Volume 563, March 2014
|Number of page(s)||21|
|Section||Interstellar and circumstellar matter|
|Published online||20 March 2014|
MCMC fitting with free β (see Sect. 4.2) produces the β and T maps shown in Fig. A.1. MCMC fitting with a constant value β = 1.8, using background-subtracted intensity maps, produces the τ250 and T maps in Fig. A.2. These maps were used in the analysis of the different regions marked in the figures. An extinction map and a τ250/τJ map (described in Sect. 4.3) are shown in Fig. A.3.
Maps of β (left) and T (right) derived by MCMC fitting with free β, using Herschel 160–500 μm maps. Background is not subtracted. Contours of the τ250 map are drawn on both maps at levels 0.0035, 0.0029, and 0.0019.
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Maps derived by MCMC fitting with a constant β = 1.8, using Herschel 250–500 μm maps at 40″ resolution. The maps are based on background-subtracted intensity maps, using the area marked BG as background. Areas of the clumps A1, A2, B, and C, and the main part of cloud (marked L1642) used in the analysis. The maps are τ250 (left) and T (right).
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(Left) Optical depth τJ map derived from 2MASS data. The resolution of the map is 180″. (Right) τ250/τJ map with resolution 180″. The black contours are drawn on τ250 levels 0.0016, 0.0008, and 0.0004. The green contours are drawn on τJ levels 2, 1, and 0.5. Areas where τJ < 0.0001 or τ250 < 0.00004 are masked. The area marked with a yellow rectangle was used as a background when subtracting the background from the two optical depth maps.
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We used a subset of the WISE catalogue to search for other YSO candidates. This subset contained sources with A photometric quality (S/N > 10) in at least three of the four bands and at least B quality (S/N > 3) in one of the bands. We searched previously classified sources in the SIMBAD and VizieR catalogues with a radius of 5″. We used the quadratic discriminant analysis (QDA, McLachlan 1992) to separate the sources with known object types (galaxies, evolved stars, single stars, ISM-related objects, and YSOs) and to determine the boundaries in the multidimensional parameter space. These boundaries were then applied to the sources with unknown object types. The sources that were similar to the known YSOs were selected as YSO candidates. The multidimensional parameter space included the following colours: J−H, H−K, K−W1, W1−W2, W2−W3, W3−W4, and also the W1 brightness. J, H, and K data are from 2MASS catalogue.
This method for YSO selection has been previously used in several studies (Tóth et al. 2013; Marton et al. 2013; Cambrésy et al. 2013) and will be discussed in more detail in a forthcoming paper (Marton et al., in prep.). Tóth et al. (2013) found that the reliability of the classification is higher than 90% compared with known YSOs. Marton et al. (in prep.) have found a quite good reliability using the current WISE catalogue. In their study, only 0.33% of all the other known sources (including galaxies, stars, etc.), 0.77% of galaxies and 73.5% of the known YSOs were classified as YSO candidates. Based on the classification in the SDSS catalogue, 6.79% of the sources classified as YSO candidates are galaxies. However, biases in the WISE catalogue might affect these results.
We located six other YSO candidates in addition to B-1, B-2, and B-3 within a 1° radius of the centre of L1642, based on WISE data. These objects are shown in Fig. B.1. Two of the
objects are within or at the edge of the densest part of the cloud on the sky, in region C. These two are plotted in our Herschel maps and can be seen in the 100 μm map as faint objects. The other four are projected on a more diffuse area, but still within the larger structure of L1642 cloud. We fitted these objects with the SED models of Robitaille et al. (2007) using optical, NIR (2MASS), and MIR (WISE) data. The most probable distances provided by the SED model fits for the objects are mostly between 350 pc and 800 pc, clearly farther away than the estimated distance of L1642. There is no evidence that any of these sources are inside the L1642 cloud, but confirming this would require more study.
Point sources B-1, B-2, and B-3 (diamonds) and other YSO candidates (crosses) marked on the Planck 857 GHz intensity map.
