Scaling relations in dynamical evolution of star clusters


Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), P.O. Box 11365-9161, Zanjan, Iran


We have carried out a series of small scale collisional N-body calculations of single-mass star clusters to investigate the dependence of the lifetime of star clusters on their initial parameters. Our models move through an external galaxy potential with a logarithmic density profile and they are limited by a cut-off radius. In order to find scaling relations between the lifetime of star clusters and their initial conditions including the initial mass, size and galactocentric distance, we vary the initial conditions and measure the final half mass radius and dissolution time of each cluster. We show that the lifetime of star clusters scales with the initial half-mass radius, galactocentric distance, and initial mass as Tdiss~R0.15h, Tdiss~R0.94 G , and TdissM0.45i , respectively. Our results are in remarkable agreement with the previous works by Baumgardt & Makino (2003) and Haghi et al. (2014) who have found some scaling relations for the lifetime of multi-mass star clusters with a large number of stars including the stellar evolution. Moreover, we find that all clusters with the same mass and different initial half-mass radius, converge to an equilibrium value of half-mass radius, after core collapse that scales with galactocentric distance as Rh~R0:8 G. We show that the exponent in this scaling relation is slightly larger for the massive star clusters.


[1] Aarseth S. J., 2003, Gravitational N-Body Simulations, Cambridge University Press, Cambridge
[2] Aarseth S. J., Heggie D. C., 1998, MNRAS, 297, 794
[3] Allen C., Santillan A., 1991, RMxAA, 22, 255
[4] Baumgardt H., Hut P., Heggie D. C., 2002, MNRAS, 336, 1069
[5] Baumgardt H., Makino J., 2003, MNRAS, 340, 227
[6] Haghi, H., Hoseini-Rad, M., Zonoozi A. H., K¨upper, A. H. W., 2014, MNRAS, 444, 3699
[7] Haghi H., Zonoozi A. H., Kroupa P., Banerjee S., Baumgardt H., 2015b, MNRAS, 454, 3872.
[8] Harris W. E., 2010, arXiv, arXiv:1012.3224
[9] Heggie, D. C., & Hut, P. 2003, The Gravitational Million-Body Problem, Cambridge Univ. Press, Cambridge
[10] Hurley J. R., Pols O. R., Tout C. A., 2000, MNRAS, 315, 543
[11] Hurley J. R., Tout C. A., Pols O. R., 2002, MNRAS, 329, 897
[12] K¨upper A. H. W., Kroupa P., Baumgardt H., 2008, MNRAS, 389, 889
[13] Mackey A. D., Wilkinson M. I., Davies M. B., Gilmore G. F., 2008, MNRAS, 386, 65
[14] Madrid J. P., Hurley J. R., Sippel A. C., 2012, ApJ, 756, 167 (MHS12)
[15] Plummer H. C., 1911, MNRAS, 71, 460
[16] Shin J., Kim S. S., Yoon S.-J., Kim J., 2013, ApJ, 762, 135
[17] Spitzer L., 1987, Dynamical Evolution of Globular Clusters. Princeton University Press, Princeton, NJ, p. 191
[18] Vesperini E. & Heggie D. C., 1997, MNRAS, 289, 898
[19] Zonoozi A. H., K¨upper A. H. W., Baumgardt H., Haghi H., KroupaP., Hilker M., 2011, MNRAS, 411, 1989
[20] Zonoozi A. H., Haghi H., K¨upper A. H. W., Baumgardt H., Frank M. J., Kroupa P., 2014, MNRAS, 440, 3172