# Constraint on Heavy Element Production in Inhomogeneous Big-Bang Nucleosynthesis from the  Light Element Observations

Authors: Riou Nakamura; Masa-aki Hashimoto; Shin-ichiro Fujimoto; Katsuhiko Sato
Journal: Journal of Astrophysics
 (2013)

---

## Abstract

We investigate the observational constraints on the inhomogeneous big-bang nucleosynthesis that Matsuura et al. (2005) suggested that states the possibility of the heavy element production beyond7Li in the early universe. From the observational constraints on light elements of 4He and D, possible regions are found on the plane of the volume fraction of the high-density region against the ratio between high- and low-density regions. In these allowed regions, we have confirmed that the heavy elements beyond Ni can be produced appreciably, where p- and/or r-process elements are produced well simultaneously.


---

## Body

## 1. Introduction

Big-bang nucleosynthesis (BBN) has been investigated to explain the origin of the light elements, such asHe4, D, He3, and Li7, during the first few minutes [1–4]. Standard model of BBN (SBBN) can succeed in explaining the observation of those elements, He4 [5–9], D [10–13], and He3 [14, 15], except for Li7. The study of SBBN has been done under the assumption of the homogeneous universe, where the model has only one parameter, the baryon-to-photon ratio η. If the present value of η is determined, SBBN can be calculated from the thermodynamical history with the use of the nuclear reaction network. We can obtain the reasonable value of η by comparing the calculated abundances with observations. In the meanwhile, the value of η is obtained as η=(5.1-6.5)×10-10 [1] from the observations of He4 and D. These values agree well with the observation of the cosmic microwave background: η=(6.19±0.14)×10-10 [16].On the other hand, BBN with the inhomogeneous baryon distribution also has been investigated. The model is called as inhomogeneous BBN (IBBN). IBBN relies on the inhomogeneity of baryon concentrations that could be induced by baryogenesis (e.g., [17]) or phase transitions such as QCD or electro-weak phase transition [18–21] during the expansion of the universe. Although a large-scale inhomogeneity is inhibited by many observations [16, 22–24], a small scale one has been advocated within the present accuracy of the observations. Therefore, it remains a possibility for IBBN to occur in some degree during the early era. In IBBN, the heavy element nucleosynthesis beyond the mass number A=8 has been proposed [17, 18, 25–35]. In addition, peculiar observations of abundances for heavy elements and/or He4 could be understood in the way of IBBN. For example, the quasar metallicity of C, N, and Si could have been explained from IBBN [36]. Furthermore, from recent observations of globular clusters, a possibility of inhomogeneous helium distribution is pointed out [37], where some separate groups of different main sequences in blue band of low mass stars are assumed due to high primordial helium abundances compared to the standard value [38, 39]. Although baryogenesis could be the origin of the inhomogeneity, the mechanism of it has not been clarified due to unknown properties of the supersymmetric Grand Unified Theory [40].Despite a negative opinion against IBBN due to insufficient consideration of the scale of inhomogeneity [41], Matsuura et al. have found that the heavy element synthesis for both p- and r-processes is possible if η>10-4 [42], where they have also shown that the high η regions are compatible with the observations of the light elements, He4 and D [43]. However, their analysis is only limited to a parameter of a specific baryon number concentration. In this paper, we extend the investigations of Matsuura et al. [42, 43] to check the validity of their conclusion from a wide parameter space of the IBBN model.In Section2, we review and give the adopted model of IBBN which is the same one as that of Matsuura et al. [43]. Constraints on the critical parameters of IBBN due to light element observations are shown in Section 3, and the possible heavy elements of nucleosynthesis are presented in Section 4. Finally, Section 5 is devoted to the summary and discussion.


