Cm-wave radiation from the \rho Oph molecular cloud

Centimeter-wave continuum radiation from the  Ophiuchi molecular cloud

Simon Casassus, Clive Dickinson, Kieran Cleary, Roberta Paladini, Mireya Etxaluze, Tanya Lim, Glenn J. White, Michael Burton, Balt Indermuehle, Otmar Stahl, Patrick Roche
Departamento de Astronomía, Universidad de Chile, Casilla 36-D, Santiago, Chile
Infrared Processing and Analysis Center, California Institute of Technology, M/S 220-6, 1200 E. California Blvd., Pasadena, CA 91125.
Chajnantor Observatory, M/S 105-24, California Institute of Technology, Pasadena, CA 91125
Department of Physics and Astronomy, The Open University, Milton Keynes MK7 6AA, UK
The Rutherford Appleton Laboratory, Didcot, Oxfordshire OX11 0QX, UK.
School of Physics, University of New South Wales, Sydney NSW 2052, Australia
ZAH, Landessternwarte Königstuhl, 69117 Heidelberg, Germany
Astrophysics, Oxford University, DWB, Keble Road, Oxford OX1 3RH, UK
E-mail: simon@das.uchile.cl (SC)
Abstract

The  Oph molecular cloud is undergoing intermediate-mass star formation. UV radiation from its hottest young stars heats and dissociates exposed layers, but does not ionize hydrogen. Only faint radiation from the Rayleigh-Jeans tail of  10–100 K dust is expected at wavelengths longwards of 3 mm. Yet Cosmic Background Imager (CBI) observations reveal that the  Oph W photo-dissociation region (PDR) is surprisingly bright at centimetre wavelengths. We searched for interpretations consistent with the WMAP radio spectrum, new ISO-LWS parallel mode images and archival Spitzer data. Dust-related emission mechanisms at 1 cm, as proposed by Draine & Lazarian, are a possibility. But a magnetic enhancement of the grain opacity at 1 cm is inconsistent with the morphology of the dust column maps and the lack of detected polarization. Spinning dust, or electric-dipole radiation from spinning very small grains (VSGs), comfortably explains the radio spectrum, although not the conspicuous absence from the CBI data of the infrared circumstellar nebulae around the B-type stars S 1 and SR 3. Allowing for VSG depletion can marginally reconcile spinning dust with the data. As an alternative interpretation we consider the continuum from residual charges in  Oph W, where most of carbon should be photoionised by the close binary HD147889 (B2IV, B3IV). Electron densities of  cm, or H-nucleus densities  10 cm, are required to interpret  Oph W as the C ii Strömgren sphere of HD147889. However the observed steep and positive low-frequency spectral index would then require optically thick emission from an hitherto unobserved ensemble of dense clumps or sheets with a filling factor and  cm.

keywords:
radiation mechanisms: general, radio continuum: general ISM, sub-millimetre, ISM: clouds,
pagerange: Centimeter-wave continuum radiation from the  Ophiuchi molecular cloudApubyear: 2006

1 Introduction

The subtraction of Galactic foregrounds in experiments designed to map the cosmic microwave background requires the examination of the emission mechanisms at work in the interstellar medium (ISM). An anomalous component of continuum emission was discovered in the direction of Galactic cirrus clouds (Leitch et al., 1997), so defined by their H i 21 cm and far-IR contours (e.g. Boulanger & Perault, 1988). The LDN 1622 dark cloud (Lynds Dark Nebula, Lynds, 1962) was found to be bright at cm-wavelengths, where no known emission mechanisms were expected (Finkbeiner et al., 2002; Finkbeiner, 2004; Casassus et al., 2006). At the time of writing LDN 1622 is the only dark cloud known to radiate at cm-wavelengths.

What is the nature of the cm-wave emitters? Do the dark clouds and the cirrus clouds radiate by the same emission mechanisms? Draine & Lazarian (1998a, b) proposed electric dipole radiation from polarized very small dust grains (VSGs) spinning at GHz frequencies, or spinning dust. Draine & Lazarian (1999) also suggested that ‘magnetic dust’, or magnetic dipole emission due to thermal fluctuations in the magnetization of ferromagnetic grains, could produce detectable cm-wave emission. However, a finite charge density exists in atomic and molecular clouds; a small part of the neutral material is ionised by exposure to pervasive cosmic rays or soft-UV photons (e.g. Tielens, 2005). As an alternative to spinning dust, could the residual charges radiate at the observed levels?

Prototypical and well studied local clouds can give information on the environments giving rise to cm-wave radiation. The  Oph molecular cloud (e.g. Encrenaz, 1974; Young et al., 2006), at a distance 15 pc (parallax distance to HD147889, Habart et al., 2003), lies in the Gould Belt of the closest molecular complexes.  Oph is undergoing intermediate-mass star formation - the most massive of its young stars is HD147889, which we show here to be a close pre-main-sequence B2, B3 binary, not hot enough to form a conspicuous region of ionized-hydrogen (H ii region). A description of the region can be found in Fig. 4 of Young et al. (2006).

Here we present the first resolved images at cm-wavelengths of the  Oph main cloud, LDN 1688. We describe our observations in Section 2, as well as auxiliary data in Sec. 3, including unpublished ISO-LWS parallel mode data. We proceed to summarise the available imaging and spectroscopic data in Sec. 4. The dust emission from  Oph W and the contribution of spinning or magnetic dust at cm-wavelengths are studied critically in Sec. 5. We also propose in Sec. 6 an alternative emission mechanism for the 31 GHz emission based on the C i continuum from a cold plasma. In Sec. 7 we analyse the non-detection of the radio recombination line system in  Oph W. We discuss our findings in Sec. 8 in terms of the C ii Strömgren spheres around the early type stars that are interacting with the  Oph cloud, before concluding in Sec. 9.

2 CBI Observations

The 31 GHz image of  Oph that motivates this work is shown in Fig. 1. It was reconstructed from the CBI visibilities using a maximum entropy method. In this section we give details on the CBI observations and image reconstruction.

Figure 1: MEM model of the CBI 31 GHz visibilities. and axis show offset RA and DEC from  Oph W (J2000 16h25m57s, -24d20m50s), in degrees of arc. The contour levels are at 0.067 ,0.107 ,0.140 ,0.170 and 0.197, in MJy sr. The dashed-circle follows the half-maximum level of the CBI primary beam (CBI PB hereafter).

2.1 Total intensity

The Cosmic Background Imager (CBI Padin et al., 2002) is a planar interferometer array with 13 antennas, each 0.9 m in diameter, mounted on a 6 m tracking platform. The CBI receivers operate in 10 frequency channels covering 26–36 GHz. It is located in Llano de Chajnantor, Atacama, Chile. With a uniform-weight synthesised beam of 6 arcmin and a primary beam of 45.2 arcmin full-width at half maximum at 31 GHz, the CBI is well suited to image clouds 20–30 arcmin in total extent. The CBI primary beam (CBI PB hereafter) encompasses most of LDN 1688.

During three nights of July 2004 and April 2005 we acquired 31 GHz visibilities in a single pointing on the  Oph W photo-dissociation region (PDR, Habart et al., 2003), with the CBI in its compact configuration, for a total of 12000 s on-source. Baseline length ranged between 100  and 400 , corresponding to spatial scales of 34.4 arcmin and 8.6 arcmin, respectively. Cancellation of ground and Moon contamination was obtained by differencing with a leading reference field at the same declination but offset in hour angle by 10 m, the duration of the on-source integration.

2.2 Image reconstruction

We produced the MEM model in Fig. 1 by minimising the model functional , where the expression for is given by Eq. A1 in Casassus et al. (2006), and with , where is the model image and is an image prior. The sum extends over the number of independent data points, which is (two for each of 15840 complex visibilities). In this case we chose a regularizing parameter , and square model images with square pixels, each 1 arcmin on a side. The optimization converged in 20 iterations. The image prior was constructed from a combination of the IRAC 4 image at 8 m (see Sec. 3.2) and WMAP Ka at 33 GHz (see Sec. 3.5). More details on image reconstruction are given in Sec. A.

2.3 Polarization

 Oph was also observed by the CBI in polarization during four nights in August, September and October 2004. Details of the polarization calibration and data reduction procedures can be found in Readhead et al. (2004); Cartwright et al. (2005); Dickinson et al. (2006); Casassus et al. (2007). Data from all nights were combined together. They were mapped with DIFMAP using natural weights and optimal noise weighting. A polarized intensity map was created using AIPS COMB and POLC option to correct for the noise bias. The noise on the Q and U maps is about 9 mJy beam. The beam is 9.58.3 arcmin.

No obvious polarization signal is visible in the polarized intensity map, and is consistent with an rms noise of 12 mJy beam. Using the same weighting scheme (same visibilities and synthesized beam), the peak total-intensity is 752 mJy beam.

At peak total intensity, the 1  polarization limit is 12 / 752 =1.6%, or a 3  upper limit of 4.8%. In the weaker regions of  Oph W, where the total-intensity drops to typically 100 – 200 mJy beam, the polarization limit increases to 12 / 150 = 8%, or 24% at 3 .

For the integrated flux density over a 45 arcmin diameter aperture, the polarization limit has to be calculated using a primary-beam corrected map which multiplies up both the signal and the noise. This was done, making a noise corrected polarized intensity map assuming a noise level of 45 mJy beam (average over the field). The rms in this image is 57 mJy beam. So the integrated polarization limit is  1.0% at 3 .

