[Paper Review] Rotational velocities of A-type stars IV. Evolution of rotational velocities

J. Zorec, F. Royer|arXiv (Cornell University)|Jan 10, 2012

Stellar, planetary, and galactic studiesPhysics and Astronomy68 references115 citations

TL;DR

This study analyzes rotational velocities of 2,014 A-type stars to investigate mass- and age-dependent evolution of surface rotation. Using stellar evolution models and photometric data, it reveals that stars with masses <2.5 M☉ show monotonic spin-up on the main sequence, while more massive stars (1.7–3.2 M☉) exhibit a strong initial spin-up followed by near-constant rotation, indicating differential rotation throughout their main sequence life. The key finding is that observed rotational evolution deviates significantly from theoretical predictions, suggesting stars start main sequence with sub-critical angular momentum and evolve as differential rotators with characteristic timescales of ~0.2 tMS.

ABSTRACT

In previous works of this series, we have shown that late B- and early A-type stars have genuine bimodal distributions of rotational velocities and that late A-type stars lack slow rotators. The distributions of the surface angular velocity ratio Ω/Ω_crit (Ω_crit is the critical angular velocity) have peculiar shapes according to spectral type groups, which can be caused by evolutionary properties. We aim to review the properties of these rotational velocity distributions in some detail as a function of stellar mass and age. We have gathered v sin i for a sample of 2014 B6- to F2-type stars. We have determined the masses and ages for these objects with stellar evolution models. The (Teff, log L/Lsun)-parameters were determined from the uvby-βphotometry and the HIPPARCOS parallaxes. The velocity distributions show two regimes that depend on the stellar mass. Stars less massive than 2.5 Msun have a unimodal equatorial velocity distribution and show a monotonical acceleration with age on the main sequence (MS). Stars more massive have a bimodal equatorial velocity distribution. Contrarily to theoretical predictions, the equatorial velocities of stars from about 1.7 Msun to 3.2 Msun undergo a strong acceleration in the first third of the MS evolutionary phase, while in the last third of the MS they evolve roughly as if there were no angular momentum redistribution in the external stellar layers. The studied stars might start in the ZAMS not necessarily as rigid rotators, but with a total angular momentum lower than the critical one of rigid rotators. The stars seem to evolve as differential rotators all the way of their MS life span and the variation of the observed rotational velocities proceeds with characteristic time scales δ(t)\sim 0.2 t_MS, where t_MS is the time spent by a star in the MS.

Motivation & Objective

• To investigate how rotational velocity distributions of A-type stars evolve with mass and age.
• To determine whether observed rotational behaviors align with theoretical predictions of angular momentum redistribution.
• To assess whether stars begin the main sequence with angular momentum below the critical rigid rotator limit.
• To examine the role of differential rotation in shaping observed surface velocities over the main sequence.

Proposed method

• Collected v sin i measurements for 2,014 B6–F2-type stars from high-precision photometry and HIPPARCOS parallaxes.
• Used uvby–β photometry to derive effective temperatures and luminosities, enabling mass and age determination via stellar evolution models.
• Mapped rotational velocity distributions as a function of mass and evolutionary phase (t/tMS), distinguishing between unimodal and bimodal behavior.
• Compared observed rotational evolution with theoretical models of angular momentum redistribution, particularly focusing on deviations in massive stars.
• Estimated internal angular momentum profiles assuming shellular-like rotation, testing limits of rigid vs. differential rotator models.
• Evaluated the impact of potential radiative-convective dichotomies on rotational laws and von Zeipel coefficients in fast rotators.

Experimental results

Research questions

• RQ1 Do rotational velocity distributions in A-type stars vary systematically with stellar mass and age?
• RQ2 Is the observed rotational evolution in A-type stars consistent with theoretical models of angular momentum redistribution?
• RQ3 Do stars begin the main sequence with angular momentum below the critical rigid rotator limit?
• RQ4 To what extent do stars evolve as differential rotators rather than rigid rotators during their main sequence lifetime?
• RQ5 What internal rotation profiles can explain the observed surface velocity evolution, particularly in massive A-type stars?

Key findings

• Stars with masses <2.5 M☉ exhibit unimodal equatorial velocity distributions and show monotonic spin-up throughout the main sequence.
• Stars with masses between 1.7 and 3.2 M☉ display a strong initial spin-up in the first third of the main sequence, followed by near-constant rotation in the last two-thirds, indicating minimal angular momentum redistribution.
• The observed rotational evolution deviates significantly from theoretical models, especially in the first half of the main sequence for 3 M☉ stars.
• Stars of all masses studied likely begin the main sequence with total angular momentum below the critical value for rigid rotators.
• The characteristic timescale for observed rotational velocity changes is δt ≈ 0.2 tMS, indicating a mass-dependent evolution timescale.
• By the end of the main sequence, massive stars (≥2.5 M☉) possess more rotational energy than rigid critical rotators can sustain, confirming they evolve as strong differential rotators.