---
abstract: |
    Detailed Monte Carlo Inversion analysis of the spectral lines from three Lyman limit systems (LLS) \[$N$(H[i]{}) $\ga 1.0\times10^{17}$ [cm$^{-2}\,$]{}\] and nine lower $N$(H[i]{}) systems \[$2\times10^{14}$ [cm$^{-2}\,$]{}$\la N$([H]{}[i]{}) $\la
    2\times10^{16}$ [cm$^{-2}\,$]{}\] observed in the VLT/UVES spectra of Q0347–3819 (in the range $2.21 \leq z \leq 3.14$) and of APM BR J0307–4945 (at $z = 4.21$ and 4.81) is presented. Combined with the results from a previous work, the analyzed LLSs show that they are a [*heterogeneous*]{} population originating in different environments. A functional dependence of the line-of-sight velocity dispersion $\sigma_{\rm v}$ on the absorber size $L$ is confirmed: the majority of the analyzed systems follow the scaling relation $\sigma_{\rm v} \sim (N_{\rm H}\,L)^{0.3}$ (with $N_{\rm H}$ being the total gas column density). This means that most absorbers may be related to virialized systems like galaxies or their halos. Previously noted enhancement of the metal content in small size systems is also confirmed: metallicities of $Z \sim (1/3-1/2)\,Z_\odot$ are found in systems with $L \la 0.4$ kpc, whereas we observe much lower metal abundances in systems with larger linear sizes. For the first time in LLSs, a pronounced \[$\alpha$-element/iron-peak\] enrichment is revealed: the absorber at [$z_{\rm abs}\,$]{}= 2.21 shows \[O/Fe\] = $0.65\pm0.11$, \[Si/Fe\] = $0.51\pm0.11$, and \[Mg/Fe\] = $0.38\pm0.11$. Several absorption systems exhibit characteristics which are very similar to that observed in high-velocity clouds in the Milky Way and may be considered as high-redshift counterparts of Galactic HVCs.
author:
- 'S. A. Levshakov, I. I. Agafonova, S. D’Odorico, A. M. Wolfe,'
- 'M. Dessauges-Zavadsky'
title: 'Metal abundances and kinematics of quasar absorbers – II. Absorption systems toward Q0347–3819 and APM BR J0307–4945 '
---

Introduction
============

With the present paper we continue to study the chemical composition and the kinematic characteristics of quasar absorption systems using a new computational procedure, – the Monte Carlo Inversion algorithm (MCI), – developed earlier in a series of papers \[see Levshakov, Agafonova & Kegel (2000); hereafter LAK\]. The MCI technique allows us to recover self-consistently the physical parameters of the intervening gas cloud (such as the average gas number density $n_0$, the column densities for different species $N_{\rm a}$, the kinetic temperature $T_{\rm kin}$, the metal abundances $Z_{\rm a}$, and the linear size $L$), the statistical characteristics of the underlying hydrodynamical fields (such as the line-of-sight velocity dispersion $\sigma_{\rm v}$, and the density dispersion $\sigma_{\rm y}$), and the line of sight density $n_{\rm H}(x)$ and velocity $v(x)$ distributions (here $x$ is the dimensionless coordinate in units of $L$). Having this comprehensive information we are able to classify the absorbers more reliably and hence to obtain important clues concerning the physical conditions in intervening galaxies, galactic halos and large scale structure objects at high redshifts. Besides, it will also be possible to constrain the existing theories of the origin of galaxy formation since the observed statistics of the damped Ly$\alpha$ (DLA) and Lyman limit (LLS) systems is believed to be a strong test of different cosmological models (e.g. Gardner et al. 2001; Prochaska & Wolfe 2001).

In the first part of our study (Levshakov et al. 2002a, hereafter Paper I) we reported results on the absorption systems at [$z_{\rm abs}\,$]{}= 1.87, 1.92 and 1.94 toward the HDF-South quasar J2233–606. These systems exhibit many metal lines with quite complex structures. It was found that all profiles can be well described with an assumption of a homogeneous metallicity and a unique photoionizing background. According to the estimated sizes, velocity dispersions and metal contents the absorbers at [$z_{\rm abs}\,$]{}= 1.92 and 1.87 were related to the galactic halos whereas the system at [$z_{\rm abs}\,$]{}= 1.94 was formed, more likely, in an irregular star-forming galaxy. It was also found, that the linear size and the line-of-sight velocity dispersion for all three absorbers obey a scaling relation of the same kind that can be expected for virialized systems.

The present paper deals with absorbers observed in the spectra of Q0347–3819 ($z_{\rm em} = 3.23$) and APM BR J0307–4945 ($z_{\rm em} = 4.75$, see § 2.1). Both spectra include several dozens of systems containing metals, but most of them are weak and severely blended and hence do not allow to estimate the underlying physical parameters with a reasonable accuracy. After preliminary analysis only 12 systems were chosen for the inversion with the MCI and their properties are described below.

The structure of the paper is as follows. § 2 describes the data sets. In § 3 our model assumptions and basic equations are specified. The estimated parameters for individual systems are given in § 4. The implication of the obtained results to the theories of LLS origin are discussed in § 5 and our conclusions are reported in § 6. Appendix contains a table with typical parameters of different absorbers which are referred to in the present study.

Observations
============

The spectroscopic observations of Q0347–3819 and APM BR J0307–4945 obtained with the UV-Visual Echelle Spectrograph UVES (D’Odorico et al. 2000) on the VLT/Kueyen 8.2 m telescope are described in detail by D’Odorico, Dessauges-Zavadsky & Molaro (2001) and by Dessauges-Zavadsky et al. (2001), respectively. Both spectra were observed with the spectral resolution FWHM $\simeq 7$ [km s$^{-1}\,$]{}. For the analysis of metal systems from the Q0347–3819 spectrum with lines in the range 4880 – 6730 Å which was not covered by the VLT observations, we used a portion of the Q0347–3819 spectrum obtained with the High-Resolution Echelle Spectrograph HIRES (Vogt et al. 1994) on the 10 m W. M. Keck I telescope (Prochaska & Wolfe 1999). The spectral resolution in this case was about 8 [km s$^{-1}\,$]{}. The VLT/UVES data are now available for public use in the VLT data archive.

The majority of the metal systems in the spectrum of Q0347–3819 were identified in Levshakov et al. (2002b), whereas the [$z_{\rm abs}\,$]{}= 4.21 system toward APM BR J0307–4945 was distinguished by Dessauges-Zavadsky et al.[^1] (2001) as consisting of two sub-systems : one at [$z_{\rm abs}\,$]{}= 4.211 and the other at [$z_{\rm abs}\,$]{}= 4.218. A new system at [$z_{\rm abs}\,$]{}= 4.81 is analyzed here for the first time.

Emission redshift of APM BR J0307–4945
--------------------------------------

The emission redshift of this distant quasar $z_{\rm em} = 4.728\pm0.015$ was previously measured by Péroux et al. (2001) from the +\] $\lambda1400.0$ and $\lambda1549.1$ lines observed in the $\sim 5$ Å resolution spectrum obtained with the 4 m Cerro Tololo Inter-American Observatory telescope.

In our VLT/UVES spectrum of this quasar a few additional lines can be identified which are useful for the redshift measurements. The most important of them is the weak $\lambda1304$ line. From earlier studies (see, e.g., Tytler & Fan 1992 and references cited therein) it is known that ‘low-ionization lines’ such as $\lambda1304$ are systematically redshifted and narrower than ‘high-ionization’ lines such as , , and Ly$\alpha$.

In Fig. 1 we compare the profile with those of and of a wide blend of the Ly$\alpha$++ lines. All these lines are shown in the same velocity scale which is defined by the $\lambda1304$ center corresponding to $z_{\rm em} = 4.7525$. This line is redshifted with respect to the $z_{\rm em}$ value deduced by Péroux et al. from the measurements of the +\] and profiles. Because the Ly$\alpha$ emission line is blended with other emission lines and its blue wing is distorted by numerous narrow absorption lines, profile comparison cannot be very accurate in this case. Nevertheless, we found a smooth fit to the $\lambda1549$ profile (which is unblended and shows significant asymmetry) and used this synthetic profile for comparison with other lines (altering the amplitude of the synthetic profile to match the line profile while keeping its center unchanged).