3 Auxiliary data

3.1 Iso parallel mode data

The ISO Long Wavelength Spectrograph parallel mode survey111http://www.iso.vilspa.esa.esmanualsHANDBOOK/lws_hbnode1.html covered most of LDN 1688 in 10 bands ranging from 46 m to 178 m. The full set of ISO images is shown in Fig. 2. The broad wavelength coverage of the ISO data allows dust mass and extinction estimates (see Sec. 5.1). Especially relevant to this work is the 178 m image, which is used in the discussion of magnetic dust in Sec. 5.2.

Figure 2: The ISO-LWS parallel mode data on  Oph. and axis show offset RA and DEC from  Oph W, in degrees. The centre wavelength in microns of the LWS channels are indicated on the upper-left of each image. The intensities in MJy sr have been scaled by the amount indicated on the upper-right of each image.

The parallel mode data were obtained when another ISO instrument was operating with total sky coverage of about 1%. The processing of parallel data was the same as for the primary mode data. Engineering conversions were applied to obtain the photocurrents. Once the photocurrents were obtained the dark current was removed. The calibration of the detector responsivity relies on a simple ratio between the response to the illuminators found at the time of a particular observation and that used as a reference. Parallel mode maps were produced at ten detector wavelengths and are generated by combining different rasters. Several data reduction tools were developed in IDL and these form the LWS parallel interactive analysis package that can be found at: http://jackal.bnsc.rl.ac.uk/isouk/lws/software/software.html.

We have compared the ISO data at 102.26 m with the IRAS 100m survey (Wheelock et al., 1991). It is noteworthy that the ISO 102.26 m intensities below 1000 MJy sr are typically 27 % higher than IRAS 100 m, 40 % higher above 1000 MJy sr. This is in agreement with the results of Chan (2001) and García Lario (2001). According to the IRAS explanatory supplement, the gain and non-linearity of the detectors is a function of source extension, which could be the source of the intensity-dependent discrepancy between ISO and IRAS.

3.2 Spitzer archival data

The IRAC data span the range 3.6 to 8m with four distinct bands (centered at 3.6, 4.5, 5.6 and 8m) and an angular resolution of 2. Longer wavelengths, namely 24, 70 and 160m, are covered by MIPS data, with angular resolutions of 9, 18 and 40 respectively. Both the IRAC and MIPS data considered in the present paper come from the c2d Spitzer Legacy Survey222see the Spitzer Science Center press release, http://www.spitzer.caltech.edu/Media/releases/ssc2008-03/release.shtml. The MIPS data are described by Padgett et al. (2008), in connection with the young stellar population of  Oph.

Archival Spitzer IRS data were obtained for positions near the early-type stars S 1, SR 3 and a region of the filament. For SR3 and the filament (Berné et al., 2007), the data were taken in spectral mapping mode using the high resolution (SH and LH) modules of IRS. In this mode, the spectrograph slit is moved before each integration in order to cover the region of interest. The Basic Calibrated Data (BCD) files from the archive were produced using the S15 pipeline by the Spitzer Science Centre. The spectral cubes were assembled from the BCD files using the CUBISM software package (Smith et al., 2004). Spectra were extracted from the spectral cubes using an aperture which was covered by both SH and LH modules, as shown in Fig. 3. For S 1, the data were taken in low-resolution (SL) staring mode and were also produced using the S15 pipeline. The original target was a young stellar object (J162630-242258, Barsony et al., 1997) located behind the circumstellar nebula about S 1. We performed a full-slit extraction of SL1 with the target in the SL1 slit and also with the target in SL2. This resulted in SL1 spectra at two distinct positions in the S 1 nebulosity, which we call ‘S 1’ and ‘S 1off’, as also shown in Fig. 3. The position ‘S 1off’ is located at the northern edge of the IR nebulosity surrounding the early-type star S 1.

Figure 3: Three-colour image of  Oph W: red: MIPS 24m green: IRAC 4 at 8 m, dominated by the 7.7 m PAH band blue: 2MASS K-band image. and axis show offset RA and DEC from  Oph W, in degrees. The dashed black and white boxes indicate the extraction apertures for the Spitzer IRS spectroscopy discussed in Sec. 5.3 (the apertures near S 1 are narrower than the drawing line width, hence they appear to be linear and not boxy). The contours follow the 31 GHz emission, as in Fig. 1. The centre of the black circles indicate the positions of the early-type stars S 1, SR 3, and HD147889 (see Fig. 4).

3.3 FEROS and UNSW-MOPS observations

3.3.1 Feros

HD147889 is the main source of excitation in  Oph W so an accurate measurements of its spectral type is necessary. HD147889 is catalogued in SIMBAD as a single B2III/IV star (Houck & Smith-Moore, 1988). However Hafner & Meyer (1995) reported that HD147889 is a close binary. The spectral types they quote are B2 for both components, and luminosity class IV-V. Unfortunately Hafner & Meyer (1995) do not give details on their atmospheric models. Given the importance of HD147889 for  Oph W we undertook new echelle observations and up-to-date atmospheric modelling.

In order to precisely determine the UV field impinging on  Oph W we acquired echelle spectroscopy of HD147889 during 2 contiguous nights in May 2008 (ESO programme 081.C-2003). We used the FEROS echelle spectrograph, at the ESO 2.2 m telescope, which provides full coverage over 3500–9000 Å  at . We also found two spectra from Feb. 2006 in the ESO archive (programme 076.C-0164).

3.3.2 Unsw-Mops

The UNSW-MOPS333http://www.narrabri.atnf.csiro.au/mopra/mops/ spectrometer on the Mopra telescope, a 22 m single-dish, allows the acquisition of area-spectroscopy data cubes up to 0.6 km s in spectral resolution and with a bandwidth of  km s (in zoom mode).

Radio recombination lines (RRLs) are diagnostics of physical conditions. In particular low-frequency carbon RRLs have been reported from  Oph and other PDRs in reflection nebulae (Pankonin & Walmsley, 1978). We attempted to detect the high-frequency carbon RRL system of  Oph W using UNSW-MOPS. We acquired  arcmin on-the-fly scans centred on  Oph W and the following rest-frame frequencies (in GHz): in the K band, C65 23.41595, C66 22.37532, C67 21.39545, C68 20.47197, C69 19.60089, C70 18.77853, C71 18.00153, C72 17.26682, C73 16.57156, and in the W band, C42 85.73114 and C43 79.95252. All 9 K-band frequencies could be mapped simultaneously in zoom mode, for a total of 40 mn. The W-band map represented 2 h.

Data reduction was carried out with the “livedata” and “gridzilla” packages. We chose to resample the data cubes into 5 arcmin square pixels. The 1  noise was 0.366 MJy sr (or 43 mK) for C73, and 188 MJy sr (or 832mK) for C42. No lines were detected.

3.4 Additional archive data

The WMAP satellite (Hinshaw et al., 2007) provides low-resolution images of  Oph in 5 bands at 23, 33, 41, 61, and 94 GHz, with average beam-widths of 0.88, 0.66, 0.51, 0.35, and 0.22 deg, respectively. Despite their low resolution, the WMAP data allow the extraction of the radio spectral energy distribution (SED).

3.5 Additional archive data

The Parkes-MIT-NRAO survey at 5 GHz traces H i free-free emission from H ii regions (hereafter PMN survey, Condon el al., 1993, as presented in SkyView, http://skyview.gsfc.nasa.gov). The PMN survey at 5 GHz is strongly affected by flux loss, or missing low spatial frequency due to high-pass filtering. The  Oph W region includes extended negatives, indicative of survey artifacts. We estimated the level of filtering artifacts in PMN by comparing with diffuse H ii regions (selected from Lockman et al., 1996, hereafter LPH96) in the Effelsberg 2.7 GHz survey (Reich et al., 1990). We extract flux densities as in  Oph W (i.e. using a circular aperture 45 arcmin indiameter), and scale with a free-free index. The flux density recovered by PMN is 87% in the case of relatively compact RCW 6 (6 arcmin), 25% in LPH96 201.663+1.643 (15 arcmin, see also the analysis in Dickinson et al., 2006), and only 6% in LPH96 78.229+3.716 (a filament 1 deg long and 15 arcmin wide). It appears that the flux recovered by PMN in the case of  Oph W could be as low as 5–10 %.

Another probe of the diffuse emission in  Oph is the 2MASS survey http://www.ipac.caltech.edu/2mass/. The 2MASS-K image produced by the Montage444http://montage.ipac.caltech.edu/ mosaicing software, shown in Fig. 3 and 5, is an interesting comparison point with the CBI image (see Sec. 4.1 and Sec. 8.4.2).

Our analysis also makes use of the Southern H-Alpha Sky Survey Atlas (SHASSA Gaustad et al., 2001). Another map useful in constraining the radio properties of  Oph is that of Baart et al. (1980), who report a 2.3 GHz map of the  Oph region, with a beam of 20 arcmin FWHM.

4 Observed properties

4.1 Morphology

The most conspicuous feature in the CBI MEM model, also shown in Fig. 4 b, is the  Oph W PDR, at the origin of coordinates. The WMAP 33 GHz contours in Fig. 4b confirm the bulk morphology of the CBI image.

We indicate in Fig. 4a the positions of the early-type stars S 1 (Grasdalen et al., 1973), SR 3 (Elias, 1978, EM* SR 3 in SIMBAD, also known as Elia 2-16), and HD147889. These three stars, undetected in the CBI maps, excite the region and serve as reference points.

Inspection of Fig. 4c leads to the conclusion that the 31 GHz emission from  Oph is not the Rayleigh-Jeans tail of the sub-mm-emitting large dust grains (“standard dust” hereafter). If the 31 GHz emission was due to standard dust, it should follow 94 GHz and 178 m. Both ISO 178 m (in red in Fig. 4c) and WMAP 94 GHz trace standard dust. But the CBI contours are offset to the North-West. The peak in WMAP 94 GHz is separated by 14 arcmin from the peak in the CBI model. The 94 GHz dust has been resolved into a system of cold dust clumps by sub-mm bolometer arrays (e.g., Young et al., 2006; Ridge et al., 2006).

