We use the open clusters ( OCs ) with known parameters available in the WEBDA database and in recently published papers to derive properties related to the disk structure such as the thin-disk scale height , displacement of the Sun above the Galactic plane , scale length and the OC age-distribution function .
The sample totals 654 OCs , consisting basically of Trumpler types I to III clusters whose spatial distribution traces out the local geometry of the Galaxy .
We find that the population of OCs with ages younger than 200 Myr distributes in the disk following an exponential-decay profile with a scale height of \mbox { $ z _ { h } $ } = 48 \pm 3 pc .
For the clusters with ages in the range 200 Myr to 1 Gyr we derive \mbox { $ z _ { h } $ } = 150 \pm 27 pc .
Clusters older than 1 Gyr distribute nearly uniformly in height from the plane so that no scale height can be derived from exponential fits .
Considering clusters of all ages we obtain an average scale height of \mbox { $ z _ { h } $ } = 57 \pm 3 pc .
We confirm previous results that z _ { h } increases with Galactocentric distance .
The scale height implied by the OCs younger than 1 Gyr outside the Solar circle is a factor \sim 1.4 - 2 larger than z _ { h } of those interior to the Solar circle .
We derive the displacement of the Sun above the Galactic plane as \mbox { $ z _ { \odot } $ } = 14.8 \pm 2.4 pc , which agrees with previous determinations using stars .
As a consequence of the completeness effects , the observed radial distribution of OCs with respect to Galactocentric distance does not follow the expected exponential profile , instead it falls off both for regions external to the Solar circle and more sharply towards the Galactic center .
We simulate the effects of completeness assuming that the observed distribution of the number of OCs with a given number of stars above the background , measured in a restricted zone outside the Solar circle , is representative of the intrinsic distribution of OCs throughout the Galaxy .
Two simulation models are considered in which the intrinsic number of observable stars are distributed : ( i ) assuming the actual positions of the OCs in the sample , and ( ii ) random selection of OC positions .
As a result we derive completeness-corrected radial distributions which agree with exponential disks throughout the observed Galactocentric distance range 5–14 kpc , with scale lengths in the range \mbox { $ R _ { D } $ } = 1.5 - 1.9 kpc , smaller than those inferred by means of stars .
In particular we retrieve the expected exponential-disk radial profile for the highly depleted regions internal to the Solar circle .
The smaller values of R _ { D } may reflect intrinsic differences in the spatial distributions of OCs and stars .
We derive a number-density of Solar-neighbourhood ( with distances from the Sun \mbox { $ d _ { \odot } $ } \leq 1.3 kpc ) OCs of \mbox { $ \rho _ { \odot } $ } = 795 \pm 70 kpc ^ { -3 } , which implies a total number of ( Trumpler types I to III ) OCs of \sim 730 of which \sim 47 \% would already have been observed .
Extrapolation of the completeness-corrected radial distributions down to the Galactic center indicates a total number of OCs in the range ( 1.8 - 3.7 ) \times 10 ^ { 5 } .
These estimates are upper-limits because they do not take into account depletion in the number of OCs by dynamical effects in the inner parts of the Galaxy .
The observed and completeness-corrected age-distributions of the OCs can be fitted by a combination of two exponential-decay profiles which can be identified with the young and old OC populations , characterized by age scales of \sim 100 Myr and \sim 1.9 Gyr , respectively .
This rules out evolutionary scenarios based on constant star-formation and OC-disruption rates .
Comparing the number of observed embedded clusters and candidates in the literature with the expected fraction of very young OCs , derived from the observed age-distribution function , we estimate that 3.4–8 % of the embedded clusters do actually emerge from the parent molecular clouds as OCs .