A theoretical framework for BL Her stars

Context. The upcoming Rubin-LSST is expected to revolutionize the field of classical pulsators by offering well-sampled multi-epoch photometric data in multiple wavelengths. Type II Cepheids (T2Cs) exhibit weak or negligible metallicity dependence on period-luminosity (PL) relations. Thus, they may potentially be used as an alternative to classical Cepheids for extragalactic distance estimations, when used together with RR Lyraes and the tip of the red giant branch. It is therefore crucial to study an updated theoretical pulsation scenario of BL Herculis stars (BL Her; the shortest period T2Cs) in the corresponding Rubin-LSST photometric system. Aims. We present new theoretical light curves in the Rubin-LSST filters for a fine grid of BL Her models computed using <ns0:sc>MESA-RSP</ns0:sc>. We have also derived new theoretical PL and period-Wesenheit (PW) relations in the Rubin-LSST filters with the aim to study the effect of convection parameters and metallicity on these relations. Methods. The grid of BL Her models was computed using the non-linear radial stellar pulsation tool <ns0:sc>MESA-RSP</ns0:sc> with the input stellar 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) and using four sets of convection parameters. Bolometric correction tables from MIST were used to transform the theoretical bolometric light curves of the BL Her models into the Rubin–LSST ugrizy filters. Results. The PL relations of the BL Her models exhibit steeper slopes but smaller dispersion with increasing wavelengths in the Rubin-LSST filters. The PL and PW slopes for the complete set of BL Her models computed with radiative cooling (sets B and D) are statistically similar across the grizy filters. The BL Her models exhibit weak or negligible effect of metallicity on the PL relations for wavelengths longer than the g filter for the case of the complete set of models as well as for the low-mass models. However, we find a significant effect of the metallicity on the PL relation in the u filter. Strong metallicity effects are observed in the PWZ relations involving the u filter and are found to have significant contribution from the high-metallicity BL Her models. Due to a negligible metallicity effect for relations involving the Wesenheit indices W(i, g − i), W(z, i − z), and W(y, g − y), we recommend these filter combinations for BL Her stars during observations with Rubin–LSST for use as reliable standard candles.