A&A 365, 275-284 (2001)
DOI: 10.1051/0004-6361:20000475
F. Bensch1 - J.-F. Panis2,3 - J. Stutzki1 - A. Heithausen1,4 - E. Falgarone3
Send offprint request: F. Bensch,
1 - I. Physikalisches Institut der Universität zu Köln, Zülpicher Straße 77, 50937 Köln, Germany
2 -
ASIAA, Academica Sinica, PO Box 1-87, Nankang, Taipei 115, Taiwan, PR China
3 -
Radioastronomie, CNRS URA 336, École Normale Supérieure, 24 rue Lhomond, 75005 Paris, France
4 -
Radioastronomisches Institut der Universität Bonn, Auf dem Hügel 71, 53121 Bonn, Germany
Received 27 January 2000 / Accepted 1 August 2000
Abstract
The goal of the IRAM key-project "Small-scale structure of pre-star
forming regions'' is to map three nearby (
), quiescent
molecular clouds with a high angular and spectral resolution to study
the molecular cloud structure down to the smallest linear
scales currently accessible by single dish radio telescopes.
Here, we give a detailed discussion of the influence and the
correction of the error beam pick-up. A new set of corrected data
is presented using the beam pattern parameters of the IRAM 30m telescope
recently published by Greve et al. (1998).
For the correction we use observations made at lower angular
resolution with the KOSMA 3m telescope.
Smeared to the resolution of the error beam,
they provide an estimate of the pick-up therein.
The error beam pick-up accounts for a significant
fraction of the observed intensity in the key-project maps:
on average 31% to 50% for the
12CO
1 maps, 10% to 35% for the
13CO
1 maps, and 16.5% in the
12CO
0 map of MCLD 123.5+24.9.
In addition, the line profiles are significantly modified by the error
beam pick-up.
The large data set available with the IRAM key-project allows us
to investigate the accuracy of the correction method and its
limitations in detail. For the corrected maps, we
determine the overall accuracy of the temperature scale to be
better than 15%, except for the 13CO
1 map
of MCLD123.5+24.9 and L1512 where we estimate an accuracy of
22% and 18%.
The key-project maps presented here and the released maps
published by Falgarone et al. (1998)
(with the correction done using the previous beam pattern parameters
determined by Garcia-Burillo et al. 1993) differ by no more than 10%
and only in localized regions. Both data sets and the supplementary
observations made with the KOSMA telescope are available
in electronic form at the CDS via anonymous ftp to
cdsarc.u-strasbg.fr (130.79.128.5) or
via http://cdsweb.u-strasbg.fr/Abstract.html
The "error beam problem'' is not limited to observations obtained
with the IRAM 30m. Similar beam pattern are found for other
large single dish (sub-)mm telescopes, although few quantitative studies
exist. In particular, for observations of spatially extended sources, the
error beam contribution has to be considered and corrected for if
necessary.
Key words: methods: data analysis - techniques: miscellaneous - radio lines: ISM - line: profiles - interstellar medium (ISM): clouds - ISM: structure
Author for correspondance: bensch@ph1.uni-koeln.de
With the increasing number of surveys covering spatially extended emission, such as those needed to study the structure of the interstellar medium (ISM), it has become clear that a significant fraction of the detected intensity can be due to pick-up in beam pattern components outside the main beam. Early studies of the influence of the stray radiation pick-up and methods for its correction have been done for HI observations (cf. Heiles & Hoffman 1968; Westerhout et al. 1973; Hartmann et al. 1996), based on accurate beam pattern measurements (cf. Baars & Mezger 1964; Hartsuijker et al. 1972; Harten 1973). Kalberla et al. (1980) have shown, that the pick-up in a relatively weak but spatially constrained stray pattern can significantly contribute to the observed intensity. For (sub-)mm wave telescopes, studies of the error beam pick-up were done by e.g. Schneider et al. (1998) for IRAM 30m observations, and Dame & Thaddeus (1994) for observations made with CfA 1.2m telescope.
Measurements of the IRAM
30 m beam pattern show that the error beam accounts for a substantial
fraction of the beam pattern (GGC and GKW),
more than 50% for observations at
wavelengths mm (frequencies
GHz).
This demonstrates that an error beam correction is
essential, in particular for observations of spatially extended
sources, such as those of the key-project.
