View source for Astronomy:Mass segregation

{{Short description|Gravitational process, eg in star clusters}}
[[File:Messier 30 Hubble WikiSky.jpg|thumb|266x266px|Many globular clusters, such as the 13-Gyr old cluster M30 (pictured), are mass segregated.]]

In [[Astronomy:Astronomy|astronomy]], '''dynamical mass segregation''' is the process by which heavier members of a gravitationally bound system, such as a [[Astronomy:Star cluster|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 [[Physics:Energy|energy]] and [[Physics:Momentum|momentum]].  Although energy can be exchanged in either direction, there is a statistical tendency for the [[Physics:Kinetic energy|kinetic energy]] 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 <ref>{{Cite book |last=Binney |first=James |url=https://www.worldcat.org/oclc/195749071 |title=Galactic dynamics |date=2008 |publisher=Princeton University Press |isbn=978-0-691-13026-2 |edition=2nd |location=Princeton |oclc=195749071}}</ref> as
:<math>t_\mathrm{relax}=\frac {N}{8\ln N}\times t_\mathrm{cross} \ ,</math>
where <math>N</math> is the number of stars in the cluster and <math> t_\mathrm{cross}</math> 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 [[Astronomy:Globular cluster|globular cluster]] with radius 10 [[Astronomy:Parsec|parsec]]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 [[Biography:Lyman Spitzer|Lyman Spitzer]] of a cluster where stars only have two possible masses (<math>m_1</math> and <math>m_2</math>). In this case, the more massive stars (mass <math>m_1</math>) will segregate in the time
:<math>t_\mathrm{m_1}=\frac {m_2}{m_1}\times t_\mathrm{relax} \ .</math>

Outward segregation of white dwarfs was observed in the globular cluster [[Astronomy:47 Tucanae|47 Tucanae]] in a [[Astronomy:Hubble Space Telescope|HST]] study of the region.<ref name=SpaceDaily-2015-05-18>{{cite news |url= http://www.spacedaily.com/reports/Hubble_Catches_Stellar_Exodus_in_Action_999.html |title= Hubble Catches Stellar Exodus in Action |date= 18 May 2015 |publisher= Space Daily }}</ref>

== Primordial mass segregation ==

[[File:W40 star-forming region.jpg|thumb|Mass segregation is occasionally seen in clusters in [[Astronomy:Star formation|star-forming regions]] like W40 (pictured).<ref name=kuhn10>{{Cite journal| last = Kuhn | first = M. A. | display-authors = etal | year=2010 | title = A Chandra Observation of the Obscured Star-forming Complex W40 | journal = Astrophysical Journal | volume = 725 | issue=2 | pages = 2485–2506 | doi=10.1088/0004-637X/725/2/2485 | bibcode=2010ApJ...725.2485K|arxiv = 1010.5434 | s2cid = 119192761 }}</ref>]]

'''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 [[Physics:Virial theorem|virialization]] timescales and the cluster's age. However, several dynamical mechanisms to accelerate virialization compared to two-body interactions have been examined.<ref name=mcmillan07>{{Cite journal| last = McMillan | first = S. L. | display-authors = etal | year=2007 | title = A Dynamical Origin for Early Mass Segregation in Young Star Clusters | journal = Astrophysical Journal | volume = 655 | issue=1 | pages = L45–L49 | doi=10.1086/511763 | bibcode=2007ApJ...655L..45M|arxiv = astro-ph/0609515 }}</ref> In star-forming regions, it is often observed that [[Astronomy:O-type star|O-type star]]s 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 [[Astronomy:Escape velocity|escape velocity]] 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 [[Astronomy:Open cluster|open cluster]]s eventually dissipate, as indicated by the fact that most existing open clusters are quite young.  [[Astronomy:Globular cluster|Globular cluster]]s, being more tightly bound, appear to be more durable.

== In the Galaxy ==
The relaxation time of the [[Astronomy:Milky Way|Milky Way]] 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.{{cn|date=October 2021}}

== See also ==
*{{annotated link|Physics:N-body problem}}
*{{annotated link|Physics:Virial theorem}}
*{{annotated link|Astronomy:Messier 67}}
*{{annotated link|Astronomy:Willman 1}}
*{{annotated link|Astronomy:Trapezium Cluster|Orion Nebula Cluster}}
*{{annotated link|Astronomy:Westerhout 40}}

== References ==
{{reflist}}

=== Sources ===
* {{cite journal
 | author=Ian A. Bonnell, Melvyn B. Davies
 | title=Mass segregation in young stellar clusters
 | journal=[[Organization:Monthly Notices of the Royal Astronomical Society|Monthly Notices of the Royal Astronomical Society]]
 | date=1998
 | volume=295
 | issue=3
 | pages=691–698
 | doi=10.1046/j.1365-8711.1998.01372.x
|bibcode = 1998MNRAS.295..691B | doi-access=free
 }}

*{{cite book
  |last = Merritt
  |first = David
  |title=Dynamics and Evolution of Galactic Nuclei
  |publisher=Princeton University Press
  |date=2013
  |isbn =  978-0-691-12101-7
  |oclc = 820123438
 }}

*{{cite book
  |last = Spitzer
  |first = Lyman S. (Jr)
  |title=Dynamical Evolution of Globular Clusters
  |publisher=Princeton University Press
  |date=1987
  |isbn = 0-691-08309-6
}}

* {{cite journal
 | author=White, S. D. M.
 | title=Mass segregation and missing mass in the Coma cluster
 | journal=Monthly Notices of the Royal Astronomical Society
 | date=April 1977
 | volume=179
 | issue=2
 | pages=33–41
 | bibcode=1977MNRAS.179...33W
 | doi=10.1093/mnras/179.2.33
| doi-access=free
 }}

[[Category:Astrophysics]]
[[Category:Effects of gravitation]]

{{Sourceattribution|Mass segregation (astronomy)|1}}