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Formation of Globular Clusters under the Influence of Ultraviolet Radiation
Kenji Hasegawa ＆ Masayuki Umemura
University of Tsukuba, JAPAN
ABSTRACT
We explore the possibility that globular clusters (GCs) form within UV radiation fields. To simulate the formation of GCs under UV radiation, we
solve gas and dark matter dynamics in spherical symmetry, consistently incorporating the radiative transfer of UV photons and non-equilibrium
chemical reactions regarding hydrogen molecules (H2). In addition, the star formation from cooled gas component is included.We also simulate the
evolution of GCs in the tidal fields, using N-body technique. As a result, we find that compact star clusters form under UV radiation fields and they
are well consistent with the recognized correlation between velocity dispersion and mass for observed GCs.
Introduction
It is expected that the formation of
GCs is affected by Pop III stars !!
Feature of GCs
Age distribution of GCs (Puzia et al. 2005)
Strong UV radiation case (I21=1)
●The star cluster formation owing to
Composed of Pop II stars
supersonic infalling.
Many GCs formed after cosmic reionization.
The energy dissipation is strong !!
Extremely high density : r =
Reionized
universe !
103 M/pc3
Compact star cluster forms at
high-s (>2s) peaks.
▲The star cluster formation owing to
self-shielding.
Low mass-to-light ratio: M/L～2
GCs could form in the UV radiation fields
Self-shielding critical density
(Tajiri ＆ Umemura (1998)）
Effects of UV radiation
・Ionizing of neutral gas
・Photodissociation of H2
・Photoheating
gas temperature
～104K
ncrit
They obstruct the
formation of stars.
Ｉt obstructs the contraction
of gas cloud with virial
mass is less than 108M.
 M 

 3.52 10  6
 10 M sun 
2
ＤＭ
Star
The compact star cluster forms
in the diffuse DM halo
LOG (Mini/M)
(100 times higher than galaxy’s density)
negative
The star component is
predominant at center.
Comparing our results with observations
Simulations
As initial cloud mass increases,
the strong energy dissipation
occurs.
The diffuse and DM dominant
star cluster forms.
1/ 5
3/ 5
I 21
s ∝L1/2
The DM component is
predominant in any area.
If self-shielding effect is
effective (n>ncrit), the gas
cloud is able to collapse.
(e.g. Kitayama et al. 2001)
The slope becomes steeper
than s ∝L1/3
If initial cloud mass is larger than
Jeans mass, the energy dissipation
is week.
ＤＭ
s ∝(M/R)1/2
Star
∝ M1/3 ∝ L1/3
Maximum compact cluster mass
It promotes the
formation of H2
・Increase of electrons
Mmax～5×106M
The main processes of H2 formation
・H ＋ e- → H- ＋ 
H- ＋ H → H2 ＋ e-
・H ＋ H+ → H2+ ＋ 
H2 + ＋ H → H2 + H+
Dynamical Evolution of GCs
We simulate the dynamical evolution of GCs in tidal field, using N-body method.
Algorithm: Block timestep method (Makino 1991)
We explore the possibility that globular clusters
(GCs) form within UV radiation fields.
Number of particles: N*=214, NDM=218
M* = 1.3×106M
Ex.)M = 2.0×106M
DM

m* = 79.3M
mDM= 7.63M
(i)
(iii) Using predicted index
1
values, determine
2
the new timestep
3
of the integrated
4
particles.
5
Select the particles
with minimum ti+dti.
(ii) Integrate the those
particles to new time.
The results obtained by our 1D simulations.
Methods
index
1
2
3
4
5
time
time
Initial condition：
Formation process of GCs
time
Isotropic velocity dispersion is assumed.
index
1
2
3
4
5
(iv) Go back to (i)
Simulation code (Kitayama et al. (2001))
・Two-body relaxation (Spitzer ＆ Hart 1971)
Star dynamics
Spherical symmetric Hydrodynamics
( with DM)
1/ 2
6.5 10 yr  M   1M sun  rh 
 6
 

trh 

ln( 0.4 N )  10 M sun   m  10pc 
10
d rs
GM ( rs )

2
2
dt
rs
2
dmb
 4rb2 r b
drb
Comic age (about 14Gyr) corresponds to 2.8trh for M=106M
 Star fromation criteria
(1) Tg < 2000K ,
(2) Vr < 0
(3) dr/dt > 0
d 2 rb
GM ( rb )
2 dP
2


4

r



H
b
0 0 rb  f rad
2
2
dt
dmb
rb
du P dr b   
 2

dt r b dt
rb
Mgalaxy=109M
Circular orbit
GC
:400pc
Time evolution
A gas shell satisfying the above criteria
becomes a star shell immediately.
k B r bT
P  (  1) r bu 
mp
Gravothermal
evolution
Radiative transfer of UV photons: (To determine the rate of heating and chemical
reaction.
)
-
Non-equilibrium chemical reactions :
e , H, H+, H-, H2, H2+ (not include metals)
Assumption : The Radiation source is
Pop III star with Teff = 105K
UV radiation is
exposed to the cloud
～100
=20
Results
are shown
by symbols
We simulated the fromation of GCs in the UV radiation fields.
The cloud with infall velocity exceeding sound speed keeps contracting even if the cloud
is fully ionized. As a result, stars are bale to form in the cloud.
 The feature of the star cluster depends on its formation process.
●Supersonic-infalling case
▲Self-shielding
case
No (or weak) UV
Time evolution of gas shells
Evaporate
collapse
0.25Gyr
1.98Gyr
3.95Gyr
8.90Gyr
11.3Gyr
13.5Gyr
Summary and Discussions
The effective intensity of HII region
around Pop III halo : 10-3< I21 < 103
I21 is intensity at Lyman limit in unit of
10-21ergs cm-2s-1Hz-1str-1
Since m* >> mDM, DM particles
are swept up on the outside and
they are easily stripped away by
tidal force. As a result, Mtot/M*
decreases.
3/ 2
Compact star cluster (GC like)
Diffuse and DM dominant star cluster (dSph-like)
To form the compact star cluster, strong UV radiation (I21>0.1) is required.
Both shells
are fully
ionized.
Our study suggests that GCs form at high-s peaks.
If elliptical galaxies form at high-s peaks (e.g. Susa ＆ Umemura 2000), we easily explain the
reason why ellipticals have high specific frequency (Harris 1991). Specific frequency is defined as the GC
population normalized to Mv,host= -15.
The substructures that formed from rare peaks (>2.5s) can reproduce the radial distribution of
GCs in the Galactic halo. (Moore et al. 2006)
Dynamical evolution of GCs
The gas cloud with infall velocity exceeding
sound speed keeps contracting even if the
cloud is fully ionized. Finally self-shielding
becomes effective and the cloud can cool via
H2 cooling.
References
We simulated the dynamical evolution of GCs in tidal field, using N-body method.
The mass-to-light ratio for GCs decreases, since DM particles are swept out.
Our results are well consistent with observations on the fundamental plane.
[1] Harris, W. E. 1991, [2] Kitayama, T., Susa, H., Umemura, M., ＆ Ikeuchi., S. 2001, MNRAS, 326, 1353, [3] Makino, J. 1991, PASJ, 43, 859, [4] Moore,B., Diemand, J., Madau, P., Zemp, M.,＆ Stadel, J. 2006, MNRAS, 368, 563, [5] Puzia, T. H., Perrett, K. M., Bridges, T. J. 2005, A＆A, 434, 909,
[6] Susa, H., ＆ Umemura, M. 2000, MNRAS, 316, L17, [7] Tajiri, Y., ＆ Umemura, M. 1998, ApJ, 502, 59,