R elativistic stellar clusters G. S. Bisnovatyi-Kogan (IKI, Moscow) ,

1. Relativistic stellar clusters G.S.Bisnovatyi-Kogan (IKI, Moscow), ГАИШ, пятница, 13 марта 2009

2. Вскоре после открытия квазаров с большим красным смещением:

3. =1 was considered by Zeldovich and Podurets (1965)

4. Star Clusters with Cutoff

7. MODELS OF CLUSTERS OF POINT MASSES WITH LARGE CENTRAL REDSHIFTS G. S. Bisnovatyi-Kogan and Ya. B. Zel'dovich Astrofizika, Vot. 5, No. 2, pp. 223-234, 1969 =2/a 0.006 r(g)/r=const~a

8. Variational principle

9. Relative binding energy E(b)/M is better for stability analysis than M

10. Publications: Earlier publications

11. E(b)/N W(0)=const, each extremum gives birth to new dynamically unstable mode . At W(0)> 15.8 all models are stable.

12. Newtonian cluster in box GR cluster with cutoff is thekinetic energy cutoff. In the Newtonian limit, formally reduces to Similarity between clusters in the box and clusters with cutoff

13. Dynamic stability against perturbations with constant adiabatic invariants. Equivalent to constant entropy for stability of gaseous star Thermodynamic stability include processes leading to thermal equilibrium, smoothing temperature over the newtonian cluster or star

14. Isolated cluster

15. Thermodynamic stability Comparison of the Newtonian curve of specific binding energyEb/N with the corresponding one forclusters in a box, of the paper of Lynden-Bell & Wood (1968), shows a good correspondence betweenthe first extrema of these curves, which lay at (-v1)=6:55, forclusters in a box, and at W0 =6:42, for open clusters with truncatedMaxwellian distribution function.

16. Clusters with cutoff : ApJ (1998), 500, 217

18. E(b)/N T=const, each extremum gives birth to new thermodynamically unstable mode

19. Large central density (central redshift) regime, loss of dynamic stability at W(0)=15.8

20. Large central density (central redshift) regime loss of dynamic stability at T=0.06

22. DU DU DS DS

23. DSTU DSTU DU T U DU T U S S S S

24. CONCLUSIONS • In Newtonian cluster thermodynamic instability leads to • gravothermal catastrophe (no dynamic instability) • All relativistic clusters with large central z are thermodynamically • unstable. • 3. Thermodynamic instability develops slowly, during a time of energy • exchange (binary collision), until dynamic instability state is reached, • and relativistic collapse starts.