1% accuracy in fundamental stellar parameters? Not without an extensive redesign of eclipsing binary models.

通过简单的几何和熟知的物理定律，双星日食可以用来确定恒星的半径和质量。在过去十年中获得的观测结果在精度上有了很大的提高，因此用于解释这些数据的理论模型需要进行大量的修订。本项目确定了需要修订的理论模型的各个方面，并提出了更新模型的途径。这将使精确（在1%以内）测量恒星质量和半径成为可能。从研究恒星的生命周期到确定整个宇宙的距离，精确确定恒星的基本特性对天体物理学的许多分支都至关重要。建模方法和分类的进步适用于天文学、物理学、工程学和应用数学中的许多问题。在一个主要的本科院校开展这个项目将为本科生提供学习现代研究工具和技术的机会。研究人员将对他们的食双星模型代码进行以下改进：(a)优化恒星表面离散化，以减轻扭曲系统中的系统性，并能够模拟更复杂的结构，如吸积盘；(b)系统地处理所有模拟双星的多普勒增强；(c)设计一个广义罗氏势的数值框架，允许组件的自旋轴向轨道轴倾斜；(d)严格处理多体系统，预测日食时间变化、第三次日食、扩展体的动态相互作用和其他相关现象；(e)修改边缘变暗处理，以解决入口/出口拟合问题，从而消除确定恒星半径的系统性；(f)基于现代嵌入算法实现新的形态学分类方案；(g)利用马尔可夫链蒙特卡罗方法和贝叶斯推理为统计误差估计提供了一种新的形式，以解决长期存在的参数误差低估问题；(h)考虑有限积分时间修正；(i)用python编写一个后端，允许在高性能计算中实现代码并行，并使其可用于更广泛的天文社区。

Eclipsing binary stars can be used to determine the radius and mass of stars by relying on simple geometry and well understood laws of physics. Observations obtained over the last decade have greatly improved in accuracy, so the theoretical models used to interpret these data require substantial revision. This project identifies the aspects of theoretical models in need of revision and proposes a path to update the models. This will enable accurate (within 1%) measurements of stellar masses and radii. Precise determination of fundamental stellar properties is critical to many branches of astrophysics, from studying the life cycles of stars to determining distances throughout the universe. The advances in modelling approaches and classification are applicable to many problems in astronomy, physics, engineering, and applied mathematics. Conducting this program at a primarily undergraduate institution will provide opportunities undergraduate students learn modern research tools and techniques.The investigators will develop the following improvements to their eclipsing binary modelling codes: (a) optimize stellar surface discretization to mitigate systematics in distorted systems and to be able to model more complicated structures such as accretion disks; (b) systematically treat Doppler boosting for all modelled binaries; (c) devise a numerical framework for the Generalized Roche Potential that will allow for tilted spin axes of components to the orbital axis; (d) rigorously treat multiple body systems, predicting eclipse timing variations, tertiary eclipses, dynamical interactions of extended bodies, and other related phenomena; (e) revise the limb darkening treatment to resolve the ingress/egress fitting problems and, consequently, eliminate systematics from the determination of stellar radii; (f) implement a new morphological classification scheme based on modern embedding algorithms; (g) provide a new formalism for statistical error estimates using Markov Chain Monte Carlo methods and Bayesian inference to resolve a long-standing issue of underestimated parameter errors; (h) account for finite integration time corrections; and (i) write a back-end in python that will allow code parallelization in high performance computing and make it available to the broader astronomical community.