Equatorial Rotation Velocity Research Articles

Inclination angles for Be stars determined using machine learning

ABSTRACT We test the viability of training machine learning algorithms with synthetic $\rm H\, \alpha$ line profiles to determine the inclination angles (the angle between the central B star’s rotation axis and the observer’s line of sight) of B emission (Be) stars from a single observed medium-resolution, moderate signal-to-noise ratio spectrum. The performances of three different machine learning algorithms were compared: neural networks tasked with regression, neural networks tasked with classification, and support vector regression. Of these three algorithms, neural networks tasked with regression consistently outperformed the other methods with a root mean squared error of 7.6° on an observational sample of 92 galactic Be stars with inclination angles known from direct $\rm H\, \alpha$ profile fitting, from the spectroscopic signature of gravitational darkening, and, in a few cases, from interferometric observations that resolved the disc. The trained neural networks enable a quick and useful determination of the inclination angles of observed Be stars, which can be used to search for correlated spin axes in young open clusters or to extract an equatorial rotation velocity from a measurement of vsin i.

Comparing Be Star Inclination Angles Determined from Hα Fitting and Gravitational Darkening

Using a sample of 92 Galactic Be stars, we compare inclination angles (the angle between a star’s rotation axis and the line of sight) determined from Hα emission-line profile fitting to those determined by the spectroscopic signature of gravitational darkening. We find good agreement: 70% of the sample (64 out of 92 stars) is consistent with zero difference between the two methods using 1σ errors, and there is a strong linear correlation coefficient between the two methods of r = +0.63 ± 0.05. There is some evidence that the Hα profile fitting method overestimates the inclination angle for i ≲ 25°, perhaps due to the neglect of incoherent electron scattering on the Hα line widths, while the gravitational darkening method underestimates the inclination angle for i ≳ 70°, perhaps due to the neglect of disk radiative transfer effects on the optical spectrum. Overall, it is demonstrated that a single Hα spectrum of modest resolution and SNR can be used to extract a useful estimate for the inclination angle of an individual Be star. This allows equatorial rotation velocities for individual Be stars to be derived from measurements and will allow Be stars to be used to search for correlated spin axes in young, open clusters if unbiased (with respect to inclination) samples of Be stars are used.

CRIRES+ detection of CO emissions lines and temperature inversions on the dayside of WASP-18b and WASP-76b

The dayside atmospheres of ultra-hot Jupiters (UHJs) are predicted to possess temperature inversion layers with extremely high temperatures at high altitudes. We observed the dayside thermal emission spectra of WASP-18b and WASP-76b with the new CRIRES+ high-resolution spectrograph at near-infrared wavelengths. Using the cross-correlation technique, we detected strong CO emission lines in both planets, which confirms the existence of temperature inversions on their dayside hemispheres. The two planets are the first UHJs orbiting F-type stars with CO emission lines detected; previous detections were mostly for UHJs orbiting A-type stars. Evidence of weak H2O emission signals is also found for both planets. We further applied forward-model retrievals on the detected CO lines and retrieved the temperature-pressure profiles along with the CO volume mixing ratios. The retrieved logarithmic CO mixing ratio of WASP-18b (−2.2−1.5+1.4) is slightly higher than the value predicted by the self-consistent model assuming solar abundance. For WASP-76b, the retrieved CO mixing ratio (−3.6−1.6+1.8) is broadly consistent with the value of solar abundance. In addition, we included the equatorial rotation velocity (υeq) in the retrieval when analyzing the line profile broadening. The obtained υeq is 7.0 ± 2.9 km s−1 for WASP-18b and 5.2−3.0+2.5 km s−1 for WASP-76b, which are consistent with the tidally locked rotational velocities.

Analysis of eight magnetic chemically peculiar stars with rotational modulation

ABSTRACT Since the end of 2018, the Transiting Exoplanet Survey Satellite (TESS) has provided stellar photometry to the astronomical community. We have used TESS data to study rotational modulation in the light curves of a sample of chemically peculiar stars with measured large-scale magnetic fields (mCP stars). In general, mCP stars show inhomogeneous distributions of elements in their atmospheres that lead to spectroscopic (line profile) and photometric (light curve) variations commensurate with the rotational period. We analyzed the available TESS data from 50 sectors for eight targets after post-processing them in order to minimize systematic instrumental trends. Analysis of the light curves allowed us to determine rotational periods for all eight of our targets. For each star, we provide a phase diagram calculated using the derived period from the light curves and from the available measurements of the disc-averaged longitudinal magnetic field 〈Bz〉. In most cases, the phased light curve and 〈Bz〉 measurements show consistent variability. Using our rotation periods, and global stellar parameters derived from fitting Balmer line profiles, and from Geneva and Strömgren–Crawford photometry, we determined the equatorial rotational velocities and calculated the respective critical rotational fractions veq/vcrit. We have shown from our sample that the critical rotational fraction decreases with stellar age, at a rate consistent with the magnetic braking observed in the larger population of mCP stars.

