Distributions and evolution of the equatorial rotation velocities of 2937 BAF-type main-sequence stars from asteroseismology

TL;DR

This study tackles how intermediate-mass stars rotate and transport angular momentum during main-sequence evolution by combining two homogeneous asteroseismic samples to measure near-core rotation frequencies $f_{ m rot}$ and derive model-independent $V_{ m eq}$, $V_{ m eq}/V_{ m crit}$, and $J/M$ for 2937 gravity-mode pulsators across $1.3-8.8\,M_\\odot$. Using a rigid-rotation framework and asteroseismic radii, the authors show predominantly unimodal distributions for $V_{ m eq}$ and $V_{ m eq}/V_{ m crit}$ at lower masses, with structure emerging at higher masses, and a clear decline of near-core rotation with MS evolution, signaling efficient angular-momentum transport. A break in the $J/M$–$M$ relation around $M\approx2.5\,M_\odot$ subdivides the sample into regimes with different angular-momentum transport, likely tied to envelope structure (convective vs radiative). These results yield population-synthesis-ready distributions and provide empirical constraints for rotation theory and angular-momentum transport processes across the main sequence, while highlighting the need for expanded metallicity coverage and future 3D MHD modelling to interpret the observed trends.

Abstract

Studies of the rotational velocities of intermediate-mass main-sequence stars are crucial for testing stellar evolution theory. They often rely on spectroscopic measurements of the projected rotation velocities. These not only suffer from the unknown projection factor but tend to ignore additional line-profile broadening mechanisms aside from rotation, such as pulsations and turbulent motions near the stellar surface. This limits the accuracy of Veq distributions. We use asteroseismic measurements to investigate the distribution of the equatorial rotation velocity, its ratio with respect to the critical rotation velocity, and the specific angular momentum for several thousands of BAF-type stars, covering a mass range from 1.3M$_\odot$ to 8.8M$_\odot$ and almost the entire core-hydrogen burning phase. We rely on high-precision model-independent internal rotation frequencies, as well as on masses and radii from asteroseismology to deduce Veq, Veq/Vcrit, and J/M for 2937 gravity-mode pulsators in the Milky Way. The sample stars have rotation frequencies between almost zero and 33$μ$Hz, corresponding to rotation periods above 0.35d. We find that intermediate-mass stars experience a break in their J/M occurring in the mass interval $[2.3,2.7]\,$M$_\odot$. We establish unimodal Veq and Veq/Vcrit distributions for the mass range $[1.3,2.5[$M$_\odot$, while stars with $M\in[2.5,8.8]$M$_\odot$ reveal some structure in their distributions. We find that the near-core rotation slows down as stars evolve, pointing to very efficient angular momentum transport. The kernel density estimators of the asteroseismic internal rotation frequency, equatorial rotation velocity, and specific angular momentum of this large sample of intermediate-mass field stars can conveniently be used for population synthesis studies and to fine-tune the theory of stellar rotation across the main sequence evolution.

Figures (5)

• Figure 1: Near-core rotation frequency $f_{\rm rot}$ versus asteroseismic gravity for two samples: 490 Kepler gravity- and gravito-inertial mode pulsators with prograde modes from Fritzewski2024b and 2447 gravito-inertial prograde dipole mode pulsators from Aerts2025. The position of the same quantities for more than a thousand red giant stars from mixed-mode asteroseismology is indicated by the red rectangle produced from Aerts2019.
• Figure 2: Kernel density estimates (full lines) and histograms constructed with optimal bandwidth for Sample 1 (orange hatched) and Sample 2 (blue). Upper left: model-independent measurement of $f_{\rm rot}$; upper right: model-dependent $V_{\rm eq}$; lower left: model-dependent $V_{\rm eq}/V_{\rm crit}$; lower right: model dependent specific angular momentum $J/M$.
• Figure 3: Specific angular momentum, $J/M$, plotted logarithmically against stellar mass (upper panel) and evolutionary stage (lower panel). The symbol size for each star scales linearly with its evolutionary stage $X_{\rm c}/X_{\rm ini}$ (upper panel) and mass (lower panel). The circles show the stars of Samples 1 and 2. Also shown are the $J/M$ values of 21 SPB stars from Pedersen2022aPedersen2022b, connected by a dotted line to the specific angular momentum of their convective core deduced from asteroseismic modelling of individual identified modes (shown as $\times$). Similarly, $J/M$ of the 37 asteroseismically modelled $\gamma\,$Dor stars from Mombarg2021 are shown as filled squares connected to the specific angular momentum of their convective core (shown as $+$). The two dashed vertical lines in the upper panel indicate the mass regime $[1.3,1.4]\,$M$_\odot$ where the Kraft break occurs. The two coloured full lines and their uncertainty regions (in grey) denote the upper limits of the $J/M$ measurements for each of the two samples.
• Figure 4: Histograms (upper panels) and KDEs (lower panels) of the near-core rotation frequency (left) and specific angular momentum (right), where the two samples are considered jointly, split up into five regimes of evolutionary stage from near-ZAMS (cyan) to near-TAMS (purple).
• Figure 5: Kernel density estimates (full lines) and histograms constructed with optimal bandwidth for the stars split up according to masses below or above 2.5 M$_\odot$. Upper panel: $V_{\rm eq}$; lower panel: $V_{\rm eq}/V_{\rm crit}$.