Multiple Main Sequence of Globular Clusters as a Result of Inhomogeneous Big Bang Nucleosynthesis

0.17 MB·English

by  Takashi Moriya

Multiple Main Sequence of Globular Clusters
as a Result of Inhomogeneous Big Bang Nucleosynthesis
Takashi Moriya
∗
Department of Astronomy, Graduate School of Science,
University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan. and
Institute for the Physics and Mathematics of the Universe,
University of Tokyo, Kashiwanoha 5-1-5, Kashiwa, Chiba 277-8568, Japan.
Toshikazu Shigeyama
Research Center for the Early Universe, Graduate School of Science,
0 University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan.
1
0 A new mechanism for enhancing the helium abundance in the blue main sequence stars of ω
2 Centauri and NGC 2808 is investigated. We suggest that helium enhancement was caused by the
n inhomogeneous big bang nucleosynthesis. Regions with extremely high baryon-to-photon ratios
a are assumed to be caused by the baryogenesis. Its mass scale is also assumed to be 106M⊙. An
J example of the mechanisms to realize these two things was already proposed as the Affleck-Dine
baryogenesis. As the baryon-to-photon ratio becomes larger, the primordial helium abundance is
2
1 enhanced. We calculated the big bang nucleosynthesis and found that there exists a parameter
region yielding enough helium to account for the split of the main sequence in the aforementioned

] globularclusterswhilekeepingtheabundancesofotherelementscompatiblewithobservations. Our
O mechanism predicts that heavy elements with the mass number of around 100 is enhanced in the
C bluemain sequencestars. Weestimatethetimescales ofdiffusionoftheenhancedheliumandmass
accretion in severalstages afterthenucleosynthesistoinvestigatewhethertheseprocesses diminish
.
h the enhancement of helium. We found that the diffusion does not influence the helium content.
p A cloud with a sufficiently large baryon-to-photon ratio to account for the multiple main sequence
- collapsedimmediatelyaftertherecombination. Subsequently,thecloudaccretedtheambientmatter
o
with the normal helium content. If the star formation occurred both in the collapsed core and the
r
t accreted envelope, then theresultant star cluster has a doublemain sequence.
s
a
[ PACSnumbers: 98.20.Gm,26.35.+c,98.80.Ft,13.60.Rj

1
v I. INTRODUCTION dowiththeirheliumcontents. Furthermore,observations
0 bytheHubbleSpaceTelescopediscoveredthetriplemain
9
sequence in another GC, NGC 2808 [8]. NGC 2808 is
7 Aglobularcluster(GC)isagravitationallyboundsys- also massive, with its mass above 106M [9]. It was
1
tem of stars with a spherical shape. The typical radius foundthat,ineitherGCs,theisochronetha⊙tmatchesthe
1. is of the order of 10 pc and its mass is about 104−6M . propertiesofthebMScanbeproducedbyassumingvery
0 Stars in a GC areknownto be veryold andtheir chem⊙i-
high helium abundances (Y), 0.35 < Y < 0.45 [5, 10].
0 calcompositionsroughlyrepresentthatoftheprimordial
As other parameters do not have much effect on colors,
1
universe.
: it is very likely that the helium enrichment is the cause
v
Among known 150GCs, ω Centauriis notoriousfor of the multiple main sequence.
Xi its unusual prope∼rties. Its mass is about 3 106M [1]
r and it is the most massive GC in the Milky×Way ga⊙laxy. The origin of the enhanced helium abundances in the
a One of the most astonishing facts about ω Centauri is bMS stars has been a mystery. It was suggested, for
that its dwarf stars split into two sequences [2–4], the example,thatthe ejectadescendedfrommassiveasymp-
blue main sequence (bMS) and the red main sequence totic giant branch (AGB) stars would enhance the he-
(rMS). 25%-35%of the dwarfstars are populated by the liumabundancesofthemainsequencestarsandsplitthe
bMS [3]. Although enhanced metallicities might split a main sequence [11]. However, it is difficult for massive
main sequence by lowering the surface temperature of AGB stars to produce as much helium as Y 0.35 [12].
