A Comparison between Anomalous 6-cm H$_2$CO Absorption and CO(1-0)
  Emission in the L1204/S140
A comparison between anomalous 6-cm H2CO absorption and
CO(1-0) emission in the L1204/S140 region
Mónica Ivette Rodŕıguez1,2
Tommy Wiklind1,3
Ronald J. Allen1
Vladimir Escalante2
Laurent Loinard2
1Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
monica, rjallen, wiklind@stsci.edu
2Centro de Radiostronomı́a y Astrof́ısica, Universidad Nacional Autónoma de México,
Apartado Postal 72 - 3, C.P. 58091, Morelia, Michoacán, México
m.rodriguez, l.loinard, v.escalante@astrosmo.unam.mx
3Affiliated with the Space Sciences Department of the European Space Agency
ABSTRACT
We report observations of the dust cloud L1204 with the Onsala 25-m tele-
scope in the 6 cm (111-110) transition of H2CO. The observed region includes the
S140 Hα arc. This spectral line is seen here in absorption against the cosmic
microwave background, indicating the presence of widespread warm molecular
gas at intermediate densities. Overall, the distributions of H2CO and CO (taken
from the literature) are fairly similar, though significant differences exist at small
scales. Most notably, while the CO peak is nearly coincident with the S140 Hα
arc, the maximum H2CO absorption is clearly separated from it by a full 10
′ beam
(∼ 3 pc). We argue that these differences result from differing abundances and ex-
citation requirements. The CO(1-0) line is more optically thick and more biased
towards warm gas than the H2CO 6 cm line. On the other hand, formaldehyde is
more easily photodissociated and is, therefore, a poorer tracer of the molecular
gas located immediately behind Photon Dominated Regions.
Subject headings: ISM: clouds — ISM: molecules – radio lines: ISM – stars:
formation – galaxies: ISM
http://arxiv.org/abs/0704.0272v1
– 2 –
1. Introduction
Since H2 –the most abundant molecule in space– lacks a permanent dipole moment, its
rotational transitions are prohibited. Although the quadrupolar transitions exist, they are
of little use for the syudy of the bulk of molecular gas in the ISM because they require high
temperature to be excited. Instead, the structure and properties of cold molecular clouds
in the interstellar medium are usually studied using low-energy rotational transitions of
simple non-symmetric polar molecules. For practical reasons, the first rotational transition
(J = 1→0) of carbon monoxide (CO), at 115.27 GHz has been the most popular choice.
This transition, however, has long been known to be nearly always optically thick, so –
for a given filling factor– its intensity is expected to increase monotonically with the kinetic
temperature of the emitting gas. Clearly, this could have adverse effects on efforts to establish
the distribution of molecular gas in the ISM from CO observations alone, because very
low temperature gas might go unnoticed in sensitivity-limited CO observations while warm
regions (& 20 K) will stand out even if they are not those with the highest molecular content.
The sources where these effects might be most noticeable are those with large temperature
gradients; for instance in molecular clouds located in the immediate vicinity of hot stars.
While all molecular emission tracers share this temperature dependance to some degree,
absorption lines can be detected even in very cold gas, provided sufficiently bright background
continuum sources are available. The scarcity of such sources at the wavelength of the
common molecular tracers, however, has limited the usefulness of absorption measurements
in the study of specific Galactic molecular clouds (e.g Evans et al. 1980). The 6-cm (110-111)
transition of ortho formaldehyde (H2CO) offers an interesting alternative. Owing to collisions
with neutral particles that selectively overpopulate the lower energy level, the excitation
temperature of the 110 → 111 transition lies below 2.7 K (Townes & Cheung 1969). This
allows the transition to be observed in absorption against the cosmic microwave background
(CMB) (Snyder et al. 1969), and makes it a potentially powerful tracer of molecular gas in
any direction of the sky. The excitation requirements are such the the 6 cm H2CO line is a
good indicator of the presence of cool to warm molecular gas (T & 10 K) at intermediate
densities (103 cm−3 ≤ n ≤ 105cm−3). Unfortunately, the absorption line is weak, so very
large amounts of telescope time are required to map large areas of the sky.
Recently, Rodŕıguez et al. (2006) conducted a blind search for H2CO absorption and
compared CO emission and H2CO absorption profiles towards the Galactic anticenter. They
found a rough, large-scale correlation between these two tracers, and concluded that both
lines preferentially trace warm and dense molecular gas. Here, we will examine this relation
between CO and H2CO at a somewhat smaller scale using observations of the well-known,
nearby star-forming region Sharpless 140 (S140 –Sharpless 1959) associated with the dark
– 3 –
dust cloud Lynds 1204 (L1204 –Lynds 1962). L1204 is centered at l = 107◦. 47, b = +4◦. 82
and covers an area of 2.5 square degrees (Lynds 1962). At its southwest edge lies S140, a
prominent compact arc-shaped H ii region with an angular size of ∼ 2′ × 6′. The ionization
of S140 is maintained by the nearby B0V star HD211880 (Blair et al. 1978). The distance of
S140/L1204 deduced from the brightness of the exciting star is 910 pc (Crampton & Fisher
1974). S140 has been the subject of many observational studies, that have usually focused on
the Photon Dominated Region (PDR) on the edge of L1204, and on the embedded infrared
sources located right behind it (e.g., Preibisch et al. 2001; Hayashi & Murata 1992; Preibisch
& Smith 2002; Bally et al. 2002). Remarkably, while the dust cloud is seen as an extended
dark feature covering more than two square degrees, the CO emission peaks immediately
behind the Hα arc (Heyer et al. 1996; Evans et al. 1987; Blair et al. 1978), while only
relatively faint emission extends deep within the dust cloud (Helfer & Blitz 1997). The 6-cm
line of H2CO was detected in absorption against the CMB in L1204 near S140 by Blair et al.
