A&A 389, 393-404 (2002)
DOI: 10.1051/0004-6361:20020646
H. Liszt
National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA 22903-2475, USA
Received 20 March 2002 / Accepted 29 April 2002
Abstract
Molecular hydrogen is quite underabundant in damped Lyman-
systems at high
redshift, when compared to the interstellar medium
near the Sun. This has been interpreted as implying that the
gas in damped Lyman-
systems is warm like the nearby neutral intercloud medium,
rather than cool, as in the clouds which give rise to most H I
absorption in the Milky Way. Other lines of evidence
suggest that the gas in damped Lyman-
systems - in whole or part - is actually
cool; spectroscopy of neutral and ionized carbon, discussed here,
shows that the damped Lyman-
systems observed at lower redshift z < 2.3 are
largely cool, while those seen at z > 2.8 are warm (though not
devoid of
). To interpret the observations
of carbon and hydrogen we constructed detailed numerical models of
formation under the conditions of two-phase thermal equilibrium,
like those which account for conditions near the Sun, but with varying
metallicity, dust-gas ratio, etc. We find that the
low metallicity of damped Lyman-
systems is enough to suppress
formation by many
orders of magnitude even in cool diffuse clouds, as long as the ambient
optical/uv radiation field is not too small. For very low metallicity
and under the most diffuse conditions,
formation will
be dominated by slow gas-phase processes not involving grains, and a
minimum molecular fraction in the range
10-8-10-7 is expected.
Key words: quasars: absorption lines - ISM: molecules
Perhaps it is something of a paradox, but large ground-based
optical telescopes like Keck and VLT routinely do absorption-line
spectroscopy of the gas in high-redshift objects which surpasses what
can be done for the interstellar medium (ISM) of our own Galaxy near
the Sun. Viewing neutral gas at high redshift makes the dominant ion
stages (C II, Fe II, etc.) accessible, to say nothing of Lyman series
in H I and D I and the Lyman and Werner bands of .
The high spectral
resolution and large collecting areas of modern ground-based
instrumentation cannot easily be matched in space-based instruments,
and certainly not for the same cost.
Thus we may have exquisitely detailed and sensitive spectra of systems
which cannot be imaged, whose nature is therefore left to be inferred
from their patterns of gas kinematics
(Prochaska & Wolfe 1997, 1998; Haehnelt et al. 1998; Ledoux et al. 1998; McDonald & Miralda-Escudé 1999) and ionization
(Wolfe & Prochaska 2000a,b). So it is with most damped Lyman-
systems, defined as those
absorption-line systems having N(H I)
when seen against the emission of background QSO's. Although well-formed
galaxian systems can and do harbor some of them at low redshift,
damped Lyman-
systems are for the most part believed to be protogalactic objects, perhaps
in disk systems (Prochaska & Wolfe) or perhaps in the ongoing merger of
protogalactic clumps (Haehnelt et al. 1998). The numbers are such that damped Lyman-
systems
seem to contain at least as many baryons as can be found in the local Universe
now, and it is of great interest to understand how these baryons become
recognizable nearby objects within a relatively short redshift interval.
The absorption-line gas in damped Lyman-
systems is easily discussed in the same terms,
using the same physical processes, that are employed locally.
Evidence that the rest-frame optical/uv radiation field is comparable
to that near the Sun (Levshakov et al. 2002; Molaro et al. 2002; Petitjean et al. 2000) and the presence
of metals at a low but non-negligible level 0.1-0.01 Solar, makes it
possible (or, perhaps, merely hopeful?) to talk about the
"interstellar medium'' in these systems. The low metallicity and general
underabundance of dust (which is not directly observed in any one
object but can be inferred statistically (Fall & Pei 1993; Pei et al. 1991) or
from patterns of gaseous abundances (Boisse et al. 1998)) may render the
gaseous medium in damped Lyman-
systems only more extreme versions of those in local
dwarf systems like the LMC and SMC
.
But it has also been argued that the apparent recognizability
of patterns in the absorption spectra has been over-interpreted
(Izotov et al. 2001), and
that the similarity of intermediate and low ion kinematics (Al III and
C II or Fe II; C IV and C II behave differently) could mean that
substantial ionization corrections to the metallicity are needed
(however, see Vladilo et al. 2001, for a contrary opinion).
At the present time there seem to be several lines of evidence suggesting
that, unlike the local ISM (where low-altitude neutral gas is perhaps
2/3 cool and 1/3 warm and the overall ratio including high-altitude
material is 1/2 and 1/2) the gas in damped Lyman-
systems is more predominantly warm.
Examples include the high H I spin temperatures inferred from comparison
of
cm and Lyman-
absorption
(Wolfe & Davis 1979; Carilli et al. 1996a,c; Chengalur & Kanekar 2000; Kanekar & Chengalur 2001)
(but see Lane et al. 2000), the similarity of low and intermediate ion
kinematics mentioned in the preceding paragraph, and the very low column
densities of
discussed here. Along lines of sight with reddening
EB-V > 0.05 mag (N(H)
)
in local
Copernicus
spectra, it is always the case that a few percent or more of the neutral
hydrogen is molecular. By contrast, the molecular hydrogen fraction in
damped Lyman-
systems is 2-4 orders of magnitude lower (i.e.