∼
metal-rich stars, it is reported that stars in the bMS are Whatis more,the amountofhelium suppliedfromAGB
moremetal-richthanthose inthe rMSinω Centauri[5]. stars is not enough to increase the helium content of all
Recently, it is reported that there also exists the third stars in the bMS up to 0.35 [12]. Helium enhance-
∼
redder MS [6]. This MS is suggested to be populated by ment by massive stars is also suggested to explain the
super metal-rich stars [7] and seems to have nothing to MS splitting [13]. Rotating low-metal massive stars can
enhance the helium abundance in the stellar winds but
such stars should accelerate the helium-rich matter by
the subsequent supernova explosions. The helium rich
∗[email protected] ejecta might be too energetic to be trapped in a GC and
2
could easily escape from it. These difficulties associated muchsmallerthanthescalesoffluctuationsintheCMBR
with the AGB and massive star scenarios might be re- that can be detected by WMAP. Recent papers by Mat-
lieved if the GC was originally the nucleus of a more suura et al. [22–24] have preformed calculations of the
massive dwarf galaxy [14]. There were much more AGB BBN with high values of η on the basis of the Affleck-
stars in the dwarf galaxy and the helium supplied from Dinebaryogenesis. SuchaninhomogeneousBBNmaybe
these AGB stars might be sufficient to produce the ob- affected by the diffusion of neutrons. Lara [25] showed
served number of bMS stars. As for the massive star thatregionswithenhancedη’sdonotleadtoabundances
scenario, a massive dwarf galaxy might be able to trap of light elements significantly deviated from those of the
the helium-richejecta due to its deeper gravitationalpo- ambient medium if their size at the temperature of 100
tential. However,there remain problems in both scenar- GKwassmallerthan104 cm. Sincethesizeoftheregion
ios. It is still difficult to produce the observed fraction weareconcernedwithinthispaperisoftheorderof1010
of bMS stars with the helium-rich matter or these sce- cm at this temperature (see Eq. (10)) and much larger
narios seem to require an initial mass function of stars than104 cm,thediffusionofneutronscannotchangethe
extremely biased toward massive stars. In addition, no yieldsoftheBBN.Stilllargerη’sinourscenariosuppress
significantspreadinmetallicities ofstarsinNGC 2808is the diffusionofneutronsfurther. Inaddition,thisregion
incompatible with the observedspreadin metallicities of extending over the event horizon even at the end of the
stars in a dwarf galaxy. BBN tolerates the diffusion of neutrons.
Inthispaper,weseekapossibilitythattheoverabun-
Most helium in the universe is believed to be pro-
dance of helium in the bMS of GCs is due to the inho-
duced by the big bang nucleosynthesis (BBN). By ob-
mogeneous BBN caused by the baryogenesis. First of
servations of extragalactic metal poor H II regions [15],
all, we determine the parameter region that reproduces
the mass fraction of helium produced during BBN (Y )
p
the helium abundance of bMS stars. The parameters
is estimated to be Y 0.25. One of the parameters
p
∼ we concerns are the baryon-to-photon ratio (η) and the
that affect Y is the baryon-to-photon ratio (η). Re-
p
degeneracy of electron neutrinos (ξ ). ξ is defined as
cently, results of the five-year observation of the cos- e e
ξ =µ /k T whereµ isthechemicalpotentialofelec-
mic microwave background radiation (CMBR) by the e νe B νe
tronneutrinos andk is the Boltzmannconstant. These
Wilkinson Microwave Anisotropy Probe (WMAP) were B
parameters are the most effective in the sense that they
released [16]. The baryon density parameter is deter-
mined to be Ω h2 = 0.02273 0.00062 where h is the can change the abundances of elements synthesized by
b
± the BBN. In Section II, we briefly summarize effects of
normalized Hubble constant given by dividing the Hub-
bleconstantby100km s 1Mpc 1. Combiningthisvalue the parameters η and ξe during the BBN. We also sum-
− −
marize calculations we have done in Section II. Results
withthewell-knowntemperatureofCMBR,2.725 0.002
K [17], η is determined to be η 6 10 10. Giv±en this are given in Section III and the evolution of the helium
−
∼ × enhanced region is discussed in Section IV. The conclu-
η, the calculation of the standardBBN yields Y 0.25,
p
≃ sion is given in Section V.
