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

¹ Armagh Observatory and Planetarium, College Hill, Armagh BT61 9DG, UK
e-mail: erin.higgins@armagh.ac.uk, jorick.vink@armagh.ac.uk
² Queen’s University of Belfast, Belfast BT7 1NN, UK
³ Dublin Institute for Advanced Studies, 31 Fitzwilliam Place, Dublin, Ireland

Received: 16 December 2019
Accepted: 16 February 2020

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 semi-convection plays a role in the post-main-sequence (MS) evolution to blue or red supergiants (RSGs), a unified treatment for all metallicities has not been achieved so far.

Aims. 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, Large Magellanic Cloud (50% solar), and Small Magellanic Cloud (20% solar) metallicities, we develop eight grids of MESA models for the mass range 20–60 M_⊙ to probe the effect of semi-convection 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 that can disable semi-convection, leading to more RSGs, but a lack of BSGs. We therefore implement α_ov = 0.1, which switches on semi-convective mixing, but for standard α_semi = 1 would result in an HD limit that is higher than observed at low Z (Large and Small Magellanic Clouds). Therefore, we need to implement very efficient semi-convection 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 semi-convection is not active at high metallicities because the envelope structure is depleted by strong mass loss such that semi-convective 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 semi-convection and low overshooting with standard Ṁ(Z), we find a natural HD limit at all metallicities.