Fig. 1 shows that this simplified procedure indeed allows us to achieve a fairly good concordance between the line and the Ly$\alpha$++ blend. This could indicate that the redshift of the quasar is higher than that measured by Péroux et al., being actually $z_{\rm em} \simeq 4.753$.

Model assumptions and the MCI procedure
=======================================

The complete description of the MCI code is given in LAK and its most updated version – in Paper I. Since this technique is relatively new, we briefly outline it here and stress its difference from the Voigt profile fitting (VPF) procedure commonly used for the QSO absorption line analysis.

The VPF deconvolution is based on the assumption that the observed complex line profiles are caused by several separate clouds randomly distributed along the line of sight. In every cloud, gas is characterized by the constant density and normally distributed velocities (the $b$ parameter usually estimated in the VPF procedure just stands for the dispersion of the velocity distribution). Because of the constant gas density, the ionizing structure inside the cloud is described by a single ionization parameter $U$ which can be estimated from the measured column densities of lines of different ions with help of some photoionization code if the spectrum of the background ionizing radiation is given.

However, numerous cosmological hydrodynamical calculations performed in the previous decade have shown that the QSO absorption lines arise more likely in the smoothly fluctuating intergalactic medium in a network of sheets, filaments, and halos (e.g., Cen et al. 1994; Miralda-Escudé et al. 1996; Theuns et al. 1998). This model finds its support also in modern high resolution spectroscopic observations: the increasing spectral resolution reveals progressively more and more complex profiles. A very important characteristic of the continuous absorbing medium is that the contribution to any point within the line profile comes not only from a single separate area (a ‘cloud’) but from all volume elements (‘clouds’) distributed along the sightline within the absorbing region and having the same radial velocity (see, for details, § 2.2 in LAK).

If the absorption systems are indeed formed in the fluctuating IGM, then the above described VPF procedure which interprets each absorption feature in the line profile as caused by one distinguished cloud is not, in general, physically justified. In some systems, this approach can produce rather erratic results like extremely varying metallicities between subcomponents, negative kinetic temperatures, exotic UV background spectra etc. (see examples in Levshakov et al. 1999; LAK; Paper I).

The MCI procedure is based on the assumption that all lines observed in a metal system arise in a continuous absorbing gas slab of a thickness $L$ with a fluctuating gas density and a random velocity field. We also assume that within the absorber the metal abundances are constant, the gas is optically thin for the ionizing UV radiation, and the gas is in the thermodynamic and ionization equilibrium. The last assumption means that the fractional ionizations of different ions are determined exclusively by the gas density and vary from point to point along the sightline. These fractional ionization variations are just the cause of the observed diversity of profile shapes between ions of low- and high-ionization stages.

Whereas most of the above mentioned assumptions are quite natural, that of the constant metallicity over the entire absorbing region needs additional discussion. On one hand, it is required from mathematical point of view. Namely, the splitting of the velocity and density fields is effective if all observed ions share the same velocity distribution but respond differently to the gas density. If in addition to the varying density and velocity one would allow for the varying metallicity, the inverse problem becomes fully degenerate, i.e. it would have infinitely large number of solutions. On the other hand, the constant metallicity has some observational support: results obtained in numerous studies of the Galactic halo chemical composition reveal no systematic differences in the gas-phase abundances within galactocentric distances of $7-10$ kpc in various directions (e.g., Savage & Sembach 1996). But, of course, we cannot exclude the case when the line of sight passes through many types of environments with different enrichment histories within a given absorber. If the metallicities within such an absorber differ only slightly ($\la 0.5$ dex), the observed lines of different ions can be well fitted to the synthetic profiles calculated with some average value of the metal content. If, however, the differences in the metallicities are really large ($\ga 1$ dex), the self-consistent fitting of all observed lines becomes impossible. In this case we have to split the absorber into separate regions having different metal abundances (see § 4.2.2 and 4.3.1 for examples).

It is well known that the measured metallicities depend in a crucial way on the adopted background ionizing spectrum. We started in all cases with the Haardt-Madau (HM) background ionizing spectra (Haardt & Madau 1996) computing the fractional ionizations and the kinetic temperatures with the photoionization code CLOUDY (Ferland 1997). If the fitting with the HM spectrum was impossible, we used another spectra, e.g. the Mathews and Ferland (MF) spectrum (Mathews & Ferland 1987).

The MCI procedure itself is implemented in the following way. Within the absorbing region the radial velocity $v(x)$ and the total hydrogen density $n_{\rm H}(x)$ along the line of sight are considered as two random fields which are represented by their sampled values at equally spaced intervals $\Delta x$, i.e. by the vectors $\{ v_1, \ldots, v_k \}$ and $\{ n_1, \ldots, n_k \}$ with $k$ large enough ($\sim 150-200$) to describe the narrowest components of the complex spectral lines. The radial velocity is assumed to be normally distributed with the dispersion $\sigma_{\rm v}$, whereas the gas density is distributed log-normally with the mean $n_0$ and the second central dimensionless moment $\sigma_{\rm y}$ ($y = n_{\rm H}/n_0$). Both stochastic fields are calculated using the Markovian processes (see LAK for mathematical basics). The model parameters estimated in the least-squares minimization of the objective function (see eqs.\[29\] and \[30\] in LAK) include $\sigma_{\rm v}$ and $\sigma_{\rm y}$ along with the total hydrogen column density $N_{\rm H}$, the mean ionization parameter $U_0$, and the metal abundances $Z_a$ for $a$ elements observed in a given absorption-line system.

The computations are carried out in two steps: firstly a point in the parameter space ($N_{\rm H}, U_0, \sigma_{\rm v}, \sigma_{\rm y},
Z_{\rm a})$ is chosen at random and then an optimal configuration of $\{v_i\}$ and $\{n_i\}$ for this parameter set is searched for. These steps are repeated till a minimum of the objective function ($\chi^2 \sim 1$ per degree of freedom) is achieved. To optimize the configurations of $\{v_i\}$ and $\{n_i\}$, the simulated annealing algorithm with Tsallis acceptance rule (Xiang et al., 1997) and an adaptive annealing temperature choice is used (details are given in Paper I).

The following important fact should be taken into account when one interprets the results obtained with the MCI technique. The mean ionization parameter $U_0$ is related to the parameters of the gas cloud as (see eq.\[28\] in LAK) $$U_0 = \frac{n_{\rm ph}}{n_0} (1 + \sigma^2_{\rm y})\; .
\label{eq:F1}$$ Here $n_{\rm ph}$ is the number density of photons with energies above 1 Ry which is determined by the intensity of the adopted background ionizing spectrum.

This equation shows that if the density field is fluctuating ($\sigma_{\rm y} > 0$), then with the same mean density $n_0$ and the same background ionizing spectrum we obtain a higher value of $U_0$ without any additional sources of the ionization. Intermittent regions of low and high ionization caused by the density fluctuations will occur in this case along the sightline. On the other hand, for a given $U_0$ the mean gas density $n_0$ is also higher in the fluctuating media as compared to the completely homogeneous gas clouds ($\sigma_{\rm y}$ = 0). Since the linear size of the absorber is $L = N_{\rm H}/n_0$, the sizes estimated with the assumption of a constant density (as, e.g., in the VPF) may occur too large.

Another important question is whether the MCI solution is unique and accurate. In general, the inverse problems are highly non-linear and ill-posed which implies multiple solutions and/or very broad uncertainty ranges for the recovered parameters. To produce a physically reasonable solution, one has to account for all available information related to the case under study. For instance, the more lines of different ionic transitions are included into the analysis, the more accurate result can be obtained since both low- and high-density regions are probed simultaneously. One may also compare the relative metal abundances predicted by nucleosynthetic theories with those provided by the MCI. An odd pattern may indicate a misleading solution. The recovered linear sizes must also be in agreement with the characteristic sizes of the absorbers stemming from observations of gravitationally lensed quasars and quasar pairs which show $L \la 100$ kpc.

One of the main problem in the analysis of the QSO high redshift spectra is the line blending which hampers significantly the inversion of the observed spectra. As compared to the VPF method, the MCI is much more robust dealing with blended lines due to the assumption that all ions trace the same underlying gas density and velocity distributions. This means that we are able to reconstruct both distributions using unblended parts of different lines. It is obvious that the accuracy of the recovered parameters improves with increasing number of lines and the variety of ions involved in the analysis. A priori we do not know which parts of the lines are blended and which are not. To clarify this, several test runs with different arrangements of lines are carried out till a self-consistent fit for the majority of lines observed in the spectrum is found.

