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=21 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 55 original IRAM CO J=21 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=21 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