Usually, models of globular star clusters are created by analyzing their luminosity and other observation parameters. The goal of this work is to create stable models of globular clusters based on the laws of mechanics. It is necessary to set the coordinates, velocities and masses of the stars so that as a result of their gravitational interaction the globular cluster is not destroyed. This is not an easy task, and it has been solved in this paper. Using an exact solution of the axisymmetric gravitational interaction of N-bodies, single-layer spherical structures were created. They are combined into multilayer models of globular clusters. An algorithm and a program for their creation is described. As a result of solving the problem of gravitational interaction of N bodies, evolution of 5-, 10-, and 15-layer structures was studied. During the inter-body interaction, there proceeds a transition from the initial specially organized structure to a structure with bodies, uniformly distributed in space. The number of inter-body collisions decreases, and the globular cluster model passes into the stable form of its existence. The collisions of bodies and the acquisition of rotational motion and thermal energy by them are considered. As a result of the passage to scaled dimensions, the results were recalculated to the conditions of globular star clusters. The periods of rotation and the temperatures of merged stars are calculated. Attention is paid to a decreased central-body mass in the analyzed models of globular star clusters.
References
[1]
King, I.R., Hedemann, E.J., Hodge, S.M. and White, R.E. (1968) The Structure of Star Clusters. V. Star Counts in 54 Globular Clusters. The Astronomical Journal, 73, 456-491. https://doi.org/10.1086/110648
[2]
Harris, W.E. (1996) A Catalog of Parameters for Globular Clusters in the Milky Way. The Astronomical Journal, 112, 1487-1488. https://doi.org/10.1086/118116
[3]
Heggie, D. and Hut, P. (2003). The Gravitational Million-Body Problem. Cambridge University Press. https://doi.org/10.1017/cbo9781139164535
[4]
Orlov, V.V., Rubinov, A.V. (2008) N-Body Problem in Stellar Dynamics: Textbook. St. Petersburg State University.
[5]
Portegies Zwart, S.F., McMillan, S.L.W. and Gieles, M. (2010) Young Massive Star Clusters. Annual Review of Astronomy and Astrophysics, 48, 431-493. https://doi.org/10.1146/annurev-astro-081309-130834
[6]
Heggie, D.C. (2014) Modelling and Understanding Globular Clusters. ISIMA.
[7]
Loktin, A.V. and Marsakov, V.A. (2009) Lectures on Stellar Astronomy. Educational and Scientific Monograph. Southern Federal University. (In Russian)
[8]
Llorente de Andrés, F. (2024) Some Old Globular Clusters (and Stars) Inferring That the Universe Is Older than Commonly Accepted. American Journal of Astronomy and Astrophysics, 11, 1-13. https://doi.org/10.11648/j.ajaa.20241101.11
[9]
Baumgardt, H., Makino, J. and Hut, P. (2005) Which Globular Clusters Contain Intermediate-Mass Black Holes? The Astrophysical Journal, 620, 238-243. https://doi.org/10.1086/426893
[10]
Mackey, A.D., Wilkinson, M.I., Davies, M.B. and Gilmore, G.F. (2008) Black Holes and Core Expansion in Massive Star Clusters. Monthly Notices of the Royal Astronomical Society, 386, 65-95. https://doi.org/10.1111/j.1365-2966.2008.13052.x
[11]
Cuevas-Otahola, B., Mayya, Y.D., Puerari, I. and Rosa-González, D. (2020) Mass-Radius Relation of Intermediate-Age Disc Super Star Clusters of M82. Monthly Notices of the Royal Astronomical Society, 500, 4422-4438. https://doi.org/10.1093/mnras/staa3513
[12]
Tully, R.B., Rizzi, L., Dolphin, A.E., Karachentsev, I.D., Karachentseva, V.E., Makarov, D.I., et al. (2006) Associations of Dwarf Galaxies. The Astronomical Journal, 132, 729-748. https://doi.org/10.1086/505466