Results on individual metal systems
===================================

All results given below in Tables 1-3 were obtained using the MCI procedure as described in Paper I. Giving the shape and the intensity at 1 Ry of the background ionizing radiation, the errors of the fitting parameters $U_0$, $N_{\rm H}$, $\sigma_{\rm  v}$, $\sigma_{\rm y}$ and $Z_{\rm a}$ are about 15-20% , the errors of the estimated column densities are less than 10%, whereas the derived parameters $n_0$ and $L$ are estimated with about 50% accuracy. These errors, however, should be considered as internal in the sense that they reflect merely the configuration of the parameter space in the vicinity of a minimum of the objective function. To what extent the recovered parameters may correspond to their real values is discussed separately for each individual absorbing system. We note in passing that the density $n_0$ and by this the linear size $L$ scales with the intensity of the radiation field (see eq.\[1\]).

The analyzed metal systems are described within three categories : (1) Lyman limit systems with $N$() $> 5\times10^{16}$ [cm$^{-2}\,$]{}, (2) Ly$\alpha$ absorbers with $N$() $< 5\times10^{16}$ [cm$^{-2}\,$]{}, and (3) Ly$\alpha$ systems with a probable metallicity gradient. Their physical properties are compared with different types of absorbers listed in Appendix.

Lyman limit systems
-------------------

### Q0347–3819, [$z_{\rm abs}\,$]{}= 2.21

This system consists of a broad saturated Ly$\alpha$ hydrogen line spread over 500 [km s$^{-1}\,$]{} and of metal lines of low and high ionized species : $\lambda1302$, $\lambda1334$, $\lambda\lambda2796,$ 2803, $\lambda1670$, $\lambda\lambda1190,$ 1193, $\lambda\lambda1608,$ 2344, 2382, 2586, 2600, $\lambda1854$, $\lambda1206$ and and doublets as well. The physical parameters obtained with the MCI are presented in Table 1 whereas the corresponding observed and synthetic spectra are shown in Fig. 2. The recovered density and velocity distributions along the line of sight are plotted in Fig. 3. The intermittent high- and low-density regions giving rise to, respectively, low- and high-ionization species (a multiphase medium) are clearly seen. This means that the lines of different ionization stages arise in different areas despite of having the same radial velocities \[see, e.g., the regions with $v(x) \simeq 0$ [km s$^{-1}\,$]{} in Fig. 3\].

According to these data, the system under study is a compact (380 pc) warm cloud ($T_{\rm kin}  \simeq 9000$ K) with a high metal content (0.6 solar value for O) and a high velocity dispersion ($\sigma_{\rm v} \simeq 80$ [km s$^{-1}\,$]{}).

The inferred column density of $4.6\times10^{17}$ [cm$^{-2}\,$]{} classifies this system as a typical LLS \[since $\log N$() $> 17$ [cm$^{-2}\,$]{}\]. In principle, this value lies beyond the applicability limit of the MCI which is formally valid for $\tau_{912} < 1$ \[if $N$() = $4.6\times10^{17}$ [cm$^{-2}\,$]{}, then $\tau_{912} = 3$\]. Besides, having only one saturated Ly$\alpha$ line we cannot in any case say for sure that the estimated value is the real hydrogen column density. But there are also reasons that make the obtained solution quite plausible.

First, we consider an absorber as a clumpy region which implies that the ionizing radiation may penetrate the cloud from different directions without being significantly altered (i.e. we assume that the density of the background ionizing radiation is not reduced much and its spectral distribution is not changed considerably in a gas cloud which is not a slab of a uniform density). Second, the observed mixture of the and lines and the and lines makes it possible to fix the mean ionization parameter $U_0$ quite strictly because the fractional ionization curves for, e.g., and are very different. Thus, the column density can hardly be less than the value estimated by the MCI since in that case the metallicity would be higher than solar. Besides, the same velocity interval covered by both the Ly$\alpha$ and $\lambda1206$ lines suggests that we observe probably the real profile of the Ly$\alpha$ (a blend with the Ly$\beta$ line from the system at [$z_{\rm abs}\,$]{}= 2.8102 which falls in the range $-40$ [km s$^{-1}\,$]{}$< \Delta v < 140$ [km s$^{-1}\,$]{} has a little influence on the Ly$\alpha$ red wing – see Fig. 2). Higher values of $N$() cannot be excluded, but additional calculations have shown that the maximum of the column density is limited : both available wings of the Ly$\alpha$ line do not allow an increase in $N$() by more than a factor of three.

This uncertainty does not change, fortunately, the main characteristic of this system – we do observe at [$z_{\rm abs}\,$]{}= 2.21398 a compact ($L < 1$ kpc) metal-rich ($Z > 0.1\,Z_\odot$) cloud. As seen from Fig. 2, the synthetic profiles represent well all unblended spectral features (broad absorption features at the position of the doublet are not consistent with each other and, hence, they cannot be attributed to the real profiles; the same is valid for the doublet). The measured relative abundances are discussed later in § 5.3. Here we note that a set of the identified species and their pattern as well as the estimated mass ($\sim 10^4 M_\odot$) resemble parameters measured in so-called high and intermediate velocity clouds (HVC, IVC) in the Local Group (Wakker 2001). Although the nature of the HVCs and IVCs is still poorly understood, they are unlikely to be phenomena isolated to the Milky Way. The system at [$z_{\rm abs}\,$]{}= 2.21 may be one of similar HVCs likely to be encountered in an high-redshift galactic halo. A more precise determination of its properties would require the higher Lyman series lines to be included in the analysis (these lines, however, can be observed with space telescopes only).

### Q0347–3819, [$z_{\rm abs}\,$]{}= 2.81

Here we identified three neutral hydrogen lines and several metal absorption lines both of low and high ionic transitions (see Fig. 4, the doublet falls, unfortunately, in a wavelength coverage gap of the Keck spectrum). The estimated physical parameters are listed in Table 1 whereas the corresponding synthetic spectra are shown in Fig. 4 by the smooth curves. It should be noted, however, that the solution with the column density of $5.5\times10^{16}$ [cm$^{-2}\,$]{} is not unique because all available hydrogen lines are saturated and partly blended in the red wings. We found also another solution with $N$() $= 10^{17}$ [cm$^{-2}\,$]{}. The solution presented in Table 1 has been chosen because it delivered a more or less consistent set of all parameters: the velocity dispersion $\sigma_{\rm v} \simeq 60$ [km s$^{-1}\,$]{}, the mean gas density $n_0 \simeq 10^{-3}$ [cm$^{-3}\,$]{}, the linear size $L \simeq 30$ kpc, and the metallicity $Z \sim 1/10Z_\odot$. For comparison, the second solution with $N$() $=10^{17}$ [cm$^{-2}\,$]{} gives the metallicity $Z \simeq 1/20Z_\odot$, the size $L \simeq 70$ kpc and the same other parameters. According to the both sets of the estimated parameters and the fact that rather strong low-ionization lines of and are observed, the [$z_{\rm abs}\,$]{}= 2.81 system could be related to an inner galactic halo.

### APM BR J0307–4945, [$z_{\rm abs}\,$]{}= 4.21

In the available spectral range we identified hydrogen lines Ly$\alpha$, Ly$\beta$ and Ly$\gamma$ as well as metal lines $\lambda1334$, $\lambda1526$, $\lambda977$, $\lambda989$, $\lambda1854$, $\lambda1206$ and the and doublets. From the metal line profiles, two main subsystems can be clearly distinguished: the first at $v \simeq -200$ [km s$^{-1}\,$]{}, and the second at $v \simeq 200$ [km s$^{-1}\,$]{}(see Fig. 5). The analysis of the [$z_{\rm abs}\,$]{}= 4.21 absorber has been carried out in two steps: ($i$) the subsystem at $v \simeq 200$ [km s$^{-1}\,$]{} was treated separately (the results are listed in column 4 in Table 1 and the corresponding synthetic spectra are shown by the solid lines in Fig. 5), ($ii$) both systems were fitted together (column 5 in Table 1, the dotted lines in Fig. 5).