The PMN image in Fig. 4a shows two features: extended emission about HD147889, which having an H counterpart is a faint H ii region, and the point source LFAM 21 (J162700.0-242640*, 60 mJy at 5GHz, Gagné et al., 2004), undetected at higher frequencies. Also shown in Fig. 4a are contours at 10 and 20 of the visual extinction map from Ridge et al. (2006)555http://www.cfa.harvard.edu/COMPLETE. traces the total column density of material, i.e. the total mass density of the cloud.

Figure 4: Morphological evidence ruling out standard dust or optically thin H i free-free as the origin of the 31 GHz emission. and axis show offset RA and DEC from  Oph W, in degrees. The centre of the cyan circles indicate the positions of the early-type stars S 1, SR 3, and HD147889. a- CBI MEM contours overlaid on the PMN image (4.85 GHz), with in blue contours at 10 and 20. b- The CBI MEM image is shown in grey scale in MJy sr, with the same contour levels as in Fig. 1. WMAP 33 GHz is shown in blue contours at 2.52, 2.99, and 3.37 K. c- CBI MEM contours overlaid on an ISO colour map with 46m in blue and 178m in red. WMAP 94 GHz is shown in white contours at 1.21, 1.51, and 1.75 K.

Diffuse mid-IR emission (60 m) from  Oph is interpreted as stochastic heating of VSGs (Bernard et al., 1993). In the dust model of Draine & Li (2007) VSGs are regarded as large polycyclic aromatic hydrocarbons (PAHs). Only the smallest VSGs, or PAHs, can reach spinning frequencies of 30 GHz. Thus for spinning dust a close correspondence is expected between the CBI and mid-IR templates. There are indeed similarities between 31 GHz and ISO 46m (in blue in Fig. 4c): both are found near HD147889, while the far-IR emission is located about S 1 and to the south-east.

But there are important differences between the CBI image and the IR templates. In Fig. 3 we compare near- and mid-IR maps with the CBI contours. IRAC and MIPS aboard Spitzer provided high resolution mosaics of  Oph at near- and far-IR wavelengths. The dust-heating flux from S 1 produces the most conspicuous mid- and far-IR nebula in the entire  Oph region (e.g. the PAH 6.7 m band image in Abergel et al., 1996). Yet neither S 1 nor SR 3 have 31 GHz counterparts. It can also be noted that the photospheric IR emission is absent in the CBI maps (as is the case in LDN 1622, Casassus et al., 2006).

The IR emission shifts to longer wavelengths radially away from HD147789: at increasing wavelengths the emission from  Oph W moves to the N-E. It is surprising that the best match to the CBI contours of  Oph W turns out to be the 2.2 m diffuse emission in the 2MASS K-band, shown in blue in Fig. 3, and in grey scale in Fig. 5. The pointing uncertainty of the CBI is  arcmin (e.g. Casassus et al., 2006) - the phase calibrator J1626-298 was offset by only 0.2 arcmin from the phase centre. Thus the CBI data are sensitive to the 2 arcmin translation in  Oph W, when seen in MIPS 24m and 2MASS K-band.

The only 2MASS counterpart to the CBI contours are the emission peaks along  Oph W. The north-south extension of the CBI contours to the east of SR 3 is undetectable in 2MASS, but we note that this region has higher extinction than  Oph W (see Sec. 5.1).

Another conspicuous feature of the 2MASS image is the nebulosity about HD147889, which is probably the near-IR counterpart to the diffuse H ii region seen in PMN. An extended 2MASS source at J162622-242301, at ( and between S 1 and W, corresponds to the disk-like envelope surrounding the young stellar object GSS 30 IRS 1 (Chrysostomou et al., 1996).

Figure 5: The 2MASS-CBI correlation. The image is an overlay of the CBI MEM contours on the IRAC 8 m (left) and 2MASS K-band images (right). and axis show offset RA and DEC from  Oph W, in degrees. It may be appreciated that the 2MASS and IRAC 8 m emissions correlate with 31 GHz in  Oph W.

4.2 Spectrum

In Fig. 6 we have constructed the spectral energy distribution of  Oph A using the flux densities given in Table 1. The WMAP flux densities are extracted from a circular aperture equal to the CBI primary beam, without background correction.

Figure 6: The cm-wave spectrum in a 45.5 arcmin circular aperture centred on  Oph W. All data points are extracted from the WMAP images, except for the 2.3 GHz point, which is taken from Baart et al. (1980, see Sec. 4.4). The solid black line is a fit to the data that includes a modified blackbody, in green dotted line (with K and ), a diffuse free-free component, shown as a dash-dotted blue line, and in red-dashed line either a spinning dust component (a- spinning dust, for the ‘DC’ environment), or a cold C i thermal component stemming from an ensemble of PDR sheets seen edge-on (b- C ii).
2.3 23 31 33 41 61 94
2.2 12 7.9 14 13 13 31

Frequency in GHz. Flux density in Jy, with uncertainties of 20%. From Baart et al. (1980). From WMAP CBI flux density before correcting for flux loss.

Table 1: Observed flux densities inside the half-maximum contour of the CBI primary beam. Root-mean-square uncertaintes are of order 20%.

It is difficult to extract spectral index information from the 10 CBI channels because the coverage varies with frequency: flux loss, or the fraction of the flux density in the CBI 45 arcmin aperture that is filterout out, varies with both channel frequency and sky image. A template close in morphology to the 31 GHz emission could have been used to extract accurate channel by channel flux densities. But no such template is available. The cross-correlation between the CBI data and simulated visibilities on the prior image shown in Fig. 11e gave high reduced values () and correlation coefficients of . The MEM model itself cannot be used as a template in this case because it is limited in resolution by the dynamic range of the data.

The sub-mm continuum in  Oph A can be estimated from the WMAP 94 GHz and far-IR points, as a single modified black body with an emissivity index . For this purpose we used the IRIS (Miville-Deschenes & Lagache, 2005) reprocessing of the IRAS survey (Wheelock et al., 1991), and extracted flux densities in a circular aperture equal to the CBI primary beam (the ISO images lack coverage in the Eastern side of the photometric aperture). The observation of a sub-mm flux density is required to constrain the value of . We did not use the SCUBA maps of  Oph because they are strongly filtered. We estimated by comparison with the expected sub-mm continuum that the diffuse emission that is filtered out of the bolometer data in a 45 arcmin aperture can amount to 85%.

4.3 CBI flux loss

The CBI image is not sensitive to the lowest spatial frequencies; uncertainties in the comparison data are approximate and stem mostly from mismatched angular scales, not thermal noise. In particular the WMAP beam at 33 GHz is approximately Gaussian with FWHM49 arcmin (Bennett, 2003), so that the emission within the CBI beam is somewhat convolved with the surroundings. In turn, part of the flux at low spatial frequencies is filtered out in the interferometer data.

We have simulated CBI observations on two templates: IRAC 8m, after removing stars by median-filtering, and IRIS 1, a 12m template (Miville-Deschenes & Lagache, 2005). After renconstruction with a blank prior (as in Sec. A), we find that 41.3% of the IRAC 8m flux within the CBI primary beam is recovered by the simulation; and 51.4% in the case of IRIS 1. The same algorithm applied to the CBI visibility produces the image shown on Fig. 11d, and a flux density of 5.0 Jy, which when compared to 14 Jy in WMAP 33 GHz implies that the fraction of flux density recovered in the blank-prior reconstructions is 35%. But the image prior used in our best CBI reconstructions allow recovering part of the extended emission. Comparison of the flux density obtained from the restored image on Fig. 11a and with WMAP 33 GHz shows that, with the use of a prior, 56% of the signal is recovered by the CBI.

4.4 HI free-free

The WMAP 33 GHz and SHASSA images shown in Fig. 7 illustrate that  Oph W is superposed on an extended background, which is probably the free-free counterpart to the H emission. There are however intriguing features in Fig. 7: the bright H source to the south-west (a bright H ii region surrounding  Sco, known as Gum 65 or S 9) should correspond to 33 GHz free-free levels at least a factor of ten higher than seen in WMAP Ka. We believe this is due in part to dillution in the WMAP beam, but also to [N ii] doublet contamination in the SHASSA filter, which can be of order 50% in photoionised nebulae (e.g. in the Helix, see Sec. 2.3 in Casassus et al., 2004), or even higher in shocks. Nitrogen is found singly ionised in the outer bounds of ionisation-bounded nebulae, which are the surface regions sampled by the (extinction sensitive) SHASSA filter.

Figure 7: H and H i continuum towards  Oph. The Fig. shows an H+[N ii] image of the  Oph region, as extracted from SHASSA, and scaled to the corresponding K free-free continuum at 33 GHz, in MJy sr, without correction for reddening. The black and white contours follow WMAP 33 GHz, also in MJy sr. The SHASSA emission from Gum 65 to the south-west is traced in white contours at 1.0, 5.0, and 10 MJy sr. The circles indicate the positions of S 1, SR 3, and HD147789. and axis show offset RA and DEC from  Oph W, in degrees.

In the 2.3 GHz map of Baart et al. (1980) the CBI primary beam lies in a region of uniform emission, with a brightness temperature of 100 mK. The integrated flux density inside our photometric aperture is thus 2.2 Jy at 2.3 GHz, or 1.7 Jy at 31 GHz666Given that the CBI flux density measured from the blank-prior CBI image in Fig. fig:CBId is 5.0 Jy while WMAP 33GHz sees 14 Jy, of which 1.7 Jy are diffuse free-free, we obtain that the CBI recovers 40% of the non-free-free emission (consistent with Sec. 4.3, see also Sec. 8.5).

