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.

I present a model to explain the mass segregation and shallow mass functions observed in the central parts of starburst stellar clusters. The model assumes that the initial pre-stellar cores mass function resulting from the turbulent fragmentation of the proto-cluster cloud is significantly altered by the cores coalescence before they collapse to form stars. With appropriate, yet realistic parameters, this model based on the competition between cores coalescence and collapse reproduces the mass spectra of the well studied Arches cluster. Namely, the slopes at the intermediate and high mass ends, as well as the peculiar bump observed at 6M⊙ This coalescence-collapse process occurs on a short timescale of the order of the free fall time of the proto-cluster cloud (i.e., a few 104 years), suggesting that mass segregation in Arches and similar clusters is primordial. The best fitting model implies the total mass of the Arches cluster is 1.45x105M⊙. which is slightly higher than the often quoted, but completeness affected, observational value of a few 104M⊙ The model implies a star formation efficiency of ~30 percent which implies that the Arches cluster is likely to a gravitationally bound system.

We have analyzed H and Ks -band images of the Arches cluster obtained using the NIRC2 instrument on Keck with the laser guide star adaptive optics (LGS AO) system. With the help of the LGS AO system, we were able to obtain the deepest ever photometry for this cluster and its neighborhood, and derive the background-subtracted present-day mass function (PDMF) down to 1.3M⊙ for the 5"-9" annulus of the cluster. We find that the previously reported turnover at 6M⊙ is simply due to a local bump in the mass function (MF), and that the MF continues to increase down to our 50 % completeness limit (1.3M⊙) with a power-law exponent of Γ= -0.91 for the mass range of 1.3 < M/M⊙ < 50. Our numerical calculations for the evolution of the Arches cluster show that the Γ values for our annulus increase by 0.1-0.2 during the lifetime of the cluster, and thus suggest that the Arches cluster initially had Γ of -1.0~-1.1 which is only slightly shallower than the Salpeter value.

We present a theoretical formalism by which the global and the local mass functions of dark matter substructures (dark subhalos) can be analytically estimated. The global subhalo mass function is defined to give the total number density of dark subhalos in the universe as a function of mass, while the local subhalo mass function counts only those sub halos included in one individual host halo. We develop our formalism by modifying the Press-Schechter theory to incorporate the followings: (i) the internal structure of dark halos; (ii) the correlations between the halos and the subhalos; (iii) the subhalo mass-loss effect driven by the tidal forces. We find that the resulting (cumulative) subhalo mass function is close to a power law with the slope of ${\~}$ 수식 이미지 -1, that the subhalos contribute approximately 10% of the total mass, and that the tidal stripping effect changes the subhalo mass function self-similarly, all consistent with recent numerical detections.

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.

The luminosity function (LF) and present day mass function(PDMF) for main sequence (MS) stars in the Praesepe and Hyades clusters are derived, showing the Wielen Dip which occurs at Mv = 9m in the LF. This dip is about 2 mag fainter than the case for the Pleiades cluster whose Wielen Dip position is consistent with that for the solar neighborhood field stars. The Wielen Dips of these clusters are reproduced by using a bimodal initial mass function (IMF).