(1978) with the NRAO 43 m telescope, and unexpectedly by Evans et al. (1987) during VLA
observations of the bright condensation just northwest of S140. However neither of those
studies provided a extensive mapping of the H2CO CMB absorption in L1204, and the exact
extension of the gas traced by H2CO remains unclear. In this article, we will present such a
extensive mapping of the 6 cm CMB absorption of H2CO over most of the large dust complex
L1204, and compare our results with existing CO observations taken from the literature.
2. Data
The H2CO observations were obtained during two sessions (January and September-
October 2004, respectively) with the 25.6-m telescope of the Onsala Space Observatory
(OSO) in Sweden. At 6 cm, the angular resolution is 10′, and our pointing precision was
always better than 20′′. Frequency-switching, with a frequency throw of 0.4 MHz was used,
and both polarizations of the incoming signal were recorded simultaneously in two indepen-
dent units of the autocorrelation spectrometer. Each of these units provided 800 2 kHz-wide
channels. At the observed frequency of 4829.660 MHz, this setup provided a total bandwidth
of 99 km s−1 and a (Hanning-smoothed) velocity resolution of 8 kHz ≡ 0.49 km s−1. The
spectrometer was centered at the systemic velocity of S140, VLSR = −8.0 km s−1. Daily
observations of the supernova remnant Cas A were used to check the overall performance of
the system. The system temperature during our observations varied from 33 to 36 K.
In order to map the entire region behind S140, we observed 72 positions on a regular
square grid with a 10′ spacing, centered at l = 107◦. 0, b = +5◦. 3; the resulting map uniformly
covers a 1◦. 0 × 1◦. 8 rectangular region (Fig. 1) . The off-line data reduction was done
– 4 –
with the CLASS program of the GILDAS software package (Guilloteau & Forveille 1989),
and involved only the subtraction of (flat) baselines from individual integrations and the
averaging of all spectra taken at the same pointing position. The total integration time for
each of these positions was about 10 hours, yielding a typical final noise level of 3 mK (T∗A).
The distribution of radio continuum sources in the region of L1204 has been studied in
detail by Allen Machalek & Jia (in preparation), using data from the Canadian Galactic Plane
Survey. Fairly bright continuum emission is associated with the Hα arc and the embedded
massive protostars located behind it –but, as we will see momentarily no formaldehyde
was detected from either of these regions. In addition, a number of extragalactic background
sources as well as diffuse emission associated with the dust cloud L1204 itself contribute to the
overall radio continuum. The typical brightness temperature average over the Onsala beam
at 6 cm, however, is only about 0.2 K, except towards the Hα arc and the embedded massive
protostars (where again, no absorption was detected). Since the brightness temperature is
so small, any H2CO absorption profiles features detected must be absorption of the cosmic
microwave background radiation at 2.7 K.
In the analysis of our new observations, we will also make use of 12CO(1-0) observations
of L1204/S140 kindly provided by Dr. Tamara Helfer, and published in Heyer et al. (1996),
and Helfer & Blitz (1997). These data were obtained with the 14-m telescope of the Five
College Radio Astronomy Observatory (FCRAO) in Amherst (MA), and have an intrinsic
angular resolution of 45′′. For comparison with our formaldehyde data, we have smoothed
the CO(1-0) observations to 10′, and resampled them on our observing grid.
3. Results
Formaldehyde absorption was detected in at least 16 of our 72 observed positions (see
Fig. 2). The maximum absorption is located 10′ arcmin behind the S140 H ii region at a
LSR velocity of −8.0 km s−1, similar to that of the CO emission detected in that area.
Table 1. Source positions.
Source Position (l, b) Size (∆α,∆δ) α(J2000.0), δ(J2000.0) Reference
L1204 107◦. 37, +4◦. 87 1◦. 0 × 2◦. 5 22h26m41s.+63◦15′36′′. Lynds (1962)
S140(Hα) 106
◦. 8, +5◦. 3 2′ × 6′ 22h19m23s.+63◦18′16′′. Sharpless (1959)
Our survey 107◦. 0, +5◦. 3 1◦. 0 × 1◦. 8 22h20m52s.+63◦24′49′′. This paper
– 5 –
Fig. 1.— This figure shows a sketch of the L1204/S140 region, with our observed positions
shown as ”+” symbols. The correspondence between Galactic coordinates (used throughout
the paper) and equatorial coordinates (that have usually been preferred for observations of
S140) is indicated. The circle represents the 2◦. 5 size of the dust cloud L1204 as reported
by Lynds (1962). The central positions of L1204 and S140 are shown as ”” symbols. The
contour represents the lowest value of the H2CO absorption.