10-4 - 10-6), which can
be interpreted as meaning that the gas temperature must be above 3000 K
(Petitjean et al. 2000) Lanzetta et al. (1989) used N(
)/N(H) to constrain
the dust/gas ratio toward Q1337+113, similar to the approach taken
in this work.
Here we consider the formation of molecular hydrogen in a gas which is in
two-phase thermal equilibrium at low metallicity. Perhaps because
has been observable so rarely in the local ISM there is not a big literature
on this subject, but the extant 1970's-era
Copernicus observations
are well-explained in this way (Liszt & Lucas 2000) using modern shielding
factors for radiative dissociation (Lee et al. 1996). The only surprise
(if there indeed is one) is the low densities that are required to start
formation locally, and the fact that even a "standard'' H I cloud
(Spitzer 1978) should have a molecular fraction of 10-30% deep inside.
Local diffuse clouds also have surprisingly high abundances of complex
polyatomic species which follow immediately upon the presence of
(Liszt & Lucas 1996; Lucas & Liszt 1996), a phenomenon which is not well understood but
which can be used to account for the observed abundancess of simpler
species such as CO (Liszt & Lucas 2000).
![]() |
Figure 1: Ionization and thermal equilibrium calculations in atomic gas. The pressure P/k is shown as a function of the density of H-nuclei n(H), for four sets of parametric variations. a) Upper left; the metallicity, (dust/gas, C/H, O/H etc.) varies in steps of 2 from 4 times to 1/32 times its reference value; b) Upper right, carbon and oxygen are removed (depleted) from the gas phase in steps of 2; c) Lower left, the "interstellar'' (ambient) radiation field (ISRF) varies from 4 times to 1/32 times the reference value; d) Lower right, the impinging flux of soft X-rays is scaled. |
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In the course of this work, we consider the ionization and
fine-structure excitation of carbon, and the inferences which may be
drawn from observations of carbon in the damped Lyman-
systems. While the importance
of carbon to the physical state of the gas and the conditions for
forming
cannot be stressed too highly, the extended discussion
here in fact arose because of something of a coincidence. Searching the
literature, it quickly became evident that there is a high degree of
overlap between the two relatively scant datasets for carbon (chiefly,
C I, C II, and C II*) and
.
The plan of the current discussion is as follows. In Sect. 2 we lay
out the basics of a calculation of two-phase equilibrium essentially
following Wolfire et al. (1995a). We examine the sensitivity of two-phase
equilibrium to variations in abundance, depletion, incident radiation
and the like, in order to extract from the calculations those aspects
which can be related to existing absorption line data on damped Lyman-
systems.
In Sect. 3 we compare the results of these calculations with observed
hydrogen and carbon column densities: we show that the observations
are consistent with an origin in largely cool gas for the damped Lyman-
systems at lower
z (z < 2.3) and in warm gas at higher redshift. In Sect.
4 we describe calculations of the
abundance in both warm and
cool diffuse gas, under conditions of varying metallicity, etc., employing
(slow) gas-phase processes to explore the minimum expected amounts of
molecular gas, and the more usual grain-catalysis (as in Liszt & Lucas 2000)
for cooler regions of higher molecular fraction. We also compute the
variation of the molecular hydrogen fraction in small gas clots of constant
density. From this, it follows that the low metallicities of damped Lyman-
systems are by
themselves sufficient to cause decreases in the molecular fraction
by many orders of magnitude, even if cool neutral clouds are present.
The ISM is so complicated that any model of it is bound to be heavily idealized and stylized, especially the assumption of a strict equilibrium. But some aspects, especially the presence of phases - discrete regimes of density and ionization - seem robust to variations in the underlying parameters. The existence of multiphase gas seems to be quite general, highly conserved across space and time.
The basis of the present work is a calculation of two-phase equilibrium
following work on the local ISM by Wolfire et al. (1995a). Notable constraints on
the model locally are the thermal pressure range
K
observed (via C I and C I*) in neutral gas locally by Jenkins et al. (1983),
and the electron density in warm gas at the Solar radius
(Taylor & Cordes 1993). As noted by Wolfire et al. (1995a),
strict two-phase equilibrium
is an idealized goal toward which the ISM may tend, but true equilibrium
is hard to attain, especially in warm gas where the cooling timescales
are long.
