A&A 383, 813-822 (2002)
DOI: 10.1051/0004-6361:20011807
S. A. Levshakov1,
- I. I. Agafonova2 - M. Centurión3 - I. E. Mazets2
1 -
Division of Theoretical Astrophysics, National Astronomical Observatory, Mitaka, Tokyo 181-8588, Japan
2 -
Department of Theoretical Astrophysics, Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia
3 -
Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34131 Trieste, Italy
Received 4 October 2001 / Accepted 18 December 2001
Abstract
The metal line profiles of different ions observed in
high H I column density
systems [N(H I) > 1016 cm-2]
in quasar spectra can be used to constrain the
ionization structure and kinematic characteristics of the absorbers.
For these purposes, a modified Monte Carlo Inversion (MCI) procedure
was applied to the study of three absorption systems in the spectrum of
the HDF-South quasar J2233-606 obtained with
the UVES spectrograph at the VLT/Kueyen telescope. The MCI does not confirm
variations of metal abundances within separate systems which were discussed
in the literature. Instead, we found that an assumption of a homogeneous
metal content and a unique photoionizing background is sufficient to describe
the observed complex metal profiles.
It was also found that the
linear size L and the line-of-sight velocity dispersion
measured within the absorbers obey a scaling relation, namely,
increases with increasing L, and that
metal abundance is inversely proportional to
the linear size of the system: the highest metallicity was measured in
the system with the smallest L.
Key words: cosmology: observations - line: formation - line: profiles - galaxies: abundances - quasars: absorption lines - quasars: individual: J2233-606
Absorption systems in quasar spectra provide unique information
on the intervening intergalactic matter (IGM) up to redshift
,
back to the time when the Universe was less than 7%
of its present age.
High resolution spectroscopic observations available nowadays
at large telescopes open new
opportunities to investigate the physical nature of quasar absorbers.
Reliable data on the
chemical composition of the IGM and on the
physical characteristics
(like velocity and density distributions,
volumetric gas density, kinetic temperature,
ionization structure etc.) of the
absorbers is an important
clue to our understanding of galaxy formation, chemical evolution
of the IGM
and the origin of the large-scale structure.
In recent investigations much attention find the metal systems which are the absorbers exhibiting as a rule numerous lines of low (like H I, C II, Si II, Mg II, Al II) and high (like C III, N III, Si III, C IV, Si IV, N V) ionized species.
Presence of metals provides a unique opportunity to study the physical conditions of matter at early epochs. Unfortunately, the computational methods usually applied to high resolution spectra lie quite often behind the quality of observational data and fail to extract from them all encoded information. The common processing method consists of the deconvolution of complex absorption profiles into an arbitrary number of separate components (assuming a constant gas density within each of them) which are then fitted to Voigt profiles. However, in many cases this procedure may not correspond to real physical conditions: observed complexity and non-similarity of the profile shapes of different ions indicate that these systems are in general absorbers with highly fluctuating density and velocity fields tightly correlated with each other. Too high or too low gas temperatures, extremely varying metallicities between subcomponents, exotic UV background spectra and other physically badly founded outcomings may be artifacts arising from the inconsistency of the applied methods (see examples in Levshakov et al. 1999; Levshakov et al. 2000b, hereafter Paper I).
In Paper I we developed a new method for the QSO spectra
inversion, - the Monte Carlo Inversion (MCI), -
assuming that the absorbing region is a cloud
with uniform metallicity but with fluctuating density and
velocity fields inside it.
This computational procedure
which is based on stochastic optimization
allows us to recover both the underlying hydrodynamical fields and
the physical parameters of the gas.
First application of the MCI to the analysis of the
system toward Q08279+5255
(Levshakov et al. 2000a)
has shown that the proposed method is very
promising especially
in the inversion of complex absorption spectra
with many metal lines.
In this paper we start a new comprehensive
survey of the metal systems for which high resolution and
high signal-to-noise spectra are available.