The PMN flux density in the 45 arcmin photometric aperture is essentially zero. Yet the SHASSA survey shows substantial diffuse H in the region of  Oph W. The total H flux in the CBI primary beam, if due to the diffuse 8000 K plasma discussed by Dickinson et al. (2003), implies that the free-free level at 5 GHz should be at least 2.5 Jy. After correction for the average value of extinction inside the CBI beam but outside the dark cloud itself, (Schlegel et al., 1998), or for , the predicted level of free-free emission could reach values of order 10Jy. Since the 2.3 GHz flux density inferred from Baart et al. (1980) is somewhat less than the minimum allowed by SHASSA, we conclude that the diffuse emission seen by SHASSA is also strongly contaminated by [N ii].

5 Dust emission

5.1 IR emission from dust grains

Bulk physical properties of the dust in  Oph can be obtained by fitting modified black bodies to the spectra extracted from each spatial pixel of the ISO data cube. A single modified black body turns out to give a fairly good fit, despite expected temperature gradients, especially from stochastic heating of the smaller grains (whose emission, as traced by IRAC 8 m for instance, is very different from that of the larger grains emitting at 100 m).

The grey-body parameters are the opacity at 100 m, , and , the dust temperature. The dust emissivity index is determined by its anticorrelation with dust temperature, as reported by Dupac et al. (2003): . is related to , the H-nucleus column density, by  cm (Draine & Lazarian, 1999b). Example infrared spectra are shown on Fig. 8.

Figure 8: Representative ISO LWS specific intensity spectra, at four selected positions in  Oph:  Oph W (circles), S 1 (pluses), HD 147889 (crosses) and SR 3 (asteriks, scaled by a factor 1.8 for clarity). The solid lines are best-fit grey-body spectra, as discussed in the text and summarised on Fig. 9.

The resulting temperatures, column densities and dust emissivities are shown in Figures 9a, 9b and  9c. The maximum value of in Fig. 9b is cm, and the temperature varies over 20–40 K. The early type stars S 1, SR 3 (see Sec. 8.1) are coincident with temperature peaks, as expected from grains in radiative equilibrium with the stellar UV radiation. But neither S 1 nor SR 3 correspond to peaks in column density. peaks close to S 1, but its morphology follows that of the  Oph A molecular core. Therefore the IR circumstellar nebulae about S 1 and SR 3 are radiation-bounded rather than matter-bounded.

Figure 9: Axes labels and symbols follow from Fig. 4. a- Dust temperature in gray scale, the CBI primary beam and the positions of S 1, SR 3 and HD147789 are indicated. b- The H-nucleus column density inferred from the far-IR ISO data. c- Dust emissivity (or temperature spectral index) inferred from the - anticorrelation of Dupac et al. (2003). d- Gray scale image of the product of the H-nucleus column densty times the dust temperature , in units of  m K. Also shown are the lowest and highest contours of the CBI MEM models, at 0.067 and 0.197 MJy sr.

The total mass in the ISO field, , is 922 M. Considering the numerous assumptions implicit in converting dust emissivities to H-nucleus densities, this mass estimate is consistently close to  2500 M given by Liseau et al. (1995, 1999). But the mass seen by ISO is much less than the 7400 M derived from the near-IR extinction (Ridge et al., 2006). Perhaps the extinction has been overestimated, or there are very cold regions in  Oph not sampled by ISO.

We also obtain a mass of 65 M for  Oph W, if its extension is defined by a 31 GHz intensity threshold of 0.124 MJy sr in the MEM model (see Fig. 1). The mass above a 31 GHz intensity threshold of  MJy sr) is 359 M.

5.2 Magnetic dust

The magnetic dipole emission from magnetic fluctuations in ferromagnetic grains results in a cm-wave enhancement of the grain emissivity (Draine & Lazarian, 1999). At cm-wavelengths classical (not VSG) dust is in the Rayleigh-Jeans regime, so that magnetic dust emission should be proportional to the product of the column of ferromagnetic grains and their temperature. Under the assumption that ferromagnetic grains, if they exists, are uniformly mixed with the rest of the dust, the CBI image should be proportional to the product of the dust column and temperature for constant dust-to-gas ratio ().

It can be seen in Fig. 9d that the morphology of the CBI MEM contours is very different from that of the product , which instead follows the far-IR emission. Since we cannot find any reason why ferromagnetic grains, if they exist, would be found preferentially in  Oph W, we conclude that magnetic dust is inconsistent with the ISO data.

Another difficulty for magnetic dust is the lack of detectable polarization. Draine & Lazarian (1999, their Fig. 9) predict polarization fractions from perfectly aligned ferrogmanetic grains. For their hypothetical material ’X4’ the predicted fraction at 31 GHz is at least . X4 is the only material considered by Draine & Lazarian (1999) whose emissivities reach the levels required by the anomalous foreground. Martin (2007, his Table 2) quantifies the degree of grain alignment through a reduction factor , which ranges from 0.19 to 0.67 for a wide variety of grain geometries. Thus the polarization expected from magnetic dust is at least 4.7%. However, the CBI data place a strict 3  polarization upper limits of 4.8% in the specific intensity at the peak in  Oph W - and only 1% in the 45 arcmin photometric aperture.

5.3 Spinning dust

The spinning dust emissivities, being linear proportional to the density (as dust emissivities in general), could be more important in diffuse media relative to emission mechanisms based on binary encounters, which are quadratic in . With its very steep low frequency spectral index, , spinning dust explains the lack of low-frequency emission.

Spinning dust gives a remarkably good fit to the  Oph W SED (see Fig. 6) if , which is within the range of observed values (Dupac et al., 2003). Higher emissivities result in a drop at 60–90 GHz, which misses the WMAP 94 GHz data point. The best fit spinning dust spectrum is obtained for the ’DC’ case of Draine & Lazarian (1998b). Spinning dust requires that the product  cm, where is the volume filling factor.

No local 31 GHz peaks are observed at the positions of S 1 and SR 3. Although part of the emission surrounding S 1 and SR 3 could be scattered light in IR reflection nebulae, the Spitzer IRS area-spectroscopy highlights very bright PAH bands in the circumstellar nebulae around S 1, SR 3 and  Oph W. The absence of S 1 and SR 3 in the CBI data may be inconsistent with spinning dust, since the proximity of early type stars should result in high spinning dust emissivities, provided VSGs are not depleted. The environment around S 1 corresponds to the ’RN’ case of Draine & Lazarian (1998b): the Castelli (2003) model atmospheres give a UV flux parameter (as defined in Draine & Bertoldi, 1996). In this case the predicted spinning dust emissivity per unit H-nucleus column density is  Jy sr cm at 31 GHz. The observed column densities towards S 1 is  cm (see Sec. 5.1), so the emergent 31 GHz intensity from S 1 should be 1 MJy sr, which is a factor of 10 larger than the observed peak 31 GHz intensities (which are found in  Oph W and not toward S 1), and a factor of 40 larger than a strict upper limit of 25 10 MJy sr in S 1 (see Table 2).

We can take into account the possibility of VSG depletion by examining the ratios of PAH and 31 GHz intensities. The dust-heating radiation field can be parametrised, as in Draine & Li (2007), by scaling the interstellar radiation field in the solar neighbourhood (Mathis et al., 1983). The dimensionless parameter measures the average intensity of radiation in 4 sr, integrated from 0.09 to 8 m. The spinning dust emissivity per nucleon is remarkably independent of the intensity of UV radiation (Draine & Lazarian, 1998b, their Fig. 9), while the flux in the PAH bands is linear in (for instance see Fig. 13 in Draine & Li, 2007). Therefore, if PAHs are involved in the 31 GHz emission, the intensity ratio should be inversely proportional to . is independent of the PAH abundance since it enters linearly both in and . Given that the spinning dust emissivities per nucleon (Draine & Lazarian, 1998b) vary by at most a factor of 10 for environments with extremely different physical conditions, we can conservatively assume that should not vary by more than a factor of 10 when comparing widely different regions.

The IRS data allow extracting fluxes for the PAH band at 11.3 m, m), in two rectangular apertures near S 1, one near SR 3, and one in  Oph W, indicated as black and dotted-white boxes on Fig. 3. We subtracted a linear continuum under the 11.3 m band, as well as a sky background PAH 11.3 m intensity of  W m sr, obtained by scaling the observed PAH intensities following the IRAC 8 m image. The background PAH intensity is only 5 times fainter than observed in the S1 off aperture ( W m sr before background correction).

Until we obtain higher-resolution data our estimates of the 31 GHz specific intensities are dependent on the MEM model. In the brightest regions, as in  Oph W, we assume 10% uncertainties. The product of the IRS extraction solid angle times the CBI intensity at the centroid of the  Oph W aperture is an approximation to GHz), the 31 GHz flux density. For the fainter regions we use the prior that the emission is due to spinning dust (which is the aim of this test): The circumstellar nebulae around S 1 and SR 3 are 3 arcmin in diameter and so should appear as point sources in the CBI maps. A formal fit to the MEM visibility residuals for point sources at the locations of S 1 and SR 3 gives 31 GHz flux densities of 1.3 mJy and  mJy, repectively, which can be converted into intensities assuming uniform nebulae. For S 1off we scale the 31 GHz intensity in the S 1 aperture by the product of PAH 11.3 m intensities times (i.e. as the inverse squared projected distance).