For the correction of the key-project data set we use observations made with the KOSMA telescope. Smeared to the spatial resolution of the error beam (appropriately scaled to account for the relative contribution of the error beam to the full beam pattern), they provide an estimate of the error beam pick-up. In Sect. 2 we summarize the beam pattern parameters of the IRAM 30 m and the correction method applied. In Sect. 3 the original and corrected maps are compared. The accuracy of the correction method and of the corrected data set is discussed in Sect. 4. In Sect. 5 we describe the self-consistent error beam correction, which is applied to the released data set (Paper I) and the data set presented here. Both independently reduced data sets are compared. A summary of our results is given in Sect. 6.
For the error beam corrected data we use the
corrected main beam temperature scale
.
The rigorous definition of
is given
in a supplementary paper (Bensch et al. 2001) where we compare two
correction methods and provide a
guideline for observers wishing to correct their own data.
The beam pattern of the IRAM 30m was determined by
GGC, and more recently by GKW.
GKW combined a larger
data set (measurements on Moon, planets and holographic data) obtained
at four different wavelengths ranging from
mm to 0.75 mm
to deduce a consistent beam pattern model.
They find that the beam pattern is
given by a tapered Airy pattern
(
)
of HPBW
,
and three Gaussian error beams
of HPBW
(
). The latter result from
three independent surface error distributions in the primary reflector.
Both more extended (second and third) error beams result from
surface errors attributed to the panel frames and the
mounting of each panel with a
array of adjustment
screws. The first error beam (
)
is due to temporally variable, large-scale
deformations of the reflector surface, suspected to result from
residual thermal deformations
(see GKW and references therein).
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||||
component | HPBW [arcsec] | pi | HPBW [arcsec] | pi | |
tapered Airy patt. |
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21 | 0.71 | 10.5 | 0.41 |
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228 | 0.08 | 114 | 0.16 |
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317 | 0.08 | 158 | 0.16 |
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1900 | 0.13 | 950 | 0.27 |
In the following, we use
The accuracy of the HPBW and the power in
the Gaussian error beams is estimated by GKW
to be
% and
5%, respectively.
This applies to the individual components,
determined from observations at one frequency, whereas the numbers
given in Table 1 are results from a consistent beam pattern
model, fitted to a larger number of observations at different
wavelengths. We therefore expect a higher accuracy for the latter.
The exception is the integral over the first error beam,
showing temporal variations of some
% with a time
constant of 1 h or more (Table 1 gives the average
p1). Therefore, a large uncertainty applies to the pick-up by
the first error beam.
The correction by de-convolution of the error beam pattern in Fourier space turned out to be not possible (Bensch et al. 2001). For each map in the data set, this correction method requires additional, fully sampled observations with the IRAM 30 m of several 104 positions, and an integration time of less than 1 s per position. Currently, this is not feasible without an excessive overhead in dead-time (due to moving of the telescope, etc.) and because of the huge amount of data to be handled in a relatively short time.
Figures 1 to 4
compare the velocity integrated maps of the original (uncorrected) and the
corrected observations.
For the uncorrected maps we use the observed spectra scaled to
.
This corresponds to a "0th
order error beam correction'' where the
forward efficiency
is used as "full beam efficiency''
(cf. Downes 1989).
Note that the signal to noise ratio is lower in the corrected maps
because the correction subtracts signal and adds noise.
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Figure 1:
Integrated spectral line maps of MCLD 123.5+24.9,
12CO
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The corrected spectral line maps show an enhanced
contrast. More details are visible at small angular scales which are
(partially) obscured in the uncorrected maps due to the smearing
with the error beam. The actual percentage of the observed
intensity attributed to the error beam pick-up significantly varies with
position and velocity. For positions where strong emission
is found nearby, the relative
contribution of the error beam is much larger than average,
accounting for up to 100% of the observed emission. Examples
are found in the North-West corner of
MCLD 123.5+24.9, 13CO
1 map (right
panel of Fig. 5) and the
South-East corner of the L1512, 13CO
1
map (right panel of Fig. 6).
In the 12CO
0 map of MCLD 123.5+24.9,
the error beam pick-up accounts (on average) for 16.5% of the
observed intensity.
The line profile of the error beam pick-up does not vary
much across the observed area, in contrast to the CO
1
observations. This is because of the larger angular extent of the
error beams for lower frequencies (
GHz), which are comparable
or larger than the observed map.
The correction therefore modifies the morphology of the
intensity distribution only to a minor degree.
Comparing the corrected (
)
and the
uncorrected (scaled to
)
spectra, we find that the latter
are larger by
30%. This can be considered as an upper limit
to the systematic error for CO
0 data, if no correction is done, scaling them
to
instead. Scaling the spectra to the antenna
temperature
gives intensities which are (on
average) smaller by
8%, and thus a better
approximation to the corrected main beam brightness temperature if
no further correction is applied.