Rotation of hot normal, peculiar and Be stars from space photometry

ABSTRACT The periods of 34 376 main-sequence stars hotter than 6000 K are derived from Kepler, K2, and TESS light curves. From the effective temperatures and GAIA DR3 luminosities, the radii, and hence the equatorial rotational velocities, can be estimated. Comparison with the projected rotational velocities shows that the photometric periods are indistinguishable from the rotational periods. Rotational light modulation in cool stars appears to continue to the hottest B stars. In fact, it is the most common type of light variation and is seen in 20–50 per cent of F, A, and B stars. The rotation rates of Am, Ap, and Bp stars do not appear to be very different from those of non-peculiar stars. Mixing of the surface layers by rotation cannot be the sole reason why element diffusion is not present in stars with normal surface abundances. The rotation rate of Be stars is well below the rate required to trigger mass-loss by non-radial pulsation. Surface activity leading to ejection of material into co-rotating clouds is suggested as the mass-loss mechanism. The rotational amplitudes of non-Be stars increases rapidly with effective temperature, possibly due to an increasing proportion of incipient Be stars in the sample. The simplest way to explain these results is to assume that surface convection is present in all main-sequence stars, from the coolest M star to the hottest B star.

Variation in solar differential rotation and activity in the period 1964–2016 determined by the Kanzelhöhe data set

Aims. Theoretical calculations predict an increased equatorial rotation and more pronounced differential rotation (DR) during the minimum of solar magnetic activity. However, the results of observational studies vary, some showing less and some more pronounced DR during the minimum of solar magnetic activity. Our study aims to gain more insight into these discrepancies. Methods. We determined the DR parameters A and B (corresponding to the equatorial rotation velocity and the gradient of the solar DR, respectively) by tracing sunspot groups in sunspot drawings of the Kanzelhöhe Observatory for Solar and Environmental Research (KSO; 1964–2008, for solar cycles 20–23) and KSO white-light images (2009–2016, for solar cycle 24). We used different statistical methods and approaches to analyse variations in DR parameters related to the cycle and to the phase of the solar cycle, together with long-term related variations. Results. The comparison of the DR parameters for individual cycles obtained from the KSO and from other sources yield statistically insignificant differences for the years after 1980, meaning that the KSO sunspot group data set is well suited for long-term cycle to cycle studies. The DR parameters A and B show statistically significant periodic variability. The periodicity corresponds to the solar cycle and is correlated with the solar activity. The changes in A related to solar cycle phase are in accordance with previously reported theoretical and experimental results (higher A during solar minimum, lower A during the maximum of activity), while changes in B differ from the theoretical predictions as we observe more negative values of B, that is, a more pronounced differential rotation during activity maximum. The main result of this paper for the long-term variations in A is the detection of a phase shift between the activity flip (in the 1970s) and the equatorial rotation velocity flip (in the early 1990s), during which both A and activity show a secular decreasing trend. This indicates that the two quantities are correlated in between 1970 and 1990. Therefore, the theoretical model fails in the phase-shift time period that occurs after the modern Gleissberg maximum, while in the time period thereafter (after the 1990s), theoretical and experimental results are consistent. The long-term variations in B in general yield an anticorrelation of B and activity, as a rise of B is observed during the entire time period (1964–2016) we analysed, during which activity decreased, with the exception of the end of solar cycle 22 and the beginning of solar cycle 23. Conclusions. We study for the first time the variation in solar DR and activity based on 53 years of KSO data. Our results agree well with the results related to the solar cycle phase from corona observations. The disagreement of the observational results for B and theoretical studies may be due to the fact that we analysed the period immediately after the modern Gleissberg maximum, where for the phase-shift period, A versus activity also entails a result that differs from theoretical predictions. Therefore, studies of rotation versus activity with data sets encompassing the Gleissberg extremes should include separate analyses of the parts of the data set in between different flips (e.g., before the activity flip, between the activity and the rotation flip, and after the rotation flip).