matchingwellwiththe observedvalues[18]. Inthe stan-
dard BBN theory, however, it is assumed that the BBN
occurred homogeneously and η has a uniform value. Al-
II. BIG BANG NUCLEOSYNTHESIS
though WMAP did not detect the inhomogeneity of the
universewithscalessmallerthanaresolutionl 2000
max
(θ 0.1 ), thereremainsapossibilityofinhom∼ogene- A. Free Parameters
min ◦
∼
ity with scales under 10 Mpc. Within regions smaller
∼
than10Mpc,η mightnottakethestandardvalue. Many The BBN occurred when the temperature of the uni-
calculationshavebeen done withvariousvalues ofη (see verse was about 1011 108 K. The parameters that gov-
−
the references of [19]). The general results are that the ern the abundance of helium synthesized during BBN
higherηbecomes,themoreabundantheliumwillbe. So, are η and ξ for a given set of the cosmological param-
e
herecomesanewcandidatefortheenigmaticmechanism eters. As η represents the density of baryons, collisions
of the helium enhancement in the bMS, inhomogeneous of baryons occur more frequently with increasing η, re-
BBN with a high value of η. sulting in larger Y . The parameter ξ represents lepton
p e
asymmetry and it can affect Y directly through the re-
We consider a baryogenesis mechanism that enhances p
actions
the baryon density in regions with the mass scale of
106M , a comparable amount of baryons to the GCs
p+e n+ν , (1)
that h⊙ave multiple main sequence. Though we do not − ←→ e
specify this baryogenesisinmoredetail,the Affleck-Dine which determines the number of neutrons and protons
mechanism [20] can realize this situation right after the before BBN. At the equilibrium of these reactions, the
inflation era. This mechanism can enhance the baryon number ratio of neutrons to protons is expressed by a
density as high as η 1 in a region with the mass scale function of the temperature T and ξ as
of 106M [21]. The∼size of inhomogeneity is a free pa- e
rameter⊙in this mechanism. The mass scale and desired nn ∆mc2
=exp ξ , (2)
η indicate that the scale of necessary inhomogeneities is np (cid:18)− kBT − e(cid:19)
3
Z A Z A Z A Z A Z A Z A
n 1 C 11-15 Mg 24-27 n 1 K 29-70 Sr 68-131
H 1-3 N 12-16 Al 25-28 H 1-3 Ca 30-73 Y 70-134
He 3,4 O 14-19 Si 28-31 He 3,4,6 Sc 32-76 Zr 72-137
Li 6-8 F 17-20 P 29-32 Li 6-9 Ti 34-80 Nb 74-140
Be 7,8 Ne 19-23 S 32 Be 7-12 V 36-83 Mo 77-144
B 8,10-12 Na 21-24 B 8,10-14 Cr 38-86 Tc 79-147
C 9-18 Mn 40-89 Ru 81-150
Table. I: Nuclei included in the small reaction network. Z is N 11-21 Fe 42-92 Rh 83-153
the name of nuclei and A is the mass number of Z included O 13-22 Co 44-96 Pd 86-156
in thenetwork. ’n’ refers to neutron. F 14,16-26 Ni 46-99 Ag 88-160
Ne 15-41 Cu 48-102 Cd 90-163
Na 17-44 Zn 51-105 In 92-166
Mg 19-47 Ga 53-108 Sn 94-169
where∆mc2 isthedifferenceoftherestenergiesbetween
Al 21-51 Ge 55-112 Sb 97-172
a proton and a neutron. As most of neutrons that had
Si 22-54 As 57-115 Te 99-176
existedbeforetheBBNerawerebroughtintoheliumnu- P 23-57 Se 59-118 I 101-179
clei,anegativeξe enhancesheliumsynthesis. Wetreatξe S 24-60 Br 61-121 Xe 103-182
as a free parameterrestrictedfromobservations[26] and Cl 26-63 Kr 63-124
assume β-equilibrium at the beginning of calculations. Ar 27-67 Rb 66-128
Allowed range with 2σ CL is
Table. II: Nuclei included in the large reaction network. See
thecaption of Table. I for details.