Figures 5 to 8
compare the line
profiles of the observed spectra (
)
and the
estimated pick-up in the second and third error
beam
. This is a
crucial test for the correction method and the beam model used for the
IRAM 30 m. Additionally, it provides information on the
accuracy of the error beam correction method and the corrected data.
An estimated error beam pick-up which
systematically exceeds the observed line profile points to a
systematic error in either the beam pattern model or the intensity
calibration of the observations made with the smaller telescope.
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Figure 5:
MCLD 123.5+24.9: The observed (uncorrected)
spectra (scaled to
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Inspection of Figs. 5 to 8
shows that this is not the case, except for a few of the 12CO
1 spectra
observed towards L134A (left panel of Fig. 7).
Here, the estimated error beam pick-up slightly exceeds the
observed line profile in the red line wing (between 3 and 4 km s-1)
for positions at
(
)
(
,
).
In addition, the estimated error beam pick-up appears to be red-shifted with
respect to the observed line profile for
.
Two possible explanations remain for the
discrepancy. Firstly, the KOSMA observations potentially suffer from
a significant error beam pick-up, which results in the error
beam pick-up of the IRAM 30 m being overestimated. Secondly, the
actual (error) beam pattern of the IRAM 30 m significantly
differs from the model used.
In either case, the thus introduced systematic error can mimic a velocity
offset between the observed line profile and the estimated error beam
pick-up, because of the velocity gradient observed for the line profiles
south of
.
A further, more quantitative
discussion is given in Sect. 4.
The line profiles shown in Figs. 5 to 7
demonstrate that the error beam pick-up not only adds intensity, but
modifies the line profile. On average, the relative contribution is
larger in the line wings than in the line core.
This is documented in Fig. 9, where the systematic variation
of the error beam pick-up with velocity channel is shown for the
map-averaged spectra. Only
for the 12CO J=
0 observations made towards
MCLD 123.5+24.9, the percentage of the observed intensity
attributed to the error beam pick-up roughly is constant across the
line profile.
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Figure 9:
Map-averaged line profiles of the 12CO
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The modification of the individual line profiles by the error beam
pick-up is more complex than suggested by the map-averaged
profiles. It depends on the position and the velocity structure of
the emission on angular scales of the error beam pattern. An inspection of
individual line profiles shows that for some positions, the intensity in the
line wing is effectively lowered with the error beam correction (e.g.
in the South-Eastern part of the MCLD 123.5+24.9,
12CO
1 map), while for other positions,
the line wings are found to be more pronounced in the corrected
spectra. The same result is suggested by maps showing the spatial
variation of the second moment, determined from the line profiles.
An example is given with Fig. 10, where the
intensity contrast is substantially higher for the corrected spectra,
consistent with a larger spatial variation of the line profile.
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Figure 10:
Maps of the second moments, determined for the
12CO
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The comparison of the error beam corrected key-project data, smoothed
to the KOSMA resolution, with the KOSMA observations provides a check
for the correction method and the intensity calibration of both data
sets. For a quantification we define
For perfectly corrected IRAM 30m data
and KOSMA observations with a negligible error beam pick-up, a
narrow distribution, centered on 1, is expected. An average value
smaller than unity suggests that the IRAM 30 m
error beam pick-up is overestimated, and hence that the
corrected main beam brightness temperature is underestimated.
For the corrected key-project maps, the x-distributions are given
in Fig. 11, together with the average (), median,
and width
(standard deviation) of the distribution.
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Figure 11:
Distribution of x, determined as the ratio of the
corrected key-project data (smoothed to angular
resolution of the KOSMA telescope) and the KOSMA observations
(Eq. 3). The ratio x was determined
for each velocity channel with an
intensity larger than three times the rms in the spectrum.
Positions which are located closer than 1 arcmin to the edge of
the map are excluded.
For each distribution, the average ![]() ![]() |
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For the 12CO
1 maps,
is found to be
equal or smaller than unity (0.82, 1.02 and 0.88 for
MCLD 123.5+24.9, L1512 and L134A, respectively),
while for the 13CO
1 maps,
is larger than
unity (1.15, 1.26 and 1.06). For the 12CO
0 map
of MCLD 123.5+24.9 we find
1.02.
The width
of the distributions is between
0.10 and 0.18, except for the 13CO
1 map of
MCLD 123.5+24.9, where
is significantly larger
(0.22). In general,
we find larger
for the 13CO
1 maps,
except for L134A where both maps have
.
The influence of the finite signal-to-noise in the spectra on the
and
is negligible.
We obtain the same results for distributions deduced with spectra
binned to a lower velocity resolution, and hence with a lower
rms noise per velocity channel. Thus, the
and
can be used to determine the
accuracy of the error beam correction method
and to examine the limiting factors.
