Please Note: the e-mail address(es) and any external links in this paper were correct when it was written in 1995, but may no longer be valid.
H. Störzer and
I. Physikalisches Institut der Universität zu Köln, Zülpicher Straße 77, D-50937 Köln, GERMANY
Molecular clouds in massive star formation regions (e.g. Orion Nebula) are irradiated by far-ultraviolet radiation (FUV, 6-13.6 eV) emitted by young, nearby, OB type stars. The theory states that these FUV photons determine the chemical and physical conditions of the cloud, creating a so called photon dominated region (PDR, in earlier papers also named photodissociation region) on the surface of individual molecular clumps.
Several UV field and density dependent processes determine the gas heating. The two most important mechanisms are photoelectric heating and UV pumping of so that in the outermost PDR layers, the temperature can increase up to several 100 K (or even more than 1000 K in case of a strong UV field). The gas cools via FIR fine structure lines, e.g. the [CII] , [OI] and lines. Deeper into the cloud, the temperature decreases and the prominent cooling lines are the [CI] fine structure line and the (sub)millimeter rotational transitions of CO. In the cold interior of the cloud the temperature is about 10 K, resulting from the balance of cosmic ray heating and low-J CO rotational line cooling.
Numerous observations of galactic and extragalactic sources in the lines given above supported the scenario of the PDR structure of molecular clouds. In this paper we briefly discuss the current state of PDR modelling and present some observational results which motivated us to develop a new PDR model for a clumpy cloud structure. Some new applications of these models are presented in the following sections.
The first theoretical PDR models were presented by Tielens & Hollenbach (1985) and Sternberg & Dalgarno (1989). Both models treated a PDR as a semi-infinite plane-parallel slab in which the UV radiation illuminates the PDR from one side and the cooling lines can only emit toward the same direction. Under these model assumptions the temperature structure and the chemical composition of a PDR is calculated, including the evaluation of the cooling line intensities. The main parameters for these model calculations are the hydrogen particle density ( typically in the range from to ) and the strength of the UV field (10 to times the mean UV interstellar radiation field, Draine (1978)). The variation of these parameters may lead to a drastic change of the chemical and physical structure of the PDR and results in a typical set of observable line intensities. The computed intensities for a wide parameter range were presented by several authors (e.g. Tielens & Hollenbach (1985),van Dishoeck & Black (1988),Sternberg & Dalgarno (1989),Burton et al. (1990)). These PDR models succeed to explain the observed line integrated intensities of e.g. the low- and mid-J rotational lines or the [CII] line both in galactic sources (star formations regions) and external galaxies (e.g. Wolfire et al. (1989),Stacey et al. (1991)).
[CII] observations in molecular clouds revealed, that the [CII] emission extends too far into the molecular cloud than could be explained by assuming a homogeneous cloud. The [CII] emission distribution can be well modelled within a clumpy cloud scenario (Stutzki et al. (1988),Howe et al. (1991),Stacey et al. (1993),Meixner & Tielens (1993)). In a clumpy cloud, provided that there is a high clump to interclump density contrast, the UV field can penetrate deep into the cloud and forms PDRs on the surface of the clumps. Detailed UV radiative transfer calculations by Boissé (1990) confirmed these results. It is thus necessary to consider a clumpy molecular cloud structure. A first step in this direction is to compute PDR models with a finite extent.
The observed intensity ratios between the and , and lines cannot be explained by a single component cloud model (e.g. Castets et al. (1990),Gierens et al. (1992)). Typically, the inter-isotopic ratios between the same transitions are in the range of 3 to 8 and the ratios between different low-J lines both for and are close to unity. In single temperature and density models the first observational result leads to the assumption of optically thin emission, whereas the second one is interpreted as optically thick, close to thermalized emission. In addition recent observations in massive star formation regions (e.g. Graf et al. (1993)) revealed surprisingly high intensities for this line.
The formation and destruction of and in the CII/CI/CO transition zone of a PDR depends on several chemical processes. Photodissociation, fractionation reactions and neutral reactions build a sensitive chemical network in the formation and destruction of CO and its isotopomers. For details refer to van Dishoeck & Black (1988), Köster et al. (1994) and Sternberg & Dalgarno (1994). In order to explain the line intensities of bearing species, it is imperative to include a realistic treatment of the chemistry in the PDR calculations. In Köster et al. (1994) we presented a PDR model which takes the clumpy structure of a molecular cloud into account by computing finite sized, plane-parallel PDRs. In these models the more accurate treatment for the calculation of the depth dependent UV radiation from Roberge et al. (1991) was used. Furthermore, we included a proper and chemistry. The calculations have been done for a wide parameter range and succeeded to explain the observed intensities, assuming high density clumps () and high UV radiation ( times the mean interstellar UV field). The observed low- and line ratios can be explained with PDR models assuming a density of about .
A PDR model with a spherical geometry which is more reasonable for a clumpy cloud structure than the presently used plane-parallel geometry is presented by Störzer et al. (1995). They point out that limb brightening and geometrical effects may lead to an increase of the [CII]/CO intensity ratio.
The [CII] fine structure line and the CO rotational lines have different emission regions in PDRs. [CII] radiation emerges from the surface of a PDR as far as the UV radiation is strong enough to ionize carbon. Deeper into the cloud, due to scattering and absorption of dust grains and self-shielding, the UV radiation decreases and CI and CO are formed. As the PDR layer () is geometrically rather thin at the relatively high densities required to explain the observed line intensities, the chemical structure of individual clumps has never been resolved observationally up to now. Several authors have investigated the correlation between [CII] and emission (e.g. Crawford et al. (1985),Wolfire et al. (1989),Jaffe et al. (1994), see 3.2).