![]() |
Figure 2:
As in Fig. 1, but the quantities shown in each panel are
the energy loss rate n![]() ![]() ![]() ![]() ![]() |
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Basically, this "standard'' model of the local diffuse ISM is driven by the heating due (in increasing order of importance in warm gas) to cosmic-rays, soft X-rays, and - the dominant mechanism in both warm and cool gas - the photoelectric effect on small grains (Bakes & Tielens 1994). The charge state of the small grains, their heating rates and the recombination of ions on them (which dominates over gas-phase processes at moderate densities in diffuse gas) are all very sensitive to the electron density, so local thermal and ionization equilbria are tightly coupled. Given that carbon is the main source of cooling in cooler gas (O I to a lesser extent) and an important source of free electrons, it follows that the equilibrium conditions and the condition of carbon in the gas are very tightly coupled.
We recently used this code (Liszt 2001) to discuss the
behaviour of the H I spin temperature in local warm gas (the H I there
is not generally thermalized by collisions in multiphase equilbrium)
and to calculate the abundances of
and CO in denser diffuse gas
(Liszt & Lucas 2000). The latter reference describes the model in more
detail than will be given here, especially the various collisional
processes which drive fine-structure cooling in the gas (they are,
of course also discussed in the original reference by Wolfire et al. 1995a).
Our basic calculation differs from that of Wolfire et al. (1995a) in two minor
ways which are subsumed by the extent of our parameter variations.
The earlier authors took the locally-determined soft X-ray flux from
Garmire et al. (1992) and decomposed it into three components, each of which
they represented by a (physically-motivated) plasma emissivity
which was then separately attenuated (or not) by an assumed column of warm
gas; the three contributions were then summed to provide the assumed
incident X-ray spectrum at a typical location. Their final spectrum
is characterized by a quantity they called Nw, the overall column of
warm gas attenuating part of the incident spectrum
whose standard value they took to be
Nw = 1019 H atoms
We
used a simpler representation of the soft X-ray flux, whereby the
observed spectrum is attenuated by a column of neutral gas Nw directly.
Our standard value of
H atoms
produces a pressure-density curve which differs little from that
of Wolfire et al. (1995a).
We also used a somewhat different set of reference (Solar) atomic
abundances whereby
,
,
namely those
which accompanied the distribution of the soft X-ray absorption cross-
sections from (Balucinska-Church & McCammon 1992), which both we and Wolfire et al. (1995a) used
(in their most recently updated version). In both calculations the
reference model has (following Wolfire et al. 1995a) little or no
depletion of the gas phase oxygen and carbon onto grains, which
might be acceptable for warm gas (where carbon does not bear the
brunt of the cooling or contribute many of the electrons, see below)
but is unlikely to be reasonable in local cool gas; if there are grains,
they have to be made of something! The gas phase depletion is considered
an adjustable parameter here, independent of the metallicity.
The net effect of these two differences is slight. With the exception of one system, the observations show that carbon is present in the gas in the same proportion as other species which are typically undepleted locally, i.e. there is low metallicity, but little global carbon depletion.
![]() |
Figure 3: As in Figs. 1 and 2, but the quantity shown in each panel here is the ratio of once-ionized to neutral carbon n(C II)/n(C I). |
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In Fig. 1 we show the basics of two-phase equilibrium and its
sensitivity to some assumed parameter variations. In these curves
of pressure vs. density (one assumes a density, calculates the
ionization and thermal equilibrium, sums the particle densities
and multiplies by the derived temperature), the regions where
dP/dn < 0 are held to be unstable and unlikely to occur in nature.
Those pressures for which there are two densities n
having
dP/d
n|n' > 0 are those for which "two-phase'' equilibrium
is possible. Two-phase heating and cooling calculations by themselves
furnish only the possibility of multi-phase equilibrium; Hennebelle (2000) and
Kritsuk & Norman (2002) elaborate on some processes by which phase transitions and
multi-phase equilibrium are actually brought about.
The curve labelled "1'' in all panels is the same (reference) model; perhaps most clearly at upper right it is apparent that the reference model provides for two-phase equilibrium over precisely the pressure range which is observed in local gas (Jenkins et al. 1983). Typically (but see below and the lower-left panel), only warm (7000 K-10 000 K) neutral gas appears if the density and pressure are below the two-phase regime and only cold (below 1000 K) neutral gas appears if the pressure and density are larger. If conditions are such that the warm gas may persist up to higher density and pressure, or when the cold medium cannot exist except at higher density and pressure, the medium is more likely to be warm.
![]() |
Figure 4:
Fine-structure excitation calculations for varying
![]() |
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At the top left, the metallicity is varied by factors of 4 to 1/32
relative to the reference value; these may be compared with the
calculations of Wolfire et al. (1995b). Many properties of the model actually
vary in concert including; the elemental and gas-phase C and O abundances
(there is no depletion); the columns of all other species heavier than
Helium providing soft X-ray absorption; and the number of grains both large
and small (the latter scales the heating rate of photoelectric ejection).
Vladilo (1998) shows that the dust/metal ratio
at
higher redshift relative to conditions in the Milky Way (MW) so
that
changes mostly because
of metallicity (Z/G), not D/Z. In fact, such an overall scaling
has a surprisingly modest effect compared to some other changes
discussed next. The warm phase may persist up to slightly higher
pressures and densities in gas of lower overall metallicity but
the existence of two-phase equilibrium is not threatened as long
as the balance between heating (small grains) and cooling (carbon)
is maintained in denser gas (as it is in this case).