0.01 ξ 0.1. (3)
e
− ≤ ≤
A. Lower Limits
Note that the Affleck-Dine mechanism prefers negative
ξ with the absolute value of the order of η because η is
e
supposed to be positive [27]. TolocateastaronthebMSinωCentauribyenhancing
theheliumcontent,theheliumfractionshouldbeashigh
as 0.35 [3]. Therefore we require η to be greater than η
b
that reproduces Y = 0.35. To estimate the amount of
p
heliumproducedduring BBN,onlythe reactionsoflight
B. Numerical Calculations
elements are essential. For this reason, we use the small
reaction network to estimate Y .
p
Becausethe horizonscale rightafter the BBNis much The results of calculations are shown in Fig. 1. We
smaller than 106M in mass, the effect of diffusion is performedthe calculationwith three differentξ ; ξ =0,
e e
negligible. Thus, w⊙e calculate the BBN with high η in 0.01, and 0.1. The horizontal line indicates Y = 0.35.
p
the same way as the homogeneous BBN ignoring inho- For ξ =0−, η yielding Y >0.35 is in the region
e p
mogeneitiesinsidetheregionandadoptthesamemethod
of numerical calculations as that of the ordinary homo- η >3 10−5. (4)
×
geneousBBN.WefirstcalculatedBBNwiththereaction
Thus η = 3 10 5. For ξ = 0.01 and ξ = 0.1,
network including 61 nuclei shown in Table. I. The nu- b − e e
η = 2 10 5×and η = 2 10 4,−respectively. η above
cleosynthesis with a larger reaction network with nuclei b − b −
× ×
these values are required to explain the bMS stars.
in Table. II is also calculated to see how much heavy el-
ements are produced. Heavy element production during
BBN with high η is discussed in [22–24]. To calculate
B. Upper Limits
BBN, we used the Kawanocode introduced in [28], with
revisedreactionratestakingfrom[29]whenevertheyare
available. Reaction rates of heavy elements are taken As previously predicted by Matsuura et al. [22–24],
from [30]. heavy elements are produced during BBN with high η.
The amount of heavy elements produced during BBN
givestheupperlimitofη. Toolargeηmightoverproduce
heavyelementsincompatiblewiththemetallicityofbMS,
which is at least a factor of a few smaller than the solar
III. RESULTS
abundances. Asnucleiwiththemassnumber(A)of 80
∼
or greater are important for this restriction, we use a
We calculate the BBN with various parameters. The large reaction network for this purpose. For calculations
calculationsarestartedfromthetimewhenthetempera- of the large reaction network, we only consider the case
tureis1011 Kandweobtainedtheabundancesat107 K. of ξ =0.
e
Thenuclearstatisticalequilibriumandtheβ-equilibrium In Fig. 2, we show the results of BBN calculations for
are assumed at the initial state. somevaluesofη. Betweenη =1 10 5andη =2 10 5,
− −
× ×
4
4
10
η=9×10-6
η=1×10-5
102 η=2×10-5
η=3×10-5
o 100
ati
R
n -2
o 10
cti
a
Fr -4
er 10
b
m
u -6
N 10
-8
10
-10
10
0 20 40 60 80 100 120 140 160
Mass Number
Fig.1: ResultsofYpforsomesetsofηandξe. Thehorizontal Fig. 2: The number fractions of the produced elements rel-
line at themiddle represents Yp=0.35. ative to the solar abundances. All the calculations are done
with ξe=0.
