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 Vsin i, 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 Vsin i 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 Vsin i, 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.

Context. Stellar physical properties of star clusters are poorly known and the cluster parameters are often quite uncertain. Aims. Our goals are to perform a spectrophotometric study of the B star population in open clusters to derive accurate stellar parameters, search for the presence of circumstellar envelopes and discuss the characteristics of these stars. Methods. The BCD spectrophotometric system is a powerful method to obtain stellar fundamental parameters from direct measurements of the Balmer discontinuity. To this end, we wrote the interactive code MIDE3700. The BCD parameters can also be used to infer the main properties of open clusters: distance modulus, color excess and age. Furthermore, we inspect the aspect of the Balmer discontinuity to put in evidence the presence of circumstellar disks and identify Be-star candidates. An additional set of high resolution spectra, in the Hα region, is used to confirm the Be nature of these stars. Results. In this work we provide T eff , log g, M v , M bol and spectral types for a sample of 68 stars in the field of the open clusters NGC 6087, NGC 6250, NGC 6383, and NGC 6530, as well as the cluster distances, ages and reddening. Then, based on a sample of 230 B stars in the direction of the eleven open clusters studied along these three series of papers, we report new six Be stars, four blue straggler candidates, and fifteen B type stars (called Bdd) with a double Balmer discontinuity which indicates the presence of circumstellar envelopes. We discuss the distribution of the fraction of B, Be and Bdd star cluster members per spectral subtype. The majority of the Be stars are dwarfs and present a maximum at the spectral type B2-B4 in young and intermediate-age open clusters (< 40 Myr). Another maximum of Be stars is observed at the spectral type B6-B8 in open clusters older than 40 Myr, where the population of Bdd stars also becomes relevant. The Bdd stars seem to be in a "passive" emission phase. Conclusions. Our results support previous statements that the Be phenomenon is present along the whole main sequence band and occurs in very different evolutionary states. We find clear evidence of an enhance of stars with circumstellar envelopes with cluster age. The Be phenomenon reaches it maximum in clusters of intermediate-age (10 − 40 Myr) and the number of B stars with circumstellar envelopes (Be plus Bdd stars) keeps also high for the older clusters (40 − 100 Myr).

Context. Spectroscopic investigations of galactic open clusters are scarce and limited to a reduced sample of cluster members. Aims. We intend to perform a complete study of the physical parameters of two galactic clusters as well as of their individual members. Methods. To carry out this study, we used the BCD (Barbier-Chalonge-Divan) spectrophotometric system, which is based on the study of the Balmer discontinuity and is independent of interstellar and circumstellar extinction. Additional physical properties were derived from the line profiles (FWHM) and stellar evolution models. We analyzed low-resolution spectra around the Balmer discontinuity for normal B-type and Be stars in two open clusters: NGC 3766 and NGC 4755. We determined the stellar fundamental parameters, such as effective temperatures, surface gravities, spectral types, luminosity classes, absolute and bolometric magnitudes, and color gradient excesses. The stellar rotation velocity was also determined. Complementary information, mainly stellar mass, age, and radius of the star population were calculated using stellar evolution models. In some cases, the stellar fundamental parameters were derived for the first time. The obtained results allowed us also to determine the reddening, age, and distance to the clusters. Results. The cluster parameters obtained through the BCD method agree very well with those derived from classical methods based on photometric data. The BCD system also provides physical properties of the star members. This study enables us to test the good behavior of M bol (λ 1 , D)-calibrations and detect systematic discrepancies between log g estimates from model atmospheres and those derived from stellar evolution models. To improve our knowledge on the formation and evolution of the clusters, more statistical studies on the initial mass luminosity and angular momentum distributions should be addressed. Therefore, the BCD spectrophotometric system could be a powerful tool for studying far galactic and extragalactic clusters with the generation of large telescopes and the multi-object technique.