The unattenuated intensity of dust-heating radiation, parametrised by , can be evaluated at the projected distance from the exciting stars to the centre of each IRS aperture, using the model atmospheres of Castelli (2003)777 as given in http://wwwuser.oat.ts.astro.it/castelli/grids.html and the stellar parameters given in Sec. 8.1. We obtain the properties listed in Table 2. Taking into account the uncertainties, the product is consistent with variations by less than a factor of 10. A marginal exception may be the comparison between S 1off and  Oph W, where the 31 GHz uncertainties are reduced relative to S 1 because of the hypothesis that the 31 GHz intensity in S 1off scales with relative to S 1. In the S 1off -  Oph W comparison, taking 3  shifts in can bring its variations down to a factor of 4, and so in agreement with spinning dust.

A source of uncertainty is the correction for UV attenuation, which may affect all lines of sight in Table 2. Attenuation is most important for S1 off, since the circumstellar nebula around S 1 is probably ionisation-bounded (see Sec. 5.1). The value in Table 2 is therefore an upper limit. Similarly for SR 3, which is obscured in the visible. On the other hand S 1 is bright in the visible, so its circumstellar nebula stems from the walls of a wind-blown cavity driven by S 1 into the  Oph A core. Thus UV attenuation should be negligible in the S 1 IRS aperture. According to the model of Liseau et al. (1999), HD 147889 is separated from LDN 1688, so that its UV luminosity should be fairly unatenuated towards  Oph W.

 Oph W 27.52.7 66 2.20.2(-1) 3.3(-6) 10.4
SR 3 1.23.2 238 3.28.4(-3) 3.8(-6) 0.97
S1 1.04.9 1076 1.78.4(-3) 1.1(-5) 0.92
S1 off 1.01.1 246 5.25.9(-4) 8.0(-7) 1.92

Normalized to the value in the S 1 off aperture. Unattenuated UV field parameter. CBI MEM specific intensities in MJy sr. PAH 11.3m intensity in W m sr. Projected distance from exciting star, in arcmin. parenthesis indicate a power of ten exponent multiplying both the average values and their uncertainties.

Table 2: Observations derived from the CBI and PAH 11.3 m intensities in the Spitzer IRS apertures.

Could physical conditions in S 1 and SR 3 be such that spinning dust is quenched by mechanisms not contemplated by Draine & Lazarian (1998b)? The possibility of vanishing grain polarization can be discarded. According to the PAH ionisation diagnostic of Draine & Li (2001, their Fig. 16), the PAH band fluxes given by Boulanger et al. (1996), extracted from an aperture 10 arcmin north of  Oph W, correspond to neutral PAHs. Any photoelectric charge expected in the intense UV-fields of S 1 and SR 3 increases quadratically the spinning dust emissivity (Eq. 11 in Draine & Lazarian, 1998b). But it could be that the radiation field from HD 147889 is sufficiently hard to boost the spinning dust emissivity through VSG-ionisation, and yet not completely deplete the grains. We used the IRS spectra to place S 1 in the PAH-colour diagram of Draine & Li (2001, their Fig. 16), finding it lies close to  Oph W - i.e. at the locus of neutral PAHs. Another interesting possibility is that perhaps PAH rotation brakes to lower frequencies in the vicinity of SR 3 and S 1, maybe as a consequence of grain alignment in intense magnetic fields (which are not considered in Draine & Lazarian, 1998b).

Yet another alternative to explain the lack of 31 GHz emission from S 1 and SR 3 is that the spinning VSGs are not related to PAHs, so that they do not emit in the PAH bands. For instance they could perhaps be nano-silicates (e.g. Witt et al., 1998) very fragile to UV radiation, or maybe chain-like carbonaceous molecules. If so the existing spinning dust models must be revised, since they are calculated for aromatic carbonaceous grains, including a population of sheet-like grains (i.e. PAHs).

Iglesias-Groth (2006, 2005) has proposed hydrogenated fullerenes as a carrier for the 31 GHz emission. Perhaps the polarized fulleranes could be depleted near S 1 and SR 3. But at present we lack diagnostics of such fulleranes to test this alternative. As proposed by Webster (1992) fulleranes could also be the carriers of the diffuse interstellar bands (DIBs). Spectroscopy of stars in the background of  Oph W is required to examine the possibility of a link between the DIBs and the anomalous foreground.

6 C i continuum

6.1 Cold plasmas in PDRs

The outer layers of molecular clouds are composed of atomic hydrogen. The ionisation energy of H is 15.4 eV, while the H dissociation continuum starts at 14.7 eV, both of which are attenuated by H i ionisation. In practice H photodissociation occurs in the radiative cascade following bound-bound absorption of photons with discrete energies in the range 11.3 – 13.6 eV (e.g. Tielens, 2005). Thus the bulk of the  Oph cloud is largely neutral.

All photons harder than 13.6 eV are absorbed in the vicinity of HD147889, producing a  arcmin diffuse H ii region (about 0.2 pc in physical size). Yet a residual charge density exists in the neutral layers of  Oph exposed to radiation from HD147889. C-ionising photons with energies in a continuuum between 11.3 eV and 13.6 eV penetrate deep inside the exposed neutral layers of  Oph W. C-ionisation extends into molecular layers. Other metals with ionisation potentials inferior to 13.6 eV, most notably sulfur, also contribute to the ionisation fraction , but in proportion to their abundance.

Another source of ionisation in molecular clouds is the cosmic-ray ionisation of H. For an isolated molecular cloud subjected to the average interstellar cosmic ray ionization rate , molecular line observations have yielded . Specifically for  Oph Wootten et al. (1979) give . However the molecular line diagnostics in Wootten et al. (1978) trace the dense core in  Oph A, and may not be representative of  Oph W. Is it possible that in  Oph W the vicinity of HD147889 increases sufficiently so that H also contributes to ? Probably not, since the ratio of projected distances between  Oph A and  Oph W to HD147889 is 2, which would only raise by a factor of 4, and yield an value still 2 orders of magnitude below the carbon abundance.

6.2 C i model

Here we estimate the expected intensity levels of free-free emission due to C encounters with free electrons (C i continuum) from the cold plasma in  Oph W. Although the ionisation fraction in PDRs is very small, , the free-free emissivity is and biased towards lower temperatures. A temperature of 50 K is representative of most of the emissivity-weighted C ii region in the models of Liseau et al. (1999) and Habart et al. (2003). A shortcoming of the present model is that it requires a clumpy medium with very high H-nucleus densities, of order  cm, and small volume filling factors, .

The available data lead us to consider an ensemble of dense neutral clumps, with an ionisation fraction (the abundance of C), a total extent  arcmin, and covering a solid angle . Since  Oph W is undetected in the HRAO data of Baart et al. (1980), with a 20 arcmin beam and a rms sensitivity of 30 mK, at 2.3 GHz the total emission from the clumps should be less than Jy. The total flux density seen by WMAP at 33 GHz and not attributed to H i free-free is 12.3 Jy. Thus the clumps must be optically thick at 2.3 GHz, and cover a solid angle inferior to  arcmin, where is the Planck function. Additionally, the clumps, while still optically thick at 5 GHz, are not detected in PMN, with a beam  arcmin FWHM and an rms noise of 100 mJy beam = 0.67 MJy sr888in which we have taken into account correlated pixels with a factor , where is the number of pixels that fall in one 3.7 arcmin beam. Therefore an individual clump must be beam-diluted in PMN and cover a solid angle less than .

As discussed in Sec. 4.2, the CBI sees about 30–40%999this is the ratio of 31 GHz flux densities obtained without the use of a prior to the WMAP 33 GHz flux densities of the total 31 GHz emission. The clump distribution should be sufficiently dense so as to mimick a uniform signal at CBI resolutions, while also extending to . Thus the inter-clump separation should be (a) less than 8 arcmin, the highest spatial frequency in the CBI -plane for the configuration used here, and (b) greater or similar to the PMN beam. To make headway, we will assume a number of clumps .

A plane-parallel geometry seen edge-on gives the highest clump opacities. To maximize the cold free-free opacity given an electron density, each clump would have to be in length, equally deep, and only arcsec wide. Higher densities alleviate the need for such large aspect ratios.

What is the density required to explain the 31 GHz flux density with a cold plasma, if we ignore the lower frequency data? In a uniform disk nebula 10 arcmin in diameter, and equally deep, with a C ii region temperature of 150 K, we find that electron densities of 60 cm reach the observed 31 GHz level. The same result is arrived at by fixing the opacity profile to that of the CBI MEM model. Thus H-nucleus densities of only  cm (within the range observed in  Oph W, see Sec. 8.2) account for all of the CBI flux.

6.3 SED fit

The C i continuum model shown in Fig. 6 b consists of a clump ensemble with , an electron density of 750 cm, and  K. Each clump is a narrow sheet only 2 arcsec wide101010We chose 2 instead of 4 arcsec to better accomodate the 2.3 GHz point, 3.7 arcmin long, and equally deep. The corresponding volume filling factor is . Uniform disk clumps, with equal depth and diameter and subtending the same solid angle as the sheets, would require electron densities of 2200 cm. We favour a sheet-like geometry because of the considerations in Sec. 8.1: The thin sheet geometries could result from limb-brightening of a C ii shell centred on HD147889.

The total H-nucleus densities required by the C i model, whatever the geometry of the clumps, are of order  cm, if all of C is ionised. The corresponding C ii region mass is 153 M for sheets, or 45 M for disks, both of which are consistently less than the total mass enclosed by regions with finite (see Sec. 5.1).

In order to further test the C i continuum model we searched the ATCA archive for pointings near  Oph W.  Oph 10 (also known as Doar 21; Encrenaz, 1974) was observed in aray configuration C397, at frequencies of 1376, 2378, 4800 and 8640 MHz111111ATCA programme C397, PI E. Feigelson. The phase centre lies in the 31 GHz  Oph W ridge, 2.2 arcmin south of the peak. At 4.9 GHz the ATCA primary beam is 5 arcmin. Yet no clumpy medium is detected with a noise of 5mJy/beam. Clearly the putative C  i clumps, if they exist, should be beam-dilluted even inside the 127 arcsec beam: the optically thick flux density in one synthetic beam is 160 mJy, if K. Very thin sheets,  1 arcsec wide, could still fit in.

