formation of globular clusters under the influence of ultraviolet radiation dynamical evolution of...

Formation of Globular Clusters under the Influence of Ultraviolet RadiationFormation of Globular Clusters under the Influence of Ultraviolet Radiation

Dynamical Evolution of GCs

ResultsResultsResultsResults

Kenji Hasegawa ＆ Masayuki UmemuraUniversity of Tsukuba, JAPAN

The gas cloud with infall velocity exceeding The gas cloud with infall velocity exceeding sound speed keeps contracting even if the sound speed keeps contracting even if the cloud is fully ionized. Finally self-shielding cloud is fully ionized. Finally self-shielding becomes effective and the cloud can cool via becomes effective and the cloud can cool via H2 cooling.H2 cooling.

Time evolution of gas shells

Both shells Both shells are fully are fully ionized.ionized.

EvaporateEvaporate

collapsecollapse

We explore the possibility that globular clusters (GCs) form within UV radiation fields. To simulate the formation of GCs under UV 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 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 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 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 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.velocity dispersion and mass for observed GCs.

Star dynamics Simulation code (Kitayama et al. (2001))

Spherical symmetric Hydrodynamics ( with DM)

Radiative transfer of UV photons:

Non-equilibrium chemical reactions :

Star fromation criteria(1) Tg < 2000K ,(2) Vr < 0 (3) d/dt > 0

p

bBb

b

b2b

radb2002

b

b

b

2b2

b2

b2

bb

b

)1(

)(4

4

m

TkuP

dt

dP

dt

du

frHr

rGM

dm

dPr

dt

rd

rdr

dm

2

s

s2s

2 )(

r

rGM

dt

rd

e-, H, H+, H-, H2, H2+ (not include metals)

A gas shell satisfying the above criteria becomes a star shell immediately.

(To determine the rate of heating and chemical reaction. )

ABSTRACTABSTRACT

Formation process of GCs

Introduction

Feature of GCs

Composed of Pop II stars

Many GCs formed after cosmic reionization.

Extremely high density : = 103 M/pc3

(100 times higher than galaxy’s density)

Low mass-to-light ratio: M/L ～ 2

GCs could form in the UV radiation fieldsGCs could form in the UV radiation fields

Effects of UV radiation Effects of UV radiation

・・ PhotoheatingPhotoheating

gas temperature ～ 101044KK

・・ Increase of electrons Increase of electrons

・・ Photodissociation of Photodissociation of HH22

・・ Ionizing of neutral Ionizing of neutral gasgas

They obstruct the They obstruct the formation of stars.formation of stars.

It promotes the It promotes the formation of Hformation of H22

The main processes of H2 formation

　・ H 　＋　 e- 　→　 H- 　＋　　　　　　　　　　　 H- 　＋　H 　→　 H2 　＋　 e-

　・ H 　＋　 H+ 　→　 H2+ 　＋　　　　　　　　　　 H2

+ 　＋　H 　→ H2 + 　 H+ 　　　

posi

tive

Age distribution of GCs (Puzia et al. 2005)It is expected that the formation of GCs is affected by Pop III stars !!

ＩＩ t obstructs the t obstructs the contraction of gas cloud contraction of gas cloud with virial mass is less than with virial mass is less than 101088MM..

If self-shielding effect is effective (n>ncrit), the gas cloud is able to collapse. (e.g. Kitayama et al. 2001)

We explore the possibility that globular clusters We explore the possibility that globular clusters (GCs) form within UV radiation fields.(GCs) form within UV radiation fields.

5/321

5/1

sun6

2crit 10

1052.3 IM

Mn

Reionized Reionized universe !universe !

Self-shielding critical density (Tajiri ＆ Umemura (1998) ）

Assumption : The Radiation source is Pop III star with Teff = 105K

The effective intensity of HII region around Pop III halo : 1010-3-3< < II2121 < 10 < 1033

I21 is intensity at Lyman limit in unit of 10-21ergs cm-2s-1Hz-1str-1

=20～ 100

Comparing our results with observationsComparing our results with observations

As initial cloud mass increases, the strong energy dissipation occurs.

The slope becomes steeper than ∝L1/3

If initial cloud mass is larger than Jeans mass, the energy dissipation is week.

Maximum compact cluster mass　

Mmax ～ 5×106M

Simulations

Vel

ocit

y di

sper

sion

∝∝LL1/21/2

∝ ∝((M/RM/R))1/21/2

∝∝ 　　 MM1/3 1/3 ∝∝ 　　LL1/31/3

●●The star cluster formation owing to The star cluster formation owing to supersonic infalling.supersonic infalling.