A second spatio-kinematical structure is detected towards the north-east (here, and in the
rest of the paper, north and all other directions refer to Galactic coordinates), at VLSR ∼
−11 km s−1. Both components are presumably associated with L1204, and have clear CO
counterparts (Fig. 2 – Blair et al. 1978; Evans et al. 1987; Sugitani & Fukui 1987; Park &
Minh 1995). There is also an isolated absorption feature towards the southeast, at VLSR ∼
−2.5 km s−1. Given its low LSR velocity, this feature is likely unrelated to L1204, and is
probably a local cloud along the line of sight. Thus, while Sugitani & Fukui (1987) identified
three molecular components associated with L1204 in their 13CO observations, we only find
two in our formaldehyde data. We do find evidence, however, for a systematic velocity
gradient across the cloud. Park & Minh (1995) argued that this complex overall spatio-
kinematical morphology was created when S140 and L1204 were swept up by an expanding
shell associated with the Cepheus bubble. Our data do not illuminate this assertion any
further, and a more thorough study is necessary to understand the detailed structure of this
region.
– 6 –
Fig. 2.— (a) Mosaic of H2CO CMB absorption spectra observed in the L1204/S140 region.
The (0,0) position corresponds to l = 107◦. 0, b = 5◦. 3, about 12′ east of S140, and about
40′ north-west of the nominal center of L1204 (Lynds 1962). (b) Corresponding CO(1-0)
observations smoothed to 10′ (see text). Note that the CO emission is located a full 10′ west
of the maximum H2CO absorption.
4. Comparison with other molecular tracers
The S140/L1204 region has been observed in many different molecular tracers (e.g.
Tafalla et al. 1993, Zhou et al. 1993, Park & Minh 1995), but most of these observations
have focused either on the S140 PDR or on the embedded infrared sources located just
behind S140, while only a few observations covered the entire dust cloud. Indeed, the first
CO observations of S140 (Blair et al. 1978) only covered a limited part of the region. To
our knowledge, the only existing large-scale CO map of L1204 is that obtained in the 90s
with the FCRAO telescope (see §2) and published by Heyer et al. (1996) and Helfer & Blitz
(1997)1. As mentioned earlier, we will use a smoothed version of that dataset here in order
to compare with our formaldehyde observations.
In general, the CO emission and H2CO absorption morphologies in this region are quite
similar (Fig. 3). This was already noticed by Blair et al. (1978) in their 6′ observations.
It is also in good agreement with the results obtained towards the Galactic anticenter by
1The region lies on the edge of, and is only partly covered by, the CfA Galactic plane survey of Dame et
al. (2001).
– 7 –
Fig. 3.— All panels show a grey-scale version of the DSS-red image of the region around
l = 107◦. 0, b = 5◦. 4. The Hα arc of S140 is clearly visible on these (red) images near l =
106◦. 8, b = 5◦. 3. In the three left panels (a1–a3), CO contours taken from the smoothed CO
data of Heyer et al. (1996) are overlaid on top of the DSS image, whereas in the three right
panels (b1–b3), our H2CO contours are overlaid. The contours in the top two panels (a1–b1)
include the entire velocity range associated with L1204 (from -12 to -5 K km s−1), whereas
in the middle two (a2–b2) and bottom two (a3–b3) panels, the contours correspond only to
the -11 K km s−1 and the -8 K km s−1 components, respectively. The asterisks correspond
to the position of the peak H2CO absorption for each component.
– 8 –
Rodŕıguez et al. (2006), and towards the Orion molecular complex by Cohen et al. (1983).
There are, however, several noteworthy differences between the CO emission and H2CO
absorption in S140. The first difference is the fact that the CO peak and the H2CO absorption
maximum are not located at the same position. The CO integrated intensity map (Fig. 3,
see also Fig. 2) shows that the maximum CO emission occurs just behind the S140 Hα arc
at the western edge of L1204, while only comparatively fainter emission extends to greater
longitudes. The maximum H2CO absorption, however, is located about 10
′ eastward of the
CO peak. A second notable difference between the CO and H2CO profile is the existence of
a CO emission ”tail” in the south/southeast part of the main cloud with little or no H2CO
counterpart (Figs. 2 and 3).
-0.35
-0.25
-0.15
-0.05
 0  10  20  30  40  50
I (12CO) K km/sec
Intensity ratio
S140 + L1204
L1204
Galactic Anticenter
Fig. 4.— Correlation between the H2CO absorption line intensity and the
12CO(1-0) emission
line intensity at corresponding points in L1204. The squares correspond to data from Table
2, the open circles correspond to H2CO upper limits and the triangles correspond to the
Galactic anticenter data previously published in Rodŕıguez et al. (2006). The horizontal
and vertical lines show the “best case” detection limit. The dashed line is the least-squares
fit for the L1204/S140 region data, and the dash-dotted line is the least-squares fit for the
Galactic anticenter data from Rodŕıguez et al. (2006). Note that the fits do not pass through
the (0,0) point, suggesting that the relation is not linear at low intensity values.
