Evolutionary tracks for Betelgeuse

Abstract: We have constructed a series of non-rotating quasi-hydrostatic evolutionary models for the M2 Iab supergiant Betelgeuse ($\alpha~Orionis$). Our models are constrained by multiple observed values for the temperature, luminosity, surface composition and mass loss for this star, along with the parallax distance and high resolution imagery that determines its radius. We have then applied our best-fit models to analyze the observed variations in surface luminosity and the size of detected surface bright spots as the result of up-flowing convective material from regions of high temperature in the surface convective zone. We also attempt to explain the intermittently observed periodic variability in a simple radial linear adiabatic pulsation model. Based upon the best fit to all observed data, we suggest a best progenitor mass estimate of $ 20 ^{+5}_{-3} M_\odot$ and a current age from the start of the zero-age main sequence of $8.0 - 8.5$ Myr based upon the observed ejected mass while on the giant branch.

• The paper presents evolutionary models using Eggleton and MESA codes to determine Betelgeuse's mass of about 20 M⊙ and an age of roughly 8.4 million years.
• The paper establishes that a mixing length parameter of 1.8–1.9 best fits observed luminosity and convective behavior while dismissing significant overshoot.
• The paper reconciles Betelgeuse's observed photospheric radius of approximately 887 R⊙ and its luminosity variability with theoretical predictions, affirming its red supergiant status.

Analytical Assessment of Betelgeuse's Evolutionary Models

The recently published work by Dolan and Mathews presents a detailed analysis of the evolutionary models pertinent to the M2 Iab supergiant Betelgeuse (α Orionis). In this paper, quasi-hydrostatic evolutionary tracks are constructed to explore the star's observable characteristics, such as its intermittent luminosity variations, surface bright spots, and periodic variability. This study synchronizes existing data on parallax distances, radii, surface characteristics, and emissive behavior against predictions from computational models.

The authors employ both the Eggleton (EG) evolution code and the MESA (Modules for Experiments in Stellar Astrophysics) code to infer the historical progression and current stage of Betelgeuse. Notably, the constraints forced by the star's magnitude, density, observed spectral distance, and other astrophysical properties have been used to achieve a best-fit model with certain physical parameters.

Major Numerical Findings

1. Mass and Age: The study estimates the present mass of Betelgeuse to be around 20 M⊙ within a confidence level of 1σ. The models suggest a current age of approximately 8.4 million years since the zero age main sequence (ZAMS), with minor variabilities depending on chosen overshoot parameters.
2. Mixing Length and Overshoot Parameter: The analysis concludes a mixing length parameter of α in the range 1.8 to 1.9 fits the observed data most effectively. Constraints implied from observed surface abundances and convective behaviors deter overshoot beyond f = 0.0, indicating a lack of substantial convective penetration past the core's boundaries.
3. Radius and Luminosity Variability: Betelgeuse's photospheric radius is constrained to approximately 887 R⊙. Given the observed variability, the paper reconciles this with differing visibility wavelengths, supporting evidence for the oversized spectral radius compared with earlier findings.

Key Implications and Model Consistencies

Betelgeuse's interior interactions are modeled with a focus on carbon-oxygen core accretion timing and hydrogen/helium burning placement, corresponding to observed isotopic abundances. The calculated ratios conform well to surface isotope measurements, indicating accurate simulation up to the first dredge-up process.

Moreover, the derived models emphasize the star's progression through the red supergiant (RSG) phase, corroborating its observed mass ejection rates. The lifetime on the RGB (Red Giant Branch) aligns with empirical age predictions derived from the Orion OB association dynamics.

Contributions to Stellar Evolution Theory

This study asserts critical insights into massive stellar evolution, particularly transitions leading to supernovae. Predicting Betelgeuse's eventual fate as a likely supernova, the authors explore parameters that may alter end-stage characteristics. The intricate balance of radiation pressure, surface convection, and mass loss rates provides a basis to anticipate the implications of various astrophysical conditions leading to stellar collapse.

Furthermore, exploring Betelgeuse's evolutionary tolerance under different theoretical boundary conditions refines stellar models for other supergiant stars undergoing similar luminosity fluctuations and mass loss behaviors. The detailed methodical approach serves to both affirm traditional methods and expands the computational horizon on stellar lifecycles.

In conclusion, Dolan and Mathews effectively leverage existing technologies and astrophysical data to reconstruct an exhaustive portrayal of Betelgeuse's evolutionary history. Their research provides significant strides toward understanding the cellular characteristics of supergiant stars, challenging previous paradigms, and predicting end-stage supernova dynamics in massive stars. Future developments may include multidimensional modeling incorporating pulsation hydrodynamics and magnetic field interactions to further refine these results.