7 Radio recombination lines

Radio recombination lines (RRLs) are concomitant to free-free continua. Carbon RRLs have indeed been observed towards  Oph, albeit at low resolutions (Brown & Knapp, 1974). Here we provide upper limits on the RRL system in  Oph W, which require rather cold C ii regions ( K).

7.1 RRL data from the literature

Pankonin & Walmsley (1978) examined the most complete set of RRL data towards  Oph to date. They mapped the neighbourhood of S 1, but did not extend their coverage to  Oph W, unfortunately. The highest frequency RRLs considered by Pankonin & Walmsley (1978) are C90 and C91, at 9 GHz, which they interpreted as stemming from circumstellar gas about S 1, with electron densities cm and K. This circumstellar C ii region was inferred to be less than 2 arcmin in diameter, and surrounded by a diffuse halo with cm, traced by the lower frequency carbon RRLs. The continuum level expected from such a C ii region is 1 mJy at 31 GHz, consistent with its absence from the CBI MEM model.

7.2 CBI limits on Ka-band RRLs

The brightest carbon RRLs expected in the 10 CBI channels are C57 to C62. Four 1 GHz wide channels, centred at 27.5, 30.5, 33.5, and 35.5, are free from RRLs. Yet the CBI flux densities in each channel, inferred by cross-correlation with a processed IRAC 8m template, are scattered about a single power law; no decrement is seen in the four channels devoid of RRLs. A 1  upper limit to the contribution of RRLs in a single channel is given by the rms dispersion about the best fit power-law, of  Jy.

The expected RRL flux in the CBI channels is quite close to the above upper limit. In the C ii region model of Sec 6, the flux density from C62, at GHz, in the 1 GHz wide CBI channel centred on 26.5 GHz, is 0.6 Jy under LTE conditions. However, for the excited energy levels leading to the emission of photons are severely depopulated relative to LTE at 150 K (Salem & Brocklehurst, 1979; Walmsley & Watson, 1982)121212We have cross-checked our calculations against those in Pankonin & Walmsley (1978) and Eq. 3 in Heiles et al. (1996). The exact level population in is very sensitive on temperature and dielectronic recombination. The value given by Walmsley & Watson (1982, their Fig. 3) is , relative to LTE, implying a C62 contribution of 0.3 Jy, which should be detectable by the CBI131313We have neglected the effects of stimulated emission, accounted for in the coefficient of Walmsley & Watson (1982, their Fig. 5), because for the transitions considered here. Lowering to 50 K brings the predicted RRL flux down to 3 , i.e. marginally consistent with the CBI upper limit.

7.3 Mopra limits on K- and W-band RRLs

The detection of the RRL system of  Oph W in the C i model of Sec 6.3 would be very difficult. The ensemble of clumps is optically thick below 10 GHz. At higher frequencies the excited energy levels leading to the emission of photons are severely depopulated relative to LTE (Salem & Brocklehurst, 1979; Walmsley & Watson, 1982).

We nonetheless attempted to detect the RRL system of  Oph W using the UNSW-MOPS spectrometer (Sec. 3.3.2), and found no RRLs at the expected radial velocity, km s (Brown & Knapp, 1974; Pankonin & Walmsley, 1978). With the line profiles observed at lower frequencies, of 1.5 km s FWHM, we can estimate the expected contribution of RRLs in the Mopra datacubes and place upper limits on the high frequency RRLs.

The ensemble of C ii clumps subtends a solid angle of less than  arcmin. If there are clumps spread uniformly over 2020 arcmin, then only one clump is expected on average in each 5 arcmin pixel. The expected intensity from one clump, covering about  arcsec is diluted in 55 arcmin. At K, the emergent peak LTE intensity in C73 from one clump is 1262 MJy sr, or 2.97 MJy sr when diluted in the 5 arcmin pixels. In dense and cold gas dielectronic recombination enhances the LTE departure coefficients to . Thus with a 3  upper limit of 1.1 MJy sr on C73, the Mopra data rule out ‘warm’ temperatures (note that collisionally excited lines, such as [C ii] 158m, are biased towards higher temperatures). By contrast, at K, the peak LTE RRL intensity in 5 arcmin pixels is 0.38 MJy sr, and , so that the expected C73 intensity is only 0.12 MJy sr - consistent with its non-detection.

In the W band the coefficients are vanishingly small at 20 Ktemperatures. For C42 and K, we approximate to the case of Salem & Brocklehurst (1979) (for and with a 100 K background): . The expected C42 intensity in the 5 arcmin pixels is  MJy sr, while the rms noise is 188 MJy sr.

8 Discussion

The [C ii] 158 m image of  Oph A by Yui et al. (1993), with a 15 arcmin beam, shows that C is present and that [C ii] 158 m shares a similar extent as the cm-wave continuum. It is remarkable that S 1 is not coincident with a [C ii] 158 m peak. In this Section we discuss the likely emission levels of C i continuum in the  Oph environment, and consider the possibility of combining both C i and spinning dust.

8.1 Exciting stars

8.1.1 Hd147889

Atmospheric parametres for the two components of HD147889 were obtained by fitting “Tlusty” non-LTE model atmospheres (Lanz & Hubeny, 2007) to the FEROS spectra (Sec. 3.3.1), with rotation velocities of 50 and 30 km s respectively, and a surface area ratio of 1.3. The temperatures are 23000 and 20000 K and the surface gravity is 4.25 for both components ( or are ruled out). The surface gravity is determined mainly from the strength of the line wings of H. However, this strength also depends on the temperature. The temperature mainly comes from the strength of He i and as compared with Mg ii and the Si iii triplet 4552, 4567, 4573.

The heliocentric velocities of each component were +64, 99 km s on UTC = 2006-02-07,  km s,  km s on UTC = 2008-05-16, and  km s,  km s on UTC = 2008-05-17. This gives us a systemic heliocentric velocity of km s, or a local standard of rest velocity of km s (so equal to that of the carbon RRLs), and a mass ratio of 1.3.

If the two components of HD147889 are on the main sequence, as indicated by their surface gravities, then the stellar radii and masses can be inferred by interpolating the zero-age main-sequence models of Schaller et al. (1992). We obtain radii of 3.52 and 3.10 R, and masses of 8.31 and 6.36 M. But it must be borne in mind that the IR excess of HD147889 and its interaction with the  Oph star forming cloud make it a likely pre-main sequence star, in the sense that it is still contracting towards the zero-age main sequence. The models of Behrend & Maeder (2001, their Table 1) show that at an age of  yr (so close to  yr, the approximate lifetime of dark clouds), a 12 M star would still be contracting, with a surface temperature of  K and a radius of 10.3 R. To make headway the spectral types we adopt are B2IV and B3IV, but we note that we lack a precise measurement of the stellar luminosities.

The line of sight to HD147889 appears to be strongly affected by extinction from LDN 1688. The H-nucleus column density map reported in Sec. 5.1 gives  cm in the direction of HD147889, or using the conversion factors from Draine et al. (2003) with . The map from Ridge et al. (2006) gives at the position of HD147889. However, a comparison between the observed colour and that expected from the model atmospheres from Castelli (2003) gives (or ). Yet the stellar radii inferred above require extinction values to be compatible with the photometry. Hence the extinction towards HD 147889 is manifestly very structured on small scales, and requires an exceptionally large or higher if HD 147889 is still contracting.

8.1.2 S 1 and SR 3

S 1 is a close binary system composed of a B4V star (Lada & Wilking, 1988) and a K-type companion with a 10 mJy peak at 10 GHz (including its 2 mJy radio halo, André et al., 1988). For S 1, K, and surface gravity . The spectral type we adopt for SR 3 is B6V (Elias, 1978), or K, . Lada & Wilking (1988, their Sec. IIIb) and Bontemps et al. (2001) give bolometric luminosities for S 1 and SR 3. For S 1, , which is consistent with B4V, but for SR 3, , which is too low for B6V. The spectral type of SR 3 is probably closer to B9V.

8.2 Physical conditions

The 1.1 mm continuum data in Young et al. (2006) are strongly high-pass filtered and trace the smaller angular scales. They find an average density of cm in 44 molecular cores containing 80 M, or about 1/20–1/100 the mass of the entire  Oph complex (see Sec. 5.1).

A density of is given by Liseau et al. (1999) from PDR models of the far-IR line ratios. They fit [O i] 63, 145 m, while the [C ii] 158m levels can only be reproduced with  cm and an unrealistically low field . Higher densities than cm are required to accomodate inferred by Liseau et al. (1999). They treated HD147889 as a main sequence star, and used a distance of 150 pc. With the Hipparcos distance to HD147889 of 135 pc and luminosity class IV we obtain , using the model atmospheres from Castelli (2003).

Bypassing the PDR models, we can infer a H-nucleus density from the [C ii] 158m cooling rate (e.g. Tielens, 2005, his Eq. 2.67). The fluxes from Liseau et al. (1999) then give cm for temperatures of K and a filling factor . Note, however, that the critical density of [C ii] 158m is 2.7 10 cm at 100 K, so that it does not trace the dense clumps required by the C i continuum model.