The energy dissipation is strong !!The energy dissipation is strong !!

The compact star cluster forms The compact star cluster forms in the diffuse DM haloin the diffuse DM halo

Compact star cluster forms at higCompact star cluster forms at high-h- (>2 (>2) peaks.) peaks.

Strong UV radiation case (Strong UV radiation case (II2121=1)=1)

MethodsMethodsMethodsMethods

We simulate the dynamical evolution of GCs in tidal field, using N-body method.

Summary and Discussions

(i)(i) Select the particles wSelect the particles with minimum tith minimum tii+dt+dtii..

(ii)(ii) Integrate the those paIntegrate the those particles to new time.rticles to new time.

(iii) Using predicted (iii) Using predicted values, determine values, determine the new timestep the new timestep of the integrated of the integrated particles.particles.

1122334455

indexindextimetime

1122334455

indexindextimetime

1122334455

indexindextimetime

(iv) Go back to (i)(iv) Go back to (i)

Initial condition ： The results obtained by our 1D simulations.

Isotropic velocity dispersion is assumed.

Algorithm: Block timestep method (Makino 1991)

Number of particles: N*=214, NDM=218

M* = 1.3×106M

MDM= 2.0×106M

m* = 79.3M

mDM= 7.63M

References

The diffuse and DM dominant The diffuse and DM dominant star cluster forms. star cluster forms.

▲▲The star cluster formation owing to The star cluster formation owing to self-shielding.self-shielding.

The DM component is The DM component is predominant in any area.predominant in any area.

ＤＭStar

The star component is The star component is predominant at center.predominant at center.

ＤＭ

Star

nega

tive

[1] Harris, W. E. 1991, [2] [1] Harris, W. E. 1991, [2] Kitayama, T., Susa, H., Umemura, M., Kitayama, T., Susa, H., Umemura, M., ＆ ＆ Ikeuchi., S. 2001, MNRAS, 326, 1353Ikeuchi., S. 2001, MNRAS, 326, 1353, [3] Makino, J. 1991, PASJ, 43, 859, [4] , [3] Makino, J. 1991, PASJ, 43, 859, [4] Moore,B., Diemand, J., Madau, P., Zemp, M.,Moore,B., Diemand, J., Madau, P., Zemp, M., ＆ ＆ Stadel, J. 2006, MNRAS, 368, 563, [5] Stadel, J. 2006, MNRAS, 368, 563, [5] Puzia, T. H., Perrett, K. M., Bridges, T. J. 2005, APuzia, T. H., Perrett, K. M., Bridges, T. J. 2005, A ＆＆ A, 434, 909, A, 434, 909, [6] Susa, H., [6] Susa, H., ＆ ＆ Umemura, M. 2000, Umemura, M. 2000, MNRAS, 316, L17MNRAS, 316, L17, [7] Tajiri, Y.,, [7] Tajiri, Y., 　＆ 　＆ Umemura, M. 1998, ApJ, 502, 59, Umemura, M. 1998, ApJ, 502, 59,

UV radiation is exposed to the cloud

Since Since mm* * >> >> mmDMDM, DM particles a, DM particles a

re swept up on the outside and thre swept up on the outside and they are easily stripped away by tiey are easily stripped away by tidal force. As a result, Mdal force. As a result, Mtottot/M/M** de de

creases. creases. GCGC

Gravothermal Gravothermal evolutionevolution

・・ Two-body relaxation (Spitzer Two-body relaxation (Spitzer ＆ ＆ Hart 1971)Hart 1971)

2/3

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yr105.6

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m

M

M

M

Nt

Comic age (about 14Gyr) corresponds to 2.8trh for M=106M

MMgalaxygalaxy=10=1099MM

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 Compact star cluster (GC like)Compact star cluster (GC like)

Diffuse and DM dominant star cluster (dSph-like)Diffuse and DM dominant star cluster (dSph-like)

Our study suggests that GCs form at high-Our study suggests that GCs form at high- peaks peaks.If elliptical galaxies form at high- 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 (>2.5) can reproduce the radial distribution of GCs in the Galactic halo. (Moore et al. 2006)

Dynamical evolution of GCsDynamical evolution of GCs

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.

We simulated the dynamical evolution of GCs in tidal field, using N-body method.

No (or weak) UV case

To form the compact star cluster, strong UV radiation (I21>0.1) is required.

Ex.)

Time evolution Circular orbitCircular orbit :400pc :400pc

Col

laps

e re

dshi

ft z

c

LOG (Mini/M)

0.25Gyr1.98Gyr3.95Gyr8.90Gyr11.3Gyr13.5Gyr

are shown by symbols