A theoretical framework for BL Her stars. II. New period-luminosity relations in Gaia passbands

Abstract

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. 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. 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 dex $), stellar mass ($0.5M_ odot -0.8M_ odot $), stellar luminosity ($50L_ odot -300L_ odot $), and effective temperature (across the full extent of the instability strip; in steps of 50K). 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. 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\ odot $) 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.