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

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 ~ 10 8 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) accretion of dwarf galaxies (Côté, Marzke & West 1998)  (Fall & Rees 1985)  Thermal instability (Fall & Rees 1985) warm 10 4 K clouds in pressure equilibrium with hot 10 6 K gas warm 10 4 K clouds in pressure equilibrium with hot 10 6 K gas   Mergers of gas-rich spirals (Ashman & Zepf 1992) massive young star clusters observed in mergers, high-pressure environment massive young star clusters observed in mergers, high-pressure environment

In hierarchical cosmology, initial conditions are 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. Art ART

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

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

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 H 2 mass  globular clusters require supergiant molecular clouds (~10 7 M  ).  gas > 10 4 M  pc -3 Elmegreen (2002): young star clusters in the Galaxy form whenever  gas > 10 4 M  pc -3 density threshold density for star cluster formation space

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

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

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

Metallicities of model GCs at z > 3 ARTGGCS 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)

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

Supergiant molecular clouds form after gas-rich mergers

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

Does reionization matter? (figure from Barkana & Loeb 2001) HI HeII H2H2 Yes! No V c = 10 km/s 100 km/s

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

Dynamical disruption of star clusters OG & Ostriker (1997) 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 21 st century: INFANT MORTALITY

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

Different types of orbits of globular clusters

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

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

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 YXX ZZ

Kinematics eccentricity e = (R a – R p )/(R a + R p ) velocity anisotropy  = 1 – V t 2 / 2 V r 2 perigalactic distance radial tangential

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 explains observed 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.

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

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