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| Plummer model | |
|---|---|
| Name | Plummer model |
| Caption | Spherical mass distribution used in stellar dynamics |
| Field | Astrophysics |
| Introduced | 1911 |
| Developer | H. C. Plummer |
Plummer model The Plummer model is an analytic, spherically symmetric model for the spatial distribution of mass in star clusters and galaxies. It was introduced to provide a simple, convergent potential-density pair useful in studies of dynamical evolution, relaxation, and N‑body simulations. The model is widely used in the literature on H. C. Plummer, James Jeans, Subrahmanyan Chandrasekhar, Henri Poincaré, and in codes developed at institutions such as Princeton University, Cambridge University, and Max Planck Institute for Astrophysics.
The Plummer model originated in early 20th‑century studies of stellar systems and was proposed by H. C. Plummer to represent globular clusters and centrally concentrated stellar associations. It complements other classic models such as the Isothermal sphere, King model, Hernquist profile, de Vaucouleurs law, Jaffe model, and Navarro–Frenk–White profile used by researchers at Harvard College Observatory, Royal Astronomical Society, and California Institute of Technology. Over time the model has been applied in comparative studies alongside work by S. Chandrasekhar, Eddington, and groups at European Southern Observatory and Space Telescope Science Institute.
The Plummer density profile is given by a spherically symmetric function with scale length a and total mass M, providing a simple analytic potential. As used in analytical derivations by James Binney and Scott Tremaine, the model admits closed‑form expressions for the gravitational potential and cumulative mass, facilitating tasks performed at University of Cambridge and University of Oxford. The model contrasts with the multi-parameter families studied by J. Navarro, C. S. Frenk, and S. D. M. White and is mathematically tractable in the manner of work from University of California, Berkeley and Institute for Advanced Study.
The Plummer sphere yields finite central density and finite total mass, features exploited in dynamical analyses by Subrahmanyan Chandrasekhar and in stability studies at Massachusetts Institute of Technology. Its potential supports bound orbits and simple expressions for velocity dispersion used in comparisons with observational programs at European Space Agency missions and surveys by Sloan Digital Sky Survey teams. Relaxation times, two‑body encounters, and core collapse phenomena have been examined in contexts involving Globular Cluster NGC 6397, Omega Centauri, and theoretical frameworks influenced by P. H. Chavanis and Douglas Heggie.
Plummer models serve as initial conditions for N‑body experiments in studies of star cluster evaporation, tidal stripping, and galaxy mergers, often employed in simulations by groups at Max Planck Institute for Astronomy, Carnegie Institution for Science, and Kavli Institute for Theoretical Physics. Observational comparisons link Plummer fits to surface brightness profiles measured by Hubble Space Telescope, Gaia astrometry surveys, and photometry from Very Large Telescope programs. The model is used in teaching materials at University of Tokyo, University of Chicago, and Cornell University to illustrate relaxation, virial equilibrium, and mass segregation in systems such as M15, M92, and other cluster catalogs curated by the International Astronomical Union.
Several generalizations extend the Plummer form to anisotropic, axisymmetric, or multi‑component systems in work by Lynden-Bell, Aarseth, and Dehnen. Multi‑component Plummer models combine stellar and dark matter components in hybrid models used by researchers at Institute of Astronomy, Cambridge and Princeton University Observatory. Other variants interpolate between Plummer and Hernquist or NFW profiles in comparative studies by Marc Balcells, Alan Dressler, and teams at European Research Council projects, and are used in analyses tied to Lambda Cold Dark Matter motivated structure formation scenarios discussed at KIPAC and Flatiron Institute.
The analytic simplicity of the Plummer potential makes it a standard choice for initial conditions in tree codes, direct N‑body integrators, and particle‑mesh methods developed in software packages from groups at University of Cambridge, University of Illinois Urbana-Champaign, and University of Washington. Implementations appear in widely used codes and libraries associated with projects at Max Planck Institute for Astrophysics, Argonne National Laboratory, and Los Alamos National Laboratory. Benchmarks comparing Plummer initial conditions are common in performance studies presented at conferences organized by American Astronomical Society and International Astronomical Union, and in tutorials produced by Harvard & Smithsonian and computational astrophysics courses at ETH Zurich.
Category:Astrophysical models