At upper right, the gas-phase abundances of C and O are decreased while all other parameters are held fixed and this actually has a much more profound effect than scaling the grain (heating) and gas (cooling) abundances in tandem. Carbon provides some heating of the gas (via its ionization, see Spitzer & Scott 1969) but is more important as a source of electrons, influencing the grain heating and recombination rates, and as a coolant. Clearly, when the ambient fluxes are maintained while the main coolants (carbon and oxygen) and source of electrons are depleted, it is substantially more difficult to provide enough pressure to maintain gas in the cool phase. This hearkens back to our discussion, slightly earlier, of the lack of inclusion of depletion in the reference model for MW conditions. In order to maintain two-phase stability over the reference range of pressures in the presence of gas-phase depletion, the incident optical/uv ionizing radiation field must be decreased somewhat. In fact this might not be unreasonable locally for cool gas, which does not occur in arbitrarily small increments and therefore exists under conditions of non-trivial extinction (especially at uv wavelengths). At lower metallicity, this sort of compensation is less obvious and (consistent with some aspects of the observations) the pressure may in fact be somewhat higher in cool gas.
At lower left, we scale the ambient optical/uv radiation field which ionizes carbon (directly) and provides heating and electrons via the photoelectric effect on small grains. Regions whose ambient radiation field (ISRF) falls even a factor four below the average will be predominantly cool. This is an inversion of the normal order of things in diffuse gas and darker clouds in the nearby ISM occur at higher, not lower, thermal pressure.
Last, at lower right, we scale the soft X-ray flux. Cool regions of higher density will probably never see the full extent of the ambient soft x-ray flux because even a small region of appreciable density accumulates a high degree of X-ray absorption. The heating due to soft X-rays tends to increase on a per-event basis as the X-ray spectrum hardens somewhat after absorption, and tends to decrease as the electrons cause more secondary ionization and less direct heating when the ionization fraction is smaller (in neutral gas).
Figure 2 shows, for the same set of parameter variations, the total
gas heating rate
and the loss of energy (
)
due to
cooling in the
C II line (discussed below at some length), in
units of ergs s-1 H-1. For the reference model, some 90%
of the heating is due to the photoelectron effect operating on small
grains, see Fig. 3 of Wolfire et al. (1995a). In warm gas, the burden of cooling
is taken up by excitation of the Ly-
lines under the
highly-idealized assumption that all photons escape; in fact, these photons
may travel substantial distances but by and large do not always
escape a two-phase galactic layer before being absorbed by
dust, at Solar metallicity: the situation may actually be very different
in three-phase models, see Neufeld (1991) and Liszt (2001). In cool gas,
the cooling is due almost entirely to carbon and oxygen fine-structure
excitation, in the reference model. The curves of
in Fig. 2
directly show the brightness (normalized; per H) of the C II*
cooling transition; in cool gas the O I* transition at
makes up most of the cooling not provided by C II.
There is really a quite profound change in the local thermodynamics when the metallicity or ionizing flux varies (Fig. 2, upper and lower left). In particular, while the energy input per H into cool and warm gas is nearly the same for the "Solar'' metallicity and the standard ISRF or higher, it is much smaller in cooler gas when the metallicity is low. In the Milky Way, the carbon cooling rate can be used to infer the heating in both cool and warm gas. In systems of low metallicity such is not the case.
In general, the brightness of the C II
line scales with metallicity
at all densities (Fig. 2, upper left) and varies nearly linearly in cool
phase-stable gas since n(C II*)/n(C II) changes little with metallicity (see
Fig. 5). It also scales with the strength of the ISRF in cool gas (Fig. 2,
lower left), due to changes in n(C II*)/n(C II) (Fig. 5). The C II
brightness varies with depletion at lower densities (Fig. 2 upper right) and
slightly, at low density, with variations in the soft X-ray flux.
From the results at upper right in Fig. 2 we see that C II may not
be the dominant host of cooling in cooler gas, at quite high densities,
if the depletion (not the metallicity) is extreme; oxygen becomes the
preferred coolant due to the higher energy separation in its ground state
fine-structure levels. There is no reason to believe that such conditions
occur widely in diffuse gas, either locally or in damped Lyman-
systems, although one
source in Table 2 (PHL957) seems quite deficient in carbon, given its
quoted metallicity.
Figure 3 shows the ratio of the two lowest ionization states of carbon n(C II)/n(C I). It differs by a factor of 40-100 between warm and cool neutral gas for the standard model, and is relatively insensitive to parameter changes, redshift, etc. This makes it a sensitive indicator of the thermodynamic state of the gas, as discussed in Sect. 3, but also causes confusion when mixtures of the two phases are observed along the same line of sight (see Sect. 2.6). Some aspects of the behaviour shown in Fig. 3 are counter-intuitive; for instance, a stronger ISRF maintains a high C II/C I ratio into denser gas, but the C II/C I ratio is actually smaller in very tenuous gas when the radiation field is higher. This arises in part because the equilibrium pressure increases with the strength of the radiation field and partly due to the level of ionization in the gas (which is not solely determined by carbon).