In order to study the relation between H2CO absorption and CO(1-0) emission in a
more quantitative way, we have computed the moments of the profiles shown in Fig. 2. The
results are listed in Table 2 (Appendix B). When two velocity components are visible at
a given pointing, the moments for each were computed separately. Intensities above 3σ are
shown as squares in Fig. 4, and were used to make least-square fits (see below). The two
– 9 –
spatio-kinematical components that we identified in our formaldehyde dataset behave quite
similarly with respect to the CO-H2CO relation, and are plotted together in Fig. 4. The
best least-squares fit to a straight line for the entire L1204 dataset yields:
I(H2CO) = (4.4± 1.1)× 10−3 I(CO) + (34± 16)× 10−3 K km s−1. (1)
We shall see momentarily that the CO emission near S140 may be particularly bright because
of local heating. Ignoring the pointings very near S140, however, yields a fairly similar
relation between CO and H2CO:
I(H2CO) = (3.8± 0.9)× 10−3 I(CO) + (31± 9)× 10−3 K km s−1. (2)
The small difference between these relations presumably reflects the differing excitation
requirements for the two lines. The relation between CO and H2CO given by Eqs. 1 and
2 for the L1204 region is almost identical to that found towards the Galactic anticenter by
Rodŕıguez et al. (2006):
I(H2CO) = (4.1± 0.5)× 10−3 I(CO) + (34± 13)× 10−3 K km s−1. (3)
It is important to note, however, that, in spite of the agreement between the fits to
the Galactic anticenter and S140 data, there is very significant scatter in the CO-H2CO
relation, some points lying nearly 10σ away from the linear relation. This situation was
already noticed by Rodŕıguez et al. (2006) in their study of the Galactic anticenter. This
lack of a detailed correspondence between CO emission and H2CO absorption presumably
reflects differences in the excitation conditions of the two tracers, as we will now discuss in
the next section.
5. Discussion
The comparison between H2CO absorption and CO(1-0) emission profiles in the Galac-
tic Anticenter and in the L1204/S140 region has led us to three important observational
conclusions:
1. Qualitatively, the morphology of CO and H2CO are quite similar, and quantitatively,
the line integrated intensities correlate quite well with one another.
– 10 –
2. The scatter in the CO-H2CO relation is, however, significantly larger than the obser-
vational errors.
3. In the specific case of S140, the CO emission peak is offset by about 3 pc from the
locus of the deepest formaldehyde absorption, and there is a region south of the main
cloud where significant CO emission is detected with little or no H2CO counterpart.
From the general large-scale correspondance between the CO(1-0) and H2CO 6 cm
integrated maps (Fig. 3), and from the fair correlation between their line intensities (Fig.
4), we conclude that the physical conditions needed for the excitation of both lines are
quite similar. The calculations presented in the Appendix A, indeed show that both lines
preferentially trace warm gas at intermediate densities (103.6< n < 105 for H2CO; n > 10
for CO). In this scheme, the offset between the CO(1-0) peak and the H2CO maximum
absorption may seem puzzling. Note that a similar trend is seen at higher resolution: while
the CO peak in the full-resolution CO map published by Heyer et al. (1996) and Helfer &
Blitz (1997) is at l = 106o.8, b = +5o.3, the H2CO absorption feature seen in the high-
resolution VLA images published by Evans et al. (1987) is centered around l = 106o.9, b =
+5o.3, again a few arcminutes to the east.
We suggest that a combination of two effects may explain this puzzling result. First, it
can be seen from the excitation analysis presented in Appendix A that the H2CO absorption
strength ”saturates” for T & 30 K, whereas the temperature of the CO emission continues
to rise at higher kinetic temperature (Fig. 5). For example, while the H2CO line strength
increases by only about 30% when the kinetic temperature goes from 20 to 40 K, the CO(1-0)
line intensity increases by more than a factor of two. According to Park & Minh (1995), the
CO brightness temperature is about 40 K at the peak and 20 K for the rest of the cloud. Thus,
the strong CO peak behind S140 may well be largely due to enhanced kinetic temperatures
related to local heating (by the external star providing the ionization of S140, and/or by
the infrared sources embedded in the cloud). As one progresses into the cloud, the local
heating diminishes, and the CO line intensity fades. Also, it should be pointed out that the
formaldehyde calculations presented in the Appendix show that the 6-cm line should be seen
in emission rather than absorption when the density exceeds 105 cm−3. The fact that this is
not the case near the CO peak (neither in our low-resolution data, nor in the high-resolution
VLA data presented by Evans 1978) suggests that the gas density there is lower than 105
cm−3. Other effects that could explain the offset between the CO and the H2CO peaks are
the lower dissociation energy, and the lower abundance (and, therefore, lower self-shielding)
of formaldehyde compared to CO (see Appendix A.3). In a photo-dissociated region, these
effects should combine to create a stratified distribution where CO survives nearer the source
of the UV photons than H2CO. This stratification, combined with the heating of the CO,
– 11 –
would naturally lead to the offset between H2CO and CO seen in the present data.