We present here the results for three absorption systems
(
= 1.87, 1.92 and 1.94) from the spectrum
of the quasar J2233-606 which have been already studied
by Prochaska & Burles (1999), and
D'Odorico & Petitjean (2001, hereafter DP)
using the common Voigt fitting method.
We re-calculate
these systems using the MCI in order
to compare the applicability of both approaches
and to show up their restrictions.
The structure of the paper is as follows. In Sect. 2 the data sets used in the MCI analysis are described. Section 3 contains the details of the applied computational procedure. The results obtained for each of the mentioned above systems are presented in Sect. 4. Conclusions are reported in Sect. 5. In Appendix the general equation of the entropy production rate is given which is used to calculate the density and velocity configurations along the line of sight exhibiting minimum dissipation.
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Figure 1:
Hydrogen and metal absorption lines associated with the
![]() ![]() ![]() ![]() ![]() ![]() |
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High-quality data of the Hubble Deep Field South (HDF-S) quasar
J2233-606 (
,
)
were obtained during the
commissioning of the UVES on the VLT 8.2 m Kueyen telescope
at Paranal (Chile) in October 1999.
The resolving power at which the spectra were recorded
in the spectral range
Å was
,
corresponding to velocity resolution of
km s-1.
The data reduction and the identification of metal absorption-line
systems in the J2233-606 spectrum
are reported in Cristiani & D'Odorico (2000).
In our study we also used the J2233-606 echelle spectrum
(
,
Å)
obtained with the HST/STIS (Savaglio 1998).
The complete description of our computational procedure is given in Paper I. Here we summarize briefly basic model assumptions and emphasize new details recently included in the MCI.
We assume that all lines observed in a metal system arise in a continuous absorbing gas slab of a thickness L (presumably the outer region of a foreground distant galaxy). The absorber exhibits a fluctuating gas density and a mixture of bulk motions such as infall and outflows, tidal flows etc., resulting in a stochastic velocity field. Metal abundances are assumed to be constant within the absorber and gas is supposed to be optically thin for the ionizing UV radiation.
Within the absorbing region the radial velocity v(s) and
total hydrogen density
distributions
along the line of sight are
the same for all ions. In the computational procedure these
two random fields
are represented by their sampled values
at equally spaced intervals
(x is dimensionless radial coordinate s/L),
i.e. by the vectors
and
with k large enough
to describe the narrowest components of complex spectral lines.
Further we suppose the thermodynamic and ionization equilibrium at each computational point along the sightline which means that fractional ionizations of different ions are determined exclusively by the gas density and vary from point to point. These fractional ionization variations are just the cause of the observed diversity of profile shapes. To calculate the kinetic temperature and fractional ionization of ions the photoionization code CLOUDY (Ferland 1997) was used.
The inputs to CLOUDY are the dimensionless ionization parameter
(
- the number density
of photons with energies above 1 Ry),
metallicity and the background ionizing spectrum for which
the Haardt-Madau spectrum (HM) was adopted (Haardt & Madau 1996).
The number density of the ionizing photons for this spectrum
Fractional ionization curves
were computed with CLOUDY for solar abundance pattern and different
metallicities and then included
in the MCI code to calculate the optical depths for ions involved in
the fitting.
If the obtained solution revealed the abundance pattern different from the solar
one,
were recalculated for this new pattern and all computations
repeated. It should be noted, however, that differences of
dex
from solar values influence the fractional ionizations only weakly.
The values of velocity and density at subsequent computational points
are considered to be correlated and are described by means of
Markovian processes. In particular, the velocity is computed as follows:
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Figure 2: Computed velocity (panel a) and density of gas (panel b) and ions (panels c-j) distributions along the line of sight for the system at z = 1.92595toward J2233-606. Shown are patterns rearranged according to the principle of minimum entropy production rate (see text). |
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Figure 3: Density-weighted velocity distribution functions, p(v), for H I, C II, Si II, N III, Si III, C IV, and Si IV as restored by the MCI procedure in the z = 1.92595 system toward J2233-606. |
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Having defined ,
the total hydrogen density can be obtained as
Before being compared with the observed spectrum,
the synthetic intensities
are convolved with the spectrograph point-spread function.
