This study investigated the initial mass function (IMF) and star formation history of high-mass stars in the Small Magellanic Cloud (SMC) using a population synthesis technique. We used the photometric survey catalog of Lee (2013) as the observable quantities and compare them with those of synthetic populations based on Bayesian inference. For the IMF slope (γ) range of -1.1 to -3.5 with steps of 0.1, five types of star formation models were tested: 1) continuous; 2) single burst at 10 Myr; 3) single burst at 60 Myr; 4) double bursts at those epochs; and 5) a complex hybrid model. In this study, a total of 125 models were tested. Based on the model calculations, it was found that the continuous model could simulate the high-mass stars of the SMC and that its IMF slope was -1.6 which is slightly steeper than Salpeter's IMF, i.e., γ=-1.35.

Five contemporary pre-main sequence (PMS) evolution model grids are compared with the photo-metric data for a nearly complete sample of low-mass members in NGC 2264. From amongst the grids compared, the models of Baraffe et al. (1998) prove to be the most reliable in mass-age distribution. To overcome the limited mass range of the models of Baraffe et al. we derived a simple transformation relation between the mass of a PMS star from Swenson et al. (1994) and that from Baraffe et al., and applied it to the PMS stars in NGC 2264 and the Orion nebula cluster (ONC). The resulting initial mass function (IMF) of the ONC shows that the previous interpretation of the IMF is not a real feature, but an artifact caused by the evolution models adopted. The IMFs of both clusters are in a good agreement with the IMF of the field stars in the solar neighborhood. This result supports the idea proposed by Lada, Strom, & Myers (1993) that the field stars originate from the stars that are formed in clusters and spread out as a result of dynamical dissociation. Nevertheless, the IMFs of OB associations and young open clusters show diverse behavior. For the low-mass regime, the current observations suffer from difficulties in membership assignment and sample incompleteness. From this, we conclude that a more thorough study of young open clusters is necessary in order to make any definite conclusions on the existence of a universal IMF.

In the best observed Pleiades cluster, the luminosity function(LF) and mass function(MF) for main sequence(MS) stars extended to Mv ≈ 15.5(V≈21) are very similar to the initial luminosity function(ILF) and initial mass function(IMF) for field stars in the solar neighborhood showing a bump at log m≃-0.05 and a dip at log m ≃ -0.12. This dip is equivalent to the Wielen dip appearing in the LF for the field stars. The occurence of these bump and dip is independent of adopted mass-luminosity relation(MLR) . and their characteristics could be explained by a time-dependent bimodal IMF. The model with this IMF gives a total cluster mass of ~700M⊙, ~25 brown dwarfs and ~3 white dwarfs if the upper mass limit of progenitor of white dwarf is greater than 4.5M⊙. The cluster age on the basis of LF for brightest stars is given by ~ 8×107yr and all stars in the cluster lie along the single age sequence in the C-M diagram without showing a large dispersion from the sequence.

The sample of sub dwarfs are selected from LHS catalogue on the bases of the reduced proper motion diagram utilizing Chui criteria, and confirmed with the available photometric and/or kinematic data. Among them, 20 sub dwarfs have trigonometric parallaxes with accuracy better than 20 % . The color­absolute magnitude relation is derived with them. By adopting this color-magnitude relation and V / V m method, we have derived the sub dwarf luminosity function over the absolute magnitude range of M v = 4.5 and 9.5. This halo luminosity function is consistent with that of Eggen(1987). By adopting the available mass-luminosity relations for halo stars, we have found that the halo IMF is steeper than disk IMFs of Scalo(1986) and Salpter(1955) in this small mass region.

The initial mass functions (IMF) of 15 selected open clusters are investigated by making use of C-M diagrams and theoretical evolutionary tracks. Among 15 clusters 13 have peaks in their IMFs and it is thought to be not due to incomplete photometry but to intrinsic property. The mass where IMF peaks is about 2 M ⊙ and it is similar to that of the second peak in the IMF of nearby field stars. The mean slope of the IMF in the high mass part is 1.9 ± 0.6 with some variations among clusters. But there seems to be no correlation between the slope and physical parameters such as ages, diameters, and metal abundances.

Combining the luminosity functions of main sequence stars in 3 associations and 22 open clusters, the initial luminosity function and mass function for these clusters are derived. For stars of m > 0.6 m ⊙ , they are well consistent with those for the field stars.

The Wielen dip over the ragne of 6 < M υ < 9 in the luminosity function (LF) for the solar neighborhood stars could be explained by the combination of two different IMFs which yields the age of 13 billion years of the solar neighborhood. This smaller age than the Galactic age, 15 billion years indicates the slow collapse model of the Galaxy, solving the G-dwarf problem. Two different IMFs suggest two different mechanisms for star formation in the solar neighborhood.

The present day mass functions of main sequence stars in the well observed open clusters, Hyades, Praesepe, Pleiades, NGC 654 and NGC 6530 arc derived and compared with those computed from the model of time-dependent initial mass function and star formation rate. The agreements between the observed and computed present day mass functions suggest the importance of fragmentation process at the early phase and fragment interaction at the later phase of cluster evolution. This process of star formation is different from that related to the evolution of the solar neighborhood, and also could explain the lack of low mass stars observed in some open clusters.

Weibull analyses given to the initial mass function (IMF) deduced by Miller and Scalo (1979) have shown that the mass dependence of IMF is an exp [ − α m ] - form in low mass range while in the high mass range it assumes an exp [ − α √ m ] / √ m -form with the break-up being at about the solar mass. Various astrophysical reasonings are given for identifying the exp [ − α m ] and exp [ − α √ m ] / √ m with halo and disk star characteristics, respectively. The physical conditions during the halo formation were such that low mass stars were preferentially formed and those in the disk high mass stars favoured. The two component nature of IMF is in general accord with the dichotomies in various stellar properties.