Finally, the origin of the other main difference between CO and H2CO in S140, namely
the existence of CO emission at the south of L1204 with no or little formaldehyde counterpart,
is likely related to another aspect of the excitation differences between the 6 cm line of
formaldehyde and the 1-0 transition of carbon monoxide. Fig. 6 of the Appendix A.2 shows
that the density detection limit for H2CO line is ∼10 times larger than the density limit for
the CO(1-0) line. We therefore suggest that the gas traced by the CO emission to the south
of L1204 is of relatively very low density. It is interesting to note, indeed, that classical
high-density molecular tracers (e.g. CS or NH3) have only been detected around the CO
peak behind S140, and not in the southern region of the cloud.
Thus, we conclude that the CO(1-0) and H2CO 6 cm lines both tend to preferentially
trace warm gas at intermediate densities. There are, however, significant differences related
either to differing excitation requirements or to differing abundances. These differences can
easily explain the large scatter in the CO–H2CO relation.
6. Conclusions
The main conclusions of this work are the following:
1. We have mapped a large region (70′ × 110′) around L1204/S140 in the 6 cm line of
formaldehyde, observing a total of 72 regularly-spaced positions every 10′ on a regular
grid. The center of our map was at l = 107◦. 0, b = +5◦. 3, and formaldehyde was
detected against the cosmic microwave background in at least 16 of our 72 positions
(Fig. 2).
2. The formaldehyde emission can be separated in three spatio-kinematical components
(Fig. 3): two (at VLSR ∼ –11 km s−1 in the northeast part of the cloud, and at VLSR
∼ –8 km s−1 just behind S140) are clearly associated with L1204, whereas the other
(an isolated component at VLSR ∼ –2.5 km s−1 towards the southeast) is most likely a
local foreground cloud unrelated to S140/L1204.
3. Both qualitatively and quantitatively, the CO(1-0) emission and the formaldehyde
6 cm absorption lines correlate fairly well. An excitation analysis shows that both
preferentially trace warm gas at intermediate densities.
4. There are, however, notable differences between the CO and H2CO lines, that can be
traced to differing excitation requirements and abundances. Those differences are most
likely the origin of the large scatter in the CO-H2CO intensity correlation.
– 12 –
We thank Professor Roy Booth, director (retired) of the radio observatory at Onsala, for
generous allocations of telescope time and for his warm hospitality during our several visits
to the observatory. We are also grateful to the observatory technical and administrative
staff for their capable assistance with our observing program. We thank Tamara Helfer
for supplying us with the CO data cube of S140. We acknowledge the financial support of
the Dirección General de Asuntos del Personal Académico (DGAPA), Universidad Nacional
Autónoma de México (UNAM) and Consejo Nacional de Ciencia y Tecnoloǵıa (CONACyT),
in México, and the Director’s Discretionary Research Fund at the Space Telescope Science
Institute. The Digitized Sky Surveys were produced at the Space Telescope Science Institute
under U.S. Government grant NAG W-2166. The images of these surveys are based on
photographic data obtained using the Oschin Schmidt Telescope on Palomar Mountain and
the UK Schmidt Telescope. The plates were processed into the present compressed digital
form with the permission of these institutions.
A. Model calculations
A.1. Collisional pumping
Observations of H2CO in dark clouds show that the anomalous absorption of the 6 and
2 cm lines is due to collisions with H2 that selectively overpopulate the lower levels of the
lines (Evans et al. 1975). We calculated the non–LTE equilibrium populations of the first
40 levels of ortho–H2CO assuming excitation by the 2.7 K background and collisions with
H2. Green (1991) has calculated excitation rates of these levels for collisions with He taking
advantage of the spherical symmetry of the He potential for kinetic temperatures T = 10 to
300 K. According to Green (1991), excitation rates by H2 collisions could be 2.2 times higher
than those by He because of the smaller reduced mass and differences in the interaction
potentials. We will show the results of the calculations under the assumption that the H2–
H2CO collisional rates are the same as the He–H2CO rates. Probabilities for the radiative
transitions were taken from Jaruschewski et al. (1986).
The optical depths of the transitions involved in the pumping mechanism are generally
larger than 1 at high densities and a radiative transfer calculation is required. Two limiting
approximations in the radiation transport are often considered in molecular clouds: the
large velocity gradient (LVG) model and the microturbulent model (Leung & Liszt 1976).
