Distribution Of Rotational Velocities Research Articles

Mapping the core of the Tarantula Nebula with VLT-MUSE

We present the spectroscopic analysis of 333 OB-type stars extracted from VLT-MUSE observations of the central 30 × 30 pc of NGC 2070 in the Tarantula Nebula on the Large Magellanic Cloud, the majority of which are analysed for the first time. The distribution of stars in the spectroscopic Hertzsprung-Russell diagram (sHRD) shows 281 stars in the main sequence. We find two groups in the main sequence, with estimated ages of 2.1 ± 0.8 and 6.2 ± 2 Myr. A subgroup of 52 stars is apparently beyond the main sequence phase, which we consider to be due to emission-type objects and/or significant nebular contamination affecting the analysis. As in previous studies, stellar masses derived from the sHRD are systematically larger than those obtained from the conventional HRD, with the differences being largest for the most massive stars. Additionally, we do not find any trend between the estimated projected rotational velocity and evolution in the sHRD. The projected rotational velocity distribution presents a tail of fast rotators that resembles findings in the wider population of 30 Doradus. We use published spectral types to calibrate the He Iλ4921/He IIλ5411 equivalent-width ratio as a classification diagnostic for early-type main sequence stars when the classical blue-visible region is not observed. Our model-atmosphere analyses demonstrate that the resulting calibration is well correlated with effective temperature.

Loss of peripheral vestibular input alters the statistics of head movement experienced during natural self-motion.

Sensory systems are adapted to the statistical structure of natural stimuli, thereby optimizing neural coding. Head motion during natural activities is first sensed and then processed by central vestibulo-motor pathways to influence subsequent behaviour, thereby establishing a feedback loop. To investigate the role of this vestibular feedback on the statistical structure of the head movements, we compared head movements in patients with unilateral vestibular loss and healthy controls. We show that the loss of vestibular feedback substantially alters the statistical structure of head motion for activities that require rapid online feedback control and predict this change by modelling the effects of increased movement variability. Our findings suggest that, following peripheral vestibular loss, changes in the reliability of the sensory input to central pathways impact the statistical structure of head motion during voluntary behaviours. It is widely believed that sensory systems are adapted to optimize neural coding of their natural stimuli. Recent evidence suggests that this is the case for the vestibular system, which senses head movement and contributes to essential functions ranging from the most automatic reflexes to voluntary motor control. During everyday behaviours, head motion is sensed by the vestibular system. In turn, this sensory feedback influences subsequent behaviour, raising the questions of whether and how real-time feedback provided by the vestibular system alters the statistical structure of head movements. We predicted that a reduction in vestibular feedback would alter head movement statistics, particularly for tasks reliant on rapid vestibular feedback. To test this proposal, we recorded six-dimensional head motion in patients with variable degrees of unilateral vestibular loss during standard balance and gait tasks, as well as dynamic self-paced activities. While distributions of linear accelerations and rotational velocities were comparable for patients and age-matched healthy controls, comparison of power spectra revealed significant differences during more dynamic and challenging activities. Specifically, consistent with our prediction, head movement power spectra were significantly altered in patients during two tasks that required rapid online vestibular feedback: active repetitive jumping and walking on foam. Using computational methods, we analysed concurrently measured torso motion and identified increases in head-torso movement variability. Taken together, our results demonstrate that vestibular loss significantly alters head movement statistics and further suggest that increased variability and impaired feedback to internal models required for accurate motor control contribute to the observed changes.

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.