Thus the proposed model is fully defined by specifying the
following values: the velocity vector ,
the total hydrogen density vector
,
the total hydrogen column density N0,
the mean ionization parameter U0,
the radial velocity dispersion
,
the density second central moment
,
the element abundances
and
the correlation coefficients
and
.
The common least-squares minimization (LSM) of the objective function
is used to estimate the model parameters
.
The computational procedure itself consists of two steps: firstly a point
in the parameter space (
is chosen and then an optimal configuration
of
and
for this parameter set is searched for.
Correlation coefficients are considered as external parameters and
remain fixed during the calculations.
![]() |
Figure 4:
Same as Fig. 1 but for the
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The optimization of
and
is the most
time-consuming part of the procedure and needs an effective algorithm
to achieve a quick and stable convergence of the computations.
In the MCI we use the simulated annealing with Tsallis acceptance
rule (Xiang et al. 1997) and an adaptive annealing temperature choice.
Namely, the annealing temperature
at iteration k+1
is decreased according to following equation:
The calculation of the uncertainty ranges
for the fitting parameters is
in our method not so
straightforward as a simple inversion of
the Hesse matrix since the
velocity and density distributions represent
additional degrees of freedom and widen, in general,
the confidence intervals.
However,
these
and
distributions themselves are nuisance parameters and should be
"integrated out'' when one computes
the errors for the other parameters.
To estimate the confidence levels,
the following procedure can be applied:
the values of the physical parameters
in the vicinity of the global minimum of the objective function
are chosen at random
and then the optimal density and velocity distributions are computed.
Assuming that the probability
of each parameter set can be linked to the derived
value
[e.g. as
]
we can estimate
from the obtained sample
the joint probability density function for parameters
and hence calculate all necessary statistical moments.
It should be noted, however, that the reliable estimation of this multidimensional function requires a very large sample which is quite time consuming. In our case the exact estimation of confidence levels is not very crucial taking into account the intrinsic uncertainties in atomic data (e.g. Savin 2000) or unknown shape and intensity of the local background ionizing radiation. Because of this we restricted our samples to a few dozens of points and estimated the accuracy of the fitting parameters only approximately.
The recovered density and velocity
patterns are not unique - many configurations are possible with
comparable probability.
But all these configurations have the same density-weighted
velocity distributions which actually determine the observed line shapes
(see Paper I).
As already mentioned above,
we represent these random fields by their values sampled at equally
spaced intervals .
In order to compare the
calculated patterns we rearrange these values
in such a way that the final configuration exhibits a lowest rate
of entropy production: according to the Prigogine theorem
(Prigogine 1967), this configuration has the minimal dissipation and,
hence, is more stable and more probable.
All necessary equations to calculate the entropy production
are presented in Appendix.
We stress, however, that
configurations produced on the base of such rearrangement
should in no case be considered as something final - they represent only
the (most) probable case of the density and velocity distributions
along the line of sight and are used here exclusively for
illustrations.
The system at
toward the quasar J2233-606
has saturated hydrogen lines (from Ly-
up to Ly-8)
and metal lines of
C II, Si II, Si III,
C IV, and Si IV.
The results obtained with the MCI
are presented in Table 1 and illustrated in
Figs. 1 and 2.
Parts of profiles included in the
minimization
are marked by horizontal lines at the panel bottoms in Fig. 1.
Profiles of the doublet N V
Å and
N V
Å were
calculated later using the obtained velocity and density
distribution and the metallicity derived from the fitting of
N III
Å.
It is seen from Fig. 1 that most spectral features can be well
represented assuming uniform
metallicities and a common HM UV background.
