ELSEVIER Nuclear Physics A718 (2003) 668~670~

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Formation of Atoms, Molecules and the First Objects in the Universe with a Variable Cosmological Term

T. Kamikawa”, M. Hashimotoa and K. Araib

“Department of Physics, Kyushu University, Fukuoka 810-8560, Japan

bDepartment of Physics, Kumamoto University, Kumamoto 860-8555, Japan

We investigate the thermal history in the universe with a variable cosmological term. In particular, we show how the formation of important molecules such as Hz and HD is influenced during the epoch for the redshift from 10000 to 1. These molecules should dominate the cooling process of primordial gas clouds which triggers the collapse of them. It is found that the molecular formation is quickened by Lz - 1000 compared with the case in the standard model due to the variable cosmological term. The qualitative estimate of the mass of the first objects has been performed with use of the time scales related to the thermal evolution. It is suggested that the formation scenarios of the first objects studied so far could be changed drastically if the variable cosmological term is included in the thermal history in the universe.

1. INTRODUCTION

Some cosmological models with a c.osmological term have been supported by the ob- servational evidence from SNe of the accelerating expansion for the universe [I]. Various theoretical models have been suggested to solve the cosmological constant problem (e.g., ‘quintessense’ of the scalar field). On the other hand, many formation scenarios of the first objects which end the ‘dark age’ have been considered actively [a]. Motivated by them, we investigate the thermal history in the universe using a phenomenological vari- able cosmological term (hereafter VCT) with time dependence [3,4]. In particular, we calculate the synthesis of first atoms and molecules for the redshift from 10000 to 1 and elucidate the effects on the formation of the first objects.

2. EVOLUTION OF THE CHEMICAL ELEMENTS WITH A VCT

Our chemical reaction network is coupled to the equation for the redshift z,

dz - = -Ho(l + 2) dt

Ro(l + z)” + AlO + ,&(l + 2)” - (Go + AlO + AZ0 _ I)(1 + z)2 (1)

with a VCT X = Xi0 + X2suF” (see [3;4] in detail) where the Hubble constant Hs = 100 h km s-i Mpc-’ and Ra is the density parameter; the radiation temperature T.0 = 2.737 K , the baryon density parameter & = 3.66 x 10-3~10h~2, h = 0.67, the baryon-to- photon ratio ~10 = 5.5, number of neutrino species N, = 3 (see Table 1 for the others).

0375~9474/03/!5 - see front matter 0 2003 Published by Elsevier Science B.V. doi: lO.l016/SO375-9474(03)00883-2

7: Kamikawa et al. /Nuclear Physics A718 (2003) 668c-670~ 669c

The reaction rates are taken from [5]. Fig. 1 shows the temperature variation against the redshift and Fig. 2 shows the evolution of Hz and HD molecules. It is noted that t,he curves of the model A and B overlap. One can see from Fig. 2 that both H2 and HD are synthesized earlier for the model C.

Table 1 Model parameters, corresponding fractional ionizations and abundances of the hydrogen molecules at z = 1.

Model 00 Xl0 ho m L [e/HI [Hz/HI A (standard) 1 0 0 0 1.2 x 10-4 1.2 x 10-G B (constant-X) 0.3 0.7 0 0 6.6 x 10-j 1.2 x 1oP C (variable-X) 0.3 0.7 0.00015 1.5 2.2 x 10-5 1.7 x 10-6

l+Z

Figure 1. Thermal history for the model B (thin lines) and model C (thick lines). Each curve represents the evolution of the radiation temperature TY (solid lines) and matter temperature T, (dotted lines).

100 1+2

Figure 2. Evolution of Ha (solid lines) and HD (dotted lines) molecules for the model B (thin lines) and model C (thick lines).

3. RELATION TO THE FIRST OBJECTS

The formation epoch of the first objects has been predicted based on the cooling diagram (see [6] in detail). I n rimordial gas clouds, Hz molecules play an important role toward p the first objects [7]. The non-equilibrium fraction of Hz with a given virial temperature can be estimated making comparisons between the time scales of recombination t,,,, Hz cooling tcooi, dissociation t&s, formation tform: When t& < min(t,,,i,t,,,), ynz = y$ where yht denotes the fraction of Ha in chemical equilibrium; t,,, < min(t,,,r; t&s), y& =

y$(trec/tdis); tcooi < min(&,,, t,-Jis); yn2 LX y$dm. Then, the possible regions for the formation of ,the first objects are determined by the competition between the time scales of free fall tff, cooling tcool and Hubble expansion tn. In Fig. 3: the region (i) indicates that no formation will occur; (ii) though not effective, the clouds will become the first objects; (iii) the cooling is the most effective and the formation of the first objects will occur most efficiently. Four lines marked with 105Mo, 106&L0, 107JJ0 and 108AJB which represent the ma.ss of clouds are described on the same plane from the lower right.

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to the upper left [8]. Three lines marked with 10; 20 and 3~ show the virial temperature of collapsing halos at the redshift 2 corresponding to 1 - g, 2 - g and 3 - 0 fluctuations, respectively.

4. CONCLUSIONS

We found that in the model C the molecular formation is quickened by &Z - 1000 compared with the cases in the model A and B. The residual fractional ionization and abundance of hydrogen molecules at z = 1 for each model are shown in Table 1. As for the hydrogen molecules, their final abundances do not depend so much on the models. The effect on the formation of the first objects was also investigated (Table 1 for models). It is found that the VCT can shift the possible emergence region of the first objects toward the higher redshift by AZ. - 20. It should be noted that this estimate is based on the comparison among the time scales of the thermal evolution. Furthermore, there might be the feedback from the formed stars on their host cloud.

The detection of the lights from the first objects has been projected with use of submil- limeter waves [9]. We hope that our study becomes a first attempt that helps to restrict the t,hermal history in the universe with the VCT related to the formation of the first objects.

Figure 3. Tvir vs. 1 + Z”ir plane divided into three regions denoted as (i) tn < tcooir (ii) tff < &d < tH, (iii) tff > kd for the model A (thin dotted lines) and model C (thick dotted lines) i respectively.

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