We estimate the total uncertainty in the
scale using
the self-consistency check (
and
)
and by comparing the observed line profiles to the
estimated error beam pick-up.
An average value
offset from unity indicates systematic
errors, which may result from
The width of the distribution ()
depends on statistical
variations from position to position. These uncertainties may
arise from
The exact amount of error beam pick-up in the KOSMA observations
is unknown because it depends on the large-scale structure
of the emission and the (unknown) details of the KOSMA error beam
pattern. If present, the KOSMA error beam pick-up is expected to play
a role for the observations of the spatially extended
12CO
1 emission only.
An estimate of the KOSMA error beam pick-up
at 230GHz is obtained by comparing
the main beam efficiency determined for bright planets
(
)
and measured on the Moon (
=
0.72). This shows that a KOSMA error beam of angular extent
is present, and that the power radiated into this error beam is
13% of the power in the main beam. Thus, for extended sources,
an error beam pick-up of
13% is expected for KOSMA
observations at 230 GHz (assuming an uniform intensity distribution).
Indeed, for the maps with the spatially most extended emission
(the 12CO
1 maps observed toward
MCLD123.5+24.9 and L134A) we find
which are
significantly smaller than unity, suggesting that the
KOSMA error beam is not negligible. The
(0.88,
respectively) suggest that the KOSMA error beam pick-up is
12 - 18% for the 12CO
1 maps, and this
only if we fully attribute the
to a KOSMA error beam.
For the 13CO
1 maps we find that the
are larger than unity. This is consistent with a negligible
KOSMA error beam pick-up for the not very extended emission
of the rarer isotopomer, and that other
systematic errors limit the accuracy of the intensity
calibration. The same applies to
the 12CO
0 map of MCLD123.5+24.9,
because of the smaller amplitude of the error beam pattern at lower
frequencies.
The correction for the first (smaller) error beam of the IRAM 30m is not possible
because of the large temporal variations of the amplitude and the
insufficient angular resolution of the KOSMA observations. Thus, an
additional error in the intensity calibration of the corrected data set
arises from the uncorrected first error beam.
This error is expected to play a significant role for maps which show
strong intensity variations
on the angular scale of the error beam (1.9' at 230GHz).
Here, the x-distribution is expected to be significantly wider
(lager
)
with an average
larger than unity,
because the pick-up in the small error beam strongly varies with the
position.
This is observed for the 13CO
map
of MCLD 123.5+24.9 and L1512. Both contain cores and/or
steep gradients extending over
1 arcmin (Figs. 1
and 2) and, at the same time, have the
largest
(1.15 and 1.26) and
(0.22 and 0.18). We therefore conclude that the
accuracy of the intensity calibration for these maps is limited by the
uncorrected first error beam, and that the
thus introduced error is up to 26%. For the other maps, the first error
beam accounts for less than 12% of the observed intensity, judged from the
in Fig. 11
and taking into account that the accuracy of the relative intensity
calibration in the maps is 9% (Panis 1995),
assuming that both errors add in quadrature.
In the 12CO
1 map of
L134A the estimated error beam pick-up
systematically exceeds the observed line profile for a few positions
at
(
,
), while both profiles appear velocity-shifted
in respect to each other for positions
.
This cannot be reconciled unless we modify the amplitude of the
error beam pattern by much more than
,
which is excluded by the
accuracy of the beam pattern parameters (GKW).
Similarly, the possible contribution of a KOSMA error beam
cannot fully account for the discrepancy because it would
imply an additional pick-up in the KOSMA observations
of far more than 20%, and thus
extended areas with strong emission outside the
maps, which is not observed (Bensch 1998).
One plausible explanation is provided by a possible deviation of the
IRAM error beam pattern from the assumed axial symmetry.
In the L134A maps, a velocity gradient is
present South of
,
extending over several arcmins.
A slight deviation from the assumed axial symmetry can mimic a velocity shift in the line
profile of the error beam pick-up. This is not excluded by the
measurements of GKW, because they used cross-scans in
East-West direction and explicitly assume axial symmetry.
Moreover, a not axially-symmetric error
beam pattern is not entirely unrealistic, given the shape of the panels/panel
frames of the IRAM 30m.
This procedure was applied to the released data set of the key-project (Paper I) and the data set presented here. However, one has to keep in mind that this is an ad hoc correction. The residual difference between the KOSMA and the corrected, smoothed IRAM spectra is not solely due to the KOSMA error beam pick-up, as shown above.