Existence of the Metal-rich Stellar Halo and High-velocity Thick Disk in the Galaxy

Abstract Based on the second Gaia data release (DR2), combined with the LAMOST and APOGEE spectroscopic surveys, we study the kinematics and metallicity distribution of the high-velocity stars that have a relative speed of at least 220 with respect to the local standard of rest in the Galaxy. The rotational velocity distribution of the high-velocity stars with [Fe/H] dex can be well described by a two-Gaussian model, with peaks at and , associated with the thick disk and halo, respectively. This implies that there should exist a high-velocity thick disk (HVTD) and a metal-rich stellar halo (MRSH) in the Galaxy. The HVTD stars have the same position as the halo in the Toomre diagram but show the same rotational velocity and metallicity as the canonical thick disk. The MRSH stars have basically the same rotational velocity, orbital eccentricity, and position in the Lindblad and Toomre diagram as the canonical halo stars, but they are more metal-rich. Furthermore, the metallicity distribution function of our sample stars are well fitted by a four-Gaussian model, associated with the outer halo, inner halo, MRSH, and HVTD, respectively. Chemical and kinematic properties and age imply that the MRSH and HVTD stars may form in situ.

Spectroscopic characterization of the known O-star population in Cygnus OB2

Context.Cygnus OB2 provides a unique insight into the high-mass stellar content in one of the largest groups of young massive stars in our Galaxy. Although several studies of its massive population have been carried out over the last decades, an extensive spectroscopic study of the whole known O-star population in the association is still lacking.Aims.We aim to carry out a spectroscopic characterization of all the currently known O stars in Cygnus OB2, determining the distribution of rotational velocities and accurate stellar parameters to obtain an improved view of the evolutionary status of the region.Methods.Based on existing and new optical spectroscopy, we performed a detailed quantitative spectroscopic analysis of all the known O-type stars identified in the association. For this purpose, we used the user-friendlyiacob-broadandiacob-gbatautomatized tools, FASTWIND stellar models, and astrometry provided by theGaiasecond data release.Results.We created the most complete spectroscopic census of O stars carried out so far in Cygnus OB2 using already existing and new spectroscopy. We present the spectra for 78 O-type stars, from which we identify new binary systems, obtain the distribution of rotational velocities, and determine the main stellar parameters for all the stars in the region that have not been detected as double-line spectroscopic binaries. We also derive radii, luminosities, and masses for those stars with reliableGaiaastrometry, in addition to creating the Hertzsprung-Russell Diagram to interpret the evolutionary status of the association. Finally, we inspect the dynamical state of the population and identify runaway candidates.Conclusions.Our spectroscopic analysis of the O-star population in Cygnus OB2 has led to the discovery of two new binary systems and the determination of the main stellar parameters, including rotational velocities, luminosities, masses, and radii for all identified stars. This work has shown the improvement reached when using accurate spectroscopic parameters and astrometry for the interpretation of the evolutionary status of a population, revealing, in the case of Cygnus OB2, at least two star-forming bursts at ~3 and ~5 Myr. We find an apparent deficit of very fast rotators in the distribution of rotational velocities. The inspection of the dynamical distribution of the sample has allowed us to identify nine O stars with peculiar proper motions and discuss a possible dynamical ejection scenario or past supernova explosions in the region.

Differential Rotation of the Halo Traced by K-giant Stars

Abstract We use K-giant stars selected from the LAMOST DR5 to study the variation of the rotational velocity of the Galactic halo at different space positions. Modeling the rotational velocity distribution with both the halo and disk components, we find that the rotational velocity of the halo population decreases almost linearly with increasing vertical distance to the Galactic disk plane, Z, at fixed galactocentric radius, R. The samples are separated into two parts with and . We derive that the decreasing rates along Z for the two subsamples are −3.07 ± 0.63 and −1.89 ± 0.37 km s−1 kpc−1, respectively. Comparing with the TNG simulations, we suggest that this trend is caused by the interaction between the disk and halo. The results from the simulations show that only an oblate halo can provide a decreasing rotational velocity with increasing Z. This indicates that the Galactic halo is oblate with galactocentric radius . On the other hand, the flaring of the disk component (mainly the thick disk) is clearly traced by this study; with R between 12 and 20 kpc, the disk can vertically extend to above the disk plane. What is more interesting is that we find the Gaia–Enceladus–Sausage component has a significant contribution only in the halo with , i.e., a fraction of 23%–47%, while in the outer subsample, the contribution is too low to be well constrained.

