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Milky Way Galaxy

Open Star Clusters

Groupings of stars come in all sizes, from binary and triplet stars to massive galaxies of many trillions of stars.  The open star clusters fall at the low-mass end of this progression.  They comprise hundreds of gravitationally-bound stars in a volume of order 10 parsecs radius.  They are important to astrophysicists because they provide some of the best star samples for testing stellar evolution theories.

Open clusters are scattered throughout the Galactic disk.  Most of them are very far from us; only ten of them lie within 300 parsecs of the Sun.  The closest of these are visible as clusters to the unaided eye.  The Pleiades (M45) are familiar to stargazers living in the northern hemisphere; this cluster in the Taurus constellation is the third closest open cluster at about 118 parsecs from the Sun.[1]  The closest open cluster is the Hyades, which is 46 parsecs from the Sun.[2]  This cluster, which is about 10° degrees to the south-east of the Pleiades, lies in the direction of Aldebaran (α Tauri), the brightest star in Taurus (Aldebaran, with a distance of 18.5 parsecs from the Sun, is not a member of the Hyades cluster).  The second-closest open cluster is also the name of a constellation, Coma Berenices.  This cluster is 87 parsecs from the Sun.[1]  In the Southern hemisphere, the open cluster IC 2602 in the Carina constellation is visibly a cluster to the unaided eye; this cluster is 152 parsecs from the Sun.[1] Other open clusters are visible to the unaided eye, some of which are farther than 300 parsecs from the Sun.

To the unaided eye, open star clusters appear to be very small.  After all, the Pleiades cluster is also called the seven sisters; it must have only seven stars in it, right?  Personally, I see less than a dozen stars in this cluster on a good night.  In fact, most of the stars in an open clusters are too faint to see with the unaided eye.  Estimates through various methods for the mass of the Pleiades cluster range from 600 to 4,000 solar masses;[3] this uncertainty reflects the difficulty of distinguishing the cluster stars from the large number of field stars in the field of view.  The Hyades cluster has a mass of 300 to 400 solar masses, with 300 observed stars associated with the cluster.[2]  Mass estimates for other clusters are comparable.  What appears as a small collection of free stars is in fact a large collection of weakly-bound stars.

Open star clusters benefit astronomers and astrophysicists by being sets of stars that differ only in their masses at birth and in their angular momenta.  The stars within an open cluster formed at the same time from the same molecular cloud.  This gives all the stars within a cluster the same chemical composition at birth and the same age.  In contrast, the individual stars of the Galactic plane different not only in the masses and angular momenta, but also in their ages and in their chemical compositions at birth.  This multiplicity of free-parameters complicates the study of stars.  For instance, the initial mass, the initial chemical composition, and the age of a star determining the star's color and luminosity.  The stars of a single open cluster show theorists how initial mass alone affects color and luminosity, and the comparison of stars from two different clusters shows theorists how initial chemical composition affects color and luminosity and how stars evolve over time.

As a practical matter, when one plots each star of a cluster on a diagram of luminosity versus color—the Hertzsprung-Russell (H-R) diagram for the cluster—one finds that the stars follow a narrow path from the red, low-luminosity corner of the diagram to the blue, high-luminosity corner.  In contrast, field stars plotted in this way are scattered all over the H-R diagram because of their different ages and chemical compositions.  In the H-R diagram for a cluster, the stars in the red, low-luminosity part of the curve are burning hydrogen at their cores, and the stars in the blue, high-luminosity part of the curve are exhausting their core hydrogen, have ceased burning hydrogen in their cores, or are now burning helium at their cores.  The theorist tries to replicate this curve on the H-R diagram by calculating the evolution of stars of different masses but the same initial composition to the same point in time.  This is how astrophysicists test their theories of stellar evolution.

One important result from a model comparison to a cluster's H-R diagram is an estimate of a cluster's age.  It is found by identifying the stars that have exhausted their core hydrogen.  The low-mass stars, which are in the hydrogen-burning phase of their lives, follow a path on the H-R diagram called the main-sequence.  The high-mass stars that have exhausted their core hydrogen deviate from the main-sequence, becoming more luminous than when they were on the main-sequence.  The extent to which the massive stars deviate from the main sequence defines an age for the cluster.  The Hyades cluster is estimated to be 625±50 million years old.  The Pleiades cluster is estimated to be 100 million years old.  Only a handful of open clusters are more than 1 billion years old.

Besides providing tests of stellar evolution, open clusters enable astronomers to study how stars lose angular momentum over time.  In particular, astronomers study how magnetic fields slow the rotation of a star.  Stars like the Sun expel winds that carry magnetic fields.  These fields enable the winds to torque the stars.  The stronger the magnetic field, the farther out a wind can travel before its torque on a star ceases.  Studies of the rate at which stars spin in different clusters shows how a star's rate of rotation changes over 1 billion years because of this torque.

The structure of several open clusters has been established, and it is like that of their larger cousins, the globular clusters and the elliptical galaxies.  An open cluster has a small core surrounded by a halo with a density that falls with increasing radius.  The core typically has a radius of 2 parsecs, while the halo typically extends beyond a 10 parsec tidal radius.  The stars within a cluster are segregated, with heavier stars and binary stars concentrated towards the core, and lighter stars predominately in the halo.  The orbital velocities of stars within the core of a cluster relative to the cluster itself are less than 1 km s−1.

The difference between an open cluster and any other large stellar system is that the open cluster is a delicate structure.  The outer limits of the open cluster are defined by the tidal force exerted by the Galaxy on the cluster.  Stars that move much beyond the point where the cluster's gravitational force equals the Galaxy's tidal force are stripped from the cluster.  As a practical matter, stars move with the cluster as long as they stay within two tidal radii of the cluster center.  As a cluster orbits the Galactic center, it encounters massive molecular clouds.  Each encounter is like a collision, transferring energy and momentum between the two systems, and like in an inelastic collision between two objects, each encounter heats the cluster, causing the stars in the cluster to move at higher velocities.  Pumping energy into a cluster in this way causes it to expand and lose stars.  Over 1 billion years, these encounters cause an open cluster to totally dissipate.

[1]Robichon, N., Arenou, F., Mermilliod, J.-C., and Turon, C.  “Open Clusters with Hipparcos: I. Mean Astrometric Parameters.”  Astronomy and Astrophysics 345 (1999): 471–484.

[2]Perryman, M.A.C., et al. “The Hyades: Distance, Structure, Dynamics, and Age.”  Astronomy and Astrophysics 331 (1998): 81–120.

[3]Raboud, D., and Mermilliod, J.-C. “Investigation of the Pleiades Cluster: IV. The Radial Structure.”  Astronomy and Astrophysics 329 (1998): 101–114.

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