The cluster M67 (= NGC 2682) in Cancer is a rich stellar cluster, usually classified as an open cluster. Using our own observations with the 0.4 m telescope, we show that M67 is a tight group of about 1200 stars. The actual radius of the cluster is about 3.1 pc and the average mass of a star in the system is about . We also show that the ratio of the mean kinetic energy of the cluster to its mean gravitational potential energy , while the value predicted by the virial theorem is equal to . So the system is a gravitationally bound. This value of is considered as an evidence of quasi-stability of the cluster and allows us to use the Chandrasekhar-Spitzer relaxation time for M67 Myr as a characteristic dynamical relaxation time of the system. As the cluster is almost twice older its half-life time , it is argued that M67 was in the past (about 4 Gyr ago, close to its forma-tion) a relatively small ( stars) globular cluster, but got “open cluster” shape due to the dynamical evapora-tion of the majority of its stars.
KeywordsPhotometersTechniquesPhotometricOpen Clusters and AssociationsM67GalaxiesStar Clusters
G. Meynet, J.-C. Mermilliod and A. Maeder, “New Dating of Galactic Open Clusters,” Astron. Astrophys. Suppl., Vol. 98, No. 3, 1993, pp. 477-504.
S. Randich, F. Primas, L. Pasquini, P. Sestito and R. Pal-lavicini, “Tracing Mixing in Stars: New Beryllium Ob-servations of the Open Clusters NGC 2516, Hyades, and M67,” Astron. Astrophys., Vol. 469, No. 1, 2007, pp. 163-172. doi:10.1051/0004-6361:20066218
A. Sarajedini, A. Dotter and A. Kirkpatrick, “Deep 2MASS Photometry of M67,” Astrophys. J., Vol. 698, No. 2, 2009, pp. 1872-1878. doi:10.1088/0004-637X/698/2/1872
X. Fan, D. Burstein, J.-S. Chen, J. Zhu et al., “Deep Wide-Field Spectrophotometry of the Open Cluster M67,” Astron. J., Vol. 112, No. 2, 1996, pp. 628-648. doi:10.1086/118039
D. A. VandenBerg and P. B. Stetson, “On the Old Open Clusters M67 and NGC 188,” Publ. Astron. Soc. Japan, Vol. 116, No. 825, 2004, pp. 997-1011. doi:10.1086/426340
V. Laugalys, A. Kazlauskas, R. P. Boyle, F. J. Vrba, P. A. Davis and V. Strai ys, “CCD Photometry of the M67 Cluster in the Vilnius System. II. New Photometry of High Accuracy,” Baltic Astron., Vol. 13, 2004, pp. 1-33.
T. M. Girard, W. M. Grundy, C. E. L pez and W. F. van Altena, “Relative Proper Motions and the Stellar Velocity Dispersion of the Open Cluster M67,” Astron. J., Vol. 98, No. 1, 1989, pp. 227-243. doi:10.1086/115139
E. K. Kharadze, R. A. Bartaya, O. B. Dluzhnevskaya, A. E. Piskunov and E. D. Pavlovskaya, “Population of the Galactic Disc in the Solar Neighbourhood. I - Parameters of Spatial Distribution for Stellar Groups of A-K Spectral and III-V Luminosity Classes,” Astrophys. Space Sci., Vol. 151, No. 2, 1989, pp. 319-334.doi:10.1007/BF00648388
J. R. Hurley, O. R. Pols, S. J. Aarseth and C. A. Tout, “A Complete N-body Model of the Old Open Cluster M67,” Monthly Not. Roy. Astron. Soc., Vol. 363, No. 1, 2005, pp. 293-314. doi:10.1111/j.1365-2966.2005.09448.x
C. Bonatto and E. Bica, “Mass Segregation in M67 with 2MASS,” Astron. Astrophys., Vol. 405, No. 2, 2003, pp. 525-530. doi:10.1051/0004-6361:20030205
J. R. A. Davenport and E. L. Sandquist, “Death of a Cluster: The Destruction of M67 as Seen by the Sloan Digital Sky Survey,” Astrophys. J., Vol. 711, No. 2, 2010, pp. 559-572. doi:10.1088/0004-637X/711/2/559
D. E. McLaughlin, J. Anderson, G. Meylan, K. Gebhardt, C. Pryor, D. Minniti and S. Phinney, “Hubble Space Telescope Proper Motions and Stellar Dynamics in the Core of the Globular Cluster 47 Tucanae,” Astrophys. J. Suppl., Vol. 166, No. 1, 2006, pp. 249-297. doi:10.1086/505692
G. Q. Liu, L. Deng, M. Ch vez, E. Bertone, A. H. Davo and M. D. Mata-Ch vez, “A Spectroscopic Study of the Blue Stragglers in M67,” Monthly Not. Roy. Astron. Soc., Vol. 390, No. 2, 2008, pp. 665-674.