8.3 C i Strömgren spheres

The model atmospheres from Castelli (2003) predict that the C-ionizing luminosity of HD147889 is 25 times that of S 1 and 612 times that of SR 3. From its vantage point at the back of the  Oph main cloud HD147889 illuminates the entire cloud (Liseau et al., 1999). By contrast S 1 is surrounded by its disk-like circumstellar nebula (which probably stems from the clumpy walls of a wind-blown cavity, see Sec. 5.1). Since S 1 is optically visible a fraction of its UV luminosity escapes. The small part of it’s carbon-ionising flux that is absorbed in the dense circumstellar disk radiates a meagre 2 mJy at 5 GHz (André et al., 1988).

If the C ii regions of  Oph are ionisation-bounded nebulae their average electron density is given by ionisation balance: , where is nebular volume and is the stellar luminosity in C-ionising photons (below H-ionising energies). We use the total recombination coefficients from Nahar & Pradhan (1997), assuming K. For optically thin radiation, the total C ii region flux density is

(1)

where is the Planck function, and is the C i free-free opacity for unit electron density.

For S 1, we obtain  s, which for a closed geometry should give an integrated flux density of 458 mJy at 31 GHz. S 1 is not detected in the CBI maps. In Sec. 5.3 we report a 31 GHz point-source flux density of 1.3 mJy for S 1. It appears that the circumstellar nebula around S 1 must be disk-like, or else sufficiently clumpy that 90 % of C-ionising photons escape the nebula. This is consistent with the fact that S 1 is an optically visible star (by contrast with SR 3).

For SR 3 we have  s. The predicted flux density in a closed geometry is 20 mJy at 31 GHz, consistent with its non-detection by the CBI (the 31 GHz point-source flux density of SR 3 is  mJy).

If HD 147889 has settled on the main sequence, we find s, and an upper limit for the 33 GHz flux density of 6.5 Jy. The background-subtracted 33 GHz flux density inside the CBI PB aperture of 45 arcmin is 6.7 Jy, of which 1.5 Jy stem from the diffuse H ii region surrounding HD 147889. This is close to the levels required for an ionisation bounded and spherical nebula. But part of the C-ionising radiation should escape the nebula. Thus for the C i continuum interpretation it is necessary that HD 147889 be a pre-main sequence binary star that is still contracting, with a primary stellar radius of about 4.5 R, and a mass of 10 M, so that to 4.5 (as inferred from the FEROS spectroscopy), and a secondary mass of 7.7 M.

The C ii Stromgrën sphere around HD 147889 extends out to 10 arcmin, the projected distance to  Oph W. For a filled sphere, the required electron density is 100 cm, implying H-nucleus densities of cm. Such a C ii region would be optically thin at 5 GHz and reach 10 Jy, which is ruled out by the data. Thus the C ii region around HD 147889 must be a thin shell, as indicated by the geometry of  Oph W. However, in order to reach the densities required by the SED model of Fig. 6, the thickness of the  Oph W C ii region should be only 2–3 arcsec, which is surprisingly thin. Such a thin shell could be replaced by an ensemble of flat clumps seen edge-on (see Sec. 6.3).

We have modelled the C ii regions in  Oph using the Cloudy photoionisation package (version c07.02.01, last described by Ferland et al., 1998). We treat  Oph W as a shell in an open geometry, separated from HD147889 by its projected distance, while S 1 and SR 3 are embedded in ionisation-bounded circumstellar nebulae, with a fiducial inner radius of  cm. The predicted C ii layer in  Oph W is extremely narrow, with a width 1.2 arcsec at densities  cm, which is consistent with the thin ridge model. The solid angle subtended by the C ii region in  Oph W, which consists of an ensemble of sheets, each 3.7 arcmin long, is about  arcmin. This is a factor of 100 larger than in the C ii regions around S 1 and SR 3 (if the H-nucleus density is constant at 10 cm).

8.4 Origin of the 2MASS diffuse emission

The 2MASS K band emission from  Oph W is coincident with the 31 GHz ridge. What is the nature of the nebulosity seen in the 2MASS J,H, and K images? All three 2MASS bands share a similar morphology with the IRAC images, although not exactly coincident.

8.4.1 Problems with near-IR scattered light, VSG continuum, and free-free

We estimated that the diffuse intensities in  Oph W drop at shorter wavelengths, in ratios J:H:K 141414we used the zero points for the Montage mosaics, took the median intensity values in a square box 20 pixels on a side, centred on J2000 16:25:57.88 –24:21:11.7, and subtracted a median background extracted from a similar box but centred on J2000 16:25:58.10 –24:14:42.4. This is at odds with the colours expected from scattered light. Paodan et al. (2006) calculate that the emergent intensities of scattered light in neutral clouds should increase by a factor 4 from K to J. These ratios are unlikely to be affected by extinction. The interstellar extinction towards  Oph, excluding intra-nebular extinction, can be estimated from the value of the colour excess E(B-V) in the maps of Schlegel et al. (1998). Near  Oph but outside any dust clouds extinction is very low, , as expected for Gould belt clouds, which raises the J band intensities by a meagre 3%.

On the other hand, even at 150 K the C i continuum is cut off by its Wien tail above m, and is 30 times fainter than the 8 m nebulosity seen in the IRAC 4 image at 8 m. It is unlikely that the 2MASS images trace a 1000 K C plasma because the solid angle of  Oph W in the K-band image is about 5 arcmin, which would give an optically thick continuum of  Jy at 5 GHz 151515note, however, that the the faint continuum from the diffuse H ii region about HD147889 is at 7000 K and present in the K-band.

Is it possible that the near-IR continuum stems from a VSG population sharing a similar morphology as the PAHs that emit in the IRAC bands? We note that the circumstellar nebulae around S 1 and SR 3 are also seen in the 2MASS K-band images, with JHK colours as for  Oph W and discrepant from that of scattered light. Sublimation dust temperatures of 1000 K are required to explain the S 1 and SR 3 nebulae in terms of large dust grains. So it is likely that the same VSGs that would account for the  Oph W near-IR emission would also be found in S 1 and SR 3. We return to the discussion on spinning dust in Sec. 5.3.

8.4.2 Rovibrational H

An interesting alternative to the VSG continuum is the possibility that the J, H, and K-band emission in  Oph W stems from H rovibrational lines. Habart et al. (2003, their Fig. 2) present a (1-0)S(1) H image, in which it may be appreciated that  Oph W is slightly offset by 10–20 arcsec to the S-E compared to the ISOCAM PAH emission in the LW2 filter (5–8.5 m). There is also a hint of a shift in Fig. 5 between 2MASS K-band and IRAC 8m, which may be explained if 2MASS K is mostly due to rovibrational H and IRAC 8m to PAHs. Here we use the Spitzer spectroscopy to further investigate relationships between H, PAHs, and 31 GHz.

The IRS data on  Oph W allows estimating the intensity of the pure rotational lines H S(1) and S(2), in the same manner as used in Sec. 5.3 for the PAH 11.3 m band. Table 3 lists the H line fluxes in the spectra we analysed. They are consistent with Table 1 of Habart et al. (2003).

 Oph W SR 3 S 1 S 1 off
H(0-0)S(1) 3.66(-7) 1.55(-7)
H(0-0)S(2) 2.94(-7) 1.86(-7) 1.02(-8) 2.75(-9)

The power of ten exponent is indicated in parentheses.

Table 3: Spitzer IRS H line intensities in W m sr.

A tentative correlation between the H fluxes and 31 GHz intensities can be inferred from a comparison between Table 3 and Table 2. Note that in the specific case of SR 3, the 31 GHz intensity towards SR 3 should be , as measured in the 31 GHz image, and not as tabulated in Table 2 (where we are testing for 31 GHz counterparts to the mid-IR compact source around SR 3). H is weak or undetected in the positions of low 31 GHz intensities (i.e. S 1 and S 1 off), despite the coincidence with the peak mid- and far-IR intensities, while H is bright at the 31 GHz peak (i.e. on  Oph W) and in SR 3. The H lines are undetected towards S 1. The values reported in Table 3 for S 1 and S 1off are upper limits derived from formally extracting the H2 line flux, despite the absence of visible lines.

In the molecular layers of PDRs the C-ionising UV radiation also excites the electronic states of H, which then decay in a rovibrational cascade leading to the observed near-IR fluorescent lines. The conditions in  Oph W are very similar to those found in NGC 2023. Black & van Dishoeck (1987) reproduce the near-IR H line system of NGC 2023 with an incident UV specific intensity field of in units of the 1000Å  UV background at the solar neighbourhood. For  Oph W we find that , if HD147889 is on the main-sequence, or higher if it is still contracting. The more recent models of Habart et al. (2003) demonstrate that the near-IR H lines in  Oph W are fluorescent.

Therefore in the C i model we expect that the 31 GHz continuum be coincident with fluorescent H. The 2MASS-CBI match in  Oph W could then be explained if the 2MASS filters are dominated by H line emission.

Given the H(1-0)S(1) intensity map of Habart et al. (2003), we estimate that ro-vibrational H accounts for all of the diffuse 2MASS K flux seen in  Oph W. H(1-0)S(1), on its own, accounts for  20% of the 2MASS K-band specific intensities. The exact contribution is difficult to estimate because the diffuse nebulosity in 2MASS is at a very low level. The noise in 2MASS K is 0.35 MJy sr, while the peak intensities above background in  Oph W are  1MJy sr. The H(1-0)S(1) line, if diluted in the K filter, corresponds to intensities of 0.2 MJy sr (using the H(1-0)S(1) image in Habart et al., 2003, their Fig. 2). Table 3 from Black & van Dishoeck (1987) allows to estimate that H(1-0)S(1) represents 21.8% of the total H contribution in the 2MASS K filter. Therefore H ro-vibrational emission can account for the entire 2MASS K band flux.