Figure 2 demonstrates the distribution of the
radial velocity and gas density (panels a and b)
along the line
of sight (rearranged in accord with the principle
of minimal entropy production rate).
The density distributions for the ions involved in the optimization
are shown in panels c-j,
whereas the density-weighted velocity distributions which
determine the shapes of the spectral lines are presented in
Fig. 3.
This figure shows that the density-weighted
velocity distributions
for low ions C II and Si II are similar, but
differ from those for high ions C IV and Si IV.
These distributions easily explain why the lines of C II and
Si II look very much alike and why their centers are displaced
by
km s-1 (DP)
with respect to C IV and Si IV.
The study of this system by DP,
who used the standard Voigt profile fitting,
produced comparable column densities (albeit 20-50% smaller).
However, the metallicities obtained by DP for two main clouds
(at v = 0 km s-1 and v = -43 km s-1) differ
nearly by two orders
of magnitude: [X/H] = -0.9 and -2.7, respectively
(in our case [X/H]
for the whole system).
As shown in Paper I,
the Voigt fitting may in general yield correct column densities
when applied to unsaturated lines, but the mean U and, hence,
the ionization corrections may not be unambiguous.
Therefore,
the conclusion made by DP that the
system contains
"a region of intense star-formation activity'' may not be well justified
since this result is model dependent.
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Figure 5: Computed velocity (upper panel) and gas density (lower panel) distributions along the line of sight for the system at z = 1.942616toward J2233-606. Shown are patterns rearranged according to the principle of minimum entropy production rate (see text). |
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The values of the average gas density n0 and kinetic temperature
,
and the
cloud thickness Lestimated in our model (see Table 1)
are typical for the Ly-
systems discussed in the literature
(e.g., Giallongo & Petitjean 1994; Viegas et al. 1999;
Prochaska & Burles 1999; Chen et al. 1998; Chen et al. 2001).
Low metallicity for the whole system ([X/H] < -2.0)
and its dimension of 20 kpc imply that this system can originate
in a galactic halo or in a large scale structure object.
This system exhibits a plenty of metal lines in different ionization stages.
The metal profiles are not very complex
and extend over the velocity range from -100 km s-1
to 100 km s-1.
Results obtained with the MCI are presented in Table 1 and
shown in Figs. 4 and 5. As in the previous system, most absorption
features can be well
described with uniform metallicities and a common HM spectrum.
The Ly-
profile is contaminated by the forest absorption
in the blue and red wings and therefore the Ly-
absorption feature
was not involved in the analysis.
The profiles of Mg II
Å
and Al II
Å were computed later using the
derived velocity and density distributions.
Mg II
Å
is contaminated by a telluric line and this explains
the difference between the computed and observed profiles.
The synthetic and observed profiles of Al II
Å
show much more pronounced discrepancy.
Fractional ionisation curves for Al II and Al III
were computed with CLOUDY.
These curves allowed us to fit the Al III doublet quite well
with the Al abundance similar to that obtained for the other metals.
However, when
the Al II profile was included
in the fitting, the Al metallicity differed by order
of magnitude from the other metals. Besides
it was impossible to fit adequately the Al III doublet.
Similar behaviour of Al was reported also by DP who noted
that "the recombination coefficients used to compute the
aluminium ionisation equilibrium
[in CLOUDY] are probably questionable''.
Column densities derived by DP coincide well (within 15%) with
that obtained in our procedure except for the
saturated Si III
Å line for which the Voigt
fitting gave nearly 2 times lower value.
The abundances estimated in DP scatter again from component
to component, but nevertheless they conclude that
"the gas in this system
is likely of quite high metallicity (larger than 0.1 solar)''.
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Figure 6:
Same as Fig. 1 but for the
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Similar to the Voigt fitting,
the MCI also delivered for this system high metal abundancies:
one third solar for carbon and silicon and nearly
two times lower for nitrogen, magnesium and aluminium.