Machine Learning for 3D Particle Tracking in Granular Gases

Dilute ensembles of granular matter (so-called granular gases) are nonlinear systems which exhibit fascinating dynamical behavior far from equilibrium, including non-Gaussian distributions of velocities and rotational velocities, clustering, and violation of energy equipartition. In order to understand their dynamic properties, microgravity experiments were performed in suborbital flights and drop tower experiments. Up to now, the experimental images were evaluated mostly manually. Here, we introduce an approach for automatic 3D tracking of positions and orientations of rod-like particles in a dilute ensemble, based on two-view video data analysis. A two-dimensional (2D) localization of particles is performed using a Mask R-CNN neural network trained on a custom data set. The problem of 3D matching of the particles is solved by minimization of the total reprojection error, and finally, particle trajectories are tracked so that ensemble statistics are extracted. Depending on the required accuracy, the software can work fully self-sustainingly or serve as a base for subsequent manual corrections. The approach can be extended to other 3D and 2D particle tracking problems.

On the origin of the bimodal rotational velocity distribution in stellar clusters: rotation on the pre-main sequence

ABSTRACT We address the origin of the observed bimodal rotational distribution of stars in massive young and intermediate age stellar clusters. This bimodality is seen as split main sequences at young ages and also has been recently directly observed in the Vsini distribution of stars within massive young and intermediate age clusters. Previous models have invoked binary interactions as the origin of this bimodality, although these models are unable to reproduce all of the observational constraints on the problem. Here, we suggest that such a bimodal rotational distribution is set-up early within a cluster’s life, i.e. within the first few Myr. Observations show that the period distribution of low-mass ($\lesssim\! 2 \, \mathrm{M}_\odot$) pre-main-sequence (PMS) stars is bimodal in many young open clusters, and we present a series of models to show that if such a bimodality exists for stars on the PMS that it is expected to manifest as a bimodal rotational velocity (at fixed mass/luminosity) on the main sequence for stars with masses in excess of ∼1.5 M⊙. Such a bimodal period distribution of PMS stars may be caused by whether stars have lost (rapid rotators) or been able to retain (slow rotators) their circumstellar discs throughout their PMS lifetimes. We conclude with a series of predictions for observables based on our model.

Exploring the Origin of Moving Groups and Diagonal Ridges by Simulations of Stellar Orbits and Birthplaces

Abstract The present paper is the culmination of a series aimed at contributing to the understanding of the kinematic structures of the solar neighborhood (SN), explaining the origin of the Local Arm, and relating the moving groups with the spiral-arms resonances in the disk. With a model for the Galactic potential, with the Sun inside the spiral corotation resonance (CR), we integrate the 2D orbits of test particles distributed in birthplaces along the main spiral arms, the Local Arm, and in the axisymmetric disk. A comparison of the resulting U–V plane of the SN with that provided by Gaia DR2 confirms our previous conclusion that the moving groups of Coma Berenices, Pleiades, and Hyades are associated with the CR, and that the Hercules stream is formed by the bulk of high-order inner Lindblad resonances. The kinematic structures result from stellar orbits trapped by the spiral resonances in a timespan of ∼1 Gyr, indicating the long-lived nature of the spiral structure and challenging recent arguments in favor of short-lived structures originated from incomplete phase mixing in the Galactic disk. As a byproduct, our simulations give some insight into the birthplaces of the stars presently located in the SN; the majority of stars of the main moving groups and the Hercules stream were likely born in the Local Arm, while stars of the Sirius group possibly originated from the outer segment of the Sagittarius–Carina arm. We also propose the spiral resonances as the dynamical origin for the diagonal ridges in the Galactic distribution of rotation velocities.

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.