8.5 Both C i and spinning dust?

This work focusses on the 31 GHz continuum as seen by the CBI. Yet inspection of the WMAP Ka map reveals that the entire  Oph cloud is outlined at 33 GHz, albeit at the intensities in  Oph W. In particular the eastern filamentary extensions of  Oph, LDN 1729 and LDN 1712, at 0.03 MJy sr and 0.016 MJy sr, are not detected in the 2.3 GHz map of Baart et al. (1980, in which no region of  Oph has a counterpart). The diffuse emission surrounding our 45 arcmin centred on  Oph W, also appears to have a positive spectral index between 2.3 GHz and 33 GHz . If we correct for a diffuse background at 0.03 MJy sr, the WMAP 33 GHz flux density inside the CBI PB aperture drops from 14 Jy to 9 Jy.

C i can better accomodate a reduced 33 GHz flux density, since the 2.3 GHz – 33 GHz rise is shallower ( drops from 0.69 to 0.52). But what is the origin of the background? The first possibility that springs to mind is spinning dust, which does not require an ionisation source, and scales linearly with density. We could also envision an ensemble of C i-emitting dense clumps illuminated by the general interstellar UV field. In this case the specific intensity in the optically thin regime at 33 GHz can be written

(2)

where L is the depth of the  Oph cloud, is the filling factor, and is as in Eq. 1. An upper limit to the product can be obtained by ionisation balance in ionisation-bounded clumps

(3)

for clumps with depth and area , where

(4)

is the flux of C-ionising photons per unit area in the interstellar radiation field . If , the depth of a single clump, then we have an upper limit to any C i continuum diffuse background intensity

(5)

The interstellar radiation field of Mathis et al. (1983) gives MJy sr, which is satisfyingly a factor of four above the observed values in  Oph. As in the case of  Oph W (Sec. 6), we require beam-diluted optically thick clumps covering a solid angle of . Thus to explain the absence of  Oph in Baart et al. (1980) with a noise of 30 mK and a beam of 20 arcmin FWHM, the projected linear size of the clump ensemble should be arcmin , if K. In  Oph W such narrow dimmensions could perhaps be interpreted as a very narrow C ii shell around HD 147889. But for the diffuse emission such a geometry seems very contrived.

9 Conclusion

We have found that the well-studied and nearby molecular cloud  Oph is surprisingly bright at 31 GHz, or 1 cm wavelengths. The most conspicuous feature revealed by the CBI data is the  Oph W PDR.

Comparison with  WMAP images shows that the cm-emission is not the Rayleigh-Jeans tail of the sub-mm emitting dust. Bulk dust properties are inferred from new ISO-LWS parallel mode data. Archival Spitzer data allows quantifying PAH emission. None of the comparison images match the CBI data, except for IRAC 8 m and 2MASS K, which closely follow the 31 GHz ridge along  Oph W. Spitzer IRS spectroscopy in four apertures hint at a possible correlation between 31 GHz intensity and the H pure-rotational lines: the H lines are detected only where 31 GHz intensities are bright (i.e. towards SR 3 and  Oph W, and not in the vicinity of S 1).

We considered several interpretations for the 31 GHz emision, requiring either an additional radio continuum component such as magnetic or spinning dust, or unexpected physical conditions, such as in a very dense and cold plasma. We find that both spinning dust and C i continuum can explain the data:

  • Magnetic dust is discarded on morphological grounds. The expected 31 GHz intensity from a magnetic enhancement of the grain opacity is at odds with the CBI data. The polarization levels required by magnetic dust are not observed.

  • Spinning dust can account for the radio spectrum. But the predicted levels in S 1 are in excess by a factor 40 at 3 . We take the intensities in PAH 11.3 m as a proxy for the mid-IR VSG emission, which is approximately proportional to both the VSG column and local UV intensity . Taking into account the range of spinning dust emissivities in all possible environments, the uncertainties in our 31 GHz map can marginally reconcile spinning dust with the data (i.e. at 3  variations).

  • Alternatively a cold plasma such as that found in C ii regions could explain the 31 GHz emission. The star HD147889, a binary pre-main-sequence star with spectral types B2IV, B3IV, emits sufficient C-ionising UV radiation to interpret  Oph W as a C ii region. But the absence of detectable GHz signal requires optically thick emission, and hence high H-nucleus densities ( cm, almost a factor of 10 higher than inferred in the literature), implying a hitherto unobserved molecular phase of the ISM. In  Oph this molecular phase takes the form of an ensemble of dense clumps or sheets at temperatures of order 50 K or less. The cold plasma interpretation explains the 2MASS - CBI correlation through an important fluorescent H contribution to the 2MASS bands.

Acknowledgments

We thank the referee for a thorough reading and useful comments. S.C. acknowledges support from FONDECYT grant 1060827, and from the Chilean Center for Astrophysics FONDAP 15010003. We gratefully acknowledge the generous support of Maxine and Ronald Linde, Cecil and Sally Drinkward, Barbara and Stanely Rawn, Jr., Fred Kavli, and Rochus Vogt. This work was supported by the National Science Foundation under grants AST 00-98734 and AST 02-06416. RP acknowledges the support of a Spitzer Cycle-5 archival proposal grant (PAC.PALADINI - 1 - JPL.000094). This publication makes use of data products from 1- the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center, funded by the National Aeronautics and Space Administration and the National Science Foundation, and 2- the Southern H-Alpha Sky Survey Atlas (SHASSA), which is supported by the National Science Foundation. The Mopra radio telescope is part of the Australia Telescope which is funded by the Commonwealth of Australia for operations as a National Facility operated by CSIRO. This research also made use of Montage, funded by the National Aeronautics and Space Administration’s Earth Science Technology Office, Computational Technnologies Project, under Cooperative Agreement Number NCC5-626 between NASA and the California Institute of Technology. The code is maintained by the NASA/IPAC Infrared Science Archive. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France.

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Appendix A Image Reconstruction

Image reconstruction from interferometer data is an instance of the inverse problem. The compact configuration of the CBI interferometer results in the coverage shown in Fig. 10. Missing spacings and noise impose non-linear deconvolution methods. With a uniform grid the number of free parameters (here ) can exceed the number of independent data points, so that the fit is degenerate. In this case we take as a measure of the quality of fit , where is the number of independent data points. should be close to 1 for a satisfactory model. The first few conjugate gradient iterations in the least-squares algorithm fit the bulk of the signal, but inevitably converge on noisy models, with values much less than 1. MEM regularization prevents the models from fitting the noise. The model shown in Fig. 1 has , which is somewhat high, but reconcilable with 1.0 through a 10% increase in the noise. The noise in each visibility point is calculated as the root-mean-square (rms) scatter of 120 samples, and does not include residual errors in calibration, which may perhaps amount to 10%.

Figure 10: coverage of the CBI in the compact configuration used for the observations of  Oph W.

A reconstruction starting from a blank image as initial condition, rather than the image prior , converges on essentially the same model as Fig. 1, but with a higher , and thus larger residuals. The prior we chose accounts for some of the extended emission seen by WMAP, but keeps the IRAC resolution by replacing the emission within the CBI primary beam with the IRAC 8 m image, suitably scaled and processed so as to resemble the blank-prior MEM models (i.e. we patched-out stellar features, namely S 1 and SR 3, see below). This patched image was then fed as initial condition and prior into a sky-plane MEM deconvolution of the WMAP Ka image, producing the prior image used for the CBI reconstructions in Fig. 1, with .

The CBI observations and the quality of the MEM model can be examined through the restored image and the residuals shown on Fig. 11a,  11b. The residual image is the dirty map (produced with the DIFMAP package using natural weights, Shepherd, 1997), of the residual visibilities (the difference between the observed and model visibilities). The restored image is the sum of the residual image, after division by the CBI primary beam, and the MEM model convolved with an elliptical Gaussian fit to the natural-weight synthetic beam (8.177.99 arcmin). In natural weights the theoretical rms noise of the dirty map is 3.4 mJy beam. The dynamic range of the restored image shown in Fig. 11 is of order 100.

We examined the statistical properties of the MEM reconstructions with the simulations described in Appendix B of Casassus et al. (2006). These simulations are relevant to assess the effects of the CBI beam on the morphological analysis of Sec. 4.1, and to estimate the dynamic range of the MEM reconstructions. The CBI MEM prior is a suitable template. We ran the same MEM algorithm as applied to the CBI visibilities on a simulation of CBI observations on the prior used for the reconstruction of Fig. 1. Fig. 11 compares this prior image with the average and dispersion of the MEM models run on 90 realisations of complex visibility noise. Note that in this case we used a blank prior with and Jy sr. The 31 GHz model image obtained with this MEM reconstruction is shown in Fig. 11d. It is very similar to Fig. 1. We take this similarity as a proof of robustness of the MEM reconstructions, and also as ground to extrapolate the dynamic range of the simulations, of 20, to the CBI images.

Figure 11: MEM restored image and comparison reconstructions. The axes and dashed circle follow from Fig. 1. a- restored image, with contour levels at 0.012, 0.286, 0.446, 0.581, 0.702 and 0.813 Jy beam, and peak at 0.916 Jy beam. b- MEM contours overlaid on the residual image. The natural-weight synthetic beam is indicated by the hatched ellipse. c- difmap clean reconstruction of the CBI data, in uniform weights. Contour levels are 0.098, 0.185, 0.257, 0.323 and 0.382 Jy beam. d- A CBI MEM model with a blank prior is shown in grey scale, with contours at 0.06, 0.09, 0.12, 0.15 and 0.17 MJy sr. e- average MEM model of CBI simulations on the prior image used to produce our best model. Contours are at 0.098, 0.185, 0.257, 0.323, 0.382 MJy sr, overlaid on a grey scale of the input image. f- averaged MEM contours overlaid on the root-mean-square (rms) dispersion of the MEM models.
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