Towards an updated theoretical framework for BL Herculis Stars

We present theoretical period-luminosity (PL), period-Wesenheit (PW) amd period-radius (PR) relations at multiple wavelengths (Johnson-Cousin-Glass bands UBVRIJHKLL'M and Gaia passbands GGBPGRP) for a fine grid of convective BL Herculis models computed using the non-linear radial stellar pulsation tool MESA-RSP. The non-linear models were computed for periods typical for BL Her stars, i.e. 1≤P (days)≤4 covering a wide range of input parameters: metallicity (-2.0 dex≤ [Fe/H]≤ 0.0 dex), stellar mass (0.5M⊙ -0.8M⊙), luminosity (50L⊙ -300L⊙) and effective temperature (full extent of the instability strip; in steps of 50K). We investigate the impact of four sets of different convection parameters on multi-wavelength properties. 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. No significant metallicity effects are seen in the PR relations. We carry out a robust light curve optimization technique to obtain the best observed-model pairs for the BL Her stars in the LMC. We also extend our study to include theoretical relations in the Rubin-LSST passbands. In addition, we also explore the mass of the prototype BL Herculis itself using simultaneous fitting of the observed light curve and radial velocity curve with those from the model that exhibits the best goodness-of-fit.