Application of Arbitrary Vortex Method in Wind Tunnel Axial Fan Design

The flow axial velocity is assumed equal everywhere in free vortex design method, and the pressure rise of flow pass through fan is assumed also equal at different radial height. But in arbitrary vortex design method, on the assumption that axial velocity along radial is variable, the flow rotational velocity along radial is not must an inverse distribution. Therefore, arbitrary vortex design method could have a more uniform axial velocity at the outlet of fan system by regulating the rotational velocity distribution. In the numerical simulation, the fan of a pilot wind tunnel is used as physical model. By comparison with the experimental data the reliability of the numerical simulation could be verified. Two fan physical models are established which are based on the designs of arbitrary vortex method and free vortex method. The result of numerical simulation indicated that compared to the free vortex method, the arbitrary vortex fan minished the separation on the tip and root of blade, obtained a more well uniform axial velocity distribution at the outlet of fan system. And the efficiency of blade is also increased by arbitrary vortex method.

A census of massive stars in NGC 346

Spectroscopy for 247 stars towards the young cluster NGC 346 in the Small Magellanic Cloud has been combined with that for 116 targets from the VLT-FLAMES Survey of Massive Stars. Spectral classification yields a sample of 47 O-type and 287 B-type spectra, while radial-velocity variations and/or spectral multiplicity have been used to identify 45 candidate single-lined (SB1) systems, 17 double-lined (SB2) systems, and one triple-lined (SB3) system. Atmospheric parameters (Teff and log g) and projected rotational velocities (ve sin i) have been estimated using TLUSTY model atmospheres; independent estimates of ve sin i were also obtained using a Fourier Transform method. Luminosities have been inferred from stellar apparent magnitudes and used in conjunction with the Teff and ve sin i estimates to constrain stellar masses and ages using the BONNSAI package. We find that targets towards the inner region of NGC 346 have higher median masses and projected rotational velocities, together with smaller median ages than the rest of the sample. There appears to be a population of very young targets with ages of less than 2 Myr, which have presumably all formed within the cluster. The more massive targets are found to have lower projected rotational velocities consistent with previous studies. No significant evidence is found for differences with metallicity in the stellar rotational velocities of early-type stars, although the targets in the Small Magellanic Cloud may rotate faster than those in young Galactic clusters. The rotational velocity distribution for single non-supergiant B-type stars is inferred and implies that a significant number have low rotational velocity (≃10% with ve < 40 km s−1), together with a peak in the probability distribution at ve≃ 300 km s−1. Larger projected rotational velocity estimates have been found for our Be-type sample and imply that most have rotational velocities between 200–450 km s−1.

A method to deconvolve stellar rotational velocities

Aims. The study of accurate methods to estimate the distribution of stellar rotational velocities is important for understanding many aspects of stellar evolution. From such observations we obtain the projected rotational speed (v sin i) in order to recover the true distribution of the rotational velocity. To that end, we need to solve a difficult inverse problem that can be posed as a Fredholm integral of the first kind. Methods. In this work we have used a novel approach based on maximum likelihood (ML) estimation to obtain an approximation of the true rotational velocity probability density function (PDF) expressed as a sum of known distribution families. In our proposal, the measurements have been treated as random variables drawn from the projected rotational velocity PDF. We analyzed the case of Maxwellian sum approximation, where we estimated the parameters that define the sum of distributions. Results. The performance of the proposed method is analyzed using Monte Carlo simulations considering two theoretical cases for the PDF of the true rotational stellar velocities: (i) an unimodal Maxwellian probability density distribution and (ii) a bimodal Maxwellian probability density distribution. The results show that the proposed method yielded more accurate estimates in comparison with the Tikhonov regularization method, especially for small sample length (N = 50). Our proposal was evaluated using real data from three sets of measurements, and our findings were validated using three statistical tests. Conclusions. The ML approach with Maxwellian sum approximation is a accurate method to deconvolve the rotational velocity PDF, even when the sample length is small (N = 50).