If the C II lines are saturated or N(C II) is otherwise unknown, but N(C I)
and N(H) are available, the thermodynamic state of the gas may also be
inferred by computing N(C)/N(H)
N(C II)/N(H)
N(C II)/N(C I)
N(C I)/N(H). Presumably, if the gas is actually cool, the
inferred carbon abundance will be much too large (inconsistent with
the metallicity) if the high n(C II)/n(C I) ratios typical of warm gas
are assumed.
The triplet fine-structure of the C I ground state is also accessible to spectroscopy. It is actually rather insensitive to the parameter variations noted above (with the slight exception that C I*/C I increases modestly with increasing X-ray flux at low density) but responds very strongly to a change in the cosmic background level because the first excited state is only 23.2 K above ground. Figure 4 (top) shows the ratio of populations in the lowest two levels as a function of cmb. Clearly, this ratio is a sensitive indicator of the ionization state at low redshift (it differs by a factor of about thirty between warm and cool gas) but is rather insensitive for redshifts above 1.5 or so. The C I*/C I ratio measures cmb at high redshift in the context of our models (see Roth & Meyer 1992). Although perhaps within observational errors, it follows from the results in Fig. 4 that quoted column densities of neutral carbon for high-z systems should include a correction factor for the excited state population.
![]() |
Figure 5: As in Figs. 1, 2 and 3, but the quantity shown in each panel here is the ratio of excited (C II*) to ground-state atoms in once-ionized carbon. |
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The rate of energy loss due to a radiative transition between two
levels k and j having statistical weights
and
,
level populations
and
(units of
),
energy separation Ekj and spontaneous emission rate Akj (
),
immersed in an isotropic radiation field characterized by cmb is
(Goldreich & Kwan 1974)
The 133.5 and 133.6 nm C II and C II* absorption lines have received
more attention because of the obvious possibility that C II is the
dominant ionization stage. But discussions of the excitation of
the C II* fine-structure levels often fail to recognize the role of
carbon in determining the conditions under which it is observed; in many
cases (see Fig. 2) C II will be the dominant coolant when it is the
dominant ionization stage. This means
that the brightness of the C II
line and the C II*/C II ratio are
determined by thermodynamic equilibrium - the energy input to the gas
which occurs at a given density and temperature. So, if the energy
input into the gas does not change, neither will the brightness of the
line or the strength of the 133.5 nm C II* absorption line. In Fig. 2 at upper right, for a density of
,
it requires a factor
8 drop in the the amount of carbon in the gas to weaken the
line
by about a factor 2, all other things being equal.
Figure 5 shows the parameter sensitivities of the C II*/C II ratio. Weak
variation in the n(C II*)/n(C II) ratio in cool gas is shown in
many ways in the panels of Fig. 5. For the reference model, the ratio
varies by only 50% between
(K = 1000 K) and n(H) 40
(K = 75 K). The variation with carbon depletion at upper
right illustrates the effects of thermodynamic considerations.
The ratio n(C II*)/n(C II) increases
as carbon is removed from the gas or n(C II) decreases, because the
brightness of the
line (and n(C II*)) must stay constant in order
to carry away a given amount of energy which is being input to the
gas (see Fig. 2). The behaviour at lower left, where the C II*/C II
ratio is a scaled representation of the cooling rate (also see
Fig. 2) shows how the brightness of the
line, or the amount
of excited-state C II*, must change proportionally as the energy input
to the gas changes.
In warm gas where its excitation is weak and C II is not the dominant coolant, the population of the C II* level is susceptible to change with cmb. This is shown in the lower two panels of Fig. 4. The ability of the C II* population to discriminate between phases may be lost at higher redshift.
Source | 3C286 | 0454+039 | 1756+237 | 1331+170 | 0013-004 | 1232+0815 | PHL957 |
z | 0.69 | 0.86 | 1.67 | 1.78 | 1.97 | 2.24 | 2.31 |
[Zn/H] | -1.22 | -1.1 | (-0.8)a | -1.27 | -0.80 | -1.20 | -1.38 |
N(H I) | 1.8E21 | 4.2E20 | 2.0E20 | 1.5E21 | 5.0E20 | 7.9E20 | 2.8E21 |
N(![]() |
6.9E19 | 6.3E16 | <5.0E15 | ||||
N(C I) | >4E13 | 4.4E13 | 1.4E13 | 1.7E13 | 6.3E13 | 4.0E13 | |
N(C II) | 4.5E16 | 2.7E16 | 7.8E15 | ||||
N(C II*) | 7.9E13 | 1.4E14 | 1.9E14 | 7.6E13 | |||
N(C II)![]() |
3.8E16 | 1.2E16 | (1.1E16) | 2.9E16 | 2.8E16 | 1.8E16 | 4.1E16 |
N(C II)/N(C I)c | (<952) | (293) | (803) | 2647 | 446 | 445 | >1734 |
N(C II*)/N(C II) | (0.0072) | 0.0031 | 0.0070 | 0.0097 |
a assumed for illustrative purposes; other (entries) follow.
b N(C II)
is the amount of carbon if [C/Zn] is Solar.
c values in parentheses use N(C II).