there is a considerable jump in the amount of heavy el- A. Diffusion
ements with A 100. Fig. 7 of Matsuura et al. [23]
showsthatη =1∼0 4 yieldsasignificantamountofheavy Helium ions in the region with a higher Y might dif-
− p
elements with A 150, comparable to the solar abun- fuse outward the surrounding region with lower helium
∼
dances. With higher η, the abundances of heavy ele- contents. This effect takes place after the horizon scale
ments continue to increase. Observations show that the exceeds the size of the region, that is, after the tem-
amounts of heavy elements are at least a factor of a few perature becomes lower than 108 107 K. The diffusion
−
less than the solar abundances in the relevant GC [31]. equation for helium is written as
Therefore the upper limit of η is somewhere between
3×10−5 and 10−4. ∂nHe =D 2nHe, (5)
∂t ∇
In Fig. 2, some elements A 100 are very close to the
∼
expected abundances ofthe GC stars. Thus, it is a good where n is the number density of helium and D is the
He
touchstone of our model to check the abundances of the diffusioncoefficientofheliumwithelectronsanditsmag-
elements A 100 in the dwarfs in bMS. nitude is estimated as
∼
λv
D = , (6)
3
where λ is the mean free path of helium ions and v =
3k T/4m is the thermal speed of helium ions. Here
B H
IV. EVOLUTION OF HELIUM ENHANCED
REGION tpheconstantmH denotesthemassofhydrogen. Thetime
scale t of the diffusion is approximated as
diff
∂lnn 1
EvenifaprimordialgaswithhighYp wasonceformed tdiff = He −
at the time of BBN, it might be mixed with other gases (cid:12) ∂t (cid:12)
in the outer regions and end up with a lower fraction = (cid:12)(cid:12)D∇2nHe(cid:12)(cid:12) −1
of helium. We briefly show that the effect of such mix- (cid:12) nHe (cid:12)
(cid:12) (cid:12)
ing would not affect the region with high helium abun- (cid:12)R2 (cid:12)
, (7)
dance. Here, we do not only consider effects of diffusion
∼ D
and accretion, but also take into account self-gravity as
a competing process. where R is the size of the region.
5
1. Before Recombination 2. After Recombination
Before the recombination of electrons, photons and Matters are assumed to completely decouple from ra-
matters had been coupled and had the same tempera- diation after the recombination. Thus, n and R after
He
ture. The number density of helium during this epoch is the recombination are denoted as functions of the gas
proportionalto the cube of the temperature and written temperature T,
as
Y (T T)3/2
n = Ypn = Yp T 3ηn . (8) nHe = 4pηnγ0 reT3 =80T3/2 cm−3, (18)
He b γ0 0
4 4 (cid:18)T (cid:19)
0
and
Here T = 2.73 K is the present temperature of CMBR
0
and nγ0 is the present number density of photons and 7 1019
expressed as nγ0 = 2ζ(3)/π2(kBT0/~c)3 = 416 cm−3 R= ×T1/2 cm. (19)
where ~ is the reduced Planck constant. For the case
of η =10−4 and Yp =0.4, Here the temperature Tre when free electrons recombine
with hydrogen ions is about 5,500 K due to the higher
n =2 10 4T3 cm 3. (9) density. We have assumed that all of helium and hy-
He − −
× drogen atoms are neutral in this stage. Therefore the
Thus, the size R is expressed as a function of the tem- cross section for helium atoms becomes of the order of
perature 10−16 cm2. Accordingly, D becomes
∼
R = 3Yp106M⊙ 1/3 = 5×1021 cm. (10) D = 3×T1017 cm2sec−1. (20)
(cid:18)16πm n (cid:19) T
H He
The diffusion timescale is obtained as a constant value.
