Abstract:
We discuss a method to use lower angular resolution spectral line
maps, e.g. from the KOSMA 3m telescope, to correct IRAM 30m high
angular resolution maps for their error beam pick-up. We show that the
corrected maps exhibit significantly stronger contrast, both spatially
and in velocity.
Garcia-Burillo et al. 1993 (A&A 274, 144) used Moon cross scans to fit
the IRAM error beam at 230 GHz with a gaussian main beam with 13.5
FWHM and a fraction
of the total intensity on
the Moon, two gaussian error beams (170
resp. 800
FWHM and
resp.
=0.13) and a ring--shaped
secondary lobe with 5
extension and
.
The
determined by Garcia--Burillo et al. do not sum up to
1. According to M. Guélin, this is due to rounding errors and non
Gaussian terms.
We simply attribute the remaining 2%
efficiency to the 800
beam and thus use
=0.15 in the
following. The observed antenna temperature (
=
/
)
is now a full beam brightness temperature
including the contributions from the different lobes, in the nomenclature
of Downes
(``Introductory courses in Galaxies'', Springer 1989) :
are the IRAM ``main beam brightness temperatures'' for each
error beam,
the respective ``main beam'' efficiencies and
the forward efficiency. From equation (1) it is obvious that
(response to an uniform, extended source of
brightness
requires
) and hence
. Due to the compactness of the 5
secondary
lobe, we assume the main beam brightness temperatures in this lobe and
the main lobe to be equal. We then get for the main beam brightness
temperature in the 13
beam :
As the main beam brightness temperature is the same at every telescope (assuming a clean gaussian beam as we have assumed in the decomposition of the IRAM 30m error beam) we can now use an independently measured map from a smaller telescope to correct the IRAM data for the pick-up from the error beams. This assumes that the smaller telescope map is not severly affected by pick-up from its error beam. It is usually a good approximation, for one because the smaller telescope error beam will be much more extended, and hence not couple significantly to the source, and for second because, if the smaller telescope has a better surface quality, its beam efficiency will be high anyway and hence error beam contributions can be regarded as "second order" effects. A similar technique is used for HI observations but to our knowledge has not been applied to molecular spectral line data so far.
The KOSMA 3m--telescope is well suited for this correction method due
to its HPBW of 132 at 1.3 mm with a main beam efficiency of 0.64
(coupling to Jupiter). The data are smoothed to 170
resp. 800
resolution with a gaussian intensity distribution, resampled on the
grid observed at IRAM, and can then be substracted from the IRAM
spectra. According to equation (2)
are replaced by the
KOSMA main beam temperatures
taking KOSMA as an "ideal"
telescope. With the values quoted above, the resulting IRAM--main
beam brightness temperature for the 13
main beam now reads :
Figure 3: The smoothed (to 170 resolution) and resampled KOSMA
CO J=2
1 data (thick line) are overlayed to the original IRAM
spectra (thin line). The temperature scale (-0.5 to 4.5 K) is in antenna
temperatures
, the velocity interval ranges from
3 to 23 km s
.
To demonstrate the applicability of this method to real observations,
we discuss in the following the results of CO observations of
the Rosette Molecular Cloud. Fig. 3 shows as an example a set of
5
5 original IRAM
CO J=2
1 spectra overlayed to the
smoothed and resampled KOSMA data. Note the very good match between
the error beam spectra synthesized from the KOSMA data and the
corresponding feature in the original IRAM line profiles. Due to the
large velocity dispersion in between individual emission regions in
the source, the error beam spectra substract a substantial fraction,
mainly the underlying broad velocity structure, in the IRAM raw data.
In fact, the good match between the spectral features, in particular
the fact that the error beam contribution is always close to, but
never exceeds, the raw spectra in the maps, is a very good
confirmation of the amplitudes
determined by Garcia--Burillo
et al., in particular the one of the 170
beam causing most of the
correction. The magnitude of the correction is up to 100% for the
extended, broad weak line emission, which can be concluded to be due
mainly to the error beam pick-up, and 20% at CO peak emission
positions. Fig. 4 shows a comparison between a large scale map before
and after the correction method was applied. The extended weak
emission is removed and the overall structure has a higher contrast,
both spatially and spectrally.
We point out that after the correction, there still remains a discrepancy between the IRAM and KOSMA temperature scales. If we smooth the corrected IRAM data to the KOSMA resolution, we find that, though the intensity matches within the noise at most positions, preferentially in more extended emission regions, the corrected and smoothed IRAM spectra still exceed the KOSMA scale by up to 30% in regions with strong emission and small scale structure. At this point we can only speculate about the origin for this discrepancy. It might partially be due to pickup in smaller scale structure whithin the error beams not accounted for by the Gaussian beam model used.
Figure 4: Contour plots of the integrated CO J=2
1 intensity
from the original (top) and corrected (bottom) IRAM data show clearly how the
extended weak emission due to the error beam pickup is removed and the
overall structure of the molecular cloud is visible with much higher
contrast. The emission was integrated between 7 and 13 km s
and the
contour levels range from
1.14 K kms
(3
) to 26.2 K km s
(original data) resp.
21.5 K km s
(corrected data) in steps of 6
.
N. Schneider, J. Stutzki
I.Physikalisches Institut, Universität zu Köln,
Zülpicher Straße 77, D-50937 Köln, Germany