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| King (1962) models | |
|---|---|
| Name | King (1962) models |
| Author | Ivan R. King |
| Year | 1962 |
| Field | Astrophysics |
King (1962) models King (1962) models are a family of isotropic, lowered isothermal stellar distribution functions introduced to describe the structure of globular clusters and spherical stellar systems. Developed by Ivan R. King in 1962, these models connect theoretical stellar dynamics with observational surface brightness and velocity-dispersion profiles of systems studied by observers at institutions such as the Mount Wilson Observatory, Palomar Observatory, Harvard College Observatory, and the Royal Observatory, Edinburgh. King models have been widely applied in comparisons involving data from facilities like the Hubble Space Telescope, the European Southern Observatory, the Keck Observatory, and space missions such as Gaia.
King (1962) models arose amid mid-20th-century efforts to reconcile theoretical equilibrium distributions with the observed truncation of stellar systems reported by surveys from the Copenhagen Observatory, the Lick Observatory, and the photographic work compiled at the Cambridge Observatory. Influences include earlier work on isothermal spheres by James Jeans, the energy-truncated distributions discussed by Lynden-Bell and Spitzer, and the Fokker–Planck treatments advanced by Chandrasekhar. The models addressed observational tensions highlighted in studies of clusters cataloged by Shapley, Harlow Shapley, and the globular cluster compilations of William Herschel and later observers at the Royal Greenwich Observatory.
Mathematically, King (1962) models specify a lowered isothermal distribution function f(E) that is constant for energies E below a cutoff and zero above, drawing on formalism developed by Lynden-Bell and Arthur Eddington. The formalism embeds the distribution into the Poisson equation encountered in stellar dynamics treatments by Binney and Tremaine, and parallels methods used in kinetic theory by Boltzmann and Maxwell. Key parameters include a dimensionless central potential W0 linked to concentration parameters used in catalogs by Harris and structural scalings comparable to those in models by Plummer and King 1966 variants. The model yields self-consistent density profiles ρ(r) and projected surface densities Σ(R) that can be compared with fits popularized in work by Meylan, Dubath, and analysts at the Instituto de Astrofísica de Canarias.
Physically, King (1962) models have been applied to model globular clusters in the Milky Way, dwarf spheroidal galaxies studied by Irwin and Hatzidimitriou, and compact stellar systems observed in surveys by Sloan Digital Sky Survey and follow-ups at Magellan Observatory. They serve to interpret surface-brightness profiles collected by observers associated with Carnegie Institution for Science, to estimate core and tidal radii often tabulated alongside catalogs maintained by NASA, and to derive mass-to-light ratios contextualized with population-synthesis results from groups at Padova Observatory and Yale University. The models also guide comparisons with dynamical friction calculations by Chandrasekhar and evaporation timescales discussed in studies by Spitzer.
Analytical properties of King (1962) models include finite total mass and a truncated radius analogous to tidal radii originally considered in analyses of cluster–galaxy interactions by Roche and later quantified in work by King (1962). The model's phase-space structure follows entropy considerations similar to those in the statistical mechanics literature of Boltzmann and Gibbs, while its moment equations relate to Jeans-equation approaches used by Binney and Tremaine. Limiting cases connect to the singular isothermal sphere discussed by Ostriker and the Plummer sphere introduced by Plummer, providing asymptotic behaviors useful in analytic approximations employed by researchers at Princeton University and Cambridge University.
Numerical implementation of King (1962) models appears in N-body simulations run on hardware and software environments developed at institutions like CERN, Los Alamos National Laboratory, and university clusters at MIT and Caltech. Techniques include direct integration exploited by groups led by Aarseth, Monte Carlo realizations following methods of Heggie and Stodółkiewicz, and Fokker–Planck solvers influenced by work at Monash University and Geneva Observatory. Simulations enable comparisons with observational data pipelines from Subaru Telescope, Very Large Telescope, and missions such as Hubble Space Telescope and Gaia.
Empirical tests use surface-brightness and velocity-dispersion profiles measured by teams at Vera C. Rubin Observatory (formerly LSST), Hubble Space Telescope programs, and spectrographs on Keck Observatory and European Southern Observatory platforms. Fits often reference the globular cluster catalog compiled by Harris and kinematic surveys published by research groups at University of Cambridge and University of California, Berkeley. Comparisons with alternative models—such as Wilson models attributed to Wilson or multi-mass models from Gunn and Griffin—are routine in papers appearing in journals by the American Astronomical Society and the Royal Astronomical Society.
Extensions include multi-mass King models developed following conceptual lines from Michie and Gunn and Griffin, anisotropic generalizations influenced by Osipkov and Merritt, and rotating or axisymmetric variants studied by groups at Max Planck Institute for Astrophysics and Institute for Advanced Study. Generalizations connect to modern distribution-function-based modeling frameworks used in analyses associated with Gaia-era dynamics, comparisons with equilibrium solutions in cosmological simulations by teams at Millennium Simulation collaborators, and hybrid approaches integrating stellar-evolution tracks from Geneva Observatory and dynamical modeling techniques from Princeton University.
Category:Stellar dynamics