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.

We present a method for deriving most optimal filter system by which the accuracy of derived physical quantities can be maximized. Using Kurucz(1978)'s model atmospheres, an optimal four filter system for F and G dwarfs is suggested, for which mean wavelengths are located at 3400|AA , 3850|AA , 4190|AA , and 4600 |AA with half-bandwidth of 200|AA . It is found that 35, 38 and 42 filters of the DDO system and the S t r ¨ o m g r e n u and ν filters are close to those of the most optimal system.

For the well observed 16 globular clusters with known metal abundance (Z), the helium abundances (Y) and ages are determined by various methods, and the relations between Y, Z and age are examined. The luminosity L R R of RR Lyrae stars is known to be dependent of evolutionary models and pulsation theory in the sense that the pulsation theory and horizontal branch (HB) models yield the anticorrelation between L R R and Z whereas main sequence (MS) and red giant branch (RGB) models yield the direct correlation between them. Similarly the anticorrelation between Y and Z is obtained from the HB models and pulsation theory whereas the direct correlation between them is obtained when the RGB model is applied. The current evolutionary models yield the anticorrelation between Z and age of clusters whenever the direct correlation between Y and Z holds. However when the anticorrelation between Y and Z is applied for age determination, the similar age of clusters is obtained as shown by Sandage (1982b). The ages, which are determined by the fitting of C-M diagrams to isochrones in the ( M v , B-V)-plane, suggest the two different chemical enrichment processes, which could be accounted for by the disk-halo model for the chemical evolution of the Galaxy (Lee and Ann 1981). Also it is known that the R-method is very useful for Y-determination and the derived Y's show the increasing rate of Δ Y Δ Z ≃ 0.5 which is comparable to the observed value of Δ Y Δ Z ≃ 0.3 from HII regions and planetary nebulae by Peimbert and Torres-Peimbert (1976). In this case, the age-metallicity relation of globular clusters could be explained by the disk-halo model.

We present the data of photoelectric photometric observations of BW Vul carried out for four nights during the period of 1982 ∼ 1984 . The light curves with asymmetric shape show a stillstand on the ascending branch at phase of ϕ ≈ 0.85 just before the maximum light, and also the ampitude and shape of light curves are changed from night to night. Using all the published data, a new ephemeris of maximum time is derived, in which the period of light variation is P = 0 d .20102977 and its increasing rate is 2.2 see/century.

Five different calibrations of metal abundances of globular clusters are examined and these are compared with metallicity ranking parameters such as ( S p ) c , . Q39 and IR-indices. Except for the calibration [ F e / H ] H by the high dispersion echelle analysis. the other calibration scales are correlated with the morphological parameters of red giant branch. In the [ F e / H ] H -scale. the clusters later than ∼ F 8 have nearly a constant metal abundance. [ F e / H ] H ≃ − 1.05 , regradless of morphological characteristics of horizontal branch and red giant branch. By the two fundamental calibration scales of [ F e / H ] L (derived by the low dispersion analysis) and [ F e / H ] Δ s (derived by the spectral analysis of RR Lyrae stars). the globular clusters are divided into the halo clusters with [Fe/H]<-1.0 and the disk clusters confined within the galactocentric distance τ G = 10 k p c and galactic plane distance |z|=3 kpc. In this case the abundance gradient is given by d[Fe/H]/ d r G ≈ − 0.05 k p c − 1 and d[Fe/H]/ d | z | ≃ − 0.08 k p c − 1 within τ G = 20 k p c and |z|=10 kpc, respectively. According to these characteristics of the spatial distribution of globular clusters. the chemical evolution of the galactic globular clusters can be accounted for by the two-zone (disk-halo) slow collapse model when the [ F e / H ] L -or [ F e / H ] Δ s -scale is applied. In the case of [ F e / H ] H -scale, the one-zone fast collapse model is preferred for the evolution of globular clusters.

The well observed 8 open clusters, NGC 6530, 2264, 654, 129, 2168, Pleiades, Praesepe and Hyades were selected on the basis of photometric observation and proper motion study. The luminosity functions (LF) and mass functions (MF) of these clusters are different with cluster age and they could be divided into three age groups (t< 10 7 yrs, 10 7 10 8 yrs, 10 8 10 9 yrs). From these LF's and MF's, the mean LF and MF of the open clusters are derived and these functions suggest the time-dependent initial mass function (IMF) and the variation of observed MF with cluster age.

