Formation of Globular Clusters under the Influence of Ultraviolet Radiation Dynamical Evolution of...
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Formation of Globular Clusters under the Influence of Ultraviolet Formation of Globular Clusters under the Influence of Ultraviolet Radiation Radiation Dynamical Evolution of GCs Resul Resul ts ts Kenji Hasegawa ＆ Masayuki Umemura University of Tsukuba, JAPAN The gas cloud with infall The gas cloud with infall velocity exceeding sound speed velocity exceeding sound speed keeps contracting even if the keeps contracting even if the cloud is fully ionized. cloud is fully ionized. Finally self-shielding becomes Finally self-shielding becomes effective and the cloud can effective and the cloud can cool via H2 cooling. cool via H2 cooling. Time evolution of gas shells Both Both shells shells are are fully fully ionized ionized . . Evapor Evapor ate ate collap collap se se We explore the possibility that globular clusters (GCs) form within UV radiation fields. To simulate the 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, 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 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 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 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 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. correlation between 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) T g < 2000K , (2) V r < 0 (3) d/dt > 0 p b B b b b 2 b rad b 2 0 0 2 b b b 2 b 2 b 2 b 2 b b b ) 1 ( ) ( 4 4 m T k u P dt d P dt du f r H r r GM dm dP r dt r d r dr dm 2 s s 2 s 2 ) ( r r GM dt r d e - , H, H + , H - , H 2 , H 2 + (not include metals) A gas shell satisfying the above criteria becomes a star shell immediately. (To determine the rate of heating and chemical reaction. ) ABSTRACT ABSTRACT rmation process of GCs ntroduction Feature of GCs Composed of Pop II stars Many GCs formed after cosmic reionization. Extremely high density : = 10 3 M /pc 3 (100 times higher than galaxy’s density) Low mass-to-light ratio: M/L ～ 2 GCs could form in the UV GCs could form in the UV radiation fields radiation fields Effects of UV radiation ・ ・ Photoheating Photoheating gas temperature ～ 10 10 4 4 K K ・ ・ Increase of Increase of electrons electrons ・ ・ Photodissociation Photodissociation of H of H 2 2 ・ ・ Ionizing of Ionizing of neutral gas neutral gas They obstruct They obstruct the formation the formation of stars. of stars. It promotes It promotes the formation the formation of H of H 2 2 The main processes of H2 formation ・ H ＋ e - → H - ＋ H - ＋ H → H 2 ＋ e - ・ H ＋ H + → H 2 + ＋ H 2 + ＋ H → H 2 + H + p o s i t i v e Age distribution of GCs (Puzia et al. 2005) It is expected that the formation of GCs is affected by Pop III stars !! Ｉ Ｉ t obstructs the t obstructs the contraction of gas contraction of gas cloud with virial cloud with virial mass is less than mass is less than 10 10 8 M M . If self-shielding e ffect is effective (n>n crit ), the gas cl oud is able to col lapse. (e.g. Kitaya ma et al. 2001) We explore the possibility that We explore the possibility that globular clusters (GCs) form globular clusters (GCs) form within UV radiation fields. within UV radiation fields. 5 / 3 21 5 / 1 sun 6 2 crit 10 10 52 . 3 I M M n Reionized Reionized universe ! universe ! Self-shielding critical density (Tajiri ＆ Umemura (1998) ） Assumption : The Radiation source is Pop III star wi th T eff = 10 5 K The effective intensity of HII region around Pop III halo : 10 10 -3 -3 < < I I 21 21 < 10 < 10 3 3 I 21 is intensity at Lyman limit in unit of 10 -21 ergs cm -2 s -1 Hz -1 str -1 =20 ～ 100 Comparing our results with observations As initial cloud mass increases, the strong energy dissipation occurs. The slope becomes steeper than ∝L 1/3 If initial cloud mass i s larger than Jeans mas s, the energy dissipati on is week. Maximum compact cluster mass M max ～ 5×10 6 M Simulations V e l o c i t y d i s p e r s i o n ∝ ∝ L L 1/2 1/2 ∝ ∝ ( ( M/R M/R ) ) 1/2 1/2 ∝ ∝ M M 1/3 1/3 ∝ ∝ L L 1/3 1/3 ● ● The star cluster The star cluster formation owing to formation owing to supersonic infalling. supersonic infalling. The energy dissipation is The energy dissipation is strong !! strong !! The compact star The compact star cluster forms in the cluster forms in the diffuse DM halo diffuse DM halo Compact star cluster f Compact star cluster f orms at high- orms at high- (>2 (>2 ) p ) p eaks. eaks. Strong UV radiation case ( Strong UV radiation case ( I I 21 21 =1) =1) Methods Methods We simulate the dynamical evolution of GCs in tidal field, using N-body method. Summary and Discussions (i) (i) Select the par Select the par ticles with mi ticles with mi nimum t nimum t i +dt +dt i . . (ii) (ii) Integrate the Integrate the those particle those particle s to new time. s to new time. (iii) Using (iii) Using predicted predicted values, values, determine determine the new the new timestep of timestep of the the integrated integrated particles. particles. 1 1 2 2 3 3 4 4 5 5 index index time time 1 1 2 2 3 3 4 4 5 5 index index time time 1 2 3 4 5 index index time time (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 * =2 14 , N DM =2 18 M * = 1.3×10 6 M M DM = 2.0×10 6 M m * = 79.3M m DM = 7.63M References The diffuse and DM The diffuse and DM dominant star cluster dominant star cluster forms. forms. ▲ ▲ The star cluster The star cluster formation owing to self- formation owing to self- shielding. shielding. The DM component The DM component is predominant in is predominant in any area. any area. ＤＭ Sta r The star component The star component is predominant at is predominant at center. center. ＤＭ Sta r negativ e [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, 1353 Ikeuchi., 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, MNR Stadel, J. 2006, MNR AS, 368, 563, [5] AS, 368, 563, [5] Puzia, T. H., Perrett, K. M., Bridges, T. J. 2005, A Puzia, 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, L17 MNRAS, 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 m m * * >> >> m m DM DM , DM pa , DM pa rticles are swept up o rticles are swept up o n the outside and they n the outside and they are easily stripped aw are easily stripped aw ay by tidal force. As ay by tidal force. As a result, M a result, M tot tot /M /M * decre decre ases. ases. GC GC Gravothermal Gravothermal evolution evolution ・ ・ Two-body relaxation (Spitzer Two-body relaxation (Spitzer ＆ ＆ Hart 1971) Hart 1971) 2 / 3 h sun 2 / 1 sun 6 10 rh pc 10 1 10 ) 4 . 0 ln( yr 10 5 . 6 r m M M M N t Comic age (about 14Gyr) corresponds to 2.8t rh for M=10 6 M M M galaxy galaxy =10 =10 9 M M 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- Diffuse and DM dominant star cluster (dSph- 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 spec ific frequency (Harris 1991). Specific frequency is defined as the GC pop ulation normalized to M v,host = -15. The substructures that formed from rare peaks (>2.5) can reprod uce the radial distribution of GCs in the Galactic halo. (Moore et al. 2006) Dynamical evolution of GCs Dynamical 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 ( I 21 >0.1) is required. Ex.) Time evolution Circular orbit Circular orbit :400pc :400pc C o l l a p s e r e d s h i f t z c LOG (M ini /M ) 0.25Gyr 1.98Gyr 3.95Gyr 8.90Gyr 11.3Gyr 13.5Gyr are shown by symbols
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Transcript of 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
hsun
2/1
sun6
10
rh pc10
1
10)4.0ln(
yr105.6
r
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
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