Rotating Halo Traced by the K-giant Stars from LAMOST and Gaia

Abstract With the help of Gaia DR2, we are able to obtain the full 6D phase space information for stars from the Large Sky Area Multi-Object Fibre Spectroscopic Telescope DR5. With high precision of the position, velocity, and metallicity, the rotation of the local stellar halo is presented using the K-giant stars with [Fe/H] < −1 dex within 4 kpc from the Sun. By fitting the rotational velocity distribution with the three-Gaussian components, stellar halo, disk, and counterrotating hot population, we find that the local halo progradely rotates with km s−1, providing the local standard of the rest velocity of V LSR = 232 km s−1. Meanwhile, we obtain the dispersion of rotational velocity is km s−1. Although the rotational velocity strongly depends on the choice of V LSR, the trend of prograde rotation is substantial even when V LSR is set at as low as 220 km s−1. Moreover, we derive the rotation for subsamples with different metallicities and find that the rotational velocity is essentially not correlated with [Fe/H]. This may hint at a secular evolution origin of the prograde rotation. It shows that the metallicity of the progradely rotating halo is peaked within −1.9 < [Fe/H] < −1.6 without considering the selection effect. We also find a small fraction of counterrotating stars with larger dispersion and a lower metallicity. Finally, the disk component rotates with km s−1 and km s−1, which is quite consistent with the metal-weak thick disk population.

Transient spiral structure and the disc velocity substructure in Gaia DR2

The second data release from ESA's Gaia mission has revealed many ridge-like structures in the velocity distribution of the Milky Way. We show that these can arise naturally from winding transient spiral structure that is commonly seen in N-body simulations of disk galaxies. We construct test particle models of the winding spiral structure, and compare the resulting distribution of orbits with the observed two-dimensional velocity distribution in the extended solar neighbourhood and with the distribution of rotational velocities over 8 kpc along the Sun--Galactic-centre--Galactic anti-centre line. We show that the ridges in these observations are well reproduced by the winding spiral model. Additionally, we demonstrate that the transient winding spiral potential can create a Hercules-like feature in the kinematics of the solar neighbourhood, either alone, or in combination with a long-slow bar potential.

Experimental study of the particle motion in flighted rotating drums by means of Magnetic Particle Tracking

The particle motion in flighted rotating drums (FRD) is still not fully understood due to the many influencing variables and its complexity. The method of Magnetic Particle Tracking (MPT) offers new possibilities for this purpose. In this work, the MPT is adopted and applied to study particle motion in FRD for the first time. The experiments were conducted using plastic balls and soybeans at 5% filling degree under various drum rotating speeds (10 rpm–40 rpm). Particle trajectories, translational velocity distributions, rotational velocity distributions, falling time of dilute phase, and instantaneous velocity of dilute phase in the equatorial region of the drum were studied. As the measurements revealed, the particle motion in flighted rotating drum is strongly influenced by the drum rotating speed and slightly affected by particle size and shape in the range investigated here.

Tentative explanation of the rotational velocity distribution in galaxies

Tentative explanation of the rotational velocity distribution in galaxies

Extended Main-sequence Turn-offs in Intermediate-age Star Clusters: Stellar Rotation Diminishes, but Does Not Eliminate, Age Spreads

Abstract Extended main-sequence turn-off (eMSTO) regions are a common feature in color–magnitude diagrams of young- and intermediate-age star clusters in the Magellanic Clouds. The nature of eMSTOs remains debated in the literature. The currently most popular scenarios are extended star formation activity and ranges of stellar rotation rates. Here we study details of differences in main-sequence turn-off (MSTO) morphology expected from spreads in age versus spreads in rotation rates, using Monte Carlo simulations with the Geneva syclist isochrone models that include the effects of stellar rotation. We confirm a recent finding of Niederhofer et al. that a distribution of stellar rotation velocities yields an MSTO extent that is proportional to the cluster age, as observed. However, we find that stellar rotation yields MSTO crosscut widths that are generally smaller than observed ones at a given age. We compare the simulations with high-quality Hubble Space Telescope data of NGC 1987 and NGC 2249, which are the two only relatively massive star clusters with an age of ∼1 Gyr for which such data is available. We find that the distribution of stars across the eMSTOs of these clusters cannot be explained solely by a distribution of stellar rotation velocities, unless the orientations of rapidly rotating stars are heavily biased toward an equator-on configuration. Under the assumption of random viewing angles, stellar rotation can account for ∼60% and ∼40% of the observed FWHM widths of the eMSTOs of NGC 1987 and NGC 2249, respectively. In contrast, a combination of distributions of stellar rotation velocities and stellar ages fits the observed eMSTO morphologies very well.

