The period-luminosity and period-radius relations of Type II and anomalous Cepheids in the Large and Small Magellanic Clouds

Context. Type II Cepheids (T2Cs) and anomalous Cepheids (ACs) are pulsating stars that follow separate period-luminosity relations. Aims. We study the period-luminosity (PL) and period-radius (PR) relations for T2Cs and ACs in the Magellanic Clouds. Methods. In an accompanying paper we determined the luminosities and effective temperatures for the 335 T2Cs and ACs in the LMC and SMC discovered in the OGLE-III survey, by constructing the spectral energy distribution (SED) and fitting this with model atmospheres and a dust radiative transfer model (in the case of dust excess). Building on these results we studied the PL and PR relations of these sources. Using existing pulsation models for RR Lyrae and classical Cepheids we derive the period-luminositymass-temperature-metallicity relations and then estimate the pulsation mass. Results. The PL relation for the T2Cs does not appear to depend on metallicity and is M-bol = +0.12-1.78 log P (for P < 50 days), excluding the dusty RV Tau stars. Relations for fundamental and first overtone LMC ACs are also presented. The PR relation for T2C also shows little or no dependence on metallicity or period. Our preferred relation combines SMC and LMC stars and all T2C subclasses and is log R = 0.846 + 0.521 log P. Relations for fundamental and first overtone LMC ACs are also presented. The pulsation masses from the RR Lyrae and classical Cepheid pulsation models agree well for the short period T2Cs, the BL Her subtype, and ACs, and are consistent with estimates in the literature, i.e. M-BLH similar to 0.49 M-circle dot and M-AC similar to 1.3 M-circle dot, respectively. The masses of the W Vir appear similar to the BL Her. The situation for the pW Vir and RV Tau stars is less clear. For many RV Tau the masses are in conflict with the standard picture of (single-star) post-AGB evolution, where the masses are either too large (greater than or similar to 1 M-circle dot) or too small (less than or similar to 0.4 M-circle dot).