J. S. Kalirai, G. G. Fahlman, H. B. Richer and P. Ventura, “The CFHT Open Star Cluster Survey. IV. Two Rich, Young Open Star Clusters: NGC 2168 (M35) and NGC 2323 (M50),” Astron. J., Vol. 126, No. 2, 2003, pp. 1402-1414. doi:10.1086/377320
S. Rosseland, “Scattering of Stars in Clusters,” Z. Astro-phys., Vol. 4, No. 1, 1932, pp. 235-254.
L. Spitzer, “Distribution of Galactic Clusters,” Astrophys. J., Vol. 127, No. 1, 1958, pp. 17-27. doi:10.1086/146435
L. Spitzer, R. Harm, “Evaporation of Stars from Isolated Clusters,” Astrophys. J., Vol. 127, No. 1, 1958, pp. 544-550. doi:10.1086/146486
E. Terlevich, “Evolution of N-body Open Clusters,” Monthly Not. Roy. Astron. Soc., Vol. 224, No. 1, 1987, pp. 193-225.
V. A. Ambartsumyan, “Stability of Stellar Clusters,” Uchenye Zapiski LGU, Vol. 22, No. 1, 1938, pp. 19-29.
L. Spitzer, “The Stability of Isolated Clusters,” Monthly Not. Roy. Astron. Soc., Vol. 100, No. 1, 1940, pp. 396-413.
T. A. Agekyan, “The Velocity Distribution Function and the Rate of Dissipation in Systems of Gravitating Bodies,” Soviet Astron., Vol. 3, No. 1, 1959, pp. 280-290.
S. Chandrasekhar, “Principles of Stellar Dynamics,” Dover, New York, 1960.
L. Spitzer and M. H. Hart, “Random Gravitational En-counters and the Evolution of Spherical Systems. I. Me-thod,” Astrophys. J., Vol. 164, No. 1, 1971, pp. 399- 409. doi:10.1086/150855
R. de Grijs, “The Long-term Survival Chances of Young Massive Star Clusters,” Astrophys. Space Sci., Vol. 324, No. 2-4, 2009, pp. 283-291. doi:10.1007/s10509-009-0100-0
J. Schneider, P. Amaro-Seoane and R. Spurzem, “High-er-order Moment Models of Dense Stellar Systems: Ap-plications to the Modelling of the Stellar Velocity Distri-bution Function,” Monthly Not. Roy. Astron. Soc., Vol. 410, No. 1, 2011, pp. 432-454. doi:10.1111/j.1365-2966.2010.17454.x
I. King, “The Escape of Stars from Clusters 11. A Simple Theory of the Evolution of an Isolated Cluster,” Astron. J., Vol. 63, No. 1258, 1958, pp. 114-117. doi:10.1086/107702
S. von Hoerner, “Die Aufl??sungszeit Offener Sternhau-fen,” Z. Astrophys., Vol. 44, No. 1, 1958, pp. 221-242.
L. P. Ossipkov, “On the Jubilee of Academician V. A. Ambartsumyan Statistical Mechanics of Stellar Systems: From Ambartsumyan Onward,” Astrophysics, Vol. 51, No. 4, 2008, pp. 428-442. doi:10.1007/s10511-008-9032-6
A. F. Alexandrov, L. S. Bogdankevich, A. A. Rukhadze, “Principles of Plasma Electrodynamics,” Springer, Berlin, 1984. doi:10.1007/978-3-642-69247-5
G. G. Kuzmin, “The Effect of Star Encounters and the Evolution of Star Clusters,” Publ. Tartu Obs., Vol. 33, No. 2, 1957, pp. 75-102.
M. N. Rosenbluth, W. M. MacDonald and D. L. Judd, “Fokker-Planck Equation for an Inverse-Square Force,” Phys. Rev., Vol. 107, No. 1, 1957, pp. 1-6. doi:10.1103/PhysRev.107.1
D. C. Montgomery and D. A. Tidman, “Plasma Kinetic Theory,” McGraw-Hill, New York, 1964.
B. A. Trubnikov, “Particle Interactions in a Fully Ionized Plasma,” in: “Reviews of Plasma Physics,” Vol. 1, M. A. Leontovich, Ed., Consultants Bureau, New York, 1965, pp. 105-140.
E. Griv, “Numerical Integration of the Landau Kinetic Equation,” in: “Order and Chaos in Stellar and Planetary Systems,” G. Byrd et al., Ed., ASP, San Francisco, 2004, pp. 352-356.
W. M. MacDonald, M. N. Rosenbluth and W. Chuck, “Relaxation of a System of Particles with Coulomb Inte-ractions,” Phys. Rev., Vol. 107, No. 2, 1957, pp. 350- 353. doi:10.1103/PhysRev.107.350
J. Killeen and A. H. Futch, “Numerical Solution of the Fokker-Planck Equations for a Hydrogen Plasma Formed by Neutral Injection,” J. Comput. Phys., Vol. 2, No. 3, 1968, pp. 236-254.