2024A&A...684A.170D

Context. In the era of the Hubble tension, it is crucial to obtain a precise calibration of the period-luminosity (PL) relations of classical pulsators. Type II Cepheids (T2Cs; often exhibiting negligible or weak metallicity dependence on PL relations) used in combination with RR Lyraes and the tip of the red giant branch may prove useful as an alternative to classical Cepheids for the determination of extragalactic distances.
Aims. We present new theoretical PL and period-Wesenheit (PW) relations for a fine grid of convective BL Her (the shortest period T2Cs) models computed using MESA-RSP in the Gaia passbands and we compare our results with the empirical relations from Gaia DR3. Our goal is to study the effect of metallicity and convection parameters on the theoretical PL and PW relations.
Methods. We used the state-of-the-art 1D non-linear radial stellar pulsation tool MESA-RSP to compute models of BL Her stars over a wide range of input parameters: metallicity (-2.0 dex ≤ [Fe/H] ≤ 0.0 dex), stellar mass (0.5 M_⊙ - 0.8 M_⊙), stellar luminosity (50 L_⊙ - 300 L_⊙), and effective temperature (across the full extent of the instability strip; in steps of 50 K). We used the Fourier decomposition technique to analyse the light curves obtained from MESA-RSP and Gaia DR3 and then compared the theoretical and empirical PL and PW relations in the Gaia passbands.
Results. The BL Her stars in the All Sky region exhibit statistically different PL slopes compared to the theoretical PL slopes computed using the four sets of convection parameters. We find the empirical PL and PW slopes from BL Her stars in the Magellanic Clouds to be statistically consistent with theoretical relations computed using the different convection parameter sets in the Gaia passbands. There is a negligible effect coming from the metallicity on the PL relations in the individual Gaia passbands. However, there is a small but significant negative coefficient of metallicity in the PWZ relations for the BL Her models using the four sets of convection parameters. This could be attributed to the increased sensitivity of bolometric corrections to metallicities at wavelengths shorter than the V band. Our BL Her models also suggest a dependence of the mass-luminosity relation on metallicity. We found the observed Fourier parameter space to be covered well by our models. Higher mass models (> 0.6 M_⊙) may be needed to reliably model the observed light curves of BL Her stars in the All-Sky region. We also found the theoretical light curve structures (especially the Fourier amplitude parameters) to be affected by the choice of convection parameters.