The recovered metallicities are high (about $1/3Z_\odot$ at $v \simeq 200$ [km s$^{-1}\,$]{}, and slightly higher at $v \simeq -200$ [km s$^{-1}\,$]{}) and their pattern is nearly solar. At low redshifts similar characteristics are measured, e.g., in high-metallicity blue compact galaxies. At high redshifts, some radio galaxies are known which show two spatially resolved emitting regions, slightly sub-solar metallicities and sizes of about tens of kpc, e.g., MRC 2104–242 at $z = 2.49$ (Overzier et al. 2001) or TN J1338–1942 at $z = 4.11$ (De Breuck et al. 1999). It is also known that galaxies showing morphological evidence of a merger have excessive velocity widths of their spectral lines (e.g. Mallén-Ornelas et al. 1999).

Thus we conclude that the LLS under study probably arises when the line of sight intersects two clumps which may be merging. The observed range of the metal lines (from $\simeq -300$ to 400 [km s$^{-1}\,$]{}) and their very complex structures are also in line with this picture.

Although the recovered values are self-consistent, we cannot guarantee their uniqueness because of the following reasons. The hydrogen lines are blended and saturated and, hence, the real $N$() value may be higher leading to lower metal abundances. Besides, in our calculations the HM background ionizing spectrum was adopted. However, it is probable that in close pair of galaxies where a significant star-forming activity is triggered by the merging, the HM spectrum can be affected by the local sources. In particular, the discrepancies between the observed and theoretical intensities seen in the and components at $v = 100$ [km s$^{-1}\,$]{} as well as the estimated overabundant ratio of \[C/Si\] $\simeq 0.1$ (usually \[Si/C\] lies between 0 and 0.4, see Appendix) may be caused by inadequate choice of the background ionizing spectrum. Nevertheless, the observed metal profiles are quite consistent with the HM spectrum and therefore we expect that the influence of the local sources may not be very strong and, hence, the interpretation of this absorption system will not be significantly altered.

Absorbers with $N$() $< 5\times10^{16}$ [cm$^{-2}\,$]{}
-------------------------------------------------------

### Q0347–3819, [$z_{\rm abs}\,$]{}= 2.53 and 2.65

These two metal systems with [$z_{\rm abs}\,$]{}= 2.5370 and 2.65044 show broad and saturated hydrogen Ly$\alpha$ lines and lines of silicon and carbon in different ionization stages. Computational results are presented in Table 2, the observed and synthetic profiles are shown in Figs. 6 and 7.

The solutions listed in Table 2 are non unique because of the sole hydrogen line and blended low-ionization lines of $\lambda$1260 and $\lambda$1334. If in reality the $\lambda$1260 absorption is absent at [$z_{\rm abs}\,$]{}= 2.5370, then the solution with a higher $U_0$ and, hence, with a large linear size can also be obtained. Therefore we consider the estimated linear size of 13 kpc as a lower limit. The system at [$z_{\rm abs}\,$]{}= 2.650 may have low-ionization $\lambda1334$ absorption resulting in a lower mean ionization parameter and a smaller linear size as compared with those listed in Table 2. A rather high overabundance ratio \[Si/C\] $\simeq 0.5$ estimated for this system also allows us to speculate that the real ionization parameter may be lower. But these considerations do not change the classification of both absorbers: most probably they are hosted by halos of some distant galaxies.

### Q0347–3819, [$z_{\rm abs}\,$]{}= 2.962 and 2.966

These two systems are separated by only 300 [km s$^{-1}\,$]{} but demonstrate very different physical characteristics (see Table 2 and Figs. 8 and 9). Multiple hydrogen lines available in their spectra make it possible to estimate quite accurately the hydrogen column densities and all other physical parameters.

The [$z_{\rm abs}\,$]{}= 2.96171 system shows a broad Ly$\alpha$ line extending over 400 [km s$^{-1}\,$]{} and weak absorption lines of highly ionized silicon and carbon \[the $\lambda977$ line is contaminated by the Ly$\gamma$ line from the [$z_{\rm abs}\,$]{}= 2.97915 system (see Fig. 11); the $\lambda$1334 line is in a wavelength coverage gap of the Keck spectrum; the $\lambda\lambda$ 1260, 1193 lines are strongly blended\]. The derived physical parameters are typical for a galactic halo absorber: a low density ($n_0 \simeq 3\times10^{-4}$ [cm$^{-3}\,$]{}), low metallicity ($Z \simeq  0.01\,Z_\odot$), hot ($T_{\rm kin} \simeq 40000$ K) cloud of $L \simeq 20$ kpc size. The large overabundance of silicon as compared with carbon (\[Si/C\] $\la 0.8$) can be explained by the uncertainty in the estimated carbon abundance: only one weak $\lambda1548$ line is available for the analysis.

The adjacent system at [$z_{\rm abs}\,$]{}= 2.96591 is on the contrary a very compact ($L \simeq 120$ pc), warm ($T_{\rm kin} \simeq 10000$ K) cloud, 5 times more denser and 30 times more metal abundant. This absorber reveals also a weak $\lambda989$ line \[contaminated in the right wing by the H$_2$ L11-0P(2) line from the [$z_{\rm abs}\,$]{}= 3.025 DLA system – see Fig. 5 in Levshakov et al. 2002b\]. We do not detect high amplitude fluctuations in the density and velocity fields in this compact system (see Fig. 10), and as a result the observed metal line profiles are almost symmetric. The low density region with the space coordinate $0 \leq x \leq 0.2$ does not contribute much to the line profiles, although a weak absorption arising in this gas can be seen in Fig. 9 in the $\lambda$977 and $\lambda1548$ lines at $v \simeq -30$ [km s$^{-1}\,$]{}.

Since it is hardly possible that a cloud with a 120 pc size could exist in space on its own, the two systems are probably physically related. For instance, this small and metal enriched cloud may be a condensation of a supernova-heated gas in a galactic halo seen in the [$z_{\rm abs}\,$]{}= 2.96171 absorption lines. This process known as a galactic fountain (Bregman 1980) is believed to give origin to the high metallicity HVCs observed in the halo of the Milky Way. The velocity excess of the HVCs is usually greater than 90 [km s$^{-1}\,$]{} which is consistent with the shift of $\simeq 120$ [km s$^{-1}\,$]{} between the redward absorption in the Ly$\alpha$ profile at [$z_{\rm abs}\,$]{}= 2.96171 and the centre of the Ly$\alpha$ line at [$z_{\rm abs}\,$]{}= 2.96591.

### Q0347–3819, [$z_{\rm abs}\,$]{}= 2.98

Although this system belongs to the most commonly observed type in the Ly$\alpha$ forest (apart from hydrogen lines only weak and doublets and no apparent absorption in other ionic species are registered), its hydrogen lines are unusually broad – extended over 600 [km s$^{-1}\,$]{}.

Available Ly$\alpha$, Ly$\beta$ and Ly$\gamma$ lines (see Fig. 11) allow us to estimate the hydrogen column density with a sufficiently high accuracy. According to the recovered physical parameters (see Table 2), in this case we are dealing with a large ($L \simeq 50$ kpc) cloud of a rarefied ($n_0 \simeq 10^{-4}$ [cm$^{-3}\,$]{}), metal-poor ($Z < 0.01\,Z_\odot$) and hot ($T_{\rm kin} \simeq 40000$ K) gas. Blending of the $\lambda977$ and $\lambda1206$ lines and the weakness of the $\lambda1393$ line do not allow us to estimate accurately the mean ionization parameter. The $U_0$ value presented in Table  2 should be considered as a lower limit. If in reality $U_0$ is higher, then the absorber may have a lower mean gas density and a larger linear size.

The most probable host for this system might be an external region of a giant galactic halo or a large scale structure object.

### Q0347–3819, [$z_{\rm abs}\,$]{}= 3.14

The unsaturated Ly$\gamma$ line gives accurate estimations of the total neutral hydrogen column density (Fig. 12, Table 2). Clean continuum windows seen at the expected positions of metal lines make it possible to estimate the upper limits on metal abundances and to calculate the total hydrogen column density $N_{\rm H}$. The result obtained shows a rather low metallicity cloud with \[C/H\] $< -2.2$ and the linear size $L > 13$ kpc. One may expect to observe similar systems in the outer parts of galactic halos.

