[Paper Review] Populations of rotating stars II. Rapid rotators and their link to Be-type stars

A. Granada, Sylvia Ekström+5 more|arXiv (Cornell University)|Mar 10, 2013

Stellar, planetary, and galactic studies7 citations

TL;DR

This study uses improved Geneva stellar evolution models to investigate rapidly rotating stars near critical rotation, showing that such stars produce decretion disks with masses of $9.4 \times 10^{-12}$ to $1.4 \times 10^{-7}\,M_\odot$, extensions of 2000–6500\,$R_\odot$, and diffusion timescales of 10–30 years—values consistent with observed Be star disks. The results support a $T_{\text{eff}}$-dependent threshold for Be star formation and confirm long-lived rotational and N/C enrichment signatures in evolved stars from initial rapid rotators.

ABSTRACT

Even though it is broadly accepted that single Be stars are rapidly rotating stars surrounded by a flat rotating circumstellar disk, there is still a debate about how fast these stars rotate and also about the mechanisms involved in the angular-momentum and mass input in the disk. We study the properties of stars that rotate near their critical-rotation rate and investigate the properties of the disks formed by equatorial mass ejections. We used the most recent Geneva stellar evolutionary tracks for rapidly rotating stars that reach the critical limit and used a simple model for the disk structure. We obtain that for a 9 Msun star at solar metallicity, the minimum average velocity during the Main Sequence phase to reach the critical velocity is around 330 km/s, whereas it would be 390 km/s at the metallicity of the Small Magellanic Cloud (SMC). Red giants or supergiants originating from very rapid rotators rotate six times faster and show N/C ratios three times higher than those originating from slowly rotating stars. This difference becomes stronger at lower metallicity. It might therefore be very interesting to study the red giants in clusters that show a large number of Be stars on the MS band. On the basis of our single-star models, we show that the observed Be-star fraction with cluster age is compatible with the existence of a temperature-dependent lower limit in the velocity rate required for a star to become a Be star. The mass, extension, and diffusion time of the disks produced when the star is losing mass at the critical velocity, obtained from simple parametrized expressions, are not too far from those estimated for disks around Be-type stars. At a given metallicity, the mass and the extension of the disk increase with the initial mass and with age on the MS phase. Denser disks are expected in low-metallicity regions.

Motivation & Objective

• To investigate the properties of stars rotating near critical velocity and their resulting decretion disks.
• To assess how initial rapid rotation affects stellar evolution and surface composition in later stages such as red giants.
• To test whether observed Be star fractions in clusters are consistent with a temperature-dependent minimum rotation rate for Be phenomenon onset.
• To estimate disk mass, size, and evolution timescale from simple parametrized models of mass loss at critical rotation.
• To evaluate the impact of angular momentum and mass loss on disk formation and long-term variability in Be stars.

Proposed method

• Utilized updated Geneva stellar evolution tracks incorporating improved numerical treatment of surface velocity, including stellar deformation and angular momentum transport.
• Accounted for the envelope's angular momentum and its coupling to the interior, enhancing accuracy in tracking total angular momentum evolution.
• Applied a parametrized model for equatorial mass ejection at critical rotation to estimate disk mass, extension, and diffusion timescale.
• Computed time-averaged mass-loss rates and disk evolution timescales under varying initial masses, metallicities, and main-sequence ages.
• Compared model predictions with observational constraints on Be star disk masses, sizes, and variability timescales from radio and H$\alpha$ studies.
• Assessed consistency with observed Be/(B+Be) fractions in clusters under a $T_{\text{eff}}$-dependent threshold for Be star formation.

Experimental results

Research questions

• RQ1 What is the minimum average surface velocity required for a 9 $M_\odot$ star to reach critical rotation at solar and SMC metallicities?
• RQ2 How do disk mass, extension, and diffusion timescale depend on initial stellar mass, metallicity, and main-sequence age?
• RQ3 Can the observed Be star fraction in open clusters be explained by a $T_{\text{eff}}$-dependent threshold for the Be phenomenon?
• RQ4 To what extent do signatures of initial rapid rotation persist in evolved stars like red giants and supergiants?
• RQ5 How do predicted disk properties compare with observational estimates from radio and H$\alpha$ studies?

Key findings

• For a 9 $M_\odot$ star, the minimum average surface velocity to reach critical rotation is ~330 km s$^{-1}$ at solar metallicity and ~390 km s$^{-1}$ at SMC metallicity.
• Red giants and supergiants from initial rapid rotators rotate six times faster and show N/C ratios three times higher than those from slowly rotating progenitors, with the difference increasing at lower metallicity.
• Disk masses produced at critical rotation range from $9.4 \times 10^{-12}$ to $1.4 \times 10^{-7}\,M_\odot$ ($3 \times 10^{-6}$ to $4.7 \times 10^{-2}$ Earth masses), with extensions between 2000 and 6500 $R_\odot$, and diffusion timescales of 10–30 years.
• The predicted disk properties are consistent with observational estimates from radio surveys (e.g., Taylor et al. 1990; Clark et al. 1998) and H$\alpha$ studies, particularly at longer wavelengths.
• Time-averaged mass-loss rates during critical rotation are $4 \times 10^{-13}$ to $4 \times 10^{-9}\,M_\odot\,\text{yr}^{-1}$, an order of magnitude lower than some observational estimates, though peak instantaneous rates agree reasonably well.
• The model supports a $T_{\text{eff}}$-dependent lower limit for the Be phenomenon, with the observed Be/(B+Be) fraction in clusters being compatible with this threshold.