Formation of Globular Clusters in  CDM Cosmology Oleg Gnedin (University of Michigan)

What we knew before HST: globular clusters are old, dense, compact – a distinct type of stellar spheroids Kormendy (1985)

Over 20 years the Hubble Space Telescope has revealed young massive star clusters in interacting and gas-rich galaxies. Example: the Antennae galaxies show recently formed star clusters and left-over molecular gas. Wilson et al. (2000)

Zhang & Fall (1999) characteristic mass The mass function of young massive clusters is a power law, while the mass function of old globular clusters is peaked

HST also measured old globular cluster systems in the Virgo and Fornax clusters Masters et al. (2010) Jordan et al. (2007) Luminosity function is effectively universal Half-light radii are independent of cluster or galaxy mass

Color and Metallicity Bimodality Peng et al. (2006) – ACS Virgo Cluster Survey Found in most galaxies Usual interpretation: red clusters are associated with host galaxy, blue clusters formed somehow independently

How to understand globular clusters in the context of galaxy formation? Beasley et al. (2002) Not easy. Assuming that GCs follow galactic star formation rate produces too many red/metal-rich clusters with a unimodal metallicity distribution. Globular clusters formed earlier than the majority of field stars in host galaxy.

Additional constraint: spatial distribution Moore et al. (2006) Simple hypothesis: if one globular cluster formed per dark matter halo at high redshift, spatial distribution of blue GCs requires z form ~ 12 However, there is a problem!

Stellar density in globular clusters:  av ~ 10 2  10 5 M  pc -3 The gas in early halos is not dense enough to form the observed globular clusters In addition, the cosmic time is less than 0.4 Gyr z=12z=0 Moore et al. (2006)

Dotter et al. (2010) Marín-Franch et al. (2009) More observational clues: globular clusters have a spread of ages and not too low metallicity – must form over an extended period age spread increases with metallicity and distance from the Galactic center

Hydrodynamic cosmological simulations can now resolve molecular clouds that could host dense and massive star clusters A. Kravtsov & OG (2005) 300 kpc (physical) 14 kpc 20 pc dark matter gas

14 kpc 20 pc M33 If star clusters form from the gas above a single density threshold in the cloud clump, 10 4 M  pc -3 their initial masses and sizes are in excellent agreement with the observations of young clusters These molecular clouds lie in the disks of high-redshift galaxies but the spatial distribution is similar to nearby disk galaxies

M GC  M host Initial mass function of model GCs is a power law as observed Size distribution is consistent, independent of redshift observed

Globular cluster formation efficiency Spitler & Forbes (2009) Georgiev et al. (2010) M GC  M host

Cluster density is key to when they can form! Mergers may be another peak of global SF not here GCs here

main disk (thick disk clusters) surviving satellite galaxy (galaxy in red) disrupted satellite galaxy The globular cluster system is gradually built up by the contributions of main disk and satellite galaxies J. Prieto & OG (2008)

A. Muratov & OG (2010) arXiv: Can a single formation mechanism produce bimodality? Yes Model: GC formation is triggered by gas-rich mergers begin with cosmological simulations of halo formation supplement halos with cold gas mass based on observations use M GC - M gas relation from hydro simulations metallicity from observed M * -Z relation for host galaxies, include evolution with time

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 What about dynamical evolution?

Dynamical evolution is partly responsible for bimodality: it removes most low-mass clusters Evolution of the cluster mass function: competition between formation and disruption Only massive clusters survive, therefore need to follow only mergers of massive protogalaxies. They are rare at low redshift.

The number of massive mergers declines with cosmic time, results in a spread of ages of red clusters of several Gyr disrupted GCs surviving GCs (64 random realizations of each cluster)

Most of globular clusters are old but they form in a variety of systems

Dotter et al. (2010 ) Marín-Franch et al. (2009) Predicted trend matches the ACS data

Globular clusters were a more dominant component of galactic star formation at z>3 than in the last 10 Gyr

Summary Globular clusters may form in giant molecular clouds in progenitor galaxies at intermediate redshifts Model explains observed sizes, masses, ages, metallicities Dynamical evolution explains the present mass function and may be important for metallicity bimodality Red clusters in the Galaxy are due to massive late gas-rich mergers Blue clusters are due to early continuous mergers and later massive mergers Break between populations is due to few late massive mergers Massive mergers produce both red and blue clusters in almost equal amounts: in large elliptical galaxies expect red fraction of about 50% (Peng et al. 2008)

Globular cluster vs. field star metallicity