### APM BR J0307–4945, [$z_{\rm abs}\,$]{}= 4.81

This is the most distant absorber in our set where a low metal abundance can be directly measured. Its hydrogen Ly$\alpha$ line is clearly seen at $\Delta v = 3000$ [km s$^{-1}\,$]{} in the wide emission blend Ly$\alpha$++ shown in Fig. 1[**c**]{}. Absorption lines in Fig. 13 give the redshift [$z_{\rm abs}\,$]{}= 4.8101 and, thus, this system has [$z_{\rm abs}\,$]{}$> z_{\rm em}$. The same order of magnitude velocity difference ($\Delta v \simeq 3000$ [km s$^{-1}\,$]{}) between the H$_2$-bearing cloud at [$z_{\rm abs}\,$]{}= 2.811 (Levshakov & Varshalovich 1985) and the quasar redshift $z_{\rm em} = 2.770$ (Foltz et al. 1988) has been observed toward PKS 0528–250. This H$_2$ cloud seems to be at a distance larger than 10 kpc from the quasar as shown by Srianand & Petitjean (1998). However, in our case we are not able to estimate the proximity of the quasar. We can only assume that the photoionization of the [$z_{\rm abs}\,$]{}= 4.8101 system could be affected by the quasar radiation.

This assumption is supported by the following facts. It turned out to be impossible to fit all available lines with the HM ionizing spectrum: the relative intensities of the $\lambda977$ and $\lambda1548, 1550$ required very high $U_0$ values ($U_0 > 0.1$) which contradicted with the shallow extended wings of the Ly$\alpha$ line. On the contrary, the MF ionizing spectrum, corresponding to the AGN, allowed to fit all lines and delivered a self-consistent set of physical parameters (Table 2, Figs. 13 and 14). The intensity at 1 Ry was set to $J_{912} = 10^{-22}$ erg cm$^{-2}$ s$^{-1}$ Hz$^{-1}$ sr$^{-1}$ which corresponds to the intensity of the HM spectrum at $z = 4.9$.

According to the recovered values, the absorber at [$z_{\rm abs}\,$]{}= 4.81 is a metal-poor cloud with the linear size of about 25 kpc and the mean density $n_0 \simeq 2\times10^{-4}$ [cm$^{-3}\,$]{}. Fig. 14 shows that the shallow wings of the Ly$\alpha$ line are produced by the streaming out low density gas whereas the central region of the cloud remains very quiet.

Since we cleary see only the doublet[^2] and have upper limits for the intensity of the $\lambda977$ and $\lambda1393$ lines, the mean ionization parameter $U_0$ listed in Table 2 should be considered as a lower limit implying that lower metal abundances and lower gas densities may also be possible. Taking into account that the density $n_0$ and by this the linear size $L$ scales with the intensity of the radiation field (see eq.\[1\]), the value of $L$ becomes quite uncertain. It could be larger or smaller than the estimated size of 25 kpc (this uncertainty is marked by ‘?’ in Table 2).

An absorption system with similar spectral characteristics (wide and shallow wings of the Ly$\alpha$ line, a weak doublet) was previously observed by Reimers et al. (2001) at [$z_{\rm abs}\,$]{}= 1.674 toward HE 0515–4414 ($z_{\rm em} = 1.73$). The system at [$z_{\rm abs}\,$]{}= 1.674 shows in addition a strong doublet which, unfortunately, cannot be identified in the [$z_{\rm abs}\,$]{}= 4.81 cloud because of blending in the dense Ly$\alpha$ forest.

Thus we may conclude that such systems are probably formed in the gas clouds affected by the QSO radiation.

Ly$\alpha$ systems with metallicity gradient
--------------------------------------------

### Q0347–3819, [$z_{\rm abs}\,$]{}= 2.848 and 2.899

These systems present several seemingly unblended hydrogen lines and pronounced lines of highly ionized silicon and carbon (Figs. 15, 16; Table 3). Additionally, the $\lambda1238$ and $\lambda1031$ lines were identified at [$z_{\rm abs}\,$]{}= 2.848.

In spite of the multiple lines, it turned out that the MCI failed to fit adequately all available ionic profiles in the apparent velocity ranges when homogeneous metallicities over the entire absorbing regions were assumed. The most sensitive restrictions in these calculations are set by the continuum windows seen in the profiles of the strong $\lambda977$ and $\lambda1206$ lines. We consider the observed lines from these systems as arising in clouds with metallicity gradients for the following reasons.

The hydrogen Ly$\alpha$ and Ly$\beta$ lines seen at [$z_{\rm abs}\,$]{}= 2.848 in the $\Delta v$ range between 100 [km s$^{-1}\,$]{} and 400 [km s$^{-1}\,$]{} do not show any metal absorption in this velocity interval. Absorption features seen in the range 140 [km s$^{-1}\,$]{}$\leq \Delta v \leq 400$ [km s$^{-1}\,$]{} in Fig. 15 (panel ) and in the range 180 [km s$^{-1}\,$]{}$\leq \Delta v \leq 400$ [km s$^{-1}\,$]{} in panel cannot be attributed to the corresponding hydrogen sub-system, otherwise we should observe pronounced lines in the same velocity range. If the redward hydrogen absorption is physically connected with the blueward one, then we may conclude that the [$z_{\rm abs}\,$]{}= 2.848 absorber has a metallicity gradient.

A very similar picture is seen in the [$z_{\rm abs}\,$]{}= 2.899 system for the blueward portions of the hydrogen lines in the range $-220$ [km s$^{-1}\,$]{}$\la \Delta v \la -80$ [km s$^{-1}\,$]{}(Fig. 16). The $\lambda977$ line (which is the most sensitive absorption line in a wide range of the ionization parameter from $\log U_0 \ga -4$ to $\log U_0 \simeq 0$) shows no absorption in this velocity range.

In principle, the [$z_{\rm abs}\,$]{}= 2.899 system may be caused by a blending effect when the line of sight intersects two separate clouds (one of them supposingly metal-free) which have approximately the same radial velocities. As for the [$z_{\rm abs}\,$]{}= 2.848 system, a fortuitous blending can be ruled out because we observe two absorption features of approximately equal depth at $v \simeq -80$ [km s$^{-1}\,$]{} in the Ly$\alpha$ and profiles – the configuration noticed previously at [$z_{\rm abs}\,$]{}= 1.385 toward HE 0515–4414 by Reimers et al. (2001), i.e. this unusual pattern is not unique and seems to indicate some special kind of absorption systems. Preliminarily we may conclude that the system at [$z_{\rm abs}\,$]{}= 2.848 as well as probably that at [$z_{\rm abs}\,$]{}= 2.899 arise when the line of sight intersects a distant halo with very low (if any) metal content and encounters a metal-rich HVC. Unfortunately, the accurate quantitative analysis of both systems cannot be carried out because the velocity excesses of the assumed HVCs are not large enough to separate the inputs to the hydrogen lines from the halos and from the clouds like it was possible in the case of the [$z_{\rm abs}\,$]{}= 2.962 and [$z_{\rm abs}\,$]{}= 2.965 systems. Therefore the results presented in Table 3 are tentative, but they are physically reasonable and self-consistent.

The corresponding synthetic spectra are shown in Figs. 15 and 16 by the solid lines. It should be noted that for both systems, only one wing of the available lines (marked with the horizontal bold lines) was included in the analysis, whereas the synthetic profiles for the entire lines of the encountered HVCs were computed using the velocity and density distributions estimated from the metal profiles.

According to the data from Table 3, the suggested HVCs belong to different types. The system at [$z_{\rm abs}\,$]{}= 2.899 has the metal abundance pattern, the set of the ions observed (notice the pronouced doublet) and the size similar to those estimated for the supposed HVC at [$z_{\rm abs}\,$]{}= 2.965 and consistent with the parameters of the HVCs observed in the Milky Way (see Appendix). The system at [$z_{\rm abs}\,$]{}= 2.848 is more higher ionized ( and and no ) and it has the size of several kiloparsecs. Highly ionized HVCs with similar parameters were observed by Sembach et al. (1999) near the Milky Way. Their origin is still uncertain. Probably the [$z_{\rm abs}\,$]{}= 2.848 absorber may belong to the intercluster gas clouds in a distant group of galaxies as it was suggested by Sembach et al. for the local highly ionized HVCs.

Discussion
==========

The origin of metal systems
---------------------------

Metal systems with $N$() $< 5\times10^{16}$ [cm$^{-2}\,$]{} are usually believed to originate in galactic halos at different galactocentric distances. At low redshifts ($z < 1$) the galaxies associated with certain metallic absorptions (e.g. ) can be in most cases identified directly (e.g. Chen et al. 2001a). Our results on absorption systems with $z \ga 2$ also support this assumption: absorbers with [$z_{\rm abs}\,$]{}= 1.87 (Paper I), 2.54, 2.65, 2.962, 2.98 (present paper) are produced by metal-enriched ($Z < 0.1\,Z_\odot$), hot ($T_{\rm kin} \ga 20000$ K), rarefied ($n_0 \simeq 10^{-4} - 10^{-3}$ [cm$^{-3}\,$]{}) gas clouds which have typical linear sizes of $L > 10$ kpc. These parameters are consistent with contemporary models of galactic halos (e.g. Viegas, Friaca & Gruenwald 1999).

