In contrast to open clusters, most globular clusters remain gravitationally bound together for time periods comparable to the lifespans of most of their stars. Strong tidal interactions with other large masses result in the dispersal of some stars, leaving behind "tidal tails" of stars removed from the cluster. After formation, the stars in the globular cluster begin to interact gravitationally with each other. The velocities of the stars steadily change, and the stars lose any history of their original velocity. The characteristic interval for this to occur is the
relaxation time, related to the characteristic length of time a star needs to cross the cluster and the number of stellar masses. The relaxation time varies by cluster, but a typical value is on the order of one billion years. Although globular clusters are generally spherical in form, ellipticity can form via tidal interactions. Clusters within the Milky Way and the Andromeda Galaxy are typically
oblate spheroids in shape, while those in the Large Magellanic Cloud are more elliptical.
Radii is classified as an open cluster. Astronomers characterize the morphology (shape) of a globular cluster by means of standard radii: the core radius (
rc), the
half-light radius (
rh), and the tidal or Jacobi radius (
rt). The radius can be expressed as a physical distance or as a subtended angle in the sky. Considering a radius around the core, the surface luminosity of the cluster steadily decreases with distance, and the core radius is the distance at which the apparent surface luminosity has dropped by half. A comparable quantity is the half-light radius, or the distance from the core containing half the total luminosity of the cluster; the half-light radius is typically larger than the core radius. Most globular clusters have a half-light radius of less than ten parsecs (pc), although some globular clusters have very large radii, like
NGC 2419 (rh = 18 pc) and
Palomar 14 (rh = 25 pc). The half-light radius includes stars in the outer part of the cluster that happen to lie along the line of sight, so theorists also use the half-mass radius (
rm)the radius from the core that contains half the total mass of the cluster. A small half-mass radius, relative to the overall size, indicates a dense core.
Messier 3 (M3), for example, has an overall visible dimension of about 18
arc minutes, but a half-mass radius of only 1.12 arc minutes. The tidal radius, or
Hill sphere, is the distance from the center of the globular cluster at which the external gravitation of the galaxy has more influence over the stars in the cluster than does the cluster itself. This is the distance at which the individual stars belonging to a cluster can unbound by the galaxy. The tidal radius of M3, for example, is about forty arc minutes, or about 113 pc.
Mass segregation, luminosity and core collapse In most Milky Way clusters, the surface brightness of a globular cluster as a function of decreasing distance to the core first increases, then levels off at a distance typically 1–2 parsecs from the core. About 20% of the globular clusters have undergone a process termed "core collapse". The luminosity in such a cluster increases steadily all the way to the core region. is the second most luminous globular cluster in the Milky Way, after Omega Centauri. Models of globular clusters predict that core collapse occurs when the more massive stars in a globular cluster encounter their less massive counterparts. Over time, dynamic processes cause individual stars to migrate from the center of the cluster to the outside, resulting in a net loss of
kinetic energy from the core region and leading the region's remaining stars to occupy a more compact volume. When this gravothermal instability occurs, the central region of the cluster becomes densely crowded with stars, and the
surface brightness of the cluster forms a
power-law cusp. A massive black hole at the core could also result in a luminosity cusp. Over a long time, this leads to a concentration of massive stars near the core, a phenomenon called
mass segregation. The dynamical heating effect of binary star systems works to prevent an initial core collapse of the cluster. When a star passes near a binary system, the orbit of the latter pair tends to contract, releasing energy. Only after this primordial supply of energy is exhausted can a deeper core collapse proceed. In contrast, the effect of
tidal shocks as a globular cluster repeatedly passes through the plane of a spiral galaxy tends to significantly accelerate core collapse. Core collapse may be divided into three phases. During a cluster's adolescence, core collapse begins with stars nearest the core. Interactions between
binary star systems prevents further collapse as the cluster approaches middle age. The central binaries are either disrupted or ejected, resulting in a tighter concentration at the core. The interaction of stars in the collapsed core region causes tight binary systems to form. As other stars interact with these tight binaries they increase the energy at the core, causing the cluster to re-expand. As the average time for a core collapse is typically less than the age of the galaxy, many of a galaxy's globular clusters may have passed through a core collapse stage, then re-expanded. is located in the Large Magellanic Cloud. The HST has provided convincing observational evidence of this stellar mass-sorting process in globular clusters. Heavier stars slow down and crowd at the cluster's core, while lighter stars pick up speed and tend to spend more time at the cluster's periphery. The cluster
47 Tucanae, made up of about one million stars, is one of the densest globular clusters in the Southern Hemisphere. This cluster was subjected to an intensive photographic survey that obtained precise velocities for nearly fifteen thousand stars in this cluster. The overall luminosities of the globular clusters within the Milky Way and the Andromeda Galaxy each have a roughly
Gaussian distribution, with an average magnitude Mv and a variance σ2. This distribution of globular cluster luminosities is called the Globular Cluster Luminosity Function (GCLF). For the Milky Way, Mv = , σ = . The GCLF has been used as a "
standard candle" for measuring the distance to other galaxies, under the assumption that globular clusters in remote galaxies behave similarly to those in the Milky Way.
N-body simulations Computing the gravitational interactions between stars within a globular cluster requires solving the
N-body problem. The naive computational cost for a dynamic simulation increases in proportion to
N 2 (where N is the number of objects), so the computing requirements to accurately simulate a cluster of thousands of stars can be enormous. In 2010 a low-density globular cluster's lifetime evolution was able to be directly computed, star-by-star. Completed N-body simulations have shown that stars can follow unusual paths through the cluster, often forming loops and falling more directly toward the core than would a single star orbiting a central mass. Additionally, some stars gain sufficient energy to escape the cluster due to gravitational interactions that result in a sufficient increase in velocity. Over long periods of time this process leads to the dissipation of the cluster, a process termed evaporation. The typical time scale for the evaporation of a globular cluster is 1010 years. or gradual shedding of stars from its outer layers.
Binary stars form a significant portion of stellar systems, with up to half of all
field stars and
open cluster stars occurring in binary systems. The present-day binary fraction in globular clusters is difficult to measure, and any information about their initial binary fraction is lost by subsequent dynamical evolution. Numerical simulations of globular clusters have demonstrated that binaries can hinder and even reverse the process of core collapse in globular clusters. When a star in a cluster has a gravitational encounter with a binary system, a possible result is that the binary becomes more tightly bound and kinetic energy is added to the solitary star. When the massive stars in the cluster are sped up by this process, it reduces the contraction at the core and limits core collapse.
Intermediate forms lies about 15,000 light-years from Earth, in the constellation of
Ophiuchus. Cluster classification is not always definitive; objects have been found that can be classified in more than one category. For example, BH 176 in the southern part of the Milky Way has properties of both an open and a globular cluster. In 2005 astronomers discovered a new, "extended" type of star cluster in the Andromeda Galaxy's halo, similar to the globular cluster. The three new-found clusters have a similar star count to globular clusters and share other characteristics, such as stellar populations and metallicity, but are distinguished by their larger sizeseveral hundred light years acrossand some hundred times lower density. Their stars are separated by larger distances; parametrically, these clusters lie somewhere between a globular cluster and a
dwarf spheroidal galaxy. It is unclear why the Milky Way lacks such clusters; Andromeda is unlikely to be the sole galaxy with them, but their presence in other galaxies remains unknown. ==Tidal encounters==