astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...

, dynamical mass segregation is the process by which heavier members of a gravitationally bound system, such as a star cluster, tend to move toward the center, while lighter members tend to move farther away from the center.

Equipartition of kinetic energy

During a close encounter of two members of the cluster, the members exchange both

energy Energy () is the physical quantity, quantitative physical property, property that is transferred to a physical body, body or to a physical system, recognizable in the performance of Work (thermodynamics), work and in the form of heat and l ...

and

momentum In Newtonian mechanics, momentum (: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. ...

. Although energy can be exchanged in either direction, there is a statistical tendency for the

kinetic energy In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion. In classical mechanics, the kinetic energy of a non-rotating object of mass ''m'' traveling at a speed ''v'' is \fracmv^2.Resnick, Rober ...

of the two members to equalize during an encounter; this statistical phenomenon is called equipartition, and is similar to the fact that the expected kinetic energy of the molecules of a gas are all the same at a given temperature. Since kinetic energy is proportional to mass times the square of the speed, equipartition requires the less massive members of a cluster to be moving faster. The more massive members will thus tend to sink into lower orbits (that is, orbits closer to the center of the cluster), while the less massive members will tend to rise to higher orbits. The time it takes for the kinetic energies of the cluster members to roughly equalize is called the relaxation time of the cluster. A relaxation time-scale assuming energy is exchanged through two-body interactions was approximated in the textbook by Binney & Tremaine as :

t_\mathrm=\frac \times t_\mathrm \ ,

where

N

is the number of stars in the cluster and

t_\mathrm

is the typical time it takes for a star to cross the cluster. This is on the order of 100 million years for a typical

globular cluster A globular cluster is a spheroidal conglomeration of stars that is bound together by gravity, with a higher concentration of stars towards its center. It can contain anywhere from tens of thousands to many millions of member stars, all orbiting ...

with radius 10

parsec The parsec (symbol: pc) is a unit of length used to measure the large distances to astronomical objects outside the Solar System, approximately equal to or (AU), i.e. . The parsec unit is obtained by the use of parallax and trigonometry, and ...

s consisting of 100 thousand stars. The most massive stars in a cluster can segregate more rapidly than the less massive stars. This time-scale can be approximated using a toy model developed by Lyman Spitzer of a cluster where stars only have two possible masses (

m_1

and

m_2

). In this case, the more massive stars (mass

m_1

) will segregate in the time :

t_\mathrm=\frac \times t_\mathrm \ .

Outward segregation of white dwarfs was observed in the globular cluster 47 Tucanae in a HST study of the region.

Primordial mass segregation

Primordial mass segregation is non-uniform distribution of masses present at the formation of a cluster. The argument that a star cluster is primordially mass segregated is typically based on a comparison of virialization timescales and the cluster's age. However, several dynamical mechanisms to accelerate virialization compared to two-body interactions have been examined. In star-forming regions, it is often observed that O-type stars are preferentially located in the center of a young cluster.

Evaporation

After relaxation, the speed of some low mass members can be greater than the

escape velocity In celestial mechanics, escape velocity or escape speed is the minimum speed needed for an object to escape from contact with or orbit of a primary body, assuming: * Ballistic trajectory – no other forces are acting on the object, such as ...

of the cluster, which results in these members being lost to the cluster. This process is called evaporation. (A similar phenomenon explains the loss of lighter gases from a planet, such as hydrogen and helium from the Earth—after equipartition, some molecules of sufficiently light gases at the top of the atmosphere will exceed the escape velocity of the planet and be lost.) Through evaporation, most

open cluster An open cluster is a type of star cluster made of tens to a few thousand stars that were formed from the same giant molecular cloud and have roughly the same age. More than 1,100 open clusters have been discovered within the Milky Way galaxy, and ...

s eventually dissipate, as indicated by the fact that most existing open clusters are quite young.

Globular cluster A globular cluster is a spheroidal conglomeration of stars that is bound together by gravity, with a higher concentration of stars towards its center. It can contain anywhere from tens of thousands to many millions of member stars, all orbiting ...

s, being more tightly bound, appear to be more durable.

In the Galaxy

The relaxation time of the

Milky Way The Milky Way or Milky Way Galaxy is the galaxy that includes the Solar System, with the name describing the #Appearance, galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars in other arms of the galax ...

galaxy is approximately 10 trillion years, on the order of thousand times the age of the galaxy itself. Thus, any observed mass segregation in our galaxy must be almost entirely primordial.

References

Sources