A theoretical framework for BL Her stars – I. Effect of metallicity and convection parameters on period–luminosity and period–radius relations

We present a new grid of convective BL Herculis models using the state-of-the-art 1D non-linear radial stellar pulsation tool mesa-rsp. We investigate the impact of metallicity and four sets of different convection parameters on multiwavelength properties. Non-linear models were computed for periods typical for BL Her stars, i.e. 1 ≤ P(d) ≤ 4 covering a wide range of input parameters – metallicity (−2.0 dex ≤ [Fe/H] ≤ 0.0 dex), stellar mass (0.5–0.8 M⊙), luminosity (50–300 L⊙), and effective temperature (full extent of the instability strip; in steps of 50 K). The total number of BL Her models with full-amplitude stable pulsations used in this study is 10 280 across the four sets of convection parameters. We obtain their multiband (UBVRIJHKLL′M) light curves and derive new theoretical period–luminosity (PL), period–Wesenheit (PW), and period–radius (PR) relations at mean light. We find that the models computed with radiative cooling show statistically similar slopes for PL, PW, and PR relations. Most empirical relations match well with the theoretical PL, PW, and PR relations from the BL Her models computed using the four sets of convection parameters. However, PL slopes of the models with radiative cooling provide a better match to empirical relations for BL Her stars in the Large Magellanic Cloud in the HKS bands. For each set of convection parameters, the effect of metallicity is significant in U and B bands and negligible in infrared bands, which is consistent with empirical results. No significant metallicity effects are seen in the PR relations.