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

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

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

8. 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
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. stellar mass M* correlates with star formation rate SFR
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
There is no “beginning epoch” for dissipational mergers, only decline towards the present time
z=9
z=1
Kravtsov, OG, Klypin 2004

14. Does reionization matter?
Vc = 10 km/s km/s HI
HeII
Yes! No H2
Reionization affects only halos with Tvir < 10^4 K where the gas cannot cool efficiently anyway and cannot form large molecular clouds
(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 = final/initial number = 0.16

18. Different types of orbits of globular clusters
Some clusters are formed in the main disk, some remain in satellite galaxies, some get accreted with their disrupted progenitor halos.

19. Rh(0) = Rh(t) = const Rh(0)  M(0)1/3, Rh(t)  M(t)
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 = final/initial mass = 0.54 final/initial number = 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. perigalactic distance
Kinematics
eccentricity e = (Ra– Rp)/(Ra+ Rp)
radial
perigalactic distance
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 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.

24. Direct detection of young globular clusters at z ~ 4
Milky Way
1 h-1 Mpc comoving (41)
HUDF Beckwith et al. (2004)

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