## 2. Model

In this section, we introduce the model of IBBN. We adopt the two-zone model for the inhomogeneous BBN. In the IBBN model, we assume the existence of spherical high-density region inside the horizon. For simplicity, we ignore in the present study the diffusion effects before(1010K<T<1011K) and during the primordial nucleosynthesis (107K<T<1010K), because the timescale of the neutron diffusion is longer than that of the cosmic expansion [25, 37].To find the parameters compatible with the observations, we consider the average abundances between the high- and low-density regions. We get at least the parameters for the extreme case by averaging the abundances in two regions. Let us define the notations,nave, nhigh, and nlow as average,  high, and low baryon number densities. fv is the volume fraction of the high baryon density region. Xiave, Xihigh, and Xilow are mass fractions of each element i in average, and high- and low-density regions, respectively. Then, basic relations are written as follows [43]:
(1)nave=fvnhigh+(1-fv)nlow,naveXiave=fvnhighXihigh+(1-fv)nlowXilow.
Here, we assume the baryon fluctuation to be isothermal as was done in previous studies (e.g., [18, 19, 30]). Under that assumption, since the baryon-to-photon ratio is defined by the number density of photon in standard BBN, (1) is rewritten as follows:
(2)ηave=fvηhigh+(1-fv)ηlow,(3)ηaveXiave=fvXihighηhigh+(1-fv)Xilowηlow,
where ηs with subscripts are the baryon-to-photon ratios in each region. In the present paper, we fix ηave=6.19×10-10 from the cosmic microwave background observation [16]. The values of ηhigh and ηlow are obtained from both fv and the density ratio between high- and low-density regions: R≡nhigh/nlow=ηhigh/ηlow.To calculate the evolution of the universe, we solve the following Friedmann equation:(4)(x˙x)2=8πG3ρ,
where x is the cosmic scale factor and G is the gravitational constant. The total energy density ρ in (4) is the sum of decomposed parts:
(5)ρ=ργ+ρν+ρe±+ρb.
Here, the subscripts γ, ν, and e± indicate photons, neutrino, and electrons/positrons, respectively. The final term is the baryon density obtained as ρb≃mpnave.We should note the energy density of baryon. To get the time evolution of the baryon density in both regions, the energy conservation law is used as follows:(6)ddt(ρx3)+pddt(x3)=0,
where p is the pressure of the fluid. When we solve (6), initial values in both regions are obtained from (2) with fv and R fixed. For ηhigh≥2×10-4, the baryon density in the high-density region, ρhigh, is larger than the radiation component at T>109 K. However, we note that the contribution to (5) is not ρhigh, but fvρhigh. In our research, the ratio of fvρhigh to ργ is about 10-7 at BBN epoch. Therefore, we can neglect the final term of (5) in the same way as it has been done in SBBN during the calculation of (4).