Taking into account this result and a compact dimension
(5 kpc, see Table 1)
of the absorbing region we come to the same conclusion as
Prochaska & Burles (1999) did: the system at z = 1.94 can hardly
be a large scale structure object (like a filament or a wall)
and should be related to a galactic system (may be a region of intense star
formation).
This is the most interesting system from the family of the absorbers at z = 1.9 toward J2233-606. The metal line profiles show a rather complex structure extending over the velocity range of about 700 km s-1. Some of these profiles are severely blended that hampers the unique Voigt profile deconvolution (e.g. DP assumed 17 components to describe metal profiles).
The MCI code turned out to be much more robust
and was able to recover the self-consistent line profiles even under such
unfavourable conditions. The physical parameters which the MCI delivered
for the z = 1.87 system together with
the underlying velocity and density distributions
are presented in Table 1 and in Figs. 6 and 7. It is seen from Fig. 6
that like in the previous two systems all lines are well described
with a single parameter set, uniform metallicities and a common
HM UV background.
The blue wing of the Ly-
line is contaminated by the forest
absorption as is clearly seen from the Ly-
and Ly-
profiles.
The synthetic
profile of the O VI
Å line
was calculated later using the derived best fitting
parameters and the oxygen abundance [O/H] = -1.0(which is about 3 times over the other
element abundances from this system).
Even with the increased abundance
the synthetic profile of O VI is still much weaker than the observed
intensities. This discrepancy
rules out the ionization of O VI by the adopted background
radiation.
Taking into account that all other elements have been well
described with a given HM spectrum and that the collisional ionization
of oxygen
can hardly be effective at low densities (
)
and temperatures of
K,
this result seems to favor the interpretation that
the O VI ion and the other ions do not arise
in the same gas (Kirkman & Tytler 1999; Reimers et al. 2001).
According to our results, the absorber at z = 1.87 could be a large size cloud with very high velocity dispersion. Its estimated linear size of 80 kpc is consistent with dimensions of extended gaseous envelopes observed around galaxies at z < 1. In these envelopes, Mg II absorption is the dominant observational signature at the distancies up to a few tens of kiloparsecs (Bergeron & Boissé 1991), whereas highly ionizied species like C IV are observed at distances of at least 100 kpc from galactic centers (Chen et al. 2001). Since the extended structure of the same order of magnitude is observed at z = 1.87, we may conclude that this system arises in the external halo at large galactocentric distances.
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Figure 7:
Same as Fig. 5 but for the
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A main goal of this work was to investigate the reliability of the physical parameters and dynamical characteristics of the metal absorption systems obtained by means of the standard Voigt fitting procedure and by the modified Monte Carlo Inversion algorithm. For comparison we used the recently obtained results on the Voigt fitting analysis of three systems toward J2233-606 (D'Odorico & Petitjean 2001).
We found that
both approaches deliver similar
total column densities of unsaturated metal
lines. The saturated
profiles may, however, be treated differently
(e.g., the Si III
Å line
in the z = 1.94 system).
We also found that metal abundances based on the Voigt deconvolution procedure differ considerably from those obtained by the MCI. For instance, instead of fluctuating metallicities found in the absorbers toward J2233-606 by DP, the MCI shows that an assumption of a homogeneous metal abundance for the whole system under study is quite sufficient to represent all observed features.
New and principal results which can be obtained only with the MCI procedure
are the kinematic characteristics of the absorbers. We estimated
selfconsistently for the first time the density and velocity dispersions
along the sightlines within the absorbers and calculated the total hydrogen
column and volumetric densities
which gave us a direct measure of their linear sizes.
The found dimensions of
kpc to
kpc are in good agreement with measurements of the extended
gaseous envelopes around the nearby galaxes which were probed by the
Mg II absorption lines (Bergeron & Boissé 1991) and by
the C IV lines (Chen et al. 2001).
A new issue obtained in the MCI analysis is
a scaling relation. Namely,
we found that the linear size L shows a positive correlation with
the line-of-sight velocity dispersion
,
i.e.
the higher L, the
larger
is observed (see Table 1).
