## 4. Multi line analysisWith the aim to understand changes in excitation conditions of molecular material in a FUV illuminated cloud like Cepheus B we try to reproduce the observed data by several model calculations. Already rather simple LTE calculations and escape probability models set reasonably good constraints on the excitation conditions, and where these models fail they indicate the necessity for more sophisticated, and realistic modelling. As a further approach we therefore apply a PDR model, which provides a self-consistent treatment of the chemical and thermal balance of a cloud together with the radiative transfer of CO line emission in spherical clouds illuminated by an isotropic FUV field. First, assuming LTE with a beam filling factor
of 1 we derive an estimate of the
average kinetic temperature, density and mass in Cepheus B. We
averaged the Since the above calculation only leads to the average density and
does not take into account non-thermal excitation nor any difference
in the kinetic temperatures of the ## 4.1. Results of the escape probability analysisWe apply the model to interpret the spectral lines observed at four
positions (Fig. 3), sampling different regions of Cepheus B. To
circumvent the problem of varying beam filling factors, we try to find
models which fit best the observed line ratios (Table 3).
## 4.1.1. Volume densitiesThe ratio of ## 4.1.2. Column densitiesH ## 4.1.3. TemperaturesWe find a temperature gradient across the surface of the cloud, as
traced by At the other two positions, it is not possible to find a single
temperature which is consistent with the emission of all three
isotopomers: The parameters at ()
indicate a temperature gradient along the line of sight - from a
warmer surface of more than 30 K, traced by the optical thick
## 4.1.4. Beam filling factorsBeam filling factors can now be determined by comparing the observed peak line temperatures with the expected values from the escape probablity analysis, given the kinetic temperatures, column and volume densities derived above (). In Table 5 we show the derived filling factors for the 2-1 transitions.
Filling factors range between 0.1
and 1.1, the values for Secondly, the C ## 4.2. Volume filling factorFor further description of the density structure in Cepheus B we
compare the average density derived
from the LTE analysis with local densities
derived from line ratios using the
escape probability model. The ratio of average over local densities,
the volume filling factor, is about
=4%. Taking into account a possible
interclump medium with the density of
, the volume filling factor can be
estimated, and becomes even lower:
the assumption of
cm Another way of putting this argument is considering the ratio of column densities over volume densities, , found via the escape probability analysis (Table 4). This ratio gives a clump diameter of pc () on average, significantly below the spatial resolution of the observations of or 0.42 pc. From the above analysis, we know that beam filling factors reach values as low as 0.1. Still, this means that about 20 clumps or more lie within one beam. The high surface temperature K,
we derive at the hot core, and the small clump diameters
pc calculated from the
N/n All this shows that only a small volume of the whole cloud is filled with molecular material in dense clumps. Such a strong clumping allows the FUV radiation of the HII region S155 and the hot core compact HII region to penetrate the cloud far more than it would be possible in a homogenous cloud. ## 4.3. The UV fieldThe UV field of O and B stars heats the molecular gas via the
photoelectric effect on dust grain surfaces and via FUV pumping of
H The far-UV luminosity where is a typical clump volume filling factor of 0.02 and the typical clump diameter of 0.02 pc. is the distance between the position inside the cloud and the cloud surface, in the direction of the exciting star. The typical scale length, , of the UV penetration is thus 1 pc. Table 6 shows the derived fluxes
, as the sum of the fluxes of all 6
stars, in units of the average interstellar radiation field,
erg s
The position represents the
north-eastern edge of Cepheus B, where the line ratios of
## 4.4. PDR modelling of CO linesThe above discussion shows that a homogeneous cloud model cannot
consistently describe the observed line ratios of all three CO
isotopomers at all positions, although such a model still provides
first estimates on column densities, densities, clump sizes, and
temperature gradients. Apparently contradictory line ratios appear to
be a widespread phenomenon in photon illuminated clouds. Castets et
al. (1990) interpreted similar findings in Orion A by temperature
gradients increasing towards the cloud surfaces. Such gradients are
naturally expected for UV irradiated clouds. Gierens et al. (1992)
modelled the line ratios found in Orion A using a spherical symmetric
PDR code including analytic temperature and density gradients.
Störzer et al. (2000) present a more realistic cloud model which
provides a self-consistent treatment of the chemical and thermal
balance of a cloud together with the radiative transfer of CO line
emission in spherical clouds illuminated by an isotropic FUV field.
The model assumes the density to increase radially inward following a
power law. Main input parameters determining the model are the average
H We compared the 4 measured peak line ratios, ## 4.4.1. PositionThis position exhibits the strongest emission in The PDR model fails however to reproduce the observed
The next two positions are of particular interest, since the escape probability model does not allow to describe consistently all observed line ratios found at these positions. ## 4.4.2. PositionWith increasing distance to the HII region, the
C ## 4.4.3. PositionThis position lies in the immediate vicinity of the hot core. Its
influence is evident in the high However, in contrast to position
, the large
## 4.5. Atomic carbonAdditionally, we observed the
transition of atomic carbon at two positions, at
(/)
position and at , near the edge to
the HII region S155. Fig. 6 presents the
[CI ] spectra in comparison with
With the CI data, the abundance ratio of molecular to atomic carbon can be estimated. Assuming optically thin [CI ] emission and LTE allows to derive a lower limit of the CI column density (Frerking et al. 1989): with taken from the 3-2 transition. To compare gas phase abundances of carbon relative to CO we calculate LTE column densities for CO by multiplying (optically thin) column densities with the abundance factor of 67 (Table 9). At the two positions observed we find that the abundance of atomic carbon is 17% and 30% of the CO column densities. As expected the CI /CO ratio is rising at the cloud edges, because more molecular material is dissociated there due to the impinging FUV field. This phenomenon is also confirmed by the decreasing FWHM ratio of CO to atomic carbon. Because of the unknown CI opcacity these abundance ratios are only lower limits. Tauber et al. (1995) derived 0.17 as lower limits for the Orion bar, and Plume et al. (1999) find values between 0.32 and 0.47 for a sample of clouds.
© European Southern Observatory (ESO) 2000 Online publication: October 30, 2000 |