Shaping the horizontal branch: The role of envelope mass in the evolution of stripped core-helium-burning stars
The location of a star along the horizontal branch (HB) during core-helium burning is primarily determined by the amount of mass lost by its progenitor. We investigate the formation and properties of stripped core-helium-burning stars, focusing on how the residual hydrogen-envelope mass ($M_{\mathrm{env}}$) and the timing of envelope removal shape their properties. We used the MESA stellar evolution code to model stars that lose their hydrogen envelopes on the first giant branch. We explored two limiting cases for the timing of stripping, corresponding to the minimum and maximum core masses for helium ignition, for progenitors with initial masses below $\sim$6 $M_{\odot}$ at two metallicities ($Z=0.02$ and $Z=0.004$), while systematically varying $M_{\mathrm{env}}$. As expected, the effective temperature along the HB decreases as $M_{\mathrm{env}}$ increases. We determined the maximum $M_{\mathrm{env}}$ required to avoid subsequent evolution through the thermally pulsing asymptotic giant branch, which ranges from $\sim0.05$ $M_{\odot}$, for low-mass progenitors to $\sim0.30$ $M_{\odot}$ for intermediate-mass progenitors. In low-mass progenitors, early envelope removal triggers a late hot flash, naturally explaining the hottest blue hook stars. In intermediate-mass systems, partial envelope stripping can produce extended pre-HB configurations consistent with puffed-up stripped stars observed in binaries with Be companions. Our post-stripping evolutionary tracks are publicly available for use in binary evolution and population synthesis studies.