UBV photoelectric observations were carried out for bright stars in M67 and the masses of clump stars and giant stars were derived in M67 and the other old open clusters, NGC 188, NGC 2420, NGC 2506 and IC 4651. The mean mass of clump stars in the five clusters ranges m = 0.5 ∼ 1.0 m ⊙ , and its ratio to the mean mass of giant stars is about 0.83. The number ratio of blue stragglers to the stars brighter than the turn-off of main sequence increases with cluster age whereas that of clump stars decreases with age. These results imply that the clump stars and blue stragglers are at the phase of horizontal branch evolution.

Analyses of an integrated form N ( τ ) = ∫ ∞ τ n ( τ ) d τ of the distribution of cluster ages, rather than its differential form n ( τ ) , demonstrate that the observed distribution has clusters older than about 500 million years in a significant excess over theoretical model distributions. Considerations on cluster disruption processes show that a single disruption time-scale, frequently employed by current theoretical models, is no longer an adequate parameter for describing survival probability of clusters over wide age range, because different initial conditions of these clusters produce corresponding spreads in their lifetimes. To take into account for the spread in initial conditions, we have introduced an age-dependent disruption time, and deduced its age-dependence from the present-day age distribution of clusters. Results show a distinct two-stage variation: The newly introduced disruption time stays constant at about 50 million years for clusters younger than about 100 million years, while for clusters older than that it increases monotonically with the cluster age. This leads us to conclude that clusters experience different types of disrupting causes as they get old.

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.

During the period between January and November in 1982, UBV photoelectric observations were made for 48 stars in NGC 2264, 66 stars in IC 1805 and 22 stars in IC 348. From these observations, various physical parameters such as distance, mean color excess, total-to-selective extinction ratio and mean age of the clusters were determined. Making use of these parameters, the star formation rates were examined for IC 348 and NGC 2264. The overall formation rate is found to be increase rapidly during the period of the active star formation. The age spread (ranging from 5 × 10 6 yrs to 10 7 yrs) of stars in a given cluster appears to be real which occurs in the extremely young open clusters.

For ∼ 240 nearby stars their age and mass were determined and kinematic parameters determined for 362 stars, applying Woolley's three-dimensional potential. Metallicity and kinematic parameters of these stars were correlated with their age, suggesting the slow collapse ( t ≳ a few billion years) of the Galaxy and the initial rapid enrichment in metal abundance ( Δ Z ≈ 1 / 3 Z 1 (present) for ∼ 4 × 10 8 yrs). The late slow enrichment rate is given by d ( Z / Z ⊙ ) / d t = 5.9 ∼ 7.0 ± 3.4 per Gyr.

Defining a metal parameter ( S p ) c , which is related to the morphological parameters of C-M diagrams, we have estimated metal abundances for 97 globular clusters in our Galaxy. A correlation between absolute magnitude of the horizontal branch and metal abundance is derived, which is used for the determining distances to globular clusters whose visual magnitudes of the horizontal branch are known. The space distribution of globular clusters and the chemical evolution of the halo are examined. Our analysis suggests an initial mean gradient of metallicity to be d[Fe/H]/ d r G = -0.06 k p c − 1 for the halo in galactocentric distance, r G <20 kpc. Our findings also imply a slow collapse of protogalaxy.