[13]
Aarseth, S.J. (2003). Gravitational N-Body Simulations. Cambridge University Press. https://doi.org/10.1017/cbo9780511535246
[14]
Baumgardt, H. (2016) n-Body Modelling of Globular Clusters: Masses, Mass-to-Light Ratios and Intermediate-Mass Black Holes. Monthly Notices of the Royal Astronomical Society, 464, 2174-2202. https://doi.org/10.1093/mnras/stw2488
[15]
King, I.R. (1966) The Structure of Star Clusters. III. Some Simple Dvriamical Models. The Astronomical Journal, 71, 64-75. https://doi.org/10.1086/109857
[16]
McLaughlin, D.E. (2000) Binding Energy and the Fundamental Plane of Globular Clusters. The Astrophysical Journal, 539, 618-640. https://doi.org/10.1086/309247
[17]
Smulsky, J.J. (2019) The Upcoming Tasks of Fundamental Science. Sputnik+ Publishing House. (In Russian) http://www.ikz.ru/~smulski/Papers/InfPrZaFN.pdf
[18]
Smulsky, J.J. (2003) The Axisymmetric Problem of Gravitational Interaction of N-Bodies. Math Modeling, 15, 27-36. (In Russian) http://www.ikz.ru/~smulski/smul1/Russian1/IntSunSyst/Osvnb4.doc
[19]
Smulsky, J.J. (2015) Exact Solution to the Problem of N Bodies Forming a Multi-Layer Rotating Structure. SpringerPlus, 4, Article No. 361. https://doi.org/10.1186/s40064-015-1141-1
[20]
Smulsky, J.J. (2016) Distributed Structures on the Sphere. Deposited in VINITI 22.08.2016, No. 112-V2016. (In Russian) http://www.ikz.ru/~smulski/Papers/SphDsSt2.pdf
[21]
Smulsky, J.J. (2019) Periodic Orbits of N Bodies on a Sphere. Cosmic Research, 57, 459-470. https://doi.org/10.1134/s001095251906008x
[22]
Smulsky, J.J. (2015) Multilayer Coulomb Structures: Mathematical Principia of Microcosm Mechanics. Open Access Library Journal, 2, 1-47. https://doi.org/10.4236/oalib.1101661
Smulsky, J.J. (2018) Future Space Problems and Their Solutions. Nova Science Publishers. http://www.ikz.ru/~smulski/Papers/InfFSPS.pdf
[25]
Smulsky, J.J. (2012) The System of Free Access Galactica to Compute Interactions of N-Bodies. International Journal of Modern Education and Computer Science, 4, 1-20. https://doi.org/10.5815/ijmecs.2012.11.01
[26]
Smulsky, J. (2014) Module of System Galactica with Coulomb’s Interaction. International Journal of Modern Education and Computer Science, 6, 1-13. https://doi.org/10.5815/ijmecs.2014.12.01
[27]
Smul’skii, I.I. and Krotov, O.I. (2015) Change of Angular Momentum in the Dynamics of the Solar System. Cosmic Research, 53, 237-245. https://doi.org/10.1134/s0010952515020094
[28]
Smulsky, J.J. (2019) Angular Momentum Due to Solar System Interactions. In: Gordon, O., Ed., A Comprehensive Guide to Angular Momentum, Nova Science Publishers, 1-40. http://www.ikz.ru/~smulski/Papers/CGAngMom1_2Cv.pdf
[29]
Laskar, J. (1996) Marginal Stability and Chaos in the Solar System. Symposium—International Astronomical Union, 172, 75-88. https://doi.org/10.1017/s0074180900127160
[30]
Laskar, J., Correia, A.C.M., Gastineau, M., Joutel, F., Levrard, B. and Robutel, P. (2004) Long Term Evolution and Chaotic Diffusion of the Insolation Quantities of Mars. Icarus, 170, 343-364. https://doi.org/10.1016/j.icarus.2004.04.005
[31]
Melnikov, V.P. and Smulsky, J.J. (2009) Astronomical Theory of Ice Ages: New Approximations. Solutions and Challenges. Academic Publishing House “Geo”. http://www.ikz.ru/~smulski/Papers/AsThAnE.pdf
[32]
Smulsky, J.J. and Smulsky, Y.J. (2012) Dynamic Problems of the Planets and Asteroids, and Their Discussion. International Journal of Astronomy and Astrophysics, 2, 129-155. https://doi.org/10.4236/ijaa.2012.23018
[33]
Smulsky, J.J. (1999) The Theory of Interaction. Publishing House of Novosibirsk University. (In Russian) http://www.ikz.ru/~smulski/TVfulA5_2.pdf
[34]
Smulsky, J.J. (2004) The Theory of Interaction. Cultural Information Bank. http://www.ikz.ru/~smulski/TVEnA5_2.pdf