Next, we estimate D before the recombination. As-
suming that the universe has no net charge, the number t =2 1022 sec. (21)
diff
density of electrons n is written as ×
e
This diffusion time is also too large.
n = n +2n (11)
e H He
3
Y T
p
= 1 ηn (12)
γ0
(cid:18) − 2 (cid:19)(cid:18)T0(cid:19) B. Accretion
= 2 10 3T3 cm 3. (13)
− −
×
Since the region with enhanced helium content has a
The last value is, again, for the case of η = 10−4 and much higher density than the surrounding region, the
Yp =0.4. From [32], region accretes matters from the outside, which might
dilute the helium fraction. For simplicity, the timescale
9k2T2 8 105T2 ofthisprocessisestimatedassumingtheBondiaccretion
λ = B = × cm, (14)
4n e4lnΛ n lnΛ [33]. The time scale of the Bondi accretion is inferred
e e
from the relation
where
M˙ ρ( )
Λ= 43e2 (cid:18)kπB3nT3(cid:19)1/2 =7×103(cid:18)Tn3(cid:19)1/2. (15) M =4πG2Mc3s(∞∞)λ(γ), (22)
e e
where M is the total mass of the region (106M in this
Thus, case), ρ( ) and c ( ) are the density and th⊙e sound
s
∞ ∞
speed at infinity. The eigen value of the steady state so-
λv 8 1011
D = = × cm2sec−1. (16) lutionλ(γ) is a function ofthe adiabatic index γ written
3 T1/2 as
From R and D derived above, tdiff is estimated to be 2 25(γ−−3γ1) (γ = 5)
tdiff ∼ 3×T31/0231 sec∼9×1020 (cid:18)10T7K(cid:19)3/2sec. (17) λ(γ) =  e(cid:16)55/−33γ(cid:17) (γ 6= 53). (23)
3

This diffusion time scale is so large that the effect of The values of ρ( ) and c ( ) are taken from those in
s
diffusion is negligible. thesurroundingr∞egionwithY∞ =0.25andη =6 10 10.
p −
×
6
They changeasthe universeexpandsandcanbe written the other hand, the Jeans mass in this region reduces to
as functions of temperature, 2 103M immediatelyaftertherecombination. Thehe-
liu×mrich⊙regioncollapsesonthetimescaleof 1.5 1011
3 ∼ ×
m ηn T sec, much shorter than the accretion time scale at the
ρ(∞) =  H γ0(cid:16)T0(cid:17) 3 (24) teeqmuapteiroantu(2re8)offoTrrbee=for5e,r5e0c0omKb,ini.aet.,io3n.)5.×Th1i0s25prseecced(isnege
m2 Hη1n0γ03(cid:16)2T√3TTr0geTcm(cid:17) 3 (before recombination) cmoalltatpersewmithighthteaavcocidretoevderaamllbmienixtinmgatotfert.heThheelriuesmultraicnht
× − − cloud consists of helium rich core surrounded by a pri-
 (25)
mordial gas with the normal helium content.
∼ 3 10 27T3/2 gcm 3 (after recombination),
× − − Though there is no widely accepted scenario for the
 formation of a GC, we raise possible routes to realize
whereT aftertherecombinationdenotesthegastemper-
GCs with multiple main sequence. Subsequent star for-
ature. Similarly, c ( ) is expressed as
s ∞ mation both in the core and envelope could lead to a
c starclusterwithdoublemainsequenceresemblingωCen-
cs(∞) =  r3(cid:16)1+34ca2Bρ(T∞4)(cid:17) (26) ltwiadiutehria.dniTdffoetrrreeinpgtgroeYrdpu’sscteainrahfGoerClmiulamikteiroNincshGiCcno2ree8as0c8ah,retowfnoereesdguiecodhntscolowcuiotdlhs-
γkBT
q2 µ1m01H0 cmsec 1 (before) rthemreoevedsiffsetraernstthYapt’sh.avTehfoercmoelldisbioenfowrei.thThaishmigahyvaellsoocritey-
 q1×+3×T103 − (27) dstuacrestinhethsetatrh-utos-fsotramresdcactltuesrteinrhmaevteamlliaciitniesse.quAesnacersewsuiltth,
∼ 
104√T cmsec 1 (after), three different helium contents and have similar metal-
−
 licities. These features are observed for stars in NGC
where µ is the mean molecular weight and a is the ra- 2808. Cloud-cloud collisions have been raised as a pos-
B
diation energy constant a = 8π5k4/15h3c3. Thus, the sible mechanism for the globular cluster formation [34].