Critical study of the distribution of rotational velocities of Be stars

Aims.We assume that stars may undergo surface differential rotation to study its impact on the interpretation ofVsiniand on the observed distributionΦ(u) of ratios of true rotational velocitiesu=V/Vc(Vcis the equatorial critical velocity). We discuss some phenomena affecting the formation of spectral lines and their broadening, which can obliterate the information carried byVsiniconcerning the actual stellar rotation.Methods.We studied the line broadening produced by several differential rotational laws, but adopted Maunder’s expression Ω(θ) = Ω0(1 +αcos2θ) as an attempt to account for all of these laws with the lowest possible number of free parameters. We studied the effect of the differential rotation parameterαon the measuredVsiniparameter and on the distributionΦ(u) of ratiosu=V/Vc.Results.We conclude that the inferredVsiniis smaller than implied by the actual equatorial linear rotation velocityVeqif the stars rotate withα< 0, but is larger if the stars haveα> 0. For a given |α| the deviations ofVsiniare larger whenα< 0. If the studied Be stars have on averageα< 0, the number of rotators withVeq≃ 0.9Vcis larger than expected from the observed distributionΦ(u); if these stars have on averageα> 0, this number is lower than expected. We discuss seven phenomena that contribute either to narrow or broaden spectral lines, which blur the information on the rotation carried byVsiniand, in particular, to decide whether the Be phenomenon mostly rely on the critical rotation. We show that two-dimensional radiation transfer calculations are needed in rapid rotators to diagnose the stellar rotation more reliably.

Critical study of the distribution of rotational velocities of Be stars

Context. Among intermediate-mass and massive stars, Be stars are the fastest rotators in the main sequence (MS) and, as such, these stars are a cornerstone to validate models of structure and evolution of rotating stars. Several phenomena, however, induce under- or overestimations either of their apparent V sini , or true velocity V .Aims. In the present contribution we aim at obtaining distributions of true rotational velocities corrected for systematic effects induced by the rapid rotation itself, macroturbulent velocities, and binarity.Methods. We study a set of 233 Be stars by assuming they have inclination angles distributed at random. We critically discuss the methods of Cranmer and Lucy-Richardson, which enable us to transform a distribution of projected velocities into another distribution of true rotational velocities, where the gravitational darkening effect on the V sini parameter is considered in different ways. We conclude that iterative algorithm by Lucy-Richardson responds at best to the purposes of the present work, but it requires a thorough determination of the stellar fundamental parameters.Results. We conclude that once the mode of ratios of the true velocities of Be stars attains the value V /V c ≃ 0.77 in the main-sequence (MS) evolutionary phase, it remains unchanged up to the end of the MS lifespan. The statistical corrections found on the distribution of ratios V /V c for overestimations of V sini, due to macroturbulent motions and binarity, produce a shift of this distribution toward lower values of V /V c when Be stars in all MS evolutionary stages are considered together. The mode of the final distribution obtained is at V /V c ≃ 0.65. This distribution has a nearly symmetric distribution and shows that the Be phenomenon is characterized by a wide range of true velocity ratios 0.3 ≲ V /V c ≲ 0.95. It thus suggests that the probability that Be stars are critical rotators is extremely low.Conclusions. The corrections attempted in the present work represent an initial step to infer indications about the nature of the Be-star surface rotation that will be studied in the second paper of this series.