The nature of Lyman limit absorbers is less understood. Mo & Miralda-Escudé (1996) associate them with cold photoionized clouds randomly moving in hot spherical halos. The clouds are supposed to form from the initial density inhomogeneities in the accreting intergalactic gas during its cooling. Both the cloud and the halo obviously reveal the equal metallicity since they are formed from the same gas. In our study two LLSs with [$z_{\rm abs}\,$]{}= 1.92 (Paper I) and 2.81 (present paper) can be related to the absorbers of this type.

However, this scenario obviously fails to explain metal abundant ($Z > 0.1\,Z_\odot$) systems since it is hard to understand how the whole halo can be metal-enriched to such a high level. It was shown by hydrodynamic simulations (e.g. Katz et al. 1996; Gardner et al. 2001) that LLSs can also arise on lines of sight that pass through small protogalaxies. We found two systems with [$z_{\rm abs}\,$]{}= 1.94 (Paper I) and 4.21 (present paper) that can be explained within this framework. These metal-rich ($Z \simeq 1/3\,Z_\odot$) absorbers with the sizes of several kpc are probably hosted by objects that may be akin to the local compact blue galaxies.

Some absorbers in our present study ([$z_{\rm abs}\,$]{}= 2.21, 2.965, and, possibly, 2.89) reveal small linear sizes ($L < 1$ kpc) together with very high metal content ($Z \simeq 1/2\,Z_\odot$). These three systems may be explained in the framework of the process known as a galactic fountain : metal-enriched (supernova-heated) gas arises from the inner region of a galaxy and condenses into the clouds within the hot galactic halo. After formation, clouds fall back toward the galaxy centre because of their higher density. It is supposed that high-metallicity HVCs observed in the Milky Way halo are formed by this mechanism (Bregman 1980). The HVCs are common objects in our Galaxy and are detected in every longitude and latitude region. If galactic fountain works also in distant galaxies, it would be quite probable to encounter such a cloud on the line of sight which intersects the galactic halo, as also discussed by Charlton et al. (2001). Another type of HVCs – hot, highly ionized clouds with sizes of several kiloparsecs – is represented by the absorption system at [$z_{\rm abs}\,$]{}= 2.848. The origin of this type of HVCs is uncertain, but they may be produced by the intergalactic metal-enriched gas falling onto metal-poor galactic halos.

Measured abundances of C and Si are depicted versus logarithmic sizes of the studied systems in Fig. 17. Systematically higher metal abundances are seen in compact systems with linear sizes $L < 4$ kpc. This result seems to indicate that the more effective metal enrichment occurs within relatively compact regions.

Our results show that Lyman limit systems are a [*heterogeneous*]{} population which is formed in at least three different environments. This should be taken into account when statistics of LLSs is used to verify different models in hydrodynamic cosmological simulations.

$\sigma_{\rm v} - N_{\rm H}\,L$ relation
----------------------------------------

If QSO metal systems are formed in gas clouds gravitationally bound with intervening galaxies, the internal kinematics of the QSO absorbers should be closely related to the total masses of the host galaxies. In case of galactic population, different types of galaxies show different scaling relations between the linear size and the velocity width of emission lines (e.g., Mallén-Ornelas et al. 1999). Possible correlation between the absorber linear size $L$ and its line-of-sight velocity dispersion $\sigma_{\rm v}$ was also mentioned in Paper I.

The correlation between $\sigma_{\rm v}$ and $L$ stems from the virial theorem which states : $$\sigma^2_{\rm v} \sim \frac{M}{L} \sim n_0\,L^2 = N_{\rm H}\,L\; .
\label{eq:E1}$$ Assuming that the gas systems are in quasi-equilibrium, one can expect $\sigma_{\rm v} \sim \sqrt{N_{\rm H}\,L}$.

In Fig. 18 we examine our systems by comparing their kinematics ($\sigma_{\rm v}$) with measured sizes ($L$) and total gas column densities ($N_{\rm H}$). Shown are the data for all QSO absorbers studied in Paper I and in the present paper except for the systems at [$z_{\rm abs}\,$]{}= 2.848 and 2.899 (Table 3) which show inhomogeneous metallicities. It is seen that in the $\log (\sigma_{\rm v})$ versus $\log (N_{\rm H}\,L)$ diagram, most systems with linear sizes $L > 1$ kpc lie along the line with the slope $\kappa = 0.30\pm0.03$ (1 $\sigma$ c.l.).

Taking into account that we know neither the impact parameters nor the halo density distributions, this result can be considered as a quite good fit to the relation (1). Hence we may conclude that most absorbers with $L > 1$ kpc are gravitationally bound with systems that appear to be in virial equilibrium at the cosmic time when the corresponding Ly$\alpha$ absorbers were formed. The possible consequence of this conclusion is that since the most metal rich absorbers identified in the QSO spectra arise in the galactic systems the question whether the intergalactic matter is metal enriched or pristine remains still open.

\[$\alpha$-element/iron-peak\] ratio
------------------------------------

The metal abundances measured in the [$z_{\rm abs}\,$]{}= 2.21 LLS (Table 1) can be used to estimate the $\alpha$-element to the iron-peak group ratio which is a good indicator of the chemical evolutionary status of high redshift gas clouds. During the chemical evolution, heavy elements produced in stars show different nucleosynthetic histories so that their relative abundances vary with cosmic time.

Oxygen and other $\alpha$-chain elements are mainly produced by Type II SNe, while iron is also a product of Type Ia SNe which have longer evolution scales. In the early stages of the chemical evolution of galaxies ($\Delta t \la
2\times10^7$ yr) the interstellar gas is likely enriched by Type II SNe products, while at $\Delta t \ga 10^8$ yr, the \[$\alpha$/Fe\] ratio should decline. Observations reveal both low \[e.g. $\simeq 0.1-0.2$ in the [$z_{\rm abs}\,$]{}= 3.390 dust-free DLA (Q0000–2621; Molaro et al. 2001) and in the [$z_{\rm abs}\,$]{}= 3.386 DLA (Q0201+1120; Ellison et al. 2000)\], and high \[e.g. $\simeq 0.7$ in the DLA I Zw 18 (Levshakov, Kegel & Agafonova 2001) and $0.68\pm0.08$ in the [$z_{\rm abs}\,$]{}= 3.025 DLA (Q0347–3819; Levshakov et al. 2002b)\] ratios of \[$\alpha$-element/iron-peak\].

Oxygen with its weak affinity with dust grains is a good tracer of the $\alpha$-element abundances. Nevertheless, the intrinsic \[$\alpha$/Fe\] ratio may be affected by depletion of iron since being a refractory element iron may be partly locked into dust grains. The dust content in the [$z_{\rm abs}\,$]{}= 2.21 LLS may not, however, be too high. The relative abundances of the $\alpha$-elements O, Mg and Si are \[Si/O\] $= -0.14\pm0.11$ and \[Mg/O\] = $-0.27\pm0.11$. In Galactic stars the $\alpha$-elements show the same behaviour relative to iron-peak elements (oversolar at \[Fe/H\] $\la -1$; see, e.g., Gaswami & Prantzos 2000). We thus expect to find solar $\alpha$-element ratios in dust-free absorbing regions, as observed, e.g., in the mentioned above [$z_{\rm abs}\,$]{}= 3.390 DLA toward Q0000–2620. A negative value of \[Mg/O\] found in this LLS may indicate the presence of some amount of dust with a depletion factor of about 0.2 dex for the magnesium abundance. If, however, only the gas-phase abundances of O and Fe are taken, the upper bound on the \[O/Fe\] ratio is $0.65\pm0.11$, which is comparable with that found, for instance, in the [$z_{\rm abs}\,$]{}= 3.025 DLA toward Q0347–3819 where the dust-to-gas ratio is $\simeq 1/30$ of the mean Galactic interstellar medium value (Levshakov et al. 2002b). The enrichment of the $\alpha$-elements in the [$z_{\rm abs}\,$]{}= 2.21 LLS is also supported by the relative abundances of Si, Mg to Fe: \[Si/Fe\] = $0.51\pm0.11$ and \[Mg/Fe\] = $0.38\pm0.11$. Thus, the absorbing cloud at [$z_{\rm abs}\,$]{}= 2.21 appears to be a chemically young object.

