Estimation of classical Cepheid’s physical parameters from NIR light curves

Recent space-borne and ground-based observations provide photometric measurements as time series. The data points are nearly continuous over a limited observational interval or randomly scattered over a long period. The effect of interstellar dust extinction in the near-infrared range is only 10% of that measured in the visual (V) range. However, the sensitivity of the light curve shape to the physical parameters in the near-infrared is significantly lower. So, interpreting these types of data sets requires new approaches like the different large-scale surveys, which create similar problems with big data. Using a selected data set, we provide a method for applying routines implemented in R to extract most information of measurements to determine physical parameters, which can also be used in automatic classification schemes and pipeline processing.

We made a multivariate classification of 131 Cepheid light curves (LC) in J,H, and K colors by applying routines of R, where all the LCs were represented in 20D parameter space in these colors separately. Performing a Principal Component Analysis (PCA), we got an orthogonal coordinate system and squared Euclidean distances between LCs. The PCA resulted in 6 significant eigenvalues, which allowed us to reduce the 20-dimension to 6. We also estimated the optimal number of partitions of similar objects and obtained it equal to 7 in each color; their dependence on the period, absolute magnitude, amplitude, and metallicity are also discussed. We computed the Spearman rank correlations, and concerning periods and absolute magnitudes, the first three PCs had correlations at a very high significance level. Similar computations revealed significant relationships between the amplitude and the first two PCs, but the LCs depend only marginally on the metallicity in H and K colors.

The method shown can be generalized and implemented in unsupervised classification schemes and analysis of mixed and biased samples. The analysis of a sample of classical Cepheids observed only in near-infrared bands resulted in the information coded in the light curves being insufficient to determine the stars’ metallicity and identified the mass as the dominating quantity to form the shape of LCs in our sample.