## 3. Constraints from Light Element Observations

In this section, we calculate the nucleosynthesis in high- and low-density regions with the use of the BBN code [44] which includes 24 nuclei from neutron to O16. We adopt the reaction rates of Descouvemont et al. [45], the neutron lifetime τN=885.7 sec [1], and consider three massless neutrinos.Let us consider the range offv. For fv≪0.1, the heavier elements can be synthesized in the high-density regions as discussed in [33]. For fv>0.1, contribution of the low-density region to ηave can be neglected, and therefore to be consistent with the  observations of light elements, we need to impose the condition of fv<0.1.Figure1 illustrates the light element synthesis in the high- and low-density regions with fv=10-6 and R = 106 that corresponds to ηhigh=3.05×10-4 and ηlow=3.05×10-10. Light elements synthesized in these calculations are shown in Table 1. In the low-density region, the evolution of the elements is almost the same as the case of SBBN. In the high-density region, while He4 is more abundant than that in the low-density region, Li7 (or Be7) is much less produced. In this case, we can see that average values such as He4 and D are overproduced as shown in Table 1. However, this overproduction can be saved by choosing the parameters carefully. We need to find the reasonable parameter ranges for both fv and R by comparing with the observation of the light elements.Table 1
The numerical abundances of light elements synthesized as shown in Figure1.
Elements
X
i
high
X
i
low
X
i
p
0.608
0.759
0.684
D
3.07
×
1
0
-
18
1.19
×
1
0
-
4
5.95
×
1
0
-
5
T +3He
1.15
×
1
0
-
13
3.41
×
1
0
-
5
1.71
×
1
0
-
5
4He
0.392
0.241
0.316
7Li + 7Be
8.2
×
1
0
-
13
6.29
×
1
0
-
10
3.14
×
1
0
-
10Illustration of the nucleosynthesis in the two-zone IBBN model withfv=10-6 and R=106. The baryon-to-photon ratios in the high (a) and low (b) density regions are ηhigh=3.05×10-4 and ηlow=3.05×10-10, respectively.
(a)
(b)Now, we put constraints onfv and R by comparing the average values of He4 and D obtained from (3) with the following observational values. First, we consider the primordial He4 abundance reported in [8]:
(7)Yp=0.2565±0.0010±0.0050,
and [9]:
(8)Yp=0.2534±0.0083.
We adopt He4 abundances as follows:
(9)0.2415<Yp<0.2617.Next, we take the primordial abundance from the D/H observation reported in [12]:
(10)DH=(2.84±0.26)×10-5,
and [13]:
(11)DH=(2.535±0.05)×10-5,DH=(2.48±0.12)×10-5.
Considering those observations with errors, we adopt the primordial D/H abundance as follows:
(12)2.36<DH×105<3.02.Figure2 illustrates the constraints on the fv-R plane from the above light element observations with contours of constant ηhigh. The solid and dashed lines indicate the upper limits from (9) and (12), respectively. From the results, we can obtain approximately the following relations between fv and R:
(13)R≤{104×fv-0.3forfv>7.4×10-6,0.13×fv-0.98forfv≤7.4×10-6.
The He4 observation (9) gives the upper bound for fv<7.4×10-6, and the limit for fv>7.4×10-6 is obtained from D observation (12). As shown in Figure 2, we can find the allowed regions which include the very high-density region such as ηhigh=10-3.Figure 2
Constraints on thefv-R plane from the observations of light element abundances. The region below the red line is an allowed one obtained from He4 observation (9). Constraints from the D/H observation (12) are shown by the region below the blue line. The gray region corresponds to the allowed parameters determined from the two observations of He4 and D/H. There is another region which is still consistent with only D/H in the upper right direction. This is the contribution of the low-density region with ηlow~10-12. The D abundance tends to decrease against the baryon density for η>10-12. The dotted lines show the contours of the baryon-to-photon ratio in the high-density region. Filled squares indicate the parameters for heavy element nucleosynthesis adopted in Section 4.We should note thatηhigh takes a larger value, nuclei which are heavier than Li7 are synthesized more and more. Then we can estimate the amount of total CNO elements in the allowed region. Figure 3 illustrates the contours of the summation of the average values of the heavier nuclei (A>7), which correspond to Figure 2 and are drawn using the constraint from He4 and D/H observations. As a consequence, we get the upper limit of total mass fractions for heavier nuclei as follows:
(14)X(A>7)≤10-5.Figure 3
Contours of the average total mass fractions which are the sum of the nuclei heavier thanLi7, where we find a consistent region of the produced elements with He4 and D observations.


