Principal Component Analysis for Estimating Parameters of the L1287 Dense Core by Fitting Model Spectral Maps into Observed Ones

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), H 13 CO + (1–0), HCN(1–0), and H 13 CN(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.