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.
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We present a collection of classical, typeII, and anomalous Cepheids detected in the OGLE fields toward the Galactic center. The sample contains 87 classical Cepheids pulsating in one, two or three radial modes, 924 type II Cepheids divided into BL Her, W Vir, peculiar W Vir, and RV Tau stars, and 20 anomalous Cepheids - first such objects found in the Galactic bulge. Additionally, we upgrade the OGLE Collection of RR Lyr stars in the Galactic bulge by adding 828 newly identified variables. For all Cepheids and RRLyr stars, we publish time-series VI photometry obtained during the OGLE-IV project, from 2010 through 2017. We discuss basic properties of our classical pulsators: their spatial distribution, light curve morphology, period-luminosity relations, and position in the Petersen diagram. We present the most interesting individual objects in our collection: a typeII Cepheid with additional eclipsing modulation, WVir stars with the period doubling effect and the RVb phenomenon, a mode-switching RR Lyr star, and a triple-mode anomalous RRd star.
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