Formation of Globular Clusters under the Influence of Ultraviolet Radiation

1. Simulations As initial cloud mass increases, the strong energy dissipation occurs. The slope becomes steeper than s ∝L1/3 s ∝L1/2 If initial cloud mass is larger than Jeans mass, the energy dissipation is week. Maximum compact cluster mass Mmax～5×106M Velocity dispersion time index (iii) Using predicted values, determine the new timestep of the integrated particles. time s ∝(M/R)1/2 ∝M1/3 ∝L1/3 1 2 3 4 5 index • Algorithm: Block timestep method (Makino 1991) 1 2 3 4 5 • Number of particles: N*=214, NDM=218 M* = 1.3×106M MDM= 2.0×106M m* = 79.3M mDM= 7.63M time index • Select the particles with minimum ti+dti. • Integrate the those particles to new time. 1 2 3 4 5 (iv) Go back to (i) • Initial condition： • The results obtained by our 1D simulations. • Isotropic velocity dispersion is assumed. Time evolution of gas shells Assumption : The Radiation source is Pop III star with Teff = 105K The effective intensity of HII region around Pop III halo : 10-3< I21 < 103 Evaporate Both shells are fully ionized. collapse I21 is intensity at Lyman limit in unit of 10-21ergs cm-2s-1Hz-1str-1 ～100 =20 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. Formation of Globular Clusters under the Influence of Ultraviolet Radiation Kenji Hasegawa＆ Masayuki Umemura University of Tsukuba, JAPAN ABSTRACT 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. Introduction The star component is predominant at center. Age distribution of GCs (Puzia et al. 2005) Strong UV radiation case (I21=1) It is expected that the formation of GCs is affected by Pop III stars !! ●The star cluster formation owing to supersonic infalling. The energy dissipation is strong !! • Feature of GCs • Composed of Pop II stars • Many GCs formed after cosmic reionization. • Extremely high density : r = 103 M/pc3 (100 times higher than galaxy’s density) • Low mass-to-light ratio: M/L～2 ＤＭ Collapse redshift zc Star Reionized universe ! The compact star cluster forms in the diffuse DM halo LOG (Mini/M) Compact star cluster forms at high-s (>2s) peaks. Comparing our results with observations ▲The star cluster formation owing to self-shielding. GCs could form in the UV radiation fields Self-shielding critical density (Tajiri ＆ Umemura (1998)） The diffuse and DM dominant star cluster forms. Effects of UV radiation ・Ionizing of neutral gas The DM component is predominant in any area. They obstruct the formation of stars. ・Photodissociation of H2 If self-shielding effect is effective (n>ncrit), the gas cloud is able to collapse. (e.g. Kitayama et al. 2001) negative Ｉt obstructs the contraction of gas cloud with virial mass is less than 108M. ・Photoheating ＤＭ Star gas temperature ～104K It promotes the formation of H2 ・Increase of electrons positive The main processes of H2 formation 　・H　＋　e-　→　H-　＋　gH-　＋　H　→　H2　＋　e- 　・H　＋　H+　→　H2+＋　gH2+　＋　H　→ H2 +H+ Dynamical Evolution of GCs We simulate the dynamical evolution of GCs in tidal field, using N-body method. We explore the possibility that globular clusters (GCs) form within UV radiation fields. Ex.) Formation process of GCs Methods • Simulation code(Kitayama et al. (2001)) • Spherical symmetric Hydrodynamics ( with DM) • Radiative transfer of UV photons: • Non-equilibrium chemical reactions : ・Two-body relaxation (Spitzer ＆ Hart 1971) • Star dynamics Since m* >> mDM, DM particles are swept up on the outside and they are easily stripped away by tidal force. As a result, Mtot/M* decreases. Comic age (about 14Gyr) corresponds to 2.8trh for M=106M Mgalaxy=109M GC • Star fromation criteria • Tg < 2000K , • Vr < 0 • dr/dt > 0 Circular orbit :400pc Time evolution A gas shell satisfying the above criteria becomes a star shell immediately. 0.25Gyr 1.98Gyr 3.95Gyr 8.90Gyr 11.3Gyr 13.5Gyr Gravothermal evolution (To determine the rate of heating and chemical reaction. ) e-, H, H+, H-, H2, H2+ (not include metals) are shown by symbols Summary and Discussions 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. UV radiation is exposed to the cloud • The feature of the star cluster depends on its formation process. Results ●Supersonic-infalling case Compact star cluster (GC like) ▲Self-shielding Diffuse and DM dominant star cluster (dSph-like) case No (or weak) UV To form the compact star cluster, strong UV radiation (I21>0.1) is required. Our study suggests that GCs form at high-s peaks. • If elliptical galaxies form at high-s 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 Mv,host= -15. • The substructures that formed from rare peaks (>2.5s) can reproduce the radial distribution of GCs in the Galactic halo. (Moore et al. 2006) Dynamical evolution of GCs We simulated the dynamical evolution of GCs in tidal field, using N-body method. • 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. References [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,