For an application to the key-project maps we merge the
ratio
and the ad hoc scaling factor for the
KOSMA data to a single scaling factor, which is
determined for each map with the x-distribution. This is
done for the 12CO
0 map of
L1512 and L134A, and for the
13CO
0 map of MCLD 123.5+24.9 and
L134A. The signal-to-noise ratio of the remaining maps
(C18O
0 maps, and the 13CO
0
map of L1512)
is too small to reliably determine the scaling factor.
For these maps the correction is done using the
KOSMA CO
1 data, assuming a constant ratio of
(Paper I).
The accuracy of this correction method is estimated by
using the 12CO
0 map of MCLD
123.5+24.9, where KOSMA observations of both lower CO transitions
are available. The key-project map, corrected with the
KOSMA 12CO
0 data, and the same map,
corrected with the KOSMA 12CO
1 observations
scaled by
,
differ by no more than 15% if the
correction is done according to Eq. (2), and
7% if the correction is done self-consistently.
The data reduction of key-project maps was done independently in Paris and Cologne. For the released data set (Paper I), the correction was done using the beam pattern parameters determined by GGC. The correction of the independently reduced data set presented here is done using the more recent beam measurements by GKW. The comparison of both data sets show that the integrated spectral line maps differ by no more than 10%, consistent with the estimated accuracy.
The released maps of the key-project, the data set presented with this paper and the complementary observations made with the KOSMA telescope are available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/Abstract.html
For the 12CO
0 map of MCLD 123.5+24.9,
the error beam pick-up is determined to be 16.5% (map average).
The intensity distribution as well as the line profiles are modified
only to a minor degree.
We apply a self-consistent error beam correction to the released data
set, where we match the KOSMA observations to
the corrected IRAM observations, smoothed to the angular
resolution of the KOSMA observations. The
accuracy of the thus corrected spectral line maps is
11% (CO
0) and 15% (CO
1),
except for the 13CO
1
map of L1512 and MCLD 123.5+24.9, where we assign
larger uncertainties (18% and 22%, respectively).
The systematic errors in the intensity calibration of the
key-project data set are dominated by the error beam
pick-up of the KOSMA telescope (accounting for
18%
in the 12CO
1 maps)
and the uncorrected first error beam of the IRAM 30 m
(resulting in the larger uncertainties for the 13CO
1
map of L1512 and MCLD 123.5+24.9). Taking both effects
into account, we find that the residual errors are in accordance with
the accuracy estimated by GKW for the beam pattern
parameters of the IRAM 30 m.
Only for the 12CO
1 map of
L134A, we find indications that the actual error beam pattern
slightly deviates from the assumed axial symmetry.
This study focuses on the observations made in the framework of the key-project with the IRAM 30m telescope. However, we expect that the error beam pick-up potentially plays a significant role for observations made with other (sub-)mm telescopes, too. An error beam pattern similar to the pattern of the IRAM 30m has been found for a number of (sub-)mm telescopes (cf. Kaufmann et al. 1987; Hills & Richter 1992; Prestage 1993). The correction methods (cf. Bensch et al. 2001) and the conclusions presented in this paper are therefore not limited to observations made with the IRAM 30 m. This should be taken into account when planning large mapping projects, where a fraction of the time should be allocated for the additional observations required to correct for the error beam pick-up.
Acknowledgements
The authors wish to thank A. Greve and C. Kramer for discussions and providing the detailed numerical results of their error beam measurements of the IRAM 30m telescope. The KOSMA 3m radio telescope at Gornergrat-Süd Observatory is operated by the University of Cologne and supported by the Deutsche Forschungsgemeinschaft through grant SFB-301, as well as special funding from the Land Nordrhein-Westfalen. The receiver development was partly funded by the Bundesminister für Forschung and Technologie. The Observatory is administered by the Internationale Stiftung Hochalpine Forschungsstationen Jungfraujoch und Gornergrat, Bern. The authors have benefitted from a joint European grant (Procope, grant# 312-pro-bmbw-gg) during the years 1995 and 1996. This research made use of NASA's Astrophysics Data System Abstract Service.
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Figure 2:
Same as Fig. 1 for L1512. The 12CO J=2
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Figure 3: Same as Fig. 1 for L134A. Because of the elongated geometry of the KOSMA maps (see Bensch et al. 2000), only a sub-set of them is shown in the panels on the left. |
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Figure 4:
Same as Fig. 1 for MCLD 123.5+24.9, 12CO J=1
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Figure 6: Same as Fig. 5 for L1512. |
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Figure 7: Same as Fig. 5 for L134A. |
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Figure 8:
Same as Fig. 5 for the 12CO
J=1
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