MESA 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.为约束超长伽马射线暴（Ultra-Long Gamma-Ray Burst，ULGRB）前身星的物理性质，我们采用MESA（恒星天体物理实验模块，Modules for Experiments in Stellar Astrophysics）模拟不同初始自转状态下低金属丰度大质量恒星的演化历程。利用核心坍缩触发阶段各模型的模拟参数，我们估算了恒星的自由下落时标。自由下落时标的估算有助于厘清中心引擎的能量供给时长，因此可将其与伽马射线暴（Gamma-Ray Bursts，GRBs）的T90持续时长进行对比。研究结果表明，在本模型所采用的参数范围及输入MESA的初始条件内，具有自转的大质量恒星有可能成为ULGRB的前身星。