References:
3C286: Boisse et al. (1998); Roth & Meyer (1992).
0454+039: Boisse et al. (1998); Steidel et al. (1995).
1756+237: Roth & Bauer (1999).
1331+170: Chaffee et al. (1988); Ge et al. (1997).
0013-004: Ge et al. (2001).
1232+0815: Black et al. (1987); Srianand et al. (2000) quote N()
= 1.5E17
.
PHL957: Black et al. (1987).
In this context it is important to note that the
K
energy separation of the C II fine-structure levels (to a lesser extent
the 232 K separation in O I), is absolutely crucial to the similarity
of two-phase equilibrium conditions out to moderate redshift, say
z < 10. If the gas locally were cooled by softer photons of
energy
such that we could observe out to some redshift
where
,
the distant gas would have to have
a different coolant. It is apparent from the behaviour of the C I*/C I
ratio in Fig. 4 that C I*, for example, could not be an important gas
coolant at z > 3. The same is true of the lower lines of CO (where
K, 11.0 K, 16.5 K, etc.).
When a property like the N(C II*)/N(C II) ratio - call it R - takes on
values
and
in warm and cool gas, respectively, and a transparent
superposition of phases is observed to have a global value
,
is related to the proportion of gas in the two phases as
![]() |
Figure 6:
Molecular fractions 2n(![]() ![]() |
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In stable two-phase gas (Fig. 3 at upper left) = 20 000 and (roughly)
= 700/n(H) in gas of Solar metallicity (
varies rather less at
low metallicity). In this case, measuring a global average of, say,
= 1000 implies only that there is some fraction
of
gas having
along the line of sight.
This ambiguity cannot generally be resolved with recourse to comparison of profiles, which are largely undifferentiated in the C II line, having been broadened due to some combination of; underlying kinematics in the host system; doppler-broadening of individual gas complexes; and, saturation. In the Milky Way, C II lines are typically fit with much larger b-values (Doppler broadening parameters) even when a single cloud or gas complex dominates the line of sight to a nearby star (cf. Morton 1975). Because of this one cannot, for instance, try to compare the C II* with only that fraction of the C II which overlaps it in velocity.
In Tables 1 and 2 we have gathered information on the neutral and
ionized carbon lines available in the literature. For each source
we show the observed column densities, and the metallicity derived from
zinc, which is believed to be (at most) only lightly depleted
(Pettini et al. 1994; Vladilo et al. 2000).
From the metallicity we derive a quantity N(C II)
which
is meant to represent the maximum amount of carbon available in
the gas phase, i.e. it is the column density of carbon assuming
that carbon and zinc have the same metallicity and depletion.
Comparison with the measured C II column densities shows that
carbon is not lacking, with the notable exception of PHL957.
N(C II)
is used as a surrogate where measured values
of N(C II) are unavailable at low redshift in Table 1.
The ratio N(C II)/N(C I) is much larger for the sources at high zin Table 2, above 13 000-30 000, consistent only with an origin in
overwhelmingly warm gas: the fraction of cool gas must be of order
a few percent at most. At lower redshift, two of the measured ratios,
and that inferred for the source 1756+237, are below 1000, consistent
with cool neutral gas in the stable region of the two-phase equilibrium,
at thermal pressures
K, and densities
.
The data for PHL957 are also consistent with
stable cool gas at
,
K,
while 1331+170 is in the marginally unstable region at
,
K. For the systems at lower
redshift, there must be a very large proportion of cool gas, though
we cannot say exactly how much.
The N(C II*)/N(C II) ratios are noticeably smaller at high redshift in Table 2, and would presumably be smaller still by a factor 2 or more, were it not for the cosmic background radiation, which has a noticeable effect (only) above z = 2.5 in warm gas (see Fig. 4). The N(C II*)/N(C II) ratios observed at lower redshift, in presumably cool gas, are 50-100% higher than in the models. This could be explained by an enhanced ISRF (Fig. 5, bottom left panel) or by some depletion of carbon for PHL957, where the metallicity of carbon is (uniquely) very low compared to that of Zn, and N(C II*)/N(C II) is rather large.