The LVG model assumes that the line profile is dominated by systematic motion of the gas
while the microturbulent model assumes that the turbulent velocity is much larger than any
systematic motion. S 140 is likely to have several velocity components, but the existence
of large systematic motions in molecular clouds and the validity of the LVG model has not
– 13 –
been well established in other molecular clouds (e.g. Evans et al. (1975), Zuckerman & Evans
(1974), Zhou et al. (1990)). We therefore use the microturbulent model, and for simplicity
we will use the escape probability formalism to account for photon trapping in a turbulent
medium in plane-parallel slab of mean total optical depth τt that is perpendicular to the line
of sight. In this case the A–value of a transition in the equations of statistical equilibrium is
multiplied by a “loss probability” P (τ, τt) that depends on the mean optical depth τ in the
slab. There are many different ways to define P (τ, τt), which can differ by several orders of
magnitude for large optical depths. We will use the form suggested by Hummer & Storey
(1992) for a uniform medium with no continuum absorption:
P (τ, τt) =
[K2(τ) +K2(τt − τ)] , (A1)
where
K2(τ) =
dx φ(x)E2[τφ(x)] , (A2)
and E2 is the second exponential integral function. The function K2(τ) can be calculated
from fits by Hummer (1981) for a normalized Doppler profile, φ(x) = exp(−x2)/
Equation (A1) can be viewed as the single flight escape probability through either side
of the slab averaged over the line profile. The probability that a photon of an isotropic
background reaches optical depth τ in this slab is also given by equation (A1), and the
blackbody continuum is thus attenuated by a factor P (τ, τt). The mean optical thickness is
given by
nu/gu
nl/gl
dz , (A3)
where σlu is the absorption cross section of the transition and ∆νD is the Doppler width.
We assumed a Doppler width of 2 km s−1 (FWHM = 2
ln 2∆νD = 3.3 km s
−1). The level
population and its statistical weight are given by n and g respectively with subindex u for
the upper and l for the lower level.
The emergent line brightness temperature with subtracted background T0 is found by
direct integration of the source function throughout the slab as
∆Tb = Tb − T0
= T0[ exp(−T )− 1]
exp(−T + τ)
nl/gl
nu/gu
dτ , (A4)
where
– 14 –
1− nu/gu
nl/gl
dz , (A5)
is the total mean optical depth of a slab of thickness L and T = τtφ(0) is the line–center
total optical depth.
Equation A4 gives the correct asymptotic limits: Tb → T0 when the density goes to
0 and Tb → T for high densities. The population densities and the optical depths as a
function of position in the slab in equations (A1) and (A3) were calculated iteratively. A
convergence of 10−3 K in Tb was achieved after a few iterations for T ≤ 40 K and H2
densities n(H2) < 10
6 cm−3. For higher densities and temperatures the procedure becomes
unstable. Fig. 5 shows the calculated ∆Tb for a 1 pc–thick slab as a function of the H2
density and a constant H2CO abundance of 2 × 10−9 with respect to H2 (Hasegawa et al.
(1992), Leung et al. (1984)). The assumed thickness of the slab has an important effect in
the anomalous absorption as shown in Fig. 5. As the thickness of the slab decreases, the
effectiveness of the pumping mechanism that cools the line decreases.
(a) (b)   (c)
Fig. 5.— (a) Brightness temperature minus background continuum vs. density for different
kinetic temperatures T of a 1–pc thick slab. (b) Contour intervals are 0.2 K from ∆Tb = −1
to 1 K. (c) Brightness temperature minus background continuum vs. density for different
slab thicknesses at T = 40 K.
Garrison et al. (1975) identified some transitions, like 111 → 312, that produce selection
effects in the excitation of some levels that cool the H2CO doublets. We have tested our model
for possible variations of the collision rates. An overall increase of collisional rates by a factor
of 2.2 decreases ∆Tb in figure 5 by 0.3 to 0.5 K for T ≥ 20 K and n(H2) > 1.6 × 104 cm−3.
For lower T and n(H2) there is very little variation in the predicted Tb.
– 15 –
A.2. A PDR model for CO
The UV field has a higher influence on the CO brightness temperature than on the
H2CO brightness temperature. Both molecules are quickly photodissociated near the edge
of clouds, but the larger abundance of the CO molecule makes its chemistry and interaction
with radiation more complex. In order to take into account the variation of CO abundance
along the line of sight, we used the Meudon PDR code to calculate the CO brightness
temperature of a plane–parallel slab irradiated by a UV field (Le Bourlot et al. 1993). A
detailed description of a revised version of the code is given by Le Petit et al. (2006).
The sharp separation between the molecular, atomic and ionized emissions suggests
that the L1204/S140 interface is a PDR viewed nearly edge–on (Hayashi & Murata 1992)
irradiated by HD 211880. The angle of incidence of the star’s radiation on the PDR boundary
is an unknown parameter but appears to be more-or-less perpendicular. Furthermore, the
infrared embedded sources are probably young stars that may also enhance the radiation
field (Evans et al. 1989).
We ran the code with its parameters set to represent a plane–parallel slab irradiated
from one side by a UV field with an enhancement factor χ = 200 with respect to the Draine
(1978) average interstellar radiation field. In a PDR, the gas is heated by the photoelec-
tric emission from grains and PAH’s, H2 formation in grains, UV pumping in the Lyman
and Werner bands, gas–grain collisions, photoionization, and photodissociation. As the UV
radiation is absorbed deeper into the cloud, other processes like cosmic rays and chemical
reaction energies become important. Cooling is produced by fine–structure and molecular
line emission. Shocks and turbulence can keep a PDR away from isobaric equilibrium. How-
ever in our model the temperature and density of the PDR were kept constant in order to
compare the results with our H2CO model in Fig. 6. We used the chemical network given
for S140 by the Meudon group at its Internet site2, which does not include H2CO. Thus the
CO and H2CO calculations represent different models, and Fig. 6 is given only as indication
of the local conditions that produce the emission and absorption for each molecule.
