Book Editors: P. Benvenuti, F. D. Macchetto, and E. J. Schreier

Electronic Editor: H. Payne

**Shin Sasaki**

Department of Physics, the University of Tokyo,
Bunkyo, Tokyo 113, Japan

**Fumio Takahara and K. Masai**

Department of Physics, Tokyo Metropolitan University,
Hachiouji, Tokyo 192-03, Japan

JSPS Research Fellow present address:Department of Physics, Tokyo Metropolitan University,Hachiouji, Tokyo 192-03, Japan

**Keywords: cosmology : absorption systems**

In quasar spectra, there are many types of absorption systems and their column density of neutral hydrogen () ranges roughly 10 orders of magnitudes. Surprisingly, their column density distribution can be well fit by a single power law. This indicates that they may be explained simultaneously by one model. Although many models have proposed to explain observational results of absorption systems, there is little agreement what they are, since we have had too little information about them. In recent years, observational progress gives us new information. In particular, recent UV observations begin to detect helium absorption and it makes it possible for us to study thermal properties of absorption systems in detail. If these systems are irradiated by diffuse UV background radiation (UVB), which is one of the most popular models, their ionization states depend on the intensity and spectrum of UVB as well as their number density and size. In this case, we can study properties of UVB besides properties of absorption systems from observations.

In order to understand new observations precisely, we need study thermal properties of absorption systems comprising of hydrogen and helium theoretically. In this paper, we study that using simple model based on photo-ionization model, and consider what types of absorption systems and UVB are favorable to explain observations. Then, we need treat radiative processes carefully even when we study absorption systems whose optical depth of neutral hydrogen is less than unity. Because optical depth of singly ionized helium is larger than that of HI unless the spectrum of UVB is too hard, it is possible that the HeII optical depth is greater than unity even when the HI optical depth is less than unity.

We adopt the photo-ionization model as absorption systems.
In this paper, we assume that they are flattened structures and
consider the homogeneous plane-parallel slab comprising of hydrogen and
helium, for simplicity.
In our model, the absorption systems are illuminated on both sides by
diffuse UV background radiation ,
whose spectrum is assumed to be a power law as
where is the ionization threshold
energy of HI, and is the Planck constant.
Furthermore, we assume that absorption systems are in thermal and
ionization equilibrium, and we use two-stream approximation
in order to calculate radiative transfer.
Our model has four model parameters:
the hydrogen number density of
absorption system , the size of absorption system **L**,
the intensity of the UVB , and the spectrum index of UVB
.
Throughout this paper, we fix the ratio of number density of
He to H to be .
The values of model parameters which we used in this paper
are summarized in Table 1.

We calculate thermal structures of absorption systems based on the model presented in the previous section. In the case of optically thin systems, thermal properties are constant everywhere in a system, but they depend on the adopted model parameters. The fraction of HI decreases as the intensity of UVB increases and as the number density of the system decreases. On the other hand, the ratio of number density of HeII to HI depends on the spectrum index of UVB strongly, and does not depend on the intensity of UVB and number density. In the case of optically thick systems, thermal properties change with depth. From these results, we can see that the thermal properties of absorption systems strongly depend on the model parameters, as expected. Thus, we expect we can put constraints on the model parameters by comparing them with observations.

Vogel & Reimers (1995) detected absorption features of HeI in optically thin Lyman limit systems whose HI column density and found that the ratio of to is . Comparison with their observational results with our numerical calculations, we expect to put constraints on our model parameters. We show the ratio of the column density of HeI and HeII to that of HI as a function of in Fig. 1. In each panel, the boxes show the result of Vogel & Reimers (1995). If number density of observed absorption systems is , is favorable. On the other hand, if their number density is , is favorable. We cannot judge which value of is correct unless we know the number density of the systems and/or other information.

Recently, Jakobsen et al. (1994) detected HeII absorption toward Q0302-003 (). Although we cannot distinguish between contributions to the absorption from Lyman clouds and diffuse intergalactic medium, this observation suggests that the spectrum of UVB must be sufficiently soft. In order to derive rigid value of , we need to know the distribution of Lyman clouds, origin of their line broadening and their contribution to the observed HeII absorption. We have not had definite information on these problems yet. However, for wide range of models, UVB must be ruled out since such hard UVB ionizes HeII too much and it is difficult to produce observed optical depth.

From these observations, we see that number density of absorption systems whose is and the spectrum index of UVB .

In order to restrict to our model parameters, it is most promising to study in addition to in optically thin systems. For optically thin systems, depends on only, does not depend on other parameters: and . From , we can decide and then, using the value of we can obtain and .

**Figure:** The ratio of column density of to that of
. The boxes in the top panels show the result of Vogel and
Reimers (1995).

We studied the ionization and thermal structures of the absorption-line systems of quasar spectra based on photo-ionization model. Comparison with the observations, we put constraints on the model parameters. We find that the spectrum index of UVB is nearly to explain HeI and HeII observations and number density of absorption systems whose is .

The author (S.S.) acknowledges the Research Fellowships of the Japan Society for the Promotion of Science.

Jakobsen, P. et al. 1994, Nature, 370, 35

Vogel, S. & Reimers, D. 1995, A&A, 294, 377

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