Astronomy & Astrophysics

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$\begin{figure} {\psfig{figure=2241fig1a.ps,width=8cm} } \par\vspace*{2mm} {\psfig{figure=2241fig1b.ps,width=8cm} }\end{figure}$ Figure 1: The predicted decrease in cluster mass due to stellar evolution and disruption for Z=0.020 and four values of the initial cluster masses: 10³, 10⁴, 10⁵ and $10^6~\mbox{$M_{\odot}$ }$ . Top panel: $\mbox{$t_0$ }=2$ Myr; lower panel: $\mbox{$t_0$ }=30$ Myr. The full lines give the exact decrease derived by numerical solution of the differential Eq. (4), and the dotted lines give the approximation (Eq. (6)). Notice the excellent agreement. The dashed lines gives the decrease in mass due to stellar evolution only.
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In the text

$\begin{figure} {\psfig{figure=2241fig2a.ps,width=8.2cm}\hspace*{2mm} \psfig{fig... ...dth=8.2cm}\hspace*{2mm} \psfig{figure=2241fig2d.ps,width=8.2cm} }\end{figure}$ Figure 2: Comparison of the decrease of the cluster mass with time between the results of the N-body simulations by BM03 ( left) and our description ( right) for clusters of different initial numbers of stars, $N_{\rm i}$ or mass $M_{\rm i}$ . The mass has been corrected to first order for the mass lost by stellar evolution. In all figures the time t is scaled to $\mbox{$t^{\rm 95\%}_{\rm dis}$ }$ , i.e. the time when 95% of the cluster mass is lost due to stellar evolution and disruption. The upper figures are for mass versus time and the lower figures are for log (Mass) versus log (time). Notice the strong similarity between the results of the N-body simulations and our simple description (Eq. (6)).
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In the text

$\begin{figure} {\psfig{figure=2241fig3.ps,width=8.4cm} }\end{figure}$ Figure 3: Comparison between the mass decrease of a cluster of $8.9\times 10^3~M_{\odot}$ predicted by N-body simulation of BM03 (full line) and our analytic approximation for $\mbox{$t_0$ }=18$ Myr (dashed and dotted line). The mass decrease has been corrected for the mass lost by stellar evolution. The timescale is normalized to the time when 95 or 96.5% of the initial mass is lost (see text).
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In the text

$\begin{figure} {\psfig{figure=2241fig4.ps,width=8.2cm} }\end{figure}$ Figure 4: The changes in the mass distribution (Eq. (15)) of a sample of clusters as a function of their age, in the case where stellar evolution can be neglected. We adopted a cluster initial mass function in the range of $10^2<M<10^6~\mbox{$M_{\odot}$ }$ with $\alpha =2.0$ and a disruption parameter $\gamma =0.62$ . The different curves refer to different ages, which are parametrized by log $t/\mbox{$t_0$ }$ . The maximum mass decreases with age due to disruption.
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In the text

$\begin{figure} {\psfig{figure=2241fig5.ps,width=8.2cm} }\end{figure}$ Figure 5: The age distribution of cluster samples formed at a constant formation rate, in cases where stellar evolution can be neglected. We adopted a cluster initial mass function in the range of $M_{\rm min}<M<M_{\rm max}$ with $M_{\rm max}=10^6~\mbox{$M_{\odot}$ }$ and different values of $M_{\rm min}$ . We adopted $\alpha =2.0$ and a disruption parameter $\gamma =0.62$ . The curves are labeled with log $(M_{\rm min}/\mbox{$M_{\odot}$ })$ .
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In the text

$\begin{figure} \par\includegraphics[width=8.2cm,clip]{2241fig6.ps} \end{figure}$ Figure 6: Top: the surface density distribution projected onto the Galactic plane of open clusters in the solar neighbourhood from the homogeneous Kharchenko et al. (2005) catalogue. Error bars indicate 1 $\sigma$ statistical uncertainties. The surface density is almost constant up to at least 600 pc and possibly 1 kpc. Bottom: the ratio between the numbers of old (> $2.5\times 10^8$ yr) and young (< $2.5\times 10^8$ yr) clusters as a function of distance. The ratio is almost constant up to 1 kpc.
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In the text

$\begin{figure} {\psfig{figure=2241fig7.ps,width=8.4cm} }\end{figure}$ Figure 7: The age histogram in units of number per year, in logarithmic age-bins of 0.2 dex, of 114 open clusters within d<600 pc from Kharchenko et al. (2005). The distributions are plotted for two sets of bins, shifted by 0.1 dex, with and without squares respectively. The error bars indicate the 1 $\sigma$ statistical uncertainty. The distribution decreases to older ages, with a small bump around $\log~ (t/{\rm yr}) \simeq 8.6$ . For $\log~ (t/{\rm yr}) < 7.5$ the distribution is uncertain due to large error bars.
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In the text

$\begin{figure} {\psfig{figure=2241fig8.ps,width=8.4cm} }\end{figure}$ Figure 8: The mass-versus-age diagram of 114 clusters of the Kharchenko et al. (2005) catalogue within a distance of 600 pc. The mass is derived from the number of main sequence stars with V<11.50.
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In the text

$\begin{figure} {\psfig{figure=2241fig9.ps,width=8.4cm} }\end{figure}$ Figure 9: The mass histogram of 114 clusters of the Kharchenko et al. (2005) catalogue within a distance of 600 pc. The steep edge at the low mass side suggests that the sample is complete for clusters with a mass $M \mathrel{\copy\gabox}100~\mbox{$M_{\odot}$ }$ .
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In the text

$\begin{figure} {\psfig{figure=2241fig10a.ps,width=8.4cm} } \par\vspace*{2mm} {\psfig{figure=2241fig10b.ps,width=8.4cm} }\end{figure}$ Figure 10: Comparison between observed and predicted age histogram of clusters in the solar neighbourhood within d<600 pc. The data are fitted to predicted relations based on our analytical expression of the cluster disruption with various values of $\mbox{$t_0$ }$ , normalized to the point at $\log~ (t/{\rm yr})=8.1$ . The clusters are formed in the mass range of $10^2 < \mbox{$M_{\rm cl}$ }< 10^5$ $M_{\odot }$ , with a CIMF of slope -2.0. Top figure: predictions for a constant CFR. The dotted line indicates the prediction if there was no cluster disruption, but only mass loss by stellar evolution. The shorter the disruption time, the steeper the decrease towards high ages. At young ages the shortest disruption time corresponds to the largest formation rate and vice versa. Lower figure: the best fit for an assumed burst between 250 and 600 Myr ago, with a CFR that was 2.5 times higher than before and after the burst.
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In the text

$\begin{figure} {\psfig{figure=2241fig8.ps,width=8.4cm} }\end{figure}$	Figure 8: The mass-versus-age diagram of 114 clusters of the Kharchenko et al. (2005) catalogue within a distance of 600 pc. The mass is derived from the number of main sequence stars with V<11.50.
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$\begin{figure} {\psfig{figure=2241fig9.ps,width=8.4cm} }\end{figure}$	Figure 9: The mass histogram of 114 clusters of the Kharchenko et al. (2005) catalogue within a distance of 600 pc. The steep edge at the low mass side suggests that the sample is complete for clusters with a mass $M \mathrel{\copy\gabox}100~\mbox{$M_{\odot}$ }$ .
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