Spectroscopic Line Modeling of the Fastest Rotating O-type Stars

We present a spectroscopic analysis of the most rapidly rotating stars currently known, VFTS 102 ( km s−1; O9: Vnnne+) and VFTS 285 ( km s−1; O7.5: Vnnn), both members of the 30 Dor complex in the Large Magellanic Cloud. This study is based on high-resolution ultraviolet spectra from Hubble Space Telescope/Cosmic Origins Spectrograph and optical spectra from the Very Large Telescope (VLT) X-shooter plus archival VLT GIRAFFE spectra. We utilize numerical simulations of their photospheres, rotationally distorted shape, and gravity darkening to calculate model spectral line profiles and predicted monochromatic absolute fluxes. We use a guided grid search to investigate parameters that yield best fits for the observed features and fluxes. These fits produce estimates of the physical parameters for these stars (plus a Galactic counterpart, ζ Oph) including the equatorial rotational velocity, inclination, radius, mass, gravity, temperature, and reddening. We find that both stars appear to be radial-velocity constant. VFTS 102 is rotating at critical velocity, has a modest He enrichment, and appears to share the motion of the nearby OB-association LH 99. These properties suggest that the star was spun up through a close binary merger. VFTS 285 is rotating at 95% of critical velocity, has a strong He enrichment, and is moving away from the R136 cluster at the center of 30 Dor. It is mostly likely a runaway star ejected by a supernova explosion that released the components of the natal binary system.

Disentangling the stellar inclination of transiting planetary systems: Fully analytic approach to the Rossiter–McLaughlin effect incorporating the stellar differential rotation

Abstract The Rossiter–McLaughlin (RM) effect has been widely used to estimate the sky-projected spin-orbit angle, λ, of transiting planetary systems. Most of the previous analysis assumes that the host stars are rigid rotators in which the amplitude of the RM velocity anomaly is proportional to v⋆ sin i⋆. When their latitudinal differential rotation is taken into account, one can break the degeneracy, and determine separately the equatorial rotation velocity v⋆ and the inclination i⋆ of the host star. We derive a fully analytic approximate formula for the RM effect adopting a parametrized model for the stellar differential rotation. For those stars that exhibit a differential rotation similar to that of the Sun, the corresponding RM velocity modulation amounts to several m s−1. We conclude that the latitudinal differential rotation offers a method to estimate i⋆, and thus the full spin-orbit angle ψ, from the RM data analysis alone.

TESS Detection of Rotation in the A1V Star α Lacertae

Abstract The A1V star α Lacertae was observed by TESS in 2019 September and October. The short-cadence photometry reveals periodic variation at the 24.6 ppm level. The 0.708 day variation is consistent with rotational modulation seen in main sequence A stars, and implies an equatorial rotation velocity of 153 km s−1. With prior spectroscopic measurement of the rotational broadening of 128 km s−1, this indicates an inclination of the rotation axis of 57°. The first harmonic of this period is present in the data, along with a two non-commensurate periods of 0.763 and 0.257 day, suggesting spot modulation with different periods, perhaps indicating differential rotation with latitude. Follow-up spectroscopy and photometry of this bright (V = 3.77) star can place valuable constraints on differential rotation and spot formation and evolution in A stars.

Exploring the Stellar Rotation of Early-type Stars in the LAMOST Medium-resolution Survey. II. Statistics

Abstract Angular momentum is a key property regulating star formation and evolution. However, the physics driving the distribution of the stellar rotation rates of early-type main-sequence stars is as yet poorly understood. Using our catalog of 40,034 early-type stars with homogeneous v sin i parameters, we review the statistical properties of their stellar rotation rates. We discuss the importance of possible contaminants, including binaries and chemically peculiar stars. Upon correction for projection effects and rectification of the error distribution, we derive the distributions of our sample’s equatorial rotation velocities, which show a clear dependence on stellar mass. Stars with masses less than 2.5 M ⊙ exhibit a unimodal distribution, with the peak velocity ratio increasing as stellar mass increases. A bimodal rotation distribution, composed of two branches of slowly and rapidly rotating stars, emerges for more massive stars (M > 2.5 M ⊙). For stars more massive than 3.0 M ⊙, the gap between the bifurcated branches becomes prominent. For the first time, we find that metal-poor ([M/H] < −0.2 dex) stars only exhibit a single branch of slow rotators, while metal-rich ([M/H] > 0.2 dex) stars clearly show two branches. The difference could be attributed to unexpectedly high spin-down rates and/or in part strong magnetic fields in the metal-poor subsample.