To summarize, comparison of the tabulated observational results with
the calculated properties of carbon in two-phase media shows quite
unambiguously that the observed gas has a substantial contribution from
cool gas at lower redshift but is very largely warm at z > 2.8. Whether
this shift from cool to warm gas is systematic or coincidental remains to be
explored. Norman & Spaans (1997) predicted that multi-phase equilibrium, cool
gas and substantial quantities of
would occur in protogalactic disks
only when the metallicity had increased to 0.03-0.1 Solar, somewhere in the
interval 1 < z < 2.
Levshakov et al. (2002) provide a summary of the molecular fractions
observed toward 14 sources (their Table 2) including most of those
discussed here. The lowest molecular fraction is seen toward
0000-262 at z = 3.39, the highest toward 0013-004 at z = 1.97
(see Tables 1-2 here). The latter is the only direction for which the
molecular fraction exceeds 1/3000, and most are below 10-5.
In this section we address the existence of damped Lyman-
systems with large
hydrogen column densities, substantial amounts of cool gas, but
very small fractions of molecular hydrogen. The models of
-formation presented here are very similar to those of
Liszt & Lucas (2000), who considered the formation of CO in local
diffuse gas, given certain other conditions like the presence of
HCO+, but there are a few differences which we now remark.
The present calculations include X-ray heating and ionization, because they are integral to the question of two-phase equilibrium. X-rays have little effect on the large neutral gas columns which harbor appreciable molecular column densities nearby in the Milky Way but are also included now because we are interested in understanding the minimum molecular fractions which can be expected, and these are presumably set by the slow gas-phase processes (not involving grains) which formed the first stars, and which occur in low-density regions of (unshielded) free space.
Source | 1337+113 | 0528-250 | 0347-382 | 0000-262 |
z | 2.80 | 2.81 | 3.03 | 3.39 |
[Zn/H] | -1.00 | -0.91 | -1.23 | -2.07 |
N(H I) | 8.0E20 | 2.2E21 | 2.52E20 | 2.6E21 |
N(![]() |
<5.0E16 | 6.0E16 | 8.2E14 | 1.1E14 |
N(C I) | <1.6E13 | <5.9E12 | <4.0E11 | |
N(C II) | 2.0E17 | 1.7E17 | 5.1E15 | |
N(C II*) | 3.6E14 | 1.9E13 | ||
N(C II)![]() |
2.8E17 | 9.6E16 | 3.1E15 | 7.9E15 |
C II/C I | >12658 | >28862 | >12700 | |
C II*/C II | 0.00211 | 0.00389 |
References:
1337+113: Lanzetta et al. (1989).
0528-250: Ge et al. (1997); Srianand & Petitjean (1998).
0347-382: Levshakov et al. (2002).
0000-262: Prochaska & Wolfe (1999); Levshakov et al. (2000).
Gas phase -formation occurs via the exothermic reaction pathways
H + e-
H- +
,
H- + H
+ e- and
H+ + H
+
,
+ H
+ H+.
Many of the basic reactions are cited by Puy et al. (1993) and
most by Haiman et al. (1996) (all can straightforwardly be located in the
UMIST reaction database) but the discussion of early-universe conditions
must be modified to include relevant values for the photodissociation of H-and
and the cosmic-ray ionization of
.
For the latter we assumed
per H and 1.08
per
), and for
the photodissociation rate of
in free space we followed Lee et al. (1996).
In order to formulate a treatment of the variation of the photodissociation
of H- with extinction, we integrated the cross-sections of Wishart (1979)
over the local ISRF, finding an unshielded rate of
s-1, just over half of which arises at wavelengths
beyond 800 nm; the photo-dissociation is, therefore, not strongly
attenuated under the conditions discussed here and we elected to
ignore extinction in this regard (the rate quoted in the UMIST
database is
s-1 but we used the smaller value).
Current values of the reaction rates for all important processes are
given in the UMIST reaction database, whose values we employed unless
otherwise noted. Species followed during modelling of the chemistry
included H I, He+, H+ and e- - all given by the calculations of
two-phase equilibrium -as well as H-,
and
.
![]() |
Figure 7:
Molecular fraction as a function of fractional distance
into cool clouds of density
![]() |
Open with DEXTER |
Figure 6 shows the free-space abundance of
arising solely from
gas-phase processes in the two-phase models under conditions of
varying metallicity and ISRF (the two left-hand panels of Fig. 1).
Unlike grain formation scenarios, which take advantage of high N(H)
to boost the molecular fraction at high density, free-space gas-phase
formation of
does not seem to distinguish between warm and cool
conditions. The molecular fractions calculated in Fig. 6 correspond
well with the smallest values in the local ISM, or, for that matter,
in damped Lyman-
systems. Unfortunately, this minimum is not diagnostic of the
host gas conditions.
formation in cool neutral gas clouds is illustrated in Fig. 7,
which indeed shows why even damped Lyman-
systems with appreciable cool gas still may
lack molecular hydrogen. To create this diagram, we considered
(following Liszt & Lucas 2000) a spherical clot of gas of constant
density, immersed in isotropic radiation fields (X-ray, cosmic-ray,
optical/uv, etc.). This was computationally divided up into 128
radial zones, in each of which we derived the temperature/ionization
structure and
abundance. The latter requires iteration, because
the maintenance of
is a sharply non-linear process dependent on the
column and extinction between any point and free-space
(Lee et al. 1996). We adopted a fairly straightforward relaxation
method which converged with gratifying rapidity.
