Abstract

An algorithm has been developed for finding the global minimum of a multidimensional error function by fitting model spectral maps into observed ones. Principal component analysis is applied to reduce the dimensionality of the model and the coupling degree between the parameters, and to determine the region of the minimum. The k-nearest neighbors method is used to calculate the optimal parameter values. The algorithm is used to estimate the physical parameters of the contracting dense star-forming core of L1287. Maps in the HCO⁺(1–0), H¹³CO⁺(1–0), HCN(1–0), and H¹³CN(1–0) lines, calculated within a 1D microturbulent model, are fitted into the observed ones. Estimates are obtained for the physical parameters of the core, including the radial profiles of density (\( \propto {\kern 1pt} {{r}^{{ - 1.7}}}\)), turbulent velocity (\( \propto {\kern 1pt} {{r}^{{ - 0.4}}}\)), and contraction velocity (\( \propto {\kern 1pt} {{r}^{{ - 0.1}}}\)). Confidence intervals are calculated for the parameter values. The power-law index of the contraction-velocity radial profile, considering the determination error, is lower in absolute terms than the expected one in the case of gas collapse onto the protostar in free fall. This result can serve as an argument in favor of a global contraction model for the L1287 core.

中文翻译：

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通过将模型光谱图拟合到观测到的谱图来估计L1287致密岩心参数的主成分分析

摘要

已经开发了一种算法，该算法通过将模型光谱图拟合到观察到的图中来找到多维误差函数的全局最小值。应用主成分分析来减少模型的维数和参数之间的耦合度，并确定最小值的区域。的K-最近邻方法用于计算最佳参数值。该算法用于估算L1287收缩致密恒星形成核的物理参数。HCO ⁺（1–0），H ¹³ CO ⁺（1–0），HCN（1–0）和H ^13中的映射在一维微湍流模型中计算出的CN（1-0）线被拟合到观察到的线中。获得了岩心物理参数的估计值，包括密度的径向分布图（\（\ propto {\ kern 1pt} {{r} ^ {{-1.7}}} \））湍流速度（\（\ propto {\ kern 1pt} {{r} ^ {{-0.4}}} \））和收缩速度（\（\ propto {\ kern 1pt} {{r} ^ {{-0.1}}} \））。计算参数值的置信区间。考虑到确定误差，收缩速度径向轮廓的幂律指数在绝对意义上低于在自由落体中气体塌陷到原恒星上的情况下的预期幂指数。该结果可以作为支持L1287磁芯的全局收缩模型的一个论据。