## 4. Heavy Element Production

In the previous section, we have obtained the amount of CNO elements produced in the two-zone IBBN model. However, it is not enough to examine the nuclear production beyondA>8 because the baryon density in the high-density region becomes so high that elements beyond CNO isotopes can be produced [17, 31, 32, 34, 42]. In this section, we investigate the heavy element nucleosynthesis in the high-density region considering the constraints shown in Figure 2. Abundance change is calculated with a large nuclear reaction network, which includes 4463 nuclei from neutron (n) and proton (p) to Americium (Z = 95 and A = 292). Nuclear data, such as reaction rates, nuclear masses, and partition functions, are the same as the ones used in [46–49] except for the neutron-proton interaction. We use the weak interaction of Kawano code [50], which is adequate for the high-temperature epoch of T>1010 K.As seen in Figure3, heavy elements of X(A>7)>10-9 are produced nearly along the upper limit of R. Therefore, to examine the efficiency of the heavy element production, we select five models with the following parameters: ηhigh = 10-3, 5.1×10-4, 10-4, 5.0×10-5, and 10-5 corresponded to (fv,R) = (3.24×10-8,1.74×106), (1.03×10-8,9.00×105), (5.41×10-7,1.84×105), (1.50×10-6,9.20×104), and (5.87×10-6,1.82×104). Adopted parameters are indicated by filled squares in Figure 2.First, we evaluate the validity of the nucleosynthesis code with4463 nuclei. Table 2 shows the results of the light elements, p, D, He4, He3, and Li7. The results of the high-density region are calculated by the extended nucleosynthesis code, and the abundances in the low-density region are obtained by BBN code. The average abundances are obtained by (3). Since the average values of He4 and D are consistent with the observations, there is no difference between BBN code and the extended nucleosynthesis code in regard to the average abundances of light elements.Table 2
Mass fractions of light elements for the four cases:ηhigh≃10-3, ηhigh=5×10-4, ηhigh≃10-4, and ηhigh=10-5. tfin and Tfin are the time and temperature at the final stage of the calculations.
(a)
For cases ofηhigh=10-3 and ηhigh=5×10-4
f
v
,
R
3.23
×
1
0
-
8
,
1.74
×
1
0
6
1.03
×
1
0
-
7
,
9.00
×
1
0
5
(
η
high
,
η
low
)
(1.02×10-3, 5.86×10-10)
(5.10×10-4, 5.67×10-10)
(
t
fin
,
T
fin
)
1.0
×
1
0
5 sec, 4.2×107 K
1.1
×
1
0
5 sec, 4.9×107 K
Elements
High
Low
Average
High
Low
Average
p
0.586
0.753
0.744
0.600
0.753
0.740
D
1.76
×
1
0
-
21
4.50
×
1
0
-
5
4.26
×
1
0
-
5
3.43
×
1
0
-
21
4.75
×
1
0
-
5
4.34
×
1
0
-
5
3He + T
2.91
×
1
0
-
14
2.18
×
1
0
-
5
2.07
×
1
0
-
5
2.77
×
1
0
-
14
2.23
×
1
0
-
5
2.04
×
1
0
-
5
4He
0.413
0.247
0.256
0.400
0.247
0.260
7Li + 7Be
1.63
×
1
0
-
13
1.78
×
1
0
-
9
1.68
×
1
0
-
9
6.80
×
1
0
-
14
1.65
×
1
0
-
9
1.52
×
1
0
-
9
(b)
For cases ofηhigh=10-4 and ηhigh=10-5
f
v
,
R
5.41
×
1
0
-
7
,
1.84
×
1
0
5
5.87
×
1
0
-
6
,
1.82
×
1
0
4
(
η
high
,
η
low
)
(1.04×10-4, 5.62×10-10)
(1.02×10-5, 5.59×10-10)
(
t
fin
,
T
fin
)
1.2
×
1
0
5 sec, 4.3×107 K
1.2
×
1
0
5 sec, 4.5×107 K
Elements
High
Low
Average
High
Low
Average
p
0.638
0.753
0.742
0.670
0.753
0.745
D
6.84
×
1
0
-
22
4.79
×
1
0
-
5
4.36
×
1
0
-
5
1.12
×
1
0
-
22
4.48
×
1
0
-
5
4.37
×
1
0
-
5
3He + T
1.63
×
1
0
-
13
2.23
×
1
0
-
5
2.04
×
1
0
-
5
1.49
×
1
0
-
9
2.25
×
1
0
-
5
2.03
×
1
0
-
5
4He
0.362
0.247
0.258
0.330
0.247
0.254
7Li + 7Be
7.42
×
1
0
-
13
1.64
×
1
0
-
9
1.49
×
1
0
-
9
6.73
×
1
0
-
8
1.62
×
1
0