Summary
=======

We have deduced the physical properties of ten absorption-line systems in the range $\Delta z = 2.21 - 2.966$ toward Q0347–3819 and of two systems at [$z_{\rm abs}\,$]{}= 4.21 and 4.81 toward APM BR J0307–4945. The main conclusions are as follows :

1.  The analyzed Lyman limit systems belong to a [*heterogeneous*]{} population which is formed by at least three groups of absorbers : ($i$) extended metal-poor gas halos of distant galaxies; ($ii$) gas in dwarf galaxies; ($iii$) metal-enriched gas arising from the inner galactic regions and condensing into the clouds within the hot galactic halo (galactic fountain). While the interpretation of a single system is sometimes subject to large uncertainties as discussed in chapter 4, the existence of a wide spread of properties in the different systems is certainly proved.

2.  A correlation between the line-of-sight velocity dispersion $\sigma_{\rm v}$ and the linear size $L$ of the absorbing systems noted in Paper I is confirmed. New results show that large size QSO absorbers ($L > 1$ kpc) obey a scaling law $\sigma_{\rm v} \sim (N_{\rm H}\,L)^{0.3}$ over two decades in velocity dispersion and in the product $(N_{\rm H}\,L)$. This means that the majority of the metal absorbers are probably bound to the galactic systems and, hence, the question whether the IGM is enriched or pristine requires further investigations.

3.  Systematically higher metal abundances are found in compact systems: in our sample there are no small size systems ($L < 1$ kpc) with metallicity lower than $0.1\,Z_\odot$.

4.  The gas-phase metal abundances from the [$z_{\rm abs}\,$]{}= 2.21 LLS reveal a pronounced \[$\alpha$-element/iron-peak\] enhancement with \[O/Fe\] = $0.65\pm0.11$ at the $6\sigma$ confidence level, the first time when this abundance pattern is unambiguously found in a LLS. The measured \[O/Fe\] ratio implies that the chemical history of this LLS is $\la 10^8$ yr.

5.  Absorption system at [$z_{\rm abs}\,$]{}= 2.21 and 2.965 and possible the systems at [$z_{\rm abs}\,$]{}= 2.848 and 2.899 toward Q0347–3819 show characteristics very similar to that observed for different types of HVCs in the Milky Way and may be interpreted as being the high-redshift counterparts of these Galactic objects.

We thank Prof. W. H. Kegel for helpful correspondence and our anonymous referee for many helpful suggestions. S.A.L. gratefully acknowledges the hospitality of the National Astronomical Observatory of Japan (Mitaka) where this work was performed. The work of S.A.L. and I.I.A. is supported in part by the RFBR grant No. 00-02-16007.

Possible counterparts of QSO absorbers
======================================

In our interpretation of the nature of the different metal systems with $N$() $\simeq 10^{14}-10^{17}$ [cm$^{-2}\,$]{} we have referred to a set of absorbers whose physical parameters are summarized in Table 4. Comparison between the reference absorbers and the QSO systems is based on following parameters :

1.  Linear sizes. The systems can be divided into small-size ($L < 1$ kpc), intermediate-size (1 kpc $\la L \la 10$ kpc), and large-size (10 kpc $\la L \la 150$ kpc) absorbing regions connected with galactic gaseous envelopes, as well as into very large-size ($L \ga$ 150 kpc) absorbers (filaments) showing correlation with the large-scale distribution of galaxies (e.g. Penton et al. 2002). Filaments are probably intergalactic material not recycled by galaxies.

2.  Metallicities. Values of $0.3 \la Z/Z_\odot \la 1$, $0.03 \la Z/Z_\odot \la 0.3$, and $Z/Z_\odot < 0.03$ classify the systems as metal rich, metal enriched, and metal poor, respectively.

3.  Metallicity patterns. Relative element abundances allow us to distinguish between chemically young and old systems (low and high relative \[$\alpha$-element/iron-peak\] ratio, respectively).

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[lcccc]{} $U_0$ & 2.1E-3 & 4.0E-2 & 7.5E-3 & 8.1E-3\
$N_{\rm H}$, [cm$^{-2}\,$]{}& 2.2E19 & 8.3E19 & 4.2E19 & 9.1E19\
$\sigma_{\rm v}$, [km s$^{-1}\,$]{}& 80.8 & 59.5 & 80.0 & 170.0\
$\sigma_{\rm y}$ & 1.0 & 1.15 & 1.2 & 1.25\
$Z^b_{\rm C}$ & 2.0E-4 & 3.1E-5 & 1.3E-4 & 2.0E-4\
$Z_{\rm N}$ & $\ldots$ & $<$4.0E-6 & $<$2.5E-5 & $<$2.5E-5\
$Z_{\rm O}$ & 4.4E-4 & $\ldots$ & $\ldots$ & $\ldots$\
$Z_{\rm Mg}$ & 1.5E-5 & $\ldots$ & $\ldots$ & $\ldots$\
$Z_{\rm Al}$ & $\ldots$ & $\ldots$ & $<$2.5E-6 & $<$2.5E-6\
$Z_{\rm Si}$ & 2.0E-5 & 4.2E-6 & 1.1E-5 & 1.5E-5\
$Z_{\rm Fe}$ & 5.0E-6 & $\ldots$ & $\ldots$ & $\ldots$\
$[Z_{\rm C}]^c$ & $-0.28$ & $-1.10$ & $-0.47$ & $-0.27$\
$[Z_{\rm N}]$ & $\ldots$ & $<-1.3$ & $<-0.5$ & $<-0.5$\
$[Z_{\rm O}]$ & $-0.10$ & $\ldots$ & $\ldots$ & $\ldots$\
$[Z_{\rm Mg}]$ & $-0.37$ & $\ldots$ & $\ldots$ & $\ldots$\
$[Z_{\rm Al}]$ & $\ldots$ & $\ldots$ & $<-0.5$ & $<-0.5$\
$[Z_{\rm Si}]$ & $-0.24$ & $-0.90$ & $-0.51$ & $-0.36$\
$[Z_{\rm Fe}]$ & $-0.75$ & $\ldots$ & $\ldots$ & $\ldots$\
$N$(H[i]{}), [cm$^{-2}\,$]{}& 4.6E17 & 5.5E16 & 1.4E17 & 2.3E17\
$N$(O[i]{}) & 1.5E14 & $\ldots$ & $\ldots$ & $\ldots$\
$N$(C[ii]{}) & 1.5E15 & 5.2E13 & 4.8E14 & 1.2E15\
$N$(Mg[ii]{})& 1.1E14 & $\ldots$ & $\ldots$ & $\ldots$\
$N$(Si[ii]{})& 2.3E14 & 8.2E12 & 4.8E13 & 1.0E14\
$N$(Fe[ii]{})& 1.3E13 & $\ldots$ & $\ldots$ & $\ldots$\
$N$(C[iii]{})& $\ldots$ & 1.6E15 & 4.3E15 & 1.3E16\
$N$(N[iii]{})& $\ldots$ & $<$2.0E14 & $<$6.3E14 & $<$1.6E15\
$N$(Al[iii]{})& $<$8.1E12 & $\ldots$ & $<$1.1E13 & $<$3.4E13\
$N$(Si[iii]{})& 2.0E14 & 1.2e14 & 2.6E14 & 6.8E14\
$N$(C[iv]{})& 7.7E13 & $\ldots$ & 5.6E14 & 2.0E15\
$N$(Si[iv]{})& 3.0E13 & 6.7E13 & 9.0E13 & 2.9E14\
$n_0$, [cm$^{-3}\,$]{}& 2.0E-2 & 9.2E-4 & 2.5E-3 & 2.5E-3\
$\langle T \rangle$, K & 9.1E3 & 2.4E4 & 1.2E4 & 1.2E4\
$T_{\rm min}$ & 8.6E3 & 1.7E4 & 1.1E4 & 1.1E4\
$T_{\rm max}$ & 9.8E3 & 3.3E4 & 1.4E4 & 1.5E4\
$L$, kpc & 0.38 & 30 & 6.0 & 13\

