Years in Seconds: An Effective Model for the 21-cm Signal with Population III Stars

摘要： 21厘米信号的观测开启了通往宇宙黎明时代（第一颗恒星形成的时代）的窗口。 这些观测通常通过半数值或流体力学模拟来解释，但这些模拟往往计算量巨大且对宇宙学或天体物理效应的变化不够灵活。 在这里，我们利用模块化代码Zeus21提出了一种针对第一颗恒星对21厘米信号影响的有效、完全解析的模型。 Zeus21采用恒星形成率密度（SFRD）的解析公式，以恢复决定21厘米信号的辐射场的完全非线性和非局部相关性。 我们在Zeus21中引入了最早期的第三星族（Pop III）恒星，它们存在于低质量分子冷却星系中，并且具有与后期第二星族（Pop II）恒星不同的光谱。 我们还自洽地建模了Lyman-Werner（LW）辐射分解$H_2$以及暗物质-重子相对速度的反馈形式，这两种机制都会抑制最低质量暗晕中的恒星形成。 由于LW光子的平均自由程很长，LW反馈会在SFRD波动上产生尺度依赖性。 相对速度在21厘米信号的空间分布中产生了“波纹”；我们提出了改进的计算方法来确定这些由速度引起的声振荡的形状，表明它们在宇宙黎明时仍然是标准的量度。 我们改进后的Zeus21版本预测的21厘米全局信号和功率谱与模拟结果一致，精度达到$\sim 10\%$级别，但速度至少快三个数量级。 这一公开代码代表了迈向宇宙黎明时期高效且灵活参数推断的重要一步，使我们能够在短短几秒内预测宇宙的最初十亿年。 显示英文摘要

摘要： Observations of the 21-cm signal are opening a window to the cosmic-dawn epoch, when the first stars formed. These observations are usually interpreted with semi-numerical or hydrodynamical simulations, which are often computationally intensive and inflexible to changes in cosmological or astrophysical effects. Here, we present an effective, fully analytic model for the impact of the first stars on the 21-cm signal, using the modular code Zeus21. Zeus21 employs an analytic prescription of the star formation rate density (SFRD) to recover the fully nonlinear and nonlocal correlations of radiative fields that determine the 21-cm signal. We introduce the earliest Population III (Pop III) stars residing in low-mass molecular-cooling galaxies in Zeus21, with distinct spectra from later Pop II stars. We also self-consistently model feedback in the form of $H_2$-dissociating Lyman-Werner (LW) radiation, as well as dark matter-baryon relative velocities, both of which suppress star formation in the lowest-mass halos. LW feedback produces a scale-dependence on the SFRD fluctuations, due to the long mean free path of LW photons. Relative velocities give rise to "wiggles" in the spatial distribution of the 21-cm signal; we present an improved calculation of the shape of these velocity-induced acoustic oscillations, showing they remain a standard ruler at cosmic dawn. Our improved version of Zeus21 predicts the 21-cm global signal and power spectra in agreement with simulations at the $\sim 10\%$ level, yet is at least three orders of magnitude faster. This public code represents a step towards efficient and flexible parameter inference at cosmic dawn, allowing us to predict the first billion years of the universe in mere seconds.