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Appendix A: Data processing

Appendix A.1: Interferometric data

We used the standard algorithms implemented in the software GILDAS/CLIC to calibrate the PdBI data. The radio-frequency bandpass was calibrated by observing the bright (12.8 Jy) quasar 3C 84. Phase and amplitude temporal variations where calibrated by fitting spline polynomials through regular measurements of two nearby (<11°) quasars (3C 84 and 0333+321). The PdBI secondary flux calibrator MWC 349 was observed once during every track, which allowed us to derive the flux scale of the interferometric data. The absolute flux accuracy is ~10%.

To produce the continuum maps, we imaged and deconvolved the WIDEX data at 2 MHz resolution. This allowed us to identify all the detected lines and to remove them before synthesizing the continuum image. To subtract the continuum from the lines, we first synthesized continuum uv tables in a ~400 MHz frequency range devoid of lines close to the targeted line. This way, we did not need to take a potential variation of the continuum level with frequency into account.

Appendix A.2: Single-dish data

Data reduction was carried out using the software GILDAS/CLASS³. The data were first calibrated to the scale using the chopper-wheel method (Penzias & Burrus 1973). The spectra were converted to main-beam temperatures (T_mb) using the forward and main-beam efficiencies (F_eff and B_eff) listed in Table 1. The resulting amplitude accuracy is 10%. A 20 MHz-wide subset of the spectra was first extracted around each line rest frequency. We computed the experimental noise after subtracting a first-order baseline from every spectrum, excluding the velocity range from 4 to 9 km s^-1 LSR where the signal resides. A systematic comparison of this noise value with the theoretical noise computed from the system temperature, the integration time, and the channel width allowed us to filter out outlier spectra (typically 3% of the data). The spectra were then gridded into a data cube through a convolution with a Gaussian kernel of FWHM ~ 1/3 of the IRAM-30 m telescope beamwidth.

Appendix A.3: Joint imaging and deconvolution of the interferometric and single-dish data

Following Rodriguez-Fernandez et al. (2008), the software GILDAS/MAPPING and the single-dish map from the IRAM-30 m were used to create the short-spacing visibilities not sampled by the Plateau de Bure interferometer. In short, the maps were deconvolved from the IRAM-30 m beam in the Fourier plane before multiplication by the PdBI primary beam in the image plane. After a last Fourier transform, pseudo-visibilities were sampled between 0 and 15 m, which is the difference between the diameters of the IRAM-30 m and the PdBI antennas.

These visibilities were then merged with the interferometric observations. Each mosaic field was imaged and a dirty mosaic was built by combining these fields in the following optimal way in terms of signal-to-noise ratio (Pety & Rodríguez-Fernández 2010). The dirty intensity distribution was corrected for primary beam attenuation, which induces a spatially inhomogeneous noise level. In particular, noise strongly increases near the edges of the field of view. To limit this effect, both the primary beams and the resulting dirty mosaics were truncated. The standard level of truncation was set at 20% of the maximum in GILDAS/MAPPING. The dirty image was deconvolved using the standard Högbom CLEAN algorithm. The resulting data cube was then scaled from Jy/beam to the T_mb temperature scale using the synthesized beam size (see Table 1).

The H₂CO emission covers most of the mosaic field of view. The emission structure thus seems to sit on a constant brightness that only depends on the frequency, not on the spatial position. CLEAN deconvolution methods have many difficulties to properly deconvolve this “constant” emission. To avoid this, we subtracted the mean spectrum over this field of view of the single-dish data before processing them to produce the short-spacings. We then imaged and deconvolved the hybrid data set as explained above and added this mean spectrum back to the hybrid synthesis data cube (30 m + PdBI) after deconvolution and conversion to the T_mb temperature scale. This treatment is correct because a constant emission is always resolved, that is, independent of the resolving power of the observatory.

Appendix B: Spectral energy distribution

	Fig. B.1 Spectral energy distribution of B1b-S (blue) and B1b-N (red). The data points are taken from Hirano & Liu (2014) and include Spitzer, Herschel, and ground-based observations. The stars show the new PdBI measurements.
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We present in Fig. B.1 the SED of B1b-N and B1b-S and provide refined positions in Table B.1. The measured continuum fluxes agree well with the values reported by Pezzuto et al. (2012) and Hirano & Liu (2014). It is interesting to observe that B1b-S is more luminous than B1b-N at far-infrared and submillimeter wavelengths while the reverse is true long-ward of ~2.5 mm. The new PdBI data help to locate the crossing point of the SEDs.

© ESO, 2015