-
9
7.96
×
1
0
-
9Figure4 shows the results of nucleosynthesis in the high-density regions with ηhigh≃10-4 and 10-3. In Figure 4(a), we see the time evolution of the abundances of Gd and Eu for the mass number 159. First, Tb159 (stable r-element) is synthesized and later Gd159and Eu159 are synthesized through the neutron captures. After t=103 sec, Eu159 decays to nuclei by way of Eu159 →Gd159→Tb159, where the half-lifes of Eu159 and Gd159 are 26.1 min and 18.479 h, respectively.Time evolution of the mass fractions in high-density regions of (a)ηhigh=1.02×10-4 and (b) ηhigh=1.06×10-3.
(a)
η
high
=
1.02
×
1
0
-
4
(b)
η
high
=
1.06
×
1
0
-
3Forηhigh≃10-3, the result is seen in Figure 4(b). Sn108, which is a proton-rich nuclei is synthesized. After that, stable nuclei Cd108 is synthesized by way of Sn108→In108→Cd108, where the half-lifes of Sn108 and In108 are 10.3 min and 58.0 min, respectively. These results are qualitatively the same as Matsuura et al. [42].In addition, we notice the production of radioactive nuclei ofNi56 and Co57, where Ni56 is produced at early times, just after the formation of He4. Usually, nuclei such as Ni56 and Co57 are produced in supernova explosions, which are assumed to be the events after the first star formation (e.g., [51]). In IBBN model, however, this production can be found to occur at an extremely high-density region of ηhigh≥10-3 as the primary elements without supernova events in the early universe.Final results (T = 4×107 K) of nucleosynthesis calculations are shown in Table 3. When we calculate the average values, we set the abundances of A>16 to be zero for low-density side. For ηhigh≃10-4, a lot of nuclei of A>7 are synthesized whose amounts are comparable to that of Li7. Produced elements in this case include both s-element (i.e., Ba138) and r-elements (for instance, Ce142 and Nd148). For ηhigh≃10-3, there are few r-elements while both s-elements (i.e., Kr82 and Y89) and p-elements (i.e., Se74 and Kr78) are synthesized such as the case of supernova explosions. For ηhigh=10-3, the heavy elements are produced slightly more than the total mass fraction (shown in Figure 3) derived from the BBN code calculations. This is because our BBN code used in Section 3 includes the elements up to A=16 and the actual abundance flow proceeds to much heavier elements.Table 3
Mass fractions of heavy elements(A>7) for three cases of ηhigh≃10-3, ηhigh=5.33×10-4, and ηhigh≃10-4.
f
v
=
3.23
×
1
0
-
8
,
R
=
1.74
×
1
0
6
f
v
=
1.03
×
1
0
-
7
,
R
=
9.00
×
1
0
5
f
v
=
5.41
×
1
0
-
7
,
R
=
1.84
×
1
0
5
(
η
high
=
1.06
×
1
0
-
3
)
(
η
high
=
5.33
×
1
0
-
4
)
(
η
high
=
1.02
×
1
0
-
4
)
Element
High
Average
Element
High
Average
Element
High
Average
Ni56
1.247
×
1
0
-
4
6.658
×
1
0
-
6
Nd142
2.051
×
1
0
-
5
1.738
×
1
0
-
6
Nd145
3.692
×
1
0
-
7
3.342
×
1
0
-
8
Co57
1.590
×
1
0
-
5
8.487
×
1
0
-
7
Ni56
1.270
×
1
0
-
5
1.077
×
1
0
-
6
Ca40
2.706
×
1
0
-
7
2.450
×
1
0
-
8
Sr86
1.061
×
1
0
-
5
5.662
×
1
0
-
7
Sm148
1.059
×
1
0
-
5
8.976
×
1
0
-
7
Mn52
2.417
×
1
0
-
7
2.188
×
1
0
-
8
Sr87
9.772
×
1
0
-
6
5.214
×
1
0
-
7
Pm147
6.996
×
1
0
-
6
5.930
×
1
0
-
7
Eu155
2.374
×
1
0
-
7
2.149
×
1
0
-
8
Se74
9.745
×
1
0
-
6
5.200
×
1
0
-
7
Pm145
6.559
×
1
0
-
6
5.559
×
1
0
-
7
Ce140
1.931
×
1
0
-
7
1.748
×
1
0
-
8
Sr84
9.172
×
1
0
-
6
4.894
×
1
0
-
7
Sm146
6.539
×
1
0
-
6
5.542
×
1
0
-
7
Cr51
1.546
×
1
0
-
7
1.400
×
1
0
-
8
Kr82
8.910
×
1
0
-
6
4.754
×
1
0
-
7
Nd143
4.146
×
1
0
-
6
3.514
×
1
0
-
7
Ce142
1.114
×
1
0
