Formation of Globular Clusters in Hierarchical Cosmology: ART and Science

1. Formation of Globular Clusters in Hierarchical Cosmology:ART and Science Oleg Gnedin Ohio State University

2. The outcome of models of GC formation depends largely on the initial conditions • Cosmological objects Jeans mass after recombination (Peebles & Dicke 1968), DM halos before reionization (Bromm & Clarke 2002), triggered by ionization fronts during reionization (Cen 2001) or by galaxy outflows (Scannapiesco et al. 2004) • Hierarchical dissipational models[ Searle-Zinn fragments ] supergiant molecular clouds ~ 108 M(Harris & Pudritz 1994),agglomeration of gas clouds at z = 5 1 (Weil & Pudritz 2001), multi-phase collapse (Forbes, Brodie, Grillmair 1997), semi-analytical galaxy formation (Beasley et al. 2002) • Hierarchical dissipationless models accretion of dwarf galaxies (Côté, Marzke & West 1998) • Thermal instability(Fall & Rees 1985) warm 104 K clouds in pressure equilibrium with hot 106 K gas • Mergers of gas-rich spirals(Ashman & Zepf 1992) massive young star clusters observed in mergers, high-pressure environment

3. In hierarchical cosmology, initial conditions are Art ART Structures in the Universe grow hierarchically, starting from primordial density fluctuations. CMB anisotropies provide, in principle, complete initial conditions to simulate the formation of galaxies and star clusters.

4. ? 300 kpc (physical) 14 kpc 20 pc Pushing the limit of current hydrodynamic simulations Milky Way-type system Kravtsov & OG (2005)

5. Clues about star cluster formation from local galaxies The Antennae and other nearby interacting galaxies show plenty of molecular gasand recently-formed globular clusters. Can incorporate these local physical conditions in the simulations, on the (unresolved) scale of parsecs Wilson et al. (2000) Zhang & Fall (1999)

6. Use simulations of galaxy formation to predict the properties (masses, sizes, turbulent velocities, metallicities) of giant molecular clouds : Following arguments of Larson and Harris & Pudritz, imagine that massive star clusters form in the same way as smaller open clusters, i.e. in the self-gravitating cores of molecular clouds. The cluster is only ~ 1% of the H2 mass  globular clusters require supergiant molecular clouds (~107 M). Elmegreen (2002): young star clusters in the Galaxy form whenevergas> 104 M pc-3 threshold density for star cluster formation density space

7. 300 kpc (physical) 14 kpc 20 pc Star clusters in spiral arms of high-redshift disks Milky Way-type system

8. Zero-age mass function of model GCs is in excellent agreement with the mass function of young clusters Cumulative mass function accumulated over all previous epochs

9. Half-mass radii of model GCs match those of the Galactic globular clusters observed

10. Metallicities of model GCs at z > 3 ART GGCS large range of metallicities of GCs formed at the same epoch: up to two orders of magnitude (absolute metallicity scale in the simulation is somewhat uncertain)

11. Clusters with different metallicity are forming at the same epoch in progenitors of different mass stellar mass M* correlates with star formation rate SFR

12. Supergiant molecular clouds form after gas-rich mergers

13. Rate of galaxy mergers declines steadily from high to low z z=9 z=1 Kravtsov, OG, Klypin 2004

14. Does reionization matter? Vc = 10 km/s 100 km/s HI HeII Yes! No H2 (figure from Barkana & Loeb 2001)

15. The mass function of young clusters deviates from the mass function of globular clusters at low masses characteristic mass Zhang & Fall (1999)

16. Dynamical disruption of star clusters OG & Ostriker (1997) Fall & Rees (1977) Spitzer (1987) + collaborators Chernoff & Weinberg (1990) Murali & Weinberg (1997) Vesperini & Heggie (1997) Ostriker & OG (1997) OG, Lee & Ostriker (1999) Fall & Zhang (2001) Baumgardt & Makino (2003) DYNAMICAL EVOLUTION: Low-mass and low-density clusters are disrupted over the Hubble time by two-body relaxation and tidal shocks. And in the 21st century: INFANT MORTALITY

17. Evolution of the GC mass function in a Milky Way-sized galaxy Jose Prieto & OG, 2006 Stellar evolution + relaxation + tidal shocks Rh(0)  M(0)1/3 Rh(t)  M(t)1/3 average density is constant final/initial mass = 0.46 final/initial number = 0.16

18. Different types of orbits of globular clusters

19. Not all initial conditions and evolutionary scenarios are consistent with the observed mass function Rh(0) = Rh(t) = const Rh(0)  M(0)1/3, Rh(t)  M(t) final/initial mass = 0.29 final/initial mass = 0.54 final/initial number = 0.54 final/initial number = 0.09

20. Mergers of progenitor galaxies ensure spheroidal distribution of GC system now z=12 z=0 Moore et al. (2006)

21. Spatial distribution Space density is consistent with a power-law, slope = –2.6 to –2.8 Azimuthal distribution is isotropic 150 kpc 50 kpc Y Z Z X X Y

22. Kinematics perigalactic distance radial eccentricity e = (Ra– Rp)/(Ra+ Rp) velocity anisotropy  = 1 – Vt2/ 2 Vr2 tangential

23. Summary • Globular clusters can form in giant molecular clouds within the disks of high-redshift galaxies, resolved by hydrodynamical simulations: • same microphysics as for young clusters in interacting galaxies • model explainsobserved ages, sizes, masses • metallicities correspond to blue/metal-poor clusters • dynamical evolution explains the present mass function, but not all initial conditions or evolutionary scenarios work • spatial distribution: isotropic, power-law as observed • velocity distribution: isotropic at the center, radial at large radii Formation of massive star clusters will soon be included self-consistently in simulations of galaxy formation. Theoretical predictions will be much less dependent on initial conditions.

24. Direct detection of young globular clusters at z ~ 4 Milky Way 1 h-1 Mpc comoving (41)

25. Metallicity bimodality: decide what we should explain Yoon, Yi, Lee (2006) astro-ph/0601526