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Local Open Clusters in the compilation by Piskunov et al. (2006) seem at first to have a random distribution in the galactic plane, with the local spiral arms barely visible and no obvious age gradients or patterns. They have been known to be grouped into star complexes (Efremov 1995) and moving groups (Eggen 1989) for a long time, but there has been little other patterning recognized. Now this is beginning to change. The groupings and complexes are better mapped using new velocity and distance information. Piskunov et al. (2006) and Kharchenko et al. (2005) catalogued "Open Cluster Complexes," in which many clusters have similar positions, velocities and ages inside each complex. For example, one is in the Hyades region and another is in Perseus-Auriga. Perseus-Auriga surrounds the Sun and lies in the galactic plane over a region 1 kpc in size with a log(age) between 8.3 and 8.6, in years. Gould's Belt is another Open Cluster Complex. It has a log age less than 7.9 and lies in a thin plane tilted to the main galactic disk by an angle of 20° surrounding the Sun.

de la Fuente Marcos & de la Fuente Marcos (2008) identified five Open Cluster Complexes from the positions and velocities of clusters within 2.5 kpc of Sun. These are: Scutum-Sagittarius at a galactic longitude of l = 12° and a distance of 1300 pc, Cygnus at l = 75° and 1400 pc, Cassiopeia-Perseus at l = 132° and 2000 pc, Orion at l = 200° and 500 pc, and Centaurus-Carina at l = 295° and 2000 pc. These authors suggest that Open Cluster Complexes are fragments from common gas clouds. Within their limiting distance of 2.5 kpc, the total gas mass in the Milky Way is ~ 5 × 107 Modot, considering a disk thickness of 300 pc and an average density of 1 cm-3. This means that each of the 5 giant gas clouds that made these Open Cluster Complexes had a mass of ~ 107 Modot. This is the Jeans mass in the galactic disk (~ sigma4 / [G2 Sigmagas] for dispersion sigma and mass column density Sigmagas), as discussed in Lecture 1. Open Cluster Complexes could be the remnants of star formation in giant clouds formed by gravitational instabilities in the Milky Way gas layer.

Elias, Alfaro & Cabrera-caño (2009) studied Gould's Belt using the Catalogue of Open Cluster Data (Kharchenko et al. 2005). They found an interesting correlation that the cluster fraction is large for the Orion OB association region and small for the Sco-Cen association. The cluster fraction is the ratio of the stellar mass that forms in bound clusters to the total stellar mass that forms at the same time. The rest of the stars form in unbound groups and associations. There is a gradient in the young cluster (age < 10 Myr) fraction of star formation and in the cluster density over the 700 pc distance separating these two associations. This suggests that star formation prefers clusters when the pressure is high, as in Orion, which is a more active region than Sco-Cen. High pressure could be a factor in bound cluster formation if high-pressure cores are more difficult to disrupt and their star formation efficiencies end up higher when star formation stops. High pressure also corresponds to a broader density probability distribution function, and so a higher mass fraction of gas exceeding the critical efficiency for bound cluster formation (Sect. 7).

This lecture reviews interstellar and stellar hierarchical structure, which gives patterns in the positions and ages of young stars and clusters. Related to this is the formation of the bound clusters themselves, and the cluster mass function. A more complete review of this topic is in Elmegreen (2010).

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