-
7
1.008
×
1
0
-
8
Kr81
7.797
×
1
0
-
6
4.160
×
1
0
-
7
Pr141
3.957
×
1
0
-
6
3.354
×
1
0
-
7
Ni56
1.100
×
1
0
-
7
9.964
×
1
0
-
9
Ge72
7.674
×
1
0
-
6
4.095
×
1
0
-
7
Nd144
3.952
×
1
0
-
6
3.350
×
1
0
-
7
Nd146
1.049
×
1
0
-
7
9.501
×
1
0
-
9
Kr78
7.602
×
1
0
-
6
4.057
×
1
0
-
7
Sm147
3.752
×
1
0
-
6
3.180
×
1
0
-
7
Eu156
9.436
×
1
0
-
8
8.542
×
1
0
-
9
Kr80
7.063
×
1
0
-
6
3.769
×
1
0
-
7
Sm149
3.322
×
1
0
-
6
2.815
×
1
0
-
7
Nd148
9.361
×
1
0
-
8
8.474
×
1
0
-
9
Kr83
6.252
×
1
0
-
6
3.336
×
1
0
-
7
Pm146
2.629
×
1
0
-
6
2.228
×
1
0
-
7
Fe52
8.974
×
1
0
-
8
8.124
×
1
0
-
9
Ge73
6.144
×
1
0
-
6
3.278
×
1
0
-
7
Sm144
2.207
×
1
0
-
6
1.870
×
1
0
-
7
Tb161
8.956
×
1
0
-
8
8.108
×
1
0
-
9
Se76
5.929
×
1
0
-
6
3.164
×
1
0
-
7
Sm150
1.683
×
1
0
-
6
1.426
×
1
0
-
7
La139
8.804
×
1
0
-
8
7.971
×
1
0
-
9
Br79
5.904
×
1
0
-
6
3.150
×
1
0
-
7
Pm144
1.581
×
1
0
-
6
1.340
×
1
0
-
7
N14
8.736
×
1
0
-
8
7.909
×
1
0
-
9
Se77
5.345
×
1
0
-
6
2.852
×
1
0
-
7
Pm143
1.575
×
1
0
-
6
1.335
×
1
0
-
7
Cr48
8.561
×
1
0
-
8
7.750
×
1
0
-
9
Y89
4.759
×
1
0
-
6
2.539
×
1
0
-
7
Sm145
1.010
×
1
0
-
6
8.568
×
1
0
-
8
Ba138
7.955
×
1
0
-
8
7.202
×
1
0
-
9
Zr90
4.412
×
1
0
-
6
2.354
×
1
0
-
7
Co57
8.643
×
1
0
-
7
7.326
×
1
0
-
8
C12
7.672
×
1
0
-
8
6.945
×
1
0
-
9
Rb85
4.324
×
1
0
-
6
2.307
×
1
0
-
7
Eu153
5.563
×
1
0
-
7
4.715
×
1
0
-
8
Dy162
6.835
×
1
0
-
8
6.188
×
1
0
-
9
Rb83
4.082
×
1
0
-
6
2.178
×
1
0
-
7
Ce140
4.944
×
1
0
-
7
4.191
×
1
0
-
8
C13
6.428
×
1
0
-
8
5.819
×
1
0
-
9
Y88
3.845
×
1
0
-
6
2.052
×
1
0
-
7
Nd145
4.376
×
1
0
-
7
3.709
×
1
0
-
8
O16
6.301
×
1
0
-
8
5.704
×
1
0
-
9
Zr88
3.546
×
1
0
-
6
1.892
×
1
0
-
7
Eu155
4.224
×
1
0
-
7
3.581
×
1
0
-
8
Gd158
5.845
×
1
0
-
8
5.292
×
1
0
-
9
As73
3.519
×
1
0
-
6
1.878
×
1
0
-
7
Eu151
4.106
×
1
0
-
7
3.480
×
1
0
-
8
Cs137
5.559
×
1
0
-
8
5.033
×
1
0
-
9
Ga71
3.388
×
1
0
-
6
1.808
×
1
0
-
7
Cr52
4.071
×
1
0
-
7
3.450
×
1
0
-
8
Nd147
3.962
×
1
0
-
8
3.587
×
1
0
-
9
Se75
2.933
×
1
0
-
6
1.565
×
1
0
-
7
Cd108
3.596
×
1
0
-
7
3.048
×
1
0
-
8
Ho165
3.770
×
1
0
-
8
3.413
×
1
0
-
9
Nb91
2.896
×
1
0
-
6
1.545
×
1
0
-
7
Gd156
3.368
×
1
0
-
7
2.854
×
1
0
-
8
Pr143
3.111
×
1
0
-
8
2.817
×
1
0
-
9
As75
2.856
×
1
0
-
6
1.524
×
1
0
-
7
Cd110
3.103
×
1
0
-
7
2.630
×
1
0
-
8
Ce141
2.998
×
1
0
-
8
2.714
×
1
0
-
9
Mo92
2.442
×
1
0
-
6
1.303
×
1
0
-
7
Eu152
2.809
×
1
0
-
7
2.381
×
1
0
-
8
Gd160
2.950
×
1
0
-
8
2.670
×
1
0
-
9
Ge70
2.318
×
1
0
-
6
1.237
×
1
0
-
7
Sm151
2.795
×
1
0
-
7
2.369
×
1
0
-
8
Xe136
2.771
×
1
0
-
8
2.509
×
1
0
-
9
Sr88
2.021
×
1
0
-
6
1.078
×
1
0
-
7
Eu154
2.759
×
1
0
-
7
2.339
×
1
0
-
8
Xe134
2.238
×
1
0
-
8
2.026
×
1
0
-
9
∑
A
>
7
X
(
A
)
3.010
×
1
0
-
4
1.652
×
1
0
-
5
∑
A
>
7
X
(
A
)
1.062
×
1
0
-
4
9.006
×
1
0
-
6
∑
A
>
7
X
(
A
)
3.850
×
1
0
-
6
3.485
×
1
0
-
7Figure5 shows the average abundances between high- and low-density regions using (3) in comparing with the solar system abundances [52]. For ηhigh≃10-4, abundance productions of 120<A<180 are comparable to the solar values. For ηhigh≃10-3, those of 50<A<100 have been synthesized well. In the case of ηhigh=5×10-4, there are two outstanding peaks: one is around A=56  (N=28) and the other can be found around A=140. Abundance patterns are very different from that of the solar system ones, because IBBN occurs under the condition of a significant amount of abundances of both neutrons and protons.Figure 5
Comparison of the average mass fractions in the two-zone model with the solar system abundances [52] (indicated by dots).