Figure 1: This shows the correlation of the observed [CII] and line intensities in three different regions in the RMC together with a theoretically predicted parameter space for hydrogen particle density ( to (thick vertical lines)) and UV-field strength ( to times the mean interstellar UV-field (thin solid lines)). The models were computed by assuming a visual extinction of 10. The arrow indicates in which direction beam filling effects would shift the observed intensities.
The Rosette Molecular Complex (RMC) was observed in the line with the KOSMA (Cologne Observatory for Submillimeter Astronomy) 3m radiotelescope and in the [CII] line with the Kuiper Airborne Observatory Schneider (1995). In Figure 1 we plot the emergent intensities of the two lines in a parameter space of hydrogen density and UV-flux used in our PDR models. We distinguish three different regions in the RMC: 1. the interface between the HII-region and the molecular cloud (marked with open triangles), 2. positions in the vicinity of the embedded IR source IR06314+0427 (marked with filled circles) and 3. the molecular cloud core (marked with filled triangles).
The measurements cover a density range of and an UV field range of . There is no overall correlation for the intensities like the one of obtained by Crawford et al. (1985) in bright galactic sources and galaxies. In contrast, the intensity ratio strongly depends on the emitting region. The strongest CO and [CII] emission is found near the IR source, which is embedded in a clump of dense () molecular gas. Schneider (1995) conclude that the central OB association of the Rosette Nebula NGC2244 is not the dominant UV source in this region, as its UV intensity at a distance of about 30pc to the IR source is too low (about a few ) to account for the observed [CII] intensity. The IR source itself could be a late O type star or a small cluster of OB type stars with lower luminosities which provide the necessary UV flux.
The cloud core and the HII interface regions yield lower CO intensities and strongly varying [CII] intensities. Due to the higher UV flux in the HII interface region, the [CII] line is quite strong. In the remote part of the molecular cloud, far away from the HII region, the UV flux is lower and the [CII] emission decreases. On the other hand the CO emission at the HII interface region is low, as in these strong UV flux regions carbon is photoionized and/or CO is photodissociated.
In the model calculations the beam filling factors for CO () and [CII] () are set to 1 which is certainly not true for all observed positions. The calculated mean density is about a factor of 10 lower than the critical density for the line. Therefore the cloud must have a clumpy substructure and might be lower than 1. Provided that CII has about the same beam filling factor as CO, the plotted values are shifted in the direction indicated by the arrow in Figure 1. Nevertheless, without knowing the correct beam filling values, the PDR models are able to fix a lower limit for the densities and the UV fluxes.
A similar investigation has been done by Jaffe et al. (1994). They compared the observed [CII] and intensities for NGC2024 with the predictions of two different PDR models: the semi-infinite PDR model of Wolfire et al. (1989) and our finite sized PDR model as described in Köster et al. (1994). They divided their observations into two regions: 1. the cloud proper with less than west of the radio peak and 2. the western edge zone with or more west of the radio continuum peak. The intensities in region 1 can be explained satisfactorily with the semi-infinite PDR models. This indicates optically thick line emission both for [CII] and CO. However in region 2 the CO line intensity drops whereas the [CII] intensity is still high. The semi-infinite models fail to explain such ratios. The authors pointed out that the most reasonable scenario is one in which the mean column densities of the clumps decreases to the east. Thus they chose the finite PDR models for low visual extinctions (, the visual extinction is a direct measure for the geometrical extent of a cloud) and thus succeed to reproduce the emission from this region with these models. The [CII] line intensities are not sensitive to the geometrical extent of a cloud, as CII always exists in the outer layers of clumps/PDRs. Thus even clouds with a very small are able to provide sufficient [CII] line intensity. On the other hand small visual extinctions and moderate UV fluxes (here models for and ) lead to low CO column densities and optical depths for the CO lines, as most of the carbon is still in the form of CII and thus the CO intensities are quite low.
To prove the existence of high density condensations in molecular clouds which are illuminated by strong UV fields, it is necessary to measure a line of a species which is exclusively formed in these high density clumps. Such a species is the OH molecule. Because of its high critical density () OH is not excited in the low density interclump medium. Theoretical model calculations show that OH is produced very efficiently in the outer layers of high density/strong UV field regions (Sternberg & Dalgarno (1994)). OH is produced by the endothermic reaction
as far as the hydrogen particle density is above and the temperatures in these layers are greater than 600 K. This leads to column densities . Thus several OH lines should be quite strong and provide an excellent tracer for high density clumps. OH rotational lines have been observed so far only in shock heated regions like Orion-KL (Melnick et al. (1987)) but not in any photon dominated region. The frequencies lie in the range which is not observable with ground based telescopes. However with the KAO or at least with the higher sensitivity of ISO (Infrared Space Observatory) the lines should be detectable. Direct observation of the OH rotational lines would thus give strong evidence for the current PDR models.
Theoretical PDR models successfully explain a wide range of emergent line intensities from atomic and molecular species with transitions in the sub-mm and FIR wavelength range, originating in photon dominated regions. The comparison of the observed ratio for the [CII] and CO (here and ) line intensities allows to estimate the density and UV-field conditions in the observed regions, i.e. to give at least a lower limit for these values. For clumps with low total column densities, e.g. at the edges of molecular clouds in more diffuse regions, models with a finite geometry are essential to explain the observations.
OH is efficiently produced and excited in high density clumps which are irradiated by strong UV fields, but not in the low density interclump medium. OH is thus an excellent tracer for high density PDRs and should be detectable with ISO.