The structure of CII in low metallicity PDRs
M.Röllig, S. Jeyakumar, J. Stutzki
I. Physikalisches Institut, Universität zu Köln, Zülpicher Str. 77, D-50937 Köln, Germany
Photon Dominated Regions (PDRs)
Metallicity effects
In principle, every boundary of a molecular cloud represents a PDR. PDRs are transition regions in
the interstellar medium between a region of ionized or atomic gas characterized by a low optical
depth for UV photons and a region of high-density, typically molecular gas and dust with a large
optical depth for UV photons. Heating by UV photons dominates the energy input in these outer
cloud layers and thus strongly influences their structure. The strength of the impinging UV field is
one characteristic of a PDR. It may vary between 105 times the average interstellar radiation field
in the vicinity of massive star formation and less than a fraction of it at large galactocentric
distances.
Both theory and observations suggest that metallicity significantly changes the structure of PDRs
(Madden et al. 1997, Madden 2000, Bolatto et al. 1999). The metallicity affects several aspects of
a PDR:
• fewer heavy elements result in an altered gas-phase chemistry (different abundances relative to
hydrogen)
• fewer heavy elements lowers the dust to gas ratio and thus change the grain surface chemistry
(e.g. formation of H2).
• less dust content of a cloud decreases the extinction, thus UV photons may penetrate deeper into
the cloud altering the radiation dependent rate coefficient (e.g. for ionization and dissociation).
Molecular hydrogen is partly affected by these effects. Because of the strong self-shielding in the
Lyman and Werner bands the enlarged UV field hardly influences the abundance of H2. But
molecules like CO are dissociated in much deeper regions into the cloud. Therefore the usually
applied XCO factors yield incorrect results. Molecular gas in low-Z systems is not well traced by
CO.
CII Balance
The dominant reaction channels for the formation and destruction of CII are:
C + ν → C+ + eC+ + e- → C + ν
and
C+ + H2 → CH2+ + ν
This figure schematically shows the structure of a PDR. FUV photons are ionizing and dissociating
Assuming that these are the only reactions which influence the CII abundance, we can write the
the atoms and molecules on the surface of the cloud. Due to continuous absorption by dust
CII balance equations as:
particles and line absorption by various species the intensity drops with increasing depth and
allows the recombination of ions and the formation of more complex molecules. These transition
Rion nCI(r,Z)=Rrec nCII(r,Z) ne(r,Z)+Rchem nCII(r,Z) nH (r)
zones are marked in the figure as rod-like structures with increasing grey-levels. Here we marked
2
the three main transition regions: a) formation of H2 from atomic hydrogen, b) C+ recombines and
with Rion , Rrec , Rchem are the reaction rate coefficients for ionization, recombination and the
CO forms, and c) O2 forms.
chemical destruction of CII respectively. The ionization rate is a function of Av : Rion=k1χE2(k3 Av
Z) with χ being the strength of the radiation field and k1,k3 the reaction coefficients taken from
UMIST95. E2(…) is the exponential integral of second order which substitutes the simple
exponential attenuation of radiation in the case of an isotropic radiation field.
Since we define the radial point r as the depth where the abundances of CI and CII are equal,
We use the spherical PDR model of Störzer et al. (1996) for our study. The model solves the
nCII=nCI . Assuming that the total carbon content is split between CII and CI, nCI and nCII can be
heating and cooling of the gas simultaneously with the chemistry in spherical symmetry. The
written as nCI(Z=1)×Z/2. All electrons are assumed to be created through ionization of CI, thus
clouds are exposed to isotropic FUV fields and we use an escape probability formalism when
ne=nCII. For the density we assume nCI(Z=1)=1.4×10-4n0, and nH2=n0/2, with the total particle
iteratively calculating the thermal structure as a balance between the gas heating and cooling.
density n0. These assumptions lead to a new balance equation:
After the final thermal and chemical structure of the PDR is established we can use a more
sophisticated multi-shell radiative transfer code (ONION) to calculate the emergent line
k1×χ× E2(k3 Av(r) Z) = Rrec× 1.4×10-4 ×n0(r) ×Z + Rchem ×n0(r)/2
intensities. The model takes into account 18 different heating and cooling terms, as well as a
complex chemical network which easily allows to add or remove chemical species into the
For a given n0(r) and χ, the above equation can be solved numerically to obtain r. We chose a
calculations.
density profile of the form n0(r)=n0×(r/Rtot)-α for r<0.2×Rtot and n=n0×0.2-α for r<0.2×Rtot. For α
we took the values 1.5 and 0 (which is equivalent for a constant density).
An online extraction tool for the PDR model results is available at:
PDR Model
http://www.ph1.uni-koeln.de/workgroups/theo_astronomy/pdr/
Results
The figure on the right shows a comparison of the detailed PDR model calculations (filled
symbols, solid lines) and the semi-analytical estimates (open symbols, dashed lines) as described
above. In this comparison we confined to a total density of n0=104 cm-3 and an UV field of χ=100.
The filled circles represent clumps of mass M=103 M~ , the filled squares represent clumps of
mass M=106 M~ (the higher mass is necessary to allow for a sufficient extinction of UV in order to
recombine C+ in the low Z clouds with uniform density) .
The squares in the figure represent models with a constant density (α=0) and the resulting CII
layer width depends on the metallicity as ~Z-1.1 which confirms the assumptions from Bolatto et al.
1999. The circles represent the models with a power-law index of the density profile of α=1.5. The
depth point can be fitted numerically with the function (1.195+5.758 Z)-1.47.
Both, detailed PDR results and semi-analytical estimate, are in good agreement, even if the
estimated widths are higher than the numerical results. This results from the very simple
assumptions made in the analytical analysis like, no UV shielding and a very rudimentary
chemical network (just 3 reactions). Nevertheless the overall dependency is reproduced very well.
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