## 5. Summary and Discussion

We extend the previous studies of Matsuura et al. [42, 43] and investigate the consistency between the light element abundances in the IBBN model and the observation of He4 and D/H.First, we have done the nucleosynthesis calculation using the BBN code with 24 nuclei for both regions. The time evolution of the light elements at the high-density region differs significantly from that at the low-density region. The nucleosynthesis begins faster andHe4 is more abundant than that in the low-density region. By comparing the average abundances with the He4 and D/H observations, we can get the allowed parameters of the two-zone model: the volume fraction fv of the high-density region and the density ratio R between the two regions.Second, we calculate the nucleosynthesis that includes 4463 nuclei in the high-density regions. Qualitatively, results of nucleosynthesis are the same as those in [42]. In the present results, we showed that p- and r-elements are synthesized simultaneously at high-density region with ηhigh≃10-4.We find that the average mass fractions in IBBN amount to as much as the solar system abundances. As seen from Figure5, there are overproduced elements around A=150 (for ηhigh = 10-4) and A = 80 (for ηhigh = 10-3). Although it seems to conflict with the chemical evolution in the universe, this problem could be solved by the careful choice of fv and/or R. Figure 6 illustrates the mass fractions with ηhigh=1.0×10-4 for three sets of fv-R. It is shown that the abundances can become lower than the solar system abundances. If we put a constraint on the fv-R plane from the heavy element observations [53–56], the parameters in IBBN model should be tightly determined.Figure 6
Same as Figure5, but ηhigh is fixed as 10-4.In the meanwhile, we would like to touch on the consistency against the primordialLi7. We have obtained interesting results about Li7 abundances in our model. For the recent study of Li7, the lithium problem arises from the discrepancy among the Li7 abundance predicted by SBBN theory, the baryon density of WMAP, and abundance inferred from the observations of metal-poor stars (see [57, 58]). As seen in Table 2, Li7 is clearly overproduced such as Li7/H|ave=1.52×10-9 for ηhigh=10-5, although we adopt the highest observational value Li7/H=(2.75-4.17)×10-10 [59]. However, for cases of ηhigh=10-3, 5×10-4 and 10-4, the values of Li7/H|ave agree with the observation. Usually, the consistency with BBN has been checked using observations of He4, D/H, and Li7/H. Then, the parameters such as ηhigh=10-5 ought to be excluded. However, the abundance of Li7/H|ave is sensitive to the values of both ηhigh and ηlow. As for the future work of IBBN, we will study in detail the Li7 production. In addition, recent He4 observation could suggest the need for a nonstandard BBN model [8]. IBBN may also give a clue to the problems.



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*Source: 587294-2013-09-01.xml*