Period–colour and amplitude–colour relations in classical Cepheid variables – IV. The multiphase relations

The superb phase resolution and quality of the Optical Gravitational Lensing Experiment (OGLE) data on the Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC) Cepheids, together with existing data on Galactic Cepheids, are combined to study the period–colour (PC) and amplitude–colour (AC) relations as a function of pulsation phase. Our results confirm earlier work that the LMC PC relation (at mean light) is more consistent with two lines of differing slopes, separated at a period of 10 d. However, our multiphase PC relations reveal much new structure which can potentially increase our understanding of Cepheid variables. These multiphase PC relations provide insight into why the Galactic PC relation is linear but the LMC PC relation is non-linear. This is because the LMC PC relation is shallower for short  (log  P < 1)  and steeper for long  (log  P > 1)  period Cepheids than the corresponding Galactic PC relation. Both of the short- and long-period Cepheids in all three galaxies exhibit the steepest and shallowest slopes at phases around 0.75–0.85, respectively. A consequence is that the PC relation at phase ～ 0.8 is highly non-linear. Further, the Galactic and LMC Cepheids with  log  P > 1  display a flat slope in the PC plane at phases close to the maximum light. When the LMC period–luminosity (PL) relation is studied as a function of phase, we confirm that it changes with the PC relation. The LMC PL relation in V and I band near the phase of 0.8 provides compelling evidence that this relation is also consistent with two lines of differing slopes joined at a period close to 10 d.