Inlists and the final models of collapsing stars from paper "Exploring Origin of Ultra-Long Gamma-ray Bursts: Lessons from GRB 221009A"

To constrain the physical properties of ULGRB progenitors, we employ MESA to simulate the evolution of low-metallicity massive stars with different initial rotations. Utilizing the simulation parameters of the models at the stage of the onset of core collapse, we estimate the free fall timescales. The estimation of free fall time is important to gain insights into how long the central engine can be fueled; thus, it can be compared with the T90 duration of the GRBs.The outcomes suggest that rotating massive stars could potentially be the progenitors of ULGRBs within the limits of the considered parameters and initial inputs to MESA in our models.为限定超长伽马射线暴（Ultra-Long Gamma-Ray Burst, ULGRB）前身天体的物理性质，我们采用MESA模拟不同初始自转参数的低金属性大质量恒星的演化过程。利用核心坍缩触发阶段的模型模拟参数，我们估算了自由下落时标。自由下落时间的估算对于理解中心引擎的供能时长具有重要意义，因此可将其与伽马射线暴（Gamma-Ray Burst, GRB）的T90持续时间进行对比。研究结果表明，在本模型所考量的参数范围及MESA初始输入条件下，自转大质量恒星有可能成为超长伽马射线暴的前身天体。