B B
accretion time scale t becomes Young stellar clustersfound in merginggalaxies[35]and
acc
nearthecenteroftheMilkyWaygalaxy[36]supportthis
3/2
3 1036 1+ 3 103 T 3 sec (before) mechanism.
t = M = × (cid:16) ×T (cid:17) − (28)
acc M˙ 
6 1011 sec (after).
× V. CONCLUSIONS

This result means that the time scale of accretion be-
fore the recombination is long enough to avoid dilution We calculated the BBN for several values of η and ξ
e
of helium, while the time scale after the recombination andlookedfortheparameterregionwheretheheliumen-
becomes significantly shorter than the Hubble time at richment in the GCs is reproduced. We set lower limits
that epoch. This indicates that the average helium con- of η to be η = 3 10 5 for ξ = 0, η = 2 10 5
b − e b −
tent reduces considerably. However, if we take the effect for ξ = 0.01, a×nd η = 2 10 4 for ξ ×= 0.1
e b − e
− ×
ofself-gravityintoaccount,starformationmightprecede . The upper limits come from metal abundances and
the dilution of helium depending on the effectiveness of the allowed parameter region for the case of ξ = 0 is
e
turbulent mixing. 3 10 5 <η <10 4. If aninhomogeneitycausedby the
− −
×
Affleck-Dinebaryogenesismadearegionwithη andξ in
e
these criterions, the helium abundance is enhanced and
C. Star Formation the region can end up with GCs, showing multiple main
sequences. Our model predicts that the abundances of
The Jeans length λ of the system before the recom- heavy elements with A 100 is enhanced in the bMS
J
∼
bination is stars. Starsinourmodelareexpectedtohavemorecon-
centrated spatial distribution of the bMS stars than the
c 1027T 3/2
λ = s = − cm, (29) rMS as was recently reported for ω Centauri [4] because
J
√Gρ 1+ 3 108 the bMS stars are formed in the central part of the he-
q ×T lium enhanced region while the rMS stars are formed in
and the Jeans mass M is the outer envelope in our model.
J
A problem of the Affleck-Dine baryogenesis is that it
4 8 1021M can be adopted to antimatters as well as ordinary mat-
MJ = 3πλ3Jρ= (T +×3 108)⊙3/2. (30) ters and can create regions with enhanced antimatters.
× As there are no observations of such regions with an-
Therefore as long as the matter is ionized the mass of timatters, there should be some mechanism that stops
the helium richregionneverexceedsthe Jeansmass. On the generation of antimatters or there must be another
7
baryogenesismechanism to exclusively enhance ordinary acknowledge K. Sato, N. Kohri, S. Matsuura, and K.
matters up to η 3 10 5 in small regions. Ichikawa for useful comments on numerical calculations
−
∼ ×
of big bang nucleosynthesis. We also wish to thank M.
KawasakiandK.Kamadafordiscussionsonbaryogenesis
Acknowledgments and cosmology. This work has been partially supported
bytheGrantsinAidforScientificResearch(21018004)of
We are grateful to an anonymous referee for helpful the Ministry of Education, Science, Culture, and Sports
suggestions to improve the presentation. We wish to in Japan.
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