From B ¨ o h m -Vitense's atmospheric model calculations, the relations, [ T e , (B-V)] and [B.C, (B-V)] with respect to heavy element abundance were obtained. Using these relations and evolutionary model calculations of Rood, and Sweigart and Gross, analytic expressions for some physical parameters relating to the C-M diagrams of globular clusters were derived, and they were applied to 21 globular clusters with observed transition periods of RR Lyrae variables. More than 20 different parameters were examined for each globular cluster. The derived ranges of some basic parameters are as follows; Y = 0.21 ∼ 0.33 , Z = 1.5 × 10 − 4 ∼ 4.5 × 10 − 3 , a g e , t = 9.5 ∼ 19 × 10 9 years, mass for red giants, m R G = 0.74 m ⊙ ∼ 0.91 m ⊙ , mass for RR Lyrae stars, m R R = 0.59 m ⊙ ∼ 0.75 m ⊙ , the visual magnitude difference between the turnoff point and the horizontal branch (HB), ${\Delta}V_{to}=3.1{\sim}3.4(<{\Delta}V_{to}>=3.32)$, the color of the blue edge of RR Lyrae gap, $(B-V)_{BE}=0.17{\sim}0.21=(<(B-V)_{BE}>=0.18),\;[\frac{m}{L}]_{RR}=-1.7{\sim}-1.9$, mass difference of m R R relative to m R G , ( m R G − m R R ) / m R G = 0.0 ∼ 0.39 . It was found that the ranges of derived parameters agree reasonably well with the observed ones and those estimated by others. Some important results obtained herein can be summarized as follows; (i) There are considerable variations in the initial helium abundance and in age of globular clusters. (ii) The radial gradient of heavy element abundance does exist for globular clusters as shown by Janes for field stars and open clusters. (iii) The helium abundance seems to have been increased with age by massive star evolution after a considerable amount (Y>0.2) of helium had been attained by the Big-Bang nucleosynthesis, but there is not seen a radial gradient of helium abundance. (iv) A considerable amount of heavy elements ( Z ∼ 10 − 3 ) might have been formed in the inner halo ( r G C <10 kpc) from the earliest galactic co1lapse, and then the heavy element abundance has been slowly enriched towards the galactic center and disk, establishing the radial gradient of heavy element abundance. (v) The final galactic disk formation might have taken much longer by about a half of the galactic age than the halo formation, supporting a slow, inhomogeneous co1lapse model of Larson. (vi) Of the three principal parameters controlling the morphology of C-M diagrams, it was found that the first parameter is heavy clement abundance, the second age and the third helium abundance. (vii) The globular clusters can be divided into three different groups, AI, BI and CII according to Z, Y an d age as well as Dickens' HB types. BI group clusters of HB types 4 and 5 like M 3 and NGC 7006 are the oldest and have the lowest helium abundance of the three groups. And also they appear in the inner halo. On the other hand, the youngest AI clusters have the highest Z and Y, and appear in the innermost halo region and in the disk. (viii) From the result of the clean separations of the clusters into three groups, a three dimensional classification with three parameters, Z, Y and age is prsented. (ix) The anomalous C-M diagrams can be expalined in terms of the three principal parameters. That is, the anomaly of NGC 362 and NGC 7006 is accounted for by the smaller age of the order of 1 ∼ 2 × 10 9 years rather than by the helium abundance difference, compared with M 3. (x) The difference in two Oosterhoff types I and II can be explained in terms of the mean mass difference of RR Lyrae variables rather than in terms of the helium abundance difference as suggested by Stobie. The mean mass of the variables in Oosterhoff type I clusters is smaller by 0.074 m ⊙ which is exactly consistent with Rood's estimate. Since it was found that the mean mass of RR Lyrae stars increases with decreasing Z, the two Oosterhoff types can be explained substantially by the metal abundance difference; the type II has Z< 3.4 × 10 − 4 , and the type I has higher Z than the type II.

The four dimensional classification of globular dusters with the parameters, Z, Y, age and HB type is presented defining two new parameters. ( B − V ) 1 / 2 a n d S 3 / 2 which are shown to be tightly correlated with Kinman's spectral types and the helium abundances obtained from the R-method, respectively. The Z- and Y- abundances are derived from ( B − V ) 1 / 2 a n d S 3 / 2 , respectively, and the latter parameters determine the age class of clusters with help of Dickens' HB type, which is a function of Z. Y and age. For the examined forty two globular clusters the computed range at Z and Y are 1.5×10 -4 ≤ Z ≤ 4.5×10 -2 and 0.23 ≤ Y ≤ 0.41. The age difference between the oldest (HB type 1) and the youngest (HB type 7) clusters is roughly estimated to be 2 − 4 × 10 9 years. Using these four parameters the known anomalous C-M diagrams seem to be reasonably interpreted without taking into account some complicate parameters such as unusually overabundant heavy elements, mass loss and mass spread, etc. The four dimensional scheme strongly suggests the slow successive collapses of the proto-Galaxy rather than a single fast collapse, and by this slow collapse model the inversion of chemical abundance gradient in the Galaxy can be explained. It is also shown that the clump position along the RGB near the HB level removes down to the fainter magnitude as the Z(Y)- abundance increases (decreases).