Calculation of the abundance of molecular hydrogen is typically made
feasible by employing a set of shielding factors which account in an
average way for the many very complicated effects of line-overlap and
radiation transport in the dissociation process. We used the shielding
factors of (Lee et al. 1996) which were calculated for local gas. The
justification for this is that the dominant effect requiring consideration
here is the order of magnitude change in the number of grains at very
low metallicity, not the factor of two differences in individual grain
properties between local grains and those seen, for instance in the
Magellanic clouds. The parametrization of Pei (1992) for the Milky
Way, LMC and SMC shows that, for a given amount of B-band extinction,
the grain distribution provides successively somewhat more extinction at
(say) Ly-
as the metallicity declines; the inference is that
graphite grains disappear and silicates do not. But this effect is
dominated by the overall diminution of the extinction with lowered
metallicity.
Figure 7 shows the radial variation of the fraction of H-nuclei in
molecular form over spherical gas clots of constant density
for different column densities N(H) through the center
of the clot. The mean line of sight averaged over the circular
face of such a body intersects it at an impact parameter of
2/3 of the radius (at a value 0.33 along the horizontal axis
in Fig. 7), where the column density is 3/4 of that through
the center.
In each panel of the figure there are 8 vertically-separated curves.
At top, shaded, is the result which would apply in the Milky Way, where
we have taken the dust/metal ratio as observed locally (the reference
model of the two-phase calculations) and depleted carbon and oxygen
in the gas phase by a factor of 2.4. The bottom curve, also shaded, is
the result when the metallicity goes to zero and only the gas-phase
formation of
is included; a modest amount of self-shielding
occurs and the molecular fraction is slightly higher than in free space
(Fig. 6). The intermediate curves assume a dust/gas ratio 0.6 relative
to the reference model for the Milky Way following Vladilo (1998) (a small
effect at higher N(H) but of real importance to the thinnest model) and
no depletion of carbon and oxygen. These curves are labelled by their
varying metallicity as in the previous diagrams.
The cloud with
would be a compact (4 pc),
cool (130 K) Spitzer (1978) "standard'' cloud in the Solar neighborhood.
It would also be very substantially molecular if found in the Solar
vicinity, but a factor 4 decline in the metallicity suffices to
reduce the molecular fraction by some four orders of magnitude. Even
the model having a four times higher column density (compare with the
entries in Tables 1-2) cannot sustain an appreciable molecular fraction
when the metallicity is reduced by a factor 10, which is hardly extreme
for one of the damped Lyman-
systems.
The role of geometry can also be inferred from Fig. 7. At any given
metallicity, a cloud with lower N(H) produces much less than one-fourth
as much
as that illustrated in the next-lower panel. This is
another reason why the molecular fraction may vary widely between two
lines of sight with similar N(H), N(C II)/N(C I), and/or metallicity
(for example). Molecular hydrogen will readily populate a region when
the circumstances are propitious, but can easily be prevented from
forming by the vagaries of local source structure.
This source (Table 2) has an overall molecular fraction
despite the lack of evidence (in carbon) for any appreciable amounts of
cool gas; earlier we asserted that (very roughly) no more than a few
percent of the gas could be cool. Carilli et al. (1996b) did not detect
21cm H I absorption, placing a
upper limit
N(H I)
.
So, the molecule-bearing gas
must be cool, occupying roughly 1% of the total gas column for
K. In the context of our models the gas must also be
fairly dense,
,
occurring over only a very
small fraction of the path length (1 kpc or more) occupied by the gas as a
whole.
The thermodynamics of the ISM near the Sun are strongly influenced
by the disposition of carbon, in grains and in the gas. Spectroscopy
of neutral and ionized carbon affords the opportunity to probe the
processes which are most basic to the structure of the gaseous medium,
nearby and in damped Lyman-
systems. For whatever reason, the very distant gas is easily
understood in the same terms as that seen nearby. Here, we have shown that
one seemingly disparate aspect of high-z systems, their small fractions
of molecular gas, can also be easily understood. Even when cool gas is
present, which must be the case for the systems discussed here at z < 2.3,
abundances of
are suppressed by many orders of magnitude at
lower metallicity as a result of the sharply non-linear nature of the
processes required to maintain substantial columns of
.
No wholesale
reorganization of the gaseous medium need be hypothesized to account
for low
abundances. Conversely, we showed that the slow gas-phase
processes which formed
in the early Universe provide for a minimum
molecular fraction in the range
10-8-10-7.
Acknowledgements
The National Radio Astronomy Observatory is operated by AUI, Inc. under a cooperative agreement with the US National Science Foundation. The referee, Mark Wolfire, is thanked for helpful comments.