TESS Observations of Be Stars: General Characteristics and the Impulsive Magnetic Rotator Model

Abstract Evidence of rotational light modulation in 30%–40% of normal B stars is presented, suggesting the presence of starspots and photospheric activity. On this basis, we propose that mass loss in Be stars is a result of magnetic reconnection coupled with rapid but not necessarily near-critical rotation. The ejected matter is trapped at two diametrically opposed locations where the magnetic and geometric equators intersect. Nonradial pulsation plays no role in the mass loss and in the short-period light and line profile variations, though Be stars may pulsate as SPB or β Cep variables. The model allows many of the major characteristics of Be stars to be understood, including the frequency pattern in the periodogram, allowing the approximate rotational frequency to be identified. From a large number of Be stars observed by TESS, it is shown that the resulting equatorial rotational velocities, v, are consistent with the projected rotational velocities, v sin i . Furthermore, it is shown that Be stars are rotating in a broad range of 30%–100% of the critical rotational velocity. This agrees with several statistical v sin i analyses, which all show that Be stars are very unlikely to be rotating at near-critical velocities.

The Second Discovery from the COCONUTS Program: A Cold Wide-orbit Exoplanet around a Young Field M Dwarf at 10.9 pc

Abstract We present the identification of the second discovery from the COol Companions ON Ultrawide orbiTS (COCONUTS) program, the COCONUTS-2 system, composed of the M3 dwarf L 34-26 and the T9 dwarf WISEPA J075108.79−763449.6. Given their common proper motions and parallaxes, these two field objects constitute a physically bound pair with a projected separation of 594″ (6471au). The primary star COCONUTS-2A has strong stellar activity (Hα, X-ray, and ultraviolet emission) and is rapidly rotating (Prot = 2.83 days), from which we estimate an age of 150–800 Myr. Comparing equatorial rotational velocity derived from the Transiting Exoplanet Survey Satellite (TESS) light curve to spectroscopic vsini, we find that COCONUTS-2A has a nearly edge-on inclination. The wide exoplanet COCONUTS-2b has an effective temperature of T eff = 434 ± 9 K, a surface gravity of log g = 4.11 − 0.18 + 0.11 dex, and a mass of M = 6.3 − 1.9 + 1.5 M Jup based on hot-start evolutionary models, leading to a mass ratio of 0.016 − 0.005 + 0.004 for the COCONUTS-2 system. COCONUTS-2b is the second coldest (after WD 0806−661B), and the second widest (after TYC 9486-927-1 b) exoplanet imaged to date. Comparison of COCONUTS-2b’s infrared photometry with ultracool model atmospheres suggests the presence of both condensate clouds and non-equilibrium chemistry in its photosphere. Similar to 51 Eri b, COCONUTS-2b has a sufficiently low luminosity ( log ( L bol / L ⊙ ) = − 6.384 ± 0.028 dex) to be consistent with the cold-start process that may form gas-giant (exo)planets, though its large separation means that such formation would not have occurred in situ. Finally, at a distance of 10.9 pc, COCONUTS-2b is the nearest imaged exoplanet to Earth known to date.

Weather on Other Worlds. V. The Three Most Rapidly Rotating Ultra-cool Dwarfs

Abstract We present the discovery of rapid photometric variability in three ultra-cool dwarfs from long-duration monitoring with the Spitzer Space Telescope. The T7, L3.5, and L8 dwarfs have the shortest photometric periods known to date: hr, hr, and hr, respectively. We confirm the rapid rotation through moderate-resolution infrared spectroscopy, which reveals projected rotational velocities between 79 and 104 km s−1. We compare the near-infrared spectra to photospheric models to determine the objects’ fundamental parameters and radial velocities. We find that the equatorial rotational velocities for all three objects are ≳100 km s−1. The three L and T dwarfs reported here are the most rapidly spinning and likely the most oblate field ultra-cool dwarfs known to date. Correspondingly, all three are excellent candidates for seeking auroral radio emission and net optical/infrared polarization. As of this writing, 78 L-, T-, and Y-dwarf rotation periods have now been measured. The clustering of the shortest rotation periods near 1 hr suggests that brown dwarfs are unlikely to spin much faster.

