Three-Dimensional Distributions of Type II Cepheids and Anomalous Cepheids in the Magellanic Clouds. Do these Stars Belong to the Old, Young or Intermediate-Age Population?

The nature of type II Cepheids and anomalous Cepheids is still not well known and their evolutionary channels leave many unanswered questions. We use complete collection of classical pulsating stars in the Magellanic Clouds discovered by the OGLE project, to compare their spatial distributions, which are one of the characteristic features directly related to the star formation history. In this analysis we use 9649 classical Cepheids, 262 anomalous Cepheids, 338 type II Cepheids and 46 443 RR Lyr stars from both Magellanic Clouds. We compute three-dimensional Kolmogorov-Smirnov tests for every possible pair of type II and anomalous Cepheids with classical Cepheids, and RR Lyr stars. We confirm that BL Her stars are as old as RR Lyr variable stars - their spatial distributions are similar, and they create a vast halo around both galaxies. We discover that spatial distribution of W Vir stars has attributes characteristic for both young and old stellar populations. Hence, it seems that these similarities are related to the concentration of these stars in the center of the Large Magellanic Cloud, and the lack of a vast halo. This leads to the conclusion that W Vir variables could be a mixture of old and intermediate-age stars. Our analysis of the three-dimensional distributions of anomalous Cepheids shows that they differ significantly from classical Cepheids. Statistical tests of anomalous Cepheids distributions with RR Lyr distributions do not give unambiguous results. We consider that these two distributions can be similar through the vast halos they create. This similarity would confirm anomalous Cepheids evolution scenario that assumes coalescence of a binary system.