Although our sample is still too small to carry out statistical analysis
of this correlation,
the scaling tendency is of the same kind that can be expected
for virialized systems. The velocity dispersion is closely
related to the total mass of the system in a stationary state
(cf. the scaling law known as the fundamental plane for
elliptical galaxies). Taking into account that the scaling laws are
different for different types of objects (see, e.g., Fig. 2 in
Mallén-Ornelas et al. 1999),
future statistical analysis may allow us to classify absorbers at
different redshifts.
It is also interesting to note another scaling relation: we observe systematically higher metal abundance with decreasing L, and vice verse, the higher L, the lower metallicity is deduced. If L reflects the linear size of a distant absorber, then we may conclude that a compact absorber has, presumably, higher metal content as compared with an extended one.
Parameter |
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Mean ionization parameter, U0 |
![]() ![]() |
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0.12 (![]() |
Total H column density, ![]() |
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Velocity dispersion,
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35 (![]() |
104 (![]() |
179 (![]() |
Density dispersion,
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1.50 (![]() |
2.31 (![]() |
1.31 (![]() |
Chemical abundances![]() |
|||
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9.8-5 (
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8.7-6 (
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2.0-6 (
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1.0-5 (
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1.7-6 (
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-0.53 | -2.21 | -1.58 |
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-0.88 | -2.17 | ![]() |
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-0.75 | ![]() |
-1.27 |
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-0.79 | ![]() |
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-0.54 | -2.14 | -1.31 |
Column densities, cm-2: | |||
N(H I) |
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N(C II) |
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N(Mg II) |
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N(Si II) |
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N(C III) | ![]() |
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N(N III) |
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N(Al III) |
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N(Si III) |
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N(C IV) |
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N(Si IV) |
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N(N V) | <3.5412 | ![]() |
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Hydrogen number density, n0, cm-3 | ![]() |
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Mean kinetic temperature, K | 143 | 253 | 253 |
Minimum kinetic temperature, K | 113 | 163 | 183 |
Maximum kinetic temperature, K | 173 | 403 | 31.53 |
Linear size, L, kpc | ![]() |
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Mass,
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Mass,
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Acknowledgements
We thank our referee Prof. Reimers for his helpfull report. S.A.L. and I.I.A. gratefully acknowledge the hospitality of the Osservatorio Astronomico di Trieste and the National Astronomical Observatory of Japan (Mitaka) where this work was performed. We also thank Valentina D'Odorico for sharing with us the calibrated VLT/UVES spectrum of J2233-606. The work of S.A.L., I.I.A. and I.E.M. is partly supported by the RFBR grant No. 00-02-16007.
General equation for the entropy production rate is given by
(Landau & Lifshits 1987):
The terms included in this equation account for only hydro- and thermodynamic processes since we assume the ionization balance in each point of the region which means that the radiative heating and cooling do not contribute to the entropy production. The second viscosity equals zero for dilute monoatomic gases (Chapman & Cowling 1970) so we omit it from further consideration.
We also assume that heat conductivity
and viscosity
are dominated by turbulence, and hence the
Prandtl number is about unity (Monin & Yaglom 1975):
From observations, only one component vx (along the sightline)
of the velocity vector v is known.
Therefore we are compelled
to neglect in (A.1) all terms including derivatives
other than
.
The second right hand term in (A.1) can be re-written in the form:
For a monatomic ideal gas
(n is the number of gram-moles and R is the universal gas constant),
and if the gas is fully ionized then
(e.g. Lang 1999).
Given the values of ,
Pr, T0,
,
and
,
we can rearrange the computational points
and
in such a manner,
that minimum of (A.4) will be achieved.
Minimization of (A.4) was carried out by means of combinatorial
simulated annealing technique (Press et al. 1992).
The obtained configuration of the density and velocity distributions
should have the least dissipation
and therefore will exist longer than all others.