[lccccccc]{} $U_0$ & 2.9E-2 & 4.2E-2 & 8.5E-2 & 2.0E-2 & 0.15 & 0.11 & 3.8E-2\
$N_{\rm H}$, [cm$^{-2}\,$]{}& 4.4E19 & 1.9E19 & 2.0E19 & 5.1E17 & 3.6E19 & 1.2E19 & 1.6E19\
$\sigma_{\rm v}$, [km s$^{-1}\,$]{}& 68.5 & 73.0 & 88.0 & 11.6 & 110.8 & 25.3 & 33.8\
$\sigma_{\rm y}$ & 1.05 & 0.7 & 0.85 & 0.92 & 1.12 & 1.0 & 0.87\
$Z^b_{\rm C}$ & 5.0E-6 & 3.7E-5 & 2.0E-6 & 1.5E-4 & 3.1E-6 & $<$ 1.8E-6 & 3.3E-6\
$Z_{\rm N}$ & $\ldots$ & $\ldots$ & $\ldots$ & 1.8E-5 & $\ldots$ & $\ldots$ & $\ldots$\
$Z_{\rm Si}$ & 1.2E-6 & 1.2E-5 & 1.1E-6 & 3.2E-5 & $<$3.5E-6 & $<$ 9.0E-7 & $<7.0$E-7\
$[Z_{\rm C}]^c$ & $-1.89$ & $-1.02$ & $>-2.3$ & $-0.42$ & $-2.07$ & $<-2.3$ & $<-2.0$\
$[Z_{\rm N}]$ & $\ldots$ & $\ldots$ & $\ldots$ & $-0.67$ & $\ldots$ & $\ldots$ & $\ldots$\
$[Z_{\rm Si}]$ & $-1.45$ & $-0.47$ & $-1.49$ & $-0.03$ & $<-1.0$ & $<-1.6$ & $<-1.7$\
$N$(H[i]{}), [cm$^{-2}\,$]{}& 2.2E16 & 6.2E15 & 2.0E15 & 3.6E14 & 1.9E15 & 8.7E14 & 3.7E15\
$N$(C[ii]{}) & $\ldots$ & $\ldots$ & $\ldots$ & 9.4E11 & $\ldots$ & $<$4.7E10 & $<$1.5E11\
$N$(Si[ii]{})& $\leq$1.2E12 & $\ldots$ & $\ldots$ & $<$1.8E11 & $\ldots$ & $<$1.6E10 & $\ldots$\
$N$(C[iii]{})& $\ldots$ & $\ldots$ & 1.1E13 & 4.3E13 & 1.8E13 & $<$4.6E12 & $<4.8$E12\
$N$(N[iii]{})& $\ldots$ & $\ldots$ & $\ldots$ & 5.2E12 & $\ldots$ & $\ldots$ & $\ldots$\
$N$(Si[iii]{})& 1.6E13 & 2.7E13 & 1.1E12 & 3.6E12 & $<$9.1E11 & $<$2.8E11 & $\ldots$\
$N$(C[iv]{})& 4.7E13 & 2.5E14 & 8.4E12 & 1.9E13 & 2.0E13 & $<$4.5E12 & 9.4E12\
$N$(Si[iv]{})& 7.3E12 & 3.7E13 & 8.5E11 & 5.2E12 & $<$1.4E12 & $<$3.0E11 & $<6.7$E11\
$n_0$, [cm$^{-3}\,$]{}& $<$1.1E-3 & 5.7E-4 & $<$3.2E-4 & 1.5E-3 & $<$2.4E-4 & $<$3.1E-4 & 2.3E-4?\
$\langle T \rangle$, K & 2.8E4 & 1.8E4 & 4.0E4 & 1.0E4 & 4.4E4 & 3.4E4 & 3.2E4\
$T_{\rm min}$ & 1.9E4 & 1.4E4 & 2.6E4 & 7.0E3 & 3.0E4 & 2.7E4 & 2.2E4\
$T_{\rm max}$ & 4.3E4 & 2.3E4 & 5.0E4 & 2.1E4 & 7.0E4 & 5.3E4 & 4.3E4\
$L$, kpc & $>$13 & 11 & $>$20 & 0.12 & $>$50 & $>$13 & 25?\

[lcc]{} $U_0$ & 0.1 & 2.2E-2\
$N_{\rm H}$, [cm$^{-2}\,$]{}& 2.3E18 & 1.9E18\
$\sigma_{\rm v}$, [km s$^{-1}\,$]{}& 34.9 & 54.3\
$\sigma_{\rm y}$ & 0.9 & 1.3\
$Z^b_{\rm C}$ & 9.1E-5 & 9.6E-5\
$Z_{\rm N}$ & $\la$2.5E-5 & $\ldots$\
$Z_{\rm O}$ & 3.5E-4 & $\ldots$\
$Z_{\rm Si}$ & $<$2.5E-5 & 2.4E-5\
$[Z_{\rm C}]^c$ & $-0.67$ & $-0.60$\
$[Z_{\rm N}]$ & $\la -0.5$ & $\ldots$\
$[Z_{\rm O}]$ & $-0.21$ & $\ldots$\
$[Z_{\rm Si}]$ & $<-0.14$ & $-0.15$\
$N$(H[i]{}), [cm$^{-2}\,$]{}& 1.8E14 & 4.1E15\
$N$(C[ii]{}) & $\ldots$ & 1.1E13\
$N$(Si[ii]{})& $\ldots$ & 3.6E12\
$N$(C[iii]{})& 2.7E13 & 1.4E14\
$N$(Si[iii]{})& $\ldots$ & 2.3E13\
$N$(C[iv]{})& 5.8E13 & 3.0E13\
$N$(Si[iv]{})& $<$1.3E12 & 1.3E13\
$N$(N[v]{}) & $\la$ 8.3E12 & $\ldots$\
$N$(O[vi]{}) & 5.3E13 & $\ldots$\
$n_0$, [cm$^{-3}\,$]{}& 2.5E-4 & 2.0E-3\
$\langle T \rangle$, K & 2.3E4 & 1.2E4\
$T_{\rm min}$ & 1.9E4 & 9.9E3\
$T_{\rm max}$ & 2.9E4 & 1.4E4\
$L$, kpc & 3.0 & 0.33\

[lcclc]{} 1. HVC-type absorbers inside& & & \[C/Fe\]$\simeq0.2$, \[N/Fe\]$\simeq0.6$ & 1,2\
galactic halos & $L < 1$ & $0.1 \la X \la 1$ & \[O/Fe\]$\simeq0.7$, \[Mg/Fe\]$\simeq0.2$ &\
& & & \[Al/Fe\]$\simeq0.3$, \[Si/Fe\]$\simeq0.3$ &\
2. Gas in dwarf galaxies of & & & &\
($i$) low-metallicity &$1 \la L \la 10$ &$0.03 \la X \la 0.06$ & \[C/Fe\]$\simeq-0.2$, \[O/Fe\]$\simeq0.3$ & 3,4\
& & &\[N/Fe\]$\simeq-0.2$, \[Si/Fe\]$\simeq0.1$ &\
($ii$) high-metallicity &$1 \la L \la 10$ &$0.06 < X \la 0.3$ & \[C/Fe\]$\simeq\,\,\,\, 0.2$, \[O/Fe\]$\simeq0.4$ &3,4\
& & &\[N/Fe\]$\simeq-0.1$, \[Si/Fe\]$\simeq0.3$ &\
3. Gaseous envelopes$^b$ & & & &\
of galaxies seen in & & & &\
($i$) H[i]{} Ly$\alpha$&$\,\,\,10h^{-1} \la L \la 160h^{-1}$ & & & 5,10\
($ii$) Mg[ii]{}$\lambda\lambda 2796, 2803$ & $15h^{-1} \la L \la 75h^{-1}$ &$X < 1$ & & 6,7\
($iii$) C[iv]{}$\lambda\lambda 1548, 1550$ & $100h^{-1} \la L \la 180h^{-1}$ &$X < 1$ & & 8,9\
\
4. Large-scale filaments & & & &\
around galaxies & $L \ga 150h^{-1}$ &$X \ll 1$ & \[Si/C\]$\simeq0.4$, \[N/C\]$\simeq-0.7$ & 10

[^1]: Data are listed in Table 5 which is only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5).

[^2]: The $\lambda$1550 Å component is slightly blended with the night sky lines, whereas the $\lambda1548$ Å line is clear as found from the comparison of the two spectra of the APM BR J0307–4945 taken in a two month interval.
