Why Do Stars Turn Red? I. Post-Main-Sequence Expansion Mechanism

Abstract

In this series of papers, we address the long-standing question of why post-main-sequence stars expand into red giants (RGs) or red supergiants (RSGs). This paper aims to identify the key physical mechanism that drives stellar evolution toward the RG/RSG phase. Using the Modules for Experiments in Stellar Astrophysics (MESA), we perform controlled numerical experiments by systematically varying stellar parameters in evolutionary models, and compare those that successfully evolve into RG/RSGs and those that do not. We show that envelope expansion toward the RG/RSG phase cannot be explained by energy absorption. Instead, it is governed by a refined form of the "mirror principle," in which the stellar envelope responds oppositely to its inner boundary, defined by the outer edge of the hydrogen-burning shell, rather than directly to the helium core. This behavior arises naturally from hydrostatic equilibrium, as the burning shell establishes a moving, nearly constant-pressure inner boundary for the envelope. We identify two evolutionary pathways toward the RG/RSG phase that both follow this refined mirror principle: (1) direct envelope expansion during helium-core contraction, and (2) continued expansion after contraction ceases, driven by a decline in nuclear energy generation rate. The final approach to the RG/RSG phase is marked by a structural transition in the envelope, characterized by mass redistribution and the development of an extended convective region. We present a unified physical framework for envelope expansion toward the RG/RSG phase, based on the refined mirror principle and the final structural transition, and outline an evolutionary roadmap leading to the RG/RSG phase.

Figures (16)

• Figure 1: Schematic diagram of the post-main-sequence stellar structure analyzed in this study, comprising a He core, an H-burning shell, and an envelope. The labeled radii and luminosities are: $R_{*}$ and $L_{s}$ at the stellar surface, $R_{\rm shell}$ and $L_{b}$ at the boundary between the envelope and the H-burning shell, and $R_{\rm core}$ at the interface between the shell and the He core.
• Figure 2: Evolution of $25\,M_{\odot}$ stars at metallicity $Z=0.001$ with different He-burning rates, parameterized by a linear scaling factor $\eta_{3\alpha}$. Model A (left panels), which adopts the standard rate ($\eta_{3\alpha}=1$), evolves into an RSG, whereas Model B (right panels), with an enhanced rate ($\eta_{3\alpha}=2$), remains a BSG. The top panels show the temporal evolution of stellar radius ($R_*$), surface luminosity ($L_s$), luminosity at the base of the envelope ($L_b$), nuclear luminosities from H burning ($L_{\rm H}$) and He burning ($L_{\rm He}$), the total nuclear luminosity ($L_{\rm nuc}$), and the gravothermal heating rates of the core ($\dot{Q}_{\rm core}$) and envelope ($\dot{Q}_{\rm env}$). The bottom panels present the corresponding evolutionary tracks in the Hertzsprung-Russell diagram.
• Figure 3: Evolution of the stellar radius ($R_*$) alongside the He core radius ($R_{\rm core}$) and the radius at the outer edge of the H-burning shell ($R_{\rm shell}$). Arrows indicate the direction of time progression during stellar evolution. Notably, $R_*$ generally evolves inversely to $R_{\rm shell}$.
• Figure 4: Evolution of the radius and luminosity at the interface between the H-burning shell and the envelope for Models A and B. The radius and luminosity at the shell-envelope boundary are denoted as $R_{\rm shell}$ and $L_b$, respectively. Arrows indicate the direction of temporal evolution.
• Figure 5: Evolution of the energy generation rates as a function of stellar radius ($R_*$) for $25\,M_{\odot}$, $Z = 0.001$ models with different values of $\eta_{3\alpha}$. The three panels show the total nuclear energy generation rate ($L_{\rm nuc}$), the contribution from hydrogen burning ($L_{\rm H}$), and from helium burning ($L_{\rm He}$). Red curves represent models with lower $\eta_{3\alpha}$ (0.1, 0.2, 0.5, 1.0, and 1.2) that eventually evolve into RSGs, while blue curves represent models with higher $\eta_{3\alpha}$ (1.33, 1.4, 1.6, 1.8, 2.0, 5.0, 10) that contract after minor expansion and remain as BSGs.