Period-Colour and Amplitude-Colour relations for OGLE-$δ$ Scuti stars in the Galactic Bulge and LMC

We present an analysis on the behaviour of the Galactic bulge and the Large Magellanic Cloud (LMC) $δ$ Scuti stars in terms of period-colour and amplitude-colour (PCAC) relations at maximum, mean and minimum light. The publicly available Optical Gravitational Lensing Experiment-IV (OGLE-IV) light curves for Galactic bulge and OGLE-III light curves for LMC $δ$ Scuti stars are exploited for the analysis. It has been found that the Galactic bulge $δ$ Scuti stars obey flat PC relations at maximum/mean/minimum light while the LMC $δ$ Scutis have sloped/sloped/flat PC relations at maximum/mean/minimum light. Both the Galactic bulge and the LMC $δ$ Scutis have sloped/flat/sloped AC relations at maximum/mean/minimum. These relations also show that Galactic $δ$ Scutis are hotter as compared to their LMC counterparts. The period-amplitude (PA) relations for $δ$ Scutis exhibit different behaviour in the Galactic bulge and the LMC. The LMC variables are found to have higher amplitudes at a given period. The amplitude of the Galactic bulge $δ$ Scuti shows a bimodal distribution which can be modelled using a two-component Gaussian Mixture Model: one component with a lower amplitude and another with a higher amplitude. The observed behaviour of the $δ$ Scuti PCAC relations can be explained using the theory of the interaction of hydrogen ionization front (HIF) and stellar photosphere as well as the PA diagram. We use MESA-RSP to calculate theoretical non-linear hydrodynamical pulsation models for $δ$ Scuti stars with input metallicities of $Z=0.02$ and $Z=0.008$ appropriate for the Galactic bulge and LMC, respectively. The observed PCAC relations and theoretical calculations support the HIF-photosphere interaction theory.