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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 It is expected that the formation of GCs is affected by Pop III stars !! Feature of GCs Age distribution of GCs (Puzia et al. 2005) Strong UV radiation case (I21=1) ●The star cluster formation owing to Composed of Pop II stars supersonic infalling. Many GCs formed after cosmic reionization. The energy dissipation is strong !! Extremely high density : r = Reionized universe ! 103 M/pc3 Compact star cluster forms at high-s (>2s) peaks. ▲The star cluster formation owing to self-shielding. Low mass-to-light ratio: M/L~2 GCs could form in the UV radiation fields Self-shielding critical density (Tajiri & Umemura (1998)) Effects of UV radiation ・Ionizing of neutral gas ・Photodissociation of H2 ・Photoheating gas temperature ~104K ncrit They obstruct the formation of stars. It obstructs the contraction of gas cloud with virial mass is less than 108M. M 3.52 10 6 10 M sun 2 DM Star The compact star cluster forms in the diffuse DM halo LOG (Mini/M) (100 times higher than galaxy’s density) negative The star component is predominant at center. Comparing our results with observations Simulations As initial cloud mass increases, the strong energy dissipation occurs. The diffuse and DM dominant star cluster forms. 1 / 5 3/ 5 I 21 s ∝L1/2 The DM component is predominant in any area. If self-shielding effect is effective (n>ncrit), the gas cloud is able to collapse. (e.g. Kitayama et al. 2001) The slope becomes steeper than s ∝L1/3 If initial cloud mass is larger than Jeans mass, the energy dissipation is week. DM s ∝(M/R)1/2 Star ∝ M1/3 ∝ L1/3 Maximum compact cluster mass It promotes the formation of H2 ・Increase of electrons Mmax~5×106M The main processes of H2 formation ・H + e- → H- + H- + H → H2 + e- ・H + H+ → H2+ + H2 + + H → H2 + H+ Dynamical Evolution of GCs We simulate the dynamical evolution of GCs in tidal field, using N-body method. Algorithm: Block timestep method (Makino 1991) We explore the possibility that globular clusters (GCs) form within UV radiation fields. Number of particles: N*=214, NDM=218 M* = 1.3×106M Ex.)M = 2.0×106M DM m* = 79.3M mDM= 7.63M (i) (iii) Using predicted index 1 values, determine 2 the new timestep 3 of the integrated 4 particles. 5 Select the particles with minimum ti+dti. (ii) Integrate the those particles to new time. The results obtained by our 1D simulations. Methods index 1 2 3 4 5 time time Initial condition: Formation process of GCs time Isotropic velocity dispersion is assumed. index 1 2 3 4 5 (iv) Go back to (i) Simulation code (Kitayama et al. (2001)) ・Two-body relaxation (Spitzer & Hart 1971) Star dynamics Spherical symmetric Hydrodynamics ( with DM) 1/ 2 6.5 10 yr M 1M sun rh 6 t rh ln( 0.4 N ) 10 M sun m 10pc 10 d rs GM ( rs ) 2 2 dt rs 2 dmb 4rb2 r b drb Comic age (about 14Gyr) corresponds to 2.8trh for M=106M Star fromation criteria (1) Tg < 2000K , (2) Vr < 0 (3) dr/dt > 0 d 2 rb GM ( rb ) 2 dP 2 4 r H b 0 0 rb f rad 2 2 dt dmb rb du P dr b 2 dt r b dt rb Mgalaxy=109M Circular orbit GC :400pc Time evolution A gas shell satisfying the above criteria becomes a star shell immediately. k B r bT P ( 1) r b u mp Gravothermal evolution Radiative transfer of UV photons: (To determine the rate of heating and chemical reaction. ) - Non-equilibrium chemical reactions : e , H, H+, H-, H2, H2+ (not include metals) Assumption : The Radiation source is Pop III star with Teff = 105K UV radiation is exposed to the cloud ~100 =20 Results are shown by symbols 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 case No (or weak) UV Time evolution of gas shells Evaporate collapse 0.25Gyr 1.98Gyr 3.95Gyr 8.90Gyr 11.3Gyr 13.5Gyr Summary and Discussions The effective intensity of HII region around Pop III halo : 10-3< I21 < 103 I21 is intensity at Lyman limit in unit of 10-21ergs cm-2s-1Hz-1str-1 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. 3/ 2 Compact star cluster (GC like) Diffuse and DM dominant star cluster (dSph-like) To form the compact star cluster, strong UV radiation (I21>0.1) is required. Both shells are fully ionized. 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 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. References 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. [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,