The initial luminosity and mass functions of the Galactic open clusters

Abstract

(... 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 $a=0.41\pm 0.01$, 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 $\alpha =1.66\pm 0.14$ in the range $\log M_c/M_{\odot }=\mathrm{3.37...4.93}$ and $\alpha =0.82\pm 0.14$ in the range $\log M_c/M_{\odot }=\mathrm{1.7...3.37}$. The average mass of open clusters at birth is $4.5\cdot 10^3{M}_{\odot }$, which should be compared to the average observed mass of about $700M_{\odot }$. 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 $22M_{\odot }{\mathrm{pc}}^{-2}$ 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.

10 pages, 8 figures, accepted for publication in A&A

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