A.3. Photodissociation of H2CO
The H2CO molecule is quickly photodissociated into CO and H2 or H in the average UV
interstellar radiation field with a rate of 1.0 × 10−9 exp(−1.7AV ) s−1 (van Dishoeck 1988).
Keene et al. (1985) estimated that far–ultraviolet radiation (FUV) from the star HD211880
2http://aristote.obspm.fr/MIS/pdr/exe.html
– 16 –
CO H CO
Fig. 6.— Brightness temperature minus background continuum vs. density for different
kinetic temperatures T for both the 12CO(1-0) line and the 6 cm H2CO line (Note that
∆Tb(k) is plotted ”negative” compared to Figure 5).
will have an enhancement factor of G0 = 150 with respect to the average interstellar field
(Habing 1968) at the ionization front, although Spaans et al. (1997) found that a more
intense radiation field may be needed to explain the H2 rotational emission. H2CO has a
dissociation energy of 3.61 ± 0.03 eV (Suto Wang & Lee 1986), and a photodissociation rate
of 1.0 × 10−9 sec−1 in the interstellar field (van Dishoeck 1988) while for CO the values
are 11.2 eV and 2.0 × 10−10 sec−1 respectively. Thus it is possible that the H2CO will be
selectively photodissociated near the S140 ionization front and the bright PDR region, where
the CO emission peaks. Detailed PDR model calculations by Li et al. (2002) show that at
20′ from the ionization front, where we observe the H2CO maximum, G0 ≤ 20 and AV ∼ 15.
We added 62 reactions involving H2CO and H2CO
+ taken from the UMIST data base
(Woodall et al., 2007) 3 to the chemical network of the Meudon group mentioned above and
ran a PDR model with G0 = 200, T = 40K and constant density of 10
3 cm−3. We found
that H2CO has significant abundance only at depths of Av > 7 while CO becomes important
at Av > 4, which shows that photodestruction could explain the offset between the CO and
the H2CO peaks.
3http://www.udfa.net/
– 17 –
B. Profile moments in detail
– 18 –
Table 2. Profile moments for each position of Fig. 2. The upper limits correspond to 3σ.
The symbol “. . . ” indicates no data were available, while “nf” indicates that data were
available but no reliable fit could be made. Values marked with “yes” in column 6 are
plotted as squares in Fig. 4, and were used for the least square fits.
Offset (l,b) 1000× I(H2CO) 〈V 〉 I(CO) 〈V 〉 Included in
arcmin K km s−1 km s−1 K km s−1 km s−1 fits
40, -70 < -24.3 nf . . . . . .
30, -70 < -18.9 nf . . . . . .
20, -70 < -25.8 nf . . . . . .
10, -70 < -23.4 nf 4.1 ± 0.7 -7.6 ± 1.3
0, -70 -42.1 ± 8.4 -7.5 ± 1.5 3.5 ± 0.6 -8.7 ± 1.5 yes
-10, -70 -30.3 ± 7.1 -6.2 ± 1.5 8.6 ± 0.8 -8.3 ± 0.8 yes
-20, -70 < -21.6 nf < 2.1 nf
40, -60 < -22.5 nf . . . . . .
30, -60 < -24.0 nf . . . . . .
20, -60 < -26.7 nf 5.9 ± 0.8 -7.0 ± 1.1
10, -60 < -23.7 nf 5.1 ± 0.6 -8.3 ± 1.0
0, -60 < -19.2 nf < 1.8 nf
-10, -60 -27.9± 7.1 -6.7 ± 0.5 < 2.1 nf
-20, -60 < -28.8 nf < 1.5 nf
40, -50 < -25.5 nf . . . . . .
30, -50 -109.3 ± 8.9 -2.6 ± 0.2 14.8 ± 1.1 -1.8 ± 0.2 yes
20, -50 < -25.2 nf 10.5 ± 0.8 -5.0 ± 0.4
10, -50 < -21.6 nf 8.2 ± 0.6 -7.0 ± 0.5
0, -50 < -18.9 nf < 2.4 nf
-10, -50 < -16.5 nf < 2.4 nf
-20, -50 < -24.6 nf < 4.8 nf
40, -40 < -23.1 nf . . . . . .
