Formation of Globular Clusters in Hierarchical Cosmology: ART and ART and

ScienceScience

Oleg GnedinOhio State University

The outcome of models of GC formation The outcome of models of GC formation depends largely on the initial conditionsdepends largely on the initial conditions

Cosmological objects

Jeans mass after recombination (Peebles & Dicke 1968), DM halos Jeans mass after recombination (Peebles & Dicke 1968), DM halos before reionization (Bromm & Clarke 2002), triggered by ionization before reionization (Bromm & Clarke 2002), triggered by ionization fronts during reionization (Cen 2001) or by galaxy outflows fronts during reionization (Cen 2001) or by galaxy outflows (Scannapiesco et al. 2004)(Scannapiesco et al. 2004)

Hierarchical dissipational models [ Searle-Zinn fragments ]

supergiant molecular clouds ~ 10supergiant molecular clouds ~ 1088 M M (Harris & Pudritz 1994),(Harris & Pudritz 1994),

agglomeration of gas clouds at z = 5 agglomeration of gas clouds at z = 5 1 (Weil & Pudritz 2001), 1 (Weil & Pudritz 2001), multi-phase collapse (Forbes, Brodie, Grillmair 1997), semi-multi-phase collapse (Forbes, Brodie, Grillmair 1997), semi-analytical galaxy formation (Beasley et al. 2002)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)

Thermal instability (Fall & Rees 1985)(Fall & Rees 1985)

warm 10warm 1044 K clouds in pressure equilibrium with hot 10 K clouds in pressure equilibrium with hot 1066 K gas K gas

Mergers of gas-rich spirals (Ashman & Zepf 1992)

massive young star clusters observed in mergers, high-pressure massive young star clusters observed in mergers, high-pressure environmentenvironment

In hierarchical cosmology, initial In hierarchical cosmology, initial conditions areconditions 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.

ArtArt

ART

Pushing the limit of current hydrodynamic Pushing the limit of current hydrodynamic simulationssimulations

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 Zhang & Fall (1999)(1999)

Wilson et al. (2000)

Clues about star cluster formation from local Clues about star cluster formation from local galaxiesgalaxies

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 H2 mass globular clusters require supergiant molecular clouds (~107 M).

Elmegreen (2002): young star clusters in the Galaxy form

whenever gasgas > 10> 1044 M M pc pc-3-3

densi

ty

threshold density for star cluster formation

space

Star clustersStar clusters in spiral arms of high-redshift disks 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 Zero-age mass function of model GCs is in excellent agreement with the mass function of excellent agreement with the mass function of

young clustersyoung clusters

Half-mass radii of model GCs Half-mass radii of model GCs match those of the Galactic match those of the Galactic

globular clustersglobular clusters

observed

Metallicities of model GCs at z > 3Metallicities of model GCs at z > 3

ARTART GGCSGGCS

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 Clusters with different metallicity are forming at the same epoch in progenitors forming at the same epoch in progenitors

of different massof different mass

stellar mass M* correlates with star formation

rate SFR

Supergiant molecular clouds form after gas-rich Supergiant molecular clouds form after gas-rich mergersmergers

Rate of galaxy mergers declines steadily from high Rate of galaxy mergers declines steadily from high to low to low zz

Kravtsov, OG, Klypin 2004

z=9

z=1

Does reionization matter?Does reionization matter?

(figure from Barkana & Loeb 2001)

HIHeII

H2

Yes!

No

Vc = 10 km/s 100 km/s

Zhang & Fall (1999)Zhang & Fall (1999)

characteristic mass

The mass function of young clusters deviates The mass function of young clusters deviates from the mass function of globular clusters from the mass function of globular clusters

at low massesat low masses

Dynamical disruption of star clustersDynamical disruption of star clusters

OOG & Ostriker (1997)G & Ostriker (1997)

Fall & Rees (1977) Fall & Rees (1977) Spitzer (1987) + collaborators Spitzer (1987) + collaborators Chernoff & Weinberg Chernoff & Weinberg (1990) Murali & Weinberg (1990) Murali & Weinberg (1997) Vesperini & Heggie (1997) Vesperini & Heggie (1997) Ostriker & OG (1997) (1997) Ostriker & OG (1997) OG, Lee & Ostriker (1999) OG, Lee & Ostriker (1999) Fall & Zhang (2001) Fall & Zhang (2001) Baumgardt & Makino (2003)Baumgardt & Makino (2003)

DYNAMICAL EVOLUTION:DYNAMICAL EVOLUTION: Low-mass and low-density Low-mass and low-density clusters are disrupted clusters are disrupted over over the Hubble timethe Hubble time by two- by two-body relaxation and tidal body relaxation and tidal shocks.shocks.

And in the 21And in the 21stst century: century: INFANT MORTALITYINFANT MORTALITY

Jose Prieto & OG, 2006

Stellar evolution

+ relaxation

+ tidal shocks

Evolution of the GC mass function in a Milky Way-Evolution of the GC mass function in a Milky Way-sized galaxysized galaxy

final/initial mass = 0.46 final/initial number = 0.16

Rh(0)

M(0)1/3

Rh(t)

M(t)1/3

average density is constant

Different types of orbits of globular clustersDifferent types of orbits of globular clusters

Not all initial conditions and evolutionary Not all initial conditions and evolutionary scenarios are consistent with the observed scenarios are consistent with the observed

mass functionmass functionRh(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

Mergers of progenitor galaxies Mergers of progenitor galaxies ensure spheroidal distribution of GC ensure spheroidal distribution of GC

system system nownow

Moore et al. (2006)

z=12 z=0

Spatial distributionSpatial distribution

Space density is consistent with a power-law, slope = –2.6 to –2.8

Azimuthal distribution is isotropic

150 kpc

50 kpc

Y

YX X

Z Z

KinematicsKinematics

eccentricity e = (Ra–

Rp)/(Ra+ Rp)

velocity anisotropy = 1 – Vt

2/ 2 Vr2

perigalactic distance

radial

tangential

SummarySummary

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 Direct detection of young globular clusters at z ~ 4clusters at z ~ 4

Metallicity bimodality: decide what we should Metallicity bimodality: decide what we should explainexplain

Yoon, Yi, Lee (2006) astro-ph/0601526