Weather on Other Worlds. V. The Three Most Rapidly Rotating Ultra-Cool Dwarfs

We present the discovery of rapid photometric variability in three ultra-cool dwarfs from long-duration monitoring with the Spitzer Space Telescope. The T7, L3.5, and L8 dwarfs have the shortest photometric periods known to date: ${1.080}^{+0.004}_{-0.005}$ h, ${1.14}^{+0.03}_{-0.01}$ h, and ${1.23}^{+0.01}_{-0.01}$ h, respectively. We confirm the rapid rotation through moderate-resolution infrared spectroscopy, which reveals projected rotational velocities between 79 and 104 km s$^{-1}$. We compare the near-infrared spectra to photospheric models to determine the objects' fundamental parameters and radial velocities. We find that the equatorial rotational velocities for all three objects are $\gtrsim$100 km s$^{-1}$. The three L and T dwarfs reported here are the most rapidly spinning and likely the most oblate field ultra-cool dwarfs known to date. Correspondingly, all three are excellent candidates for seeking auroral radio emission and net optical/infrared polarization. As of this writing, 78 L-, T-, and Y-dwarf rotation periods have now been measured. The clustering of the shortest rotation periods near 1 h suggests that brown dwarfs are unlikely to spin much faster.

Binary-driven stellar rotation evolution at the main-sequence turn-off in star clusters

ABSTRACT The impact of stellar rotation on the morphology of star cluster colour–magnitude diagrams is widely acknowledged. However, the physics driving the distribution of the equatorial rotation velocities of main-sequence turn-off stars is as yet poorly understood. Using Gaia Data Release 2 photometry and new Southern African Large Telescope medium-resolution spectroscopy, we analyse the intermediate-age ($\sim 1\text{-}{\rm Gyr}$-old) Galactic open clusters NGC 3960, NGC 6134, and IC 4756 and develop a novel method to derive their stellar rotation distributions based on SYCLIST stellar rotation models. Combined with literature data for the open clusters NGC 5822 and NGC 2818, we find a tight correlation between the number ratio of slow rotators and the clusters’ binary fractions. The blue-main-sequence stars in at least two of our clusters are more centrally concentrated than their red-main-sequence counterparts. The origin of the equatorial stellar rotation distribution and its evolution remains as yet unidentified. However, the observed correlation in our open cluster sample suggests a binary-driven formation mechanism.

The Betelgeuse Project. III. Merger Characteristics

Abstract We previously proposed that Betelgeuse might have been spun up by accreting a companion of about 1 M ⊙. Here we explore in more detail the possible systematics of such a merger and a larger range of accreted masses. We use the stellar evolutionary code mesa to add angular momentum to a primary star in core helium burning, core carbon burning, or shell carbon burning. Our models provide a reasonable “natural” explanation for why Betelgeuse has a large, but sub-Keplerian equatorial velocity. They eject sufficient mass and angular momentum in rotationally induced mass loss to reproduce the observed ratio of the equatorial velocity to escape velocity of Betelgeuse, ≈0.23, within a factor of 3 nearly independent of the primary mass, the secondary mass, and the epoch at which merger occurs. Our models suggest that merger of a primary of somewhat less than 15 M ⊙ with secondaries from 1 to 10 M ⊙ during core helium burning or core carbon burning could yield the equatorial rotational velocity of ∼15 km s−1 attributed to Betelgeuse. For accreting models, a wave of angular momentum is halted at the composition boundary at the edge of the helium core. The inner core is thus not affected by the accretion of the companion in these simulations. Accretion has relatively little effect on the production of magnetic fields in the inner core. Our results do not prove, but do not negate, that Betelgeuse might have ingested a companion of several M ⊙.

On the rotational velocity of Sirius A

ABSTRACT With an aim of getting information on the equatorial rotation velocity (ve) of Sirius A separated from the inclination effect (sin i), a detailed profile analysis based on the Fourier transform technique was carried out for a large number of spectral lines, while explicitly taking into account the line-by-line differences in the centre–limb behaviours and the gravity darkening effect (which depend on the physical properties of each line) based on model calculations. The simulations showed that how the first-zero frequencies (q1) of Fourier transform amplitudes depends on ve is essentially determined by the temperature-sensitivity parameter (K) differing from line to line, and that Fe i lines (especially those of very weak ones) are more sensitive to ve than Fe ii lines. The following conclusions were drawn by comparing the theoretical and observed q1 values for many Fe i and Fe ii lines: (1) The projected rotational velocity (vesin i) for Sirius A is fairly well established at 16.3(±0.1) km s−1 by requiring that both Fe i and Fe ii lines yield consistent results. (2) Although precise separation of ve and i is difficult, ve is concluded to be in the range of $16 \le v_{\rm e} \lesssim$ 30–40 km s−1, which corresponds to $25^{\circ } \lesssim i \le 90^{\circ }$. Accordingly, Sirius A is an intrinsically slow rotator for an A-type star, being consistent with its surface chemical peculiarity.

