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

TL;DR

This study develops a comprehensive grid of BL Her star models using advanced pulsation tools to analyze how metallicity and convection parameters influence period-luminosity and period-radius relations across multiple wavelengths.

Contribution

It introduces a large set of non-linear pulsation models for BL Her stars, exploring the effects of metallicity and convection parameters on their observable relations, and compares these with empirical data.

Findings

Radiative cooling models have similar PL, PW, PR slopes.

Models with radiative cooling better match LMC empirical relations.

Metallicity significantly affects optical bands, negligible in infrared.

Abstract

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 multi-wavelength properties. Non-linear models were computed for periods typical for BL Her stars, i.e. $1 \leq \mathrm{P (days)} \leq 4$ covering a wide range of input parameters - metallicity ($-2.0\; \mathrm{dex} \leq \mathrm{[Fe/H]} \leq 0.0\; \mathrm{dex}$), stellar mass (0.5M$_{\odot}$-0.8M$_{\odot}$), luminosity (50L$_{\odot}$-300L$_{\odot}$) and effective temperature (full extent of the instability strip; in steps of 50K). The total number of BL Her models with full-amplitude stable pulsations used in this study is 10280 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 LMC in the $HK_S$ 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.