Theoretical investigation of the Humphreys–Davidson limit at high and low metallicity

Abstract

Context. Current massive star evolution grids are not able to simultaneously reproduce the empirical upper luminosity limit of red supergiants, the Humphrey-Davidson (HD) limit, nor the blue-to-red (B/R) supergiant ratio at high and low metallicity. Although previous studies have shown that the treatment of convection and semiconvection play a role in the post-main sequence (MS) evolution to blue/red supergiants, a unified treatment for all metallicities has not yet been achieved. Aims. In this study, we focus on developing a better understanding of what drives massive star evolution to blue and red supergiant phases, with the ultimate aim of reproducing the HD limit at varied metallicities. We discuss the consequences of classifying B and R in the B/R ratio and clarify what is required to quantify a relatable theoretical B/R ratio for comparison with observations. Methods. For solar, LMC (50% solar), and SMC (20% solar) metallicities, we develop eight grids of MESA models for the mass range 20-60 M to probe the effect of semiconvection and overshooting on the core helium-burning phase. We compare rotating and non-rotating models with efficient (α semi = 100) and inefficient semi-convection (α semi = 0.1), with high and low amounts of core overshooting (α ov of 0.1 or 0.5). The red and blue supergiant evolutionary phases are investigated by comparing the fraction of core He-burning lifetimes spent in each phase for a range of masses and metallicities. Results. We find that the extension of the convective core by overshooting α ov = 0.5 has an effect on the post-MS evolution which can disable semiconvection leading to more RSGs, but a lack of BSGs. We therefore implement α ov = 0.1 which switches on semiconvective mixing, though for standard α semi = 1, would result in an HD limit which is higher than observed at low Z (LMC, SMC). Therefore, we need to implement very efficient semiconvection of α semi = 100 which reproduces the HD limit at log L/ L ∼ 5.5 for the Magellanic Clouds while simultaneously reproducing the Galactic HD limit of log L/ L ∼ 5.8 naturally. The effect of semiconvection is not active at high metallicities due to the depletion of the envelope structure by strong mass loss such that semiconvective regions could not form. Conclusions. Metallicity dependent mass loss plays an indirect, yet decisive role in setting the HD limit as a function of Z. For a combination of efficient semiconvection and low overshooting with standardṀ(Z), we find a natural HD limit at all metallicities.

Convection Theory and Related Problems in Stellar Structure, Evolution, and Pulsational Stability II. Turbulent Convection and Pulsational Stability of Stars

“…These influences of non-local convective mixing on the structure and evolution of stars increase toward lower mass, because the relative increase of convective core size increases with the decreasing mass of the star. These theoretical predictions have been confirmed by later theoretical studies (Stothers, 1991;Chiosi et al, 1992;Schootemeijer et al, 2019;Higgins and Vink, 2020). This means that the evolution masses for given luminosity is reduced in comparison with those calculated using the local MLT, for which the convective overshooting mixing has been neglected.…”

The excess of cool supergiants from contemporary stellar evolution models defies the metallicity-independent Humphreys–Davidson limit

“…When considering only RSGs, we find that the dependence of the excess on the overshooting extent is non-monotonic for efficient semiconvective mixing (α sc = 100). Recent studies by Schootemeijer et al (2019) and Higgins & Vink (2020) advocate for highly efficient mixing in regions of semiconvection to account for the properties of supergiants in the LMC and SMC. Schootemeijer et al (2019) also claim that convective overshooting can be constrained by the properties of the populations, such as the ratio between RSGs and BSGs.…”

“…The lowest value for α ov that we use is α ov = 0.1 (e.g. Ekström et al 2012;Higgins & Vink 2020), followed by α ov = 0.335 as calibrated by Brott et al (2011), with higher values starting at α ov = 0.5 (e.g. Vink et al 2010 ; Higgins & Vink 2019), and ad- ditional higher values of α ov = 0.8, α ov = 1 and α ov = 1.2 1 .…”

“…However, initial rotation rates in the excess of ≈ 200 km s −1 (at which strong rotational mixing starts) seem to be inconsistent with observed rotation rates of massive stars (Ramírez-Agudelo et al 2015Ramachandran et al 2019), and models using realistic rotation rates do not reproduce the apparently Z-independent HD limit . Higgins & Vink (2020) recently explored this problem by investigating the impact of mixing parameters on RSG stellar models. They found that enhanced semi-convection can reproduce the observed HD limit.…”

Forming an “Impossible” 85 solar mass Black Hole

“…An accompanying ingredient is to keep the amount of core overshooting under control by not unnecessarily applying large core overshooting [17]. We therefore employ a small amount of overshooting as is common in massive star evolution [9].…”