30, -40 < -22.8 nf 3.1 ± 0.6 -6.2 ± 1.2
20, -40 < -22.2 nf 7.2 ± 0.8 -7.2 ± 0.9
10, -40 < -23.1 nf 4.5 ± 0.5 -8.8 ± 1.1
0, -40 < -22.5 nf < 2.7 nf
-10, -40 < -26.1 nf < 2.7 nf
-20, -40 < -18.6 nf < 3.0 nf
40, -30 < -22.5 nf 3.4 ± 0.5 -9.0 ± 1.5
30, -30 < -22.8 nf 4.0 ± 0.7 -8.9 ± 1.5
– 19 –
Table 2—Continued
Offset (l,b) 1000× I(H2CO) 〈V 〉 I(CO) 〈V 〉 Included in
arcmin K km s−1 km s−1 K km s−1 km s−1 fits
20, -30 < -25.5 nf < 1.8 nf
10, -30 < -30.9 nf 5.2 ± 0.6 -8.6 ± 1.0
0, -30 < -20.1 nf < 4.2 nf
-10, -30 < -26.7 nf < 1.8 nf
-20, -30 < -22.2 nf < 2.1 nf
40, -20 . . . . . . < 2.7 nf
30, -20 < -30.9 nf 3.5 ± 0.7 -9.4 ± 1.9
20, -20 < -24.0 nf < 2.7 nf
10, -20 -31.6 ± 6.0 -8.2 ± 1.6 8.2 ± 1.1 -8.9 ± 1.2 yes
0, -20 < -29.1 nf 8.5 ± 1.4 -9.5 ± 1.7
-10, -20 < -19.5 nf 6.8 ± 0.3 -8.7 ± 0.9
-20, -20 < -22.2 nf < 1.5 nf
40, -10 . . . . . . < 1.8 nf
30, -10 < -35.7 nf < 2.4 nf
20, -10 < -16.8 nf < 3.0 nf
10, -10 -43.1 ± 8.2 -8.1 ± 1.6 4.7 ± 1.1 -10.3 ± 2.8 yes
0, -10 -76.2 ± 13.8 -9.5 ± 1.8 11.7 ± 0.8 -9.0 ± 0.6 yes
-10, -10 -82.7 ± 7.7 -8.1 ± 0.8 18.6 ± 0.6 -8.2 ± 0.3 yes
-20, -10 < -24.3 nf < 2.7 nf
40, 0 < -33.0 nf 2.8 ± 0.5 -11.6 ± 2.3
30, 0 < -28.8 nf < 3.3 nf
20, 0 -63.8 ± 7.8 -7.8 ± 0.9 3.8 ± 1.1 -8.9 ± 3.0 yes
10, 0 -93.7 ± 11.3 -8.7 ± 1.1 9.4 ± 0.7 -9.9 ± 0.8 yes
0, 0 -272.6 ± 9.8 -7.8 ± 0.3 21.6 ± 0.7 -8.0 ± 0.3 yes
-10, 0 -159.8 ± 8.6 -8.0 ± 0.4 46.5 ± 1.6 -7.8 ± 0.3 yes
-20, 0 < -24.0 nf 10.2 ± 0.7 -7.7 ± 0.6
40,+10 . . . . . . < 1.7 nf
30, +10 < -28.8 nf < 0.9 nf
20, +10 -52.0 ± 8.2 -8.7 ± 1.4 5.3 ± 0.4 -9.1 ± 0.7 yes
10, +10 -114.1 ± 9.7 -6.2 ± 0.6 11.1 ± 1.3 -7.1 ± 0.9 yes
– 20 –
Table 2—Continued
Offset (l,b) 1000× I(H2CO) 〈V 〉 I(CO) 〈V 〉 Included in
arcmin K km s−1 km s−1 K km s−1 km s−1 fits
-70.3 ± 7.7 -10.3 ± 1.2 13.5 ± 1.1 -10.6 ± 1.0 yes
0, +10 -247.0 ± 10.1 -7.6 ± 0.3 22.8 ± 1.6 -8.5 ± 0.6 yes
-10, +10 -118.9 ± 9.2 -8.1 ± 0.6 22.3 ± 2.0 -8.6 ± 0.8 yes
-20, +10 < -19.2 nf < 0.9 nf
40, +20 . . . . . . < 1.2 nf
30, +20 < -25.2 nf 3.1 ± 0.4 -8.3 ± 1.7
20, +20 -42.3 ± 9.3 -7.1 ± 1.6 6.7 ± 0.7 -9.9 ± 1.0 yes
-82.0 ± 7.4 -11.3 ± 1.1 nf nf
10, +20 -49.8 ± 6.9 -6.9 ± 1.0 7.0 ± 1.2 -8.0 ± 1.4 yes
-63.1 ± 5.5 -10.8 ± 1.0 8.3 ± 0.9 -11.0 ± 1.4 yes
0, +20 -68.3 ± 9.7 -8.9 ± 1.3 6.1 ± 0.7 -10.8 ± 1.3 yes
-10, +20 -56.4 ± 6.8 -8.6 ± 1.1 5.5 ± 0.5 -10.8 ± 1.1 yes
-20, +20 < -29.7 nf < 2.7 nf
40, +30 . . . . . . < 1.6 nf
30, +30 < -27.9 nf < 1.6 nf
20, +30 < -19.5 nf 3.4 ± 0.8 -11.4 ± 2.7
10, +30 -54.1 ± 8.8 -9.3 ± 1.6 5.6 ± 0.7 -10.3 ± 1.2 yes
0, +30 < -18.0 nf 5.0 ± 0.6 -11.1 ± 1.3
-10, +30 < -27.0 nf 2.0 ± 0.4 -10.2 ± 2.2
-20, +30 < -23.4 nf < 3.0 nf
– 21 –
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This preprint was prepared with the AAS LATEX macros v5.2.
	Introduction
	Data
	Results
	Comparison with other molecular tracers
	Discussion
	Conclusions
	Model calculations
	Collisional pumping
	A PDR model for CO
	Photodissociation of H2CO
	Profile moments in detail