Two New Rapidly Rotating ON Stars Found with LAMOST

Abstract The ON stars are a rare subtype of O stars of uncertain origin. We report two new, rapidly rotating ON stars found in data acquired with the Large Sky Area Multi-Object Fiber Spectroscopic Telescope. LS I +61 28 is an ON8.5 Vn dwarf with a projected equatorial rotational velocity of , while HDE 236672 is an ON9 IVn subgiant with . The former is the first rapidly rotating ON dwarf to be found, and the latter is only the third ON subgiant. The luminosity classes of non-supergiant ON stars appear to be influenced by the axial inclination angle i: the rapidly rotating giants are close to equator-on, while ON dwarfs with lower values are viewed more nearly pole-on. Combining parallaxes and proper motions from Gaia Data Release 2 with radial-velocity measurements, we investigate the kinematics of non-supergiant ON stars and infer that the dynamics, rapid rotation, and surface nitrogen characteristics may all be consequences of binary interaction.

Rotation and spots in normal A and Am/Fm stars

ABSTRACT Frequency analysis of long-term ultraprecise photometry can lead to precise values of rotation frequencies of rotating stars with ‘hump and spike’ features in their periodograms. Using these features, we computed the rotation frequencies and amplitudes. The corresponding equatorial rotational velocity ($V_{\rm{rot}}$) and spot size were estimated. On fitting the autocorrelation functions of the light curves with the appropriate model, we determined the star-spot decay time-scale. The $\rm \mathit{ V}_{rot}$ agrees well with the projected rotational velocity ($\rm \nu ~sin$ i) in the literature. Considering a single circular and black spot, we estimate its radius from the amplitude of the ‘spike’. No evidence for a significant difference in the average ‘spike’ amplitude and spot radius was found for Am/Fm and normal A stars. Indeed, we derived an average value of $\rm \sim\! 21\pm 2$ and $\rm \sim\! 19\pm 2$ ppm for the photometric amplitude and of $\rm 1.01\, \pm \, 0.13$ and $\rm 1.16\, \pm \, 0.12$ $R_\mathrm{ E}$ for the spot radius (where $\rm \mathit{ R}_E$ is the Earth radius), respectively. We do find a significant difference for the average spot decay time-scale, which amounts to 3.6 ± 0.2 and 1.5 ± 0.2 d for Am/Fm and normal A stars, respectively. In general, spots on normal A stars are similar in size to those on Am/Fm stars, and both are weaker than previously estimated. The existence of the ‘spikes’ in the frequency spectra may not be strongly dependent on the appearance of star-spots on the stellar surface. In comparison with G, K, and M stars, spots in normal A and Am/Fm stars are weak, which may indicate the presence of a weak magnetic field.

The single star path to Be stars

Context. Be stars are rapidly rotating B main sequence stars that show line emission due to an outflowing disc. By studying the evolution of rotating single star models, we can assess their contribution to the observed Be star populations. Aims. We identify the main effects that cause single stars to approach critical rotation as functions of initial mass and metallicity, and predict the properties of populations of rotating single stars. Methods. We perform population synthesis with single-star models of initial masses ranging between 3 and 30 M⊙ and initial equatorial rotation velocities between 0 and 600 km s−1 at compositions representing the Milky Way and the Large and Small Magellanic Clouds. These models include efficient core–envelope coupling mediated by internal magnetic fields and correspond to the maximum efficiency of Be star production. We predict Be star fractions and the positions of fast-rotating stars in the colour–magnitude diagram. Results. We identify stellar wind mass-loss and the convective core mass fraction as the key parameters determining the time dependance of the stellar rotation rates. Using empirical distributions of initial rotational velocities, our single-star models can reproduce the trends observed in Be star fractions with mass and metallicity. However, they fail to produce a significant number of stars rotating very close to the critical velocity. We also find that rapidly rotating Be stars in the Magellanic Clouds should have significant surface nitrogen enrichment, which may be in conflict with abundance determinations of Be stars. Conclusions. Single-star evolution might explain the high number of Be stars if 70 to 80% of critical rotation would be sufficient to produce the Be phenomenon. However, even in this case, the unexplained presence of many Be stars far below the cluster turn-off indicates the importance of the binary channel for Be star production.