1. Formation of Globular Clusters under the Influence of Ultraviolet Radiation Dynamical Evolution of GCs ResultsResults Kenji Hasegawa ＆ Masayuki Umemura University of Tsukuba, JAPAN The gas cloud with infall velocity exceeding sound speed keeps contracting even if the cloud is fully ionized. Finally self-shielding becomes effective and the cloud can cool via H2 cooling. Time evolution of gas shells Both shells are fully ionized. Evaporate collapse We explore the possibility that globular clusters (GCs) form within UV radiation fields. To simulate the formation of GCs under UV radiation, we solve gas and dark matter dynamics in spherical symmetry, consistently incorporating the radiative transfer of UV photons and non-equilibrium chemical reactions regarding hydrogen molecules (H2). In addition, the star formation from cooled gas component is included.We also simulate the evolution of GCs in the tidal fields, using N-body technique. As a result, we find that compact star clusters form under UV radiation fields and they are well consistent with the recognized correlation between velocity dispersion and mass for observed GCs.  Star dynamics Simulation code (Kitayama et al. (2001))  Spherical symmetric Hydrodynamics ( with DM)  Radiative transfer of UV photons:  Non-equilibrium chemical reactions :  Star fromation criteria (1) T g < 2000K, (2) V r < 0 (3) d  /dt > 0 e -, H, H +, H -, H 2, H 2 + (not include metals) A gas shell satisfying the above criteria becomes a star shell immediately. (To determine the rate of heating and chemical reaction. ) ABSTRACT Formation process of GCs Introduction Feature of GCs  Composed of Pop II stars  Many GCs formed after cosmic reionization.  Extremely high density :  = 10 3 M  /pc 3 (100 times higher than galaxy’s density)  Low mass-to-light ratio: M/L ～ 2 GCs could form in the UV radiation fields Effects of UV radiation ・ Photoheating 10 4 K gas temperature ～ 10 4 K ・ Increase of electrons ・ Photodissociation of H 2 ・ Ionizing of neutral gas They obstruct the formation of stars. It promotes the formation of H 2 The main processes of H2 formation ・ H ＋ e - → H - ＋  H - ＋ H → H 2 ＋ e - ・ H ＋ H + → H 2 + ＋  H 2 + ＋ H → H 2 + H + positive Age distribution of GCs (Puzia et al. 2005) It is expected that the formation of GCs is affected by Pop III stars !! Ｉ t obstructs the contraction of gas cloud with virial mass is less than 10 8 M . If self-shielding effect is effective (n>n crit ), the gas cloud is able to collapse. (e.g. Kitayama et al. 2001) We explore the possibility that globular clusters (GCs) form within UV radiation fields. Reionized universe ! Self-shielding critical density (Tajiri ＆ Umemura (1998) ） Assumption : The Radiation source is Pop III star with T eff = 10 5 K 10 -3 < I 21 < 10 3 The effective intensity of HII region around Pop III halo : 10 -3 < I 21 < 10 3 I 21 is intensity at Lyman limit in unit of 10 -21 ergs cm -2 s -1 Hz -1 str -1 =20 ～ 100 Comparing our results with observations As initial cloud mass increases, the strong energy dissipation occurs. The slope becomes steeper than  ∝ L 1/3 If initial cloud mass is larger than Jeans mass, the energy dissipation is week. Maximum compact cluster mass M max ～ 5×10 6 M  Simulations Velocity dispersion  ∝ L 1/2  ∝ (M/R) 1/2 ∝ M 1/3 ∝ L 1/3 ● The star cluster formation owing to supersonic infalling. The energy dissipation is strong !! The compact star cluster forms in the diffuse DM halo Compact star cluster forms at high-  (>2  ) peaks. Strong UV radiation case (I 21 =1) MethodsMethods We simulate the dynamical evolution of GCs in tidal field, using N-body method. Summary and Discussions (i)Select the particles with minimum t i +dt i. (ii)Integrate the those particles to new time. (iii) Using predicted values, determine the new timestep of the integrated particles. 12345 index time 12345 index time 12345 index time (iv) Go back to (i)  Initial condition ： The results obtained by our 1D simulations. Isotropic velocity dispersion is assumed.  Algorithm: Block timestep method (Makino 1991)  Number of particles: N * =2 14, N DM =2 18 M * = 1.3×10 6 M  M DM = 2.0×10 6 M  m * = 79.3M  m DM = 7.63M  References The diffuse and DM dominant star cluster forms. ▲ The star cluster formation owing to self-shielding. The DM component is predominant in any area. ＤＭ Star The star component is predominant at center. ＤＭ Star negative [1] Harris, W. E. 1991, [2] Kitayama, T., Susa, H., Umemura, M., ＆ Ikeuchi., S. 2001, MNRAS, 326, 1353, [3] Makino, J. 1991, PASJ, 43, 859, [4] Moore,B., Diemand, J., Madau, P., Zemp, M., ＆ Stadel, J. 2006, MNRAS, 368, 563, [5] Puzia, T. H., Perrett, K. M., Bridges, T. J. 2005, A ＆ A, 434, 909, [6] Susa, H., ＆ Umemura, M. 2000, MNRAS, 316, L17, [7] Tajiri, Y., ＆ Umemura, M. 1998, ApJ, 502, 59, UV radiation is exposed to the cloud Since m * >> m DM, DM particles are swept up on the outside and they are easily stripped away by tidal force. As a result, M tot /M * decreases. GC Gravothermal evolution ・ Two-body relaxation (Spitzer ＆ Hart 1971) Comic age (about 14Gyr) corresponds to 2.8t rh for M=10 6 M  M galaxy =10 9 M  We simulated the fromation of GCs in the UV radiation fields. The cloud with infall velocity exceeding sound speed keeps contracting even if the cloud is fully ionized. As a result, stars are bale to form in the cloud. The feature of the star cluster depends on its formation process. ● Supersonic-infalling case ▲ Self-shielding Compact star cluster (GC like) Diffuse and DM dominant star cluster (dSph-like) Our study suggests that GCs form at high-  peaks Our study suggests that GCs form at high-  peaks.  If elliptical galaxies form at high-  peaks (e.g. Susa ＆ Umemura 2000), we easily explain the reason why ellipticals have high specific frequency (Harris 1991). Specific frequency is defined as the GC population normalized to M v,host = -15.  The substructures that formed from rare peaks (>2.5  ) can reproduce the radial distribution of GCs in the Galactic halo. (Moore et al. 2006) Dynamical evolution of GCs The mass-to-light ratio for GCs decreases, since DM particles are swept out. Our results are well consistent with observations on the fundamental plane. We simulated the dynamical evolution of GCs in tidal field, using N-body method. No (or weak) UV case To form the compact star cluster, strong UV radiation (I 21 >0.1) is required. Ex.) Time evolution Circular orbit :400pc Collapse redshift z c LOG (M ini /M  ) 0.25Gyr 1.98Gyr 3.95Gyr 8.90Gyr 11.3Gyr 13.5Gyr are shown by symbols