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(... abridged) The observed luminosity function can be constructed in a range of absolute integrated magnitudes $I_{M_V}= [-10, -0.5]$ mag, i.e. about 5 magnitudes deeper than in the most nearby galaxies. It increases linearly from the brightest limit to a turnover at about $I_{M_V}approx-2.5$. The slope of this linear portion is $a=0.41pm0.01$, which agrees perfectly with the slope deduced for star cluster observations in nearby galaxies. (...) We find that the initial mass function of open clusters (CIMF) has a two-segment structure with the slopes $alpha=1.66pm0.14$ in the range $log M_c/M_odot=3.37...4.93$ and $alpha=0.82pm0.14$ in the range $log M_c/M_odot=1.7...3.37$. The average mass of open clusters at birth is $4.5cdot 10^3 M_odot$, which should be compared to the average observed mass of about $700 M_odot$. The average cluster formation rate derived from the comparison of initial and observed mass functions is $bar{upsilon}=0.4 mathrm{kpc}^{-2}mathrm{Myr}^{-1}$. Multiplying by the age of the Galactic disc (T = 13 Gyr) the predicted surface density of Galactic disc field stars originating from dissolved open clusters amounts to $22 M_odot mathrm{pc}^{-2}$ which is about 40% of the total surface density of the Galactic disc in the solar neighbourhood. Thus, we conclude that almost half of all field stars were born in open clusters, a much higher fraction than previously thought.
Over the past decades open clusters have been the subject of many studies. Such studies are crucial considering that the universality of the Initial Mass Function is still a subject of current investigations. Praesepe is an interesting open cluster f
We provide a review of the current status of several topics on the ages, distances, and mass functions of open clusters, with a particular emphasis on illuminating the areas of uncertainty. Hipparcos has obtained parallaxes for nearby open clusters t
We present UBVRI photometry of the open cluster NGC 2422 (age $sim 10^8$ yr) down to a limiting magnitude $Vsimeq19$. These data are used to derive the Luminosity and Mass Functions and to study the cluster spatial distribution. By considering the co
In this paper we compare the mass function slopes of Galactic globular clusters recently determined by Sollima & Baumgardt (2017) with a set of dedicated N-body simulations of star clusters containing between 65,000 to 200,000 stars. We study cluster
We predict near-infrared luminosity functions of young (5 Myr to 1 Gyr) star clusters by combining evolutionary models of very low-mass ($1 M_J$ to $0.15 M_{odot}$) dwarfs with empirical bolometric corrections. We identify several characteristic feat