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Relation between the Planck Legacy Archive CO maps and the SEST CO data of Russeil et al. (2003) using Planck Type 3 J = 1–0 data (left, 6′ resolution) and using Type 2 data (15′ resolution) for J = 1–0 (middle) and J = 2–1 (right). The blue crosses show the relation between Planck CO and the SEST 12CO line area, the red crosses the relation between Planck CO and the sum of SEST 12CO and 13CO line areas.
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We used the SEST CO data of Russeil et al. (2003) to correct the Planck 217 and 353 GHz maps for the contribution of CO line emission. We compared the SEST data with the maps of integrated CO line area that have been derived from Planck data and are available in the Planck Legacy Archive10. The Planck archive includes three separate estimates of the CO emission. Type 1 products are based on the bandpass measurements of individual Planck channels, include separate estimates of the J = 1–0, J = 2–1, and J = 3–2 line intensities, but have relatively low SN. Type 2 maps include estimates of the CO J = 1–0 and J = 2–1 emission that were obtained by a joint analysis of multiple Planck frequency channels and have a higher S/N. Type 3 maps additionally use prior information of the CO line ratios resulting in a combined CO emission map with a good S/N.
The comparison between SEST and the Type 2 and Type 3 data is shown in Fig. C.1. The correlation is very good between Type III J = 1–0 line areas and the sum of SEST 12CO(1–0) and 13CO(1–0) data (left panel). Type 2 (1–0) maps give slightly higher line areas than Type 3 maps, and Type 2 (2–1) maps give lower values than SEST. However, because the calibration errors of the SEST data can be ~10% , the correlations are still quite good. Note that the SEST values are antenna temperatures corrected using the Moon efficiency.
We carried out radiative transfer modelling of L1642 to qualitatively estimate the effects that LOS temperature variations have on estimates of the optical depth and the emissivity spectral index. The initial model is based on the column density map derived from observations, the Mathis et al. (1983) model of the interstellar radiation field (ISRF), and the dust properties corresponding to observations of diffuse interstellar medium (Draine 2003). However, to be consistent with the previous analysis, the dust model was adjusted so that the spectral index was exactly β = 1.8 for all wavelengths λ > 100 μm.
The density distribution was defined using a 1323 Cartesian grid with a cell size corresponding to 6″. Thus the model covers an area of 13.2′× 13.2′ that includes the sources B-1, B-2, B-3, and B-4. The initial column density distribution was obtained from the analysis of Herschel observations. The LOS density distribution was assumed to be Gaussian with a FWHM corresponding to the value of ~6′ visible in the plane of the sky. The external radiation field was assumed to be isotropic. Corresponding to the sources B-1, B-2, and B-3, we added three radiation sources inside the cloud. In the plane of the sky these are the positions of the local peaks measured in the 250 μm surface brightness maps, and along the LOS they are in the middle of the cloud. We treated B-4 as a clump heated from the outside, and did not add an internal source there. A non-LTE radiative transfer program was used to estimate the dust temperature distributions and to calculate synthetic surface brightness maps at the Herschel wavelengths (Juvela & Padoan 2003).
The initial model was optimised by comparing the observed and modelled surface brightness maps. We used observations that were background subtracted using a reference area around the position RA = 4h34m52s, Dec = −14°25′15″ (J2000.0). For each LOS, the densities of the model cloud were scaled so that one reproduces the observed 250 μm surface brightness data at the observed resolution. The ISRF was scaled to reproduce the observed surface brightness ratio 160 μm/500 μm that was estimated from the central area of 4.4′ × 4.4′. The embedded sources B-1, B-2, and B-3 were assumed to be black-bodies at a temperature of 8000 K. Their luminosities were adjusted so that the surface brightness ratios between 160 μm and 250 μm bands had the observed values when measured towards the sources, using the resolution of the observed maps (12.0″ and 18.3″ for 160 μm and 250 μm, respectively). The calculations were iterated until the 250 μm surface brightness, the average colour of the central regions, and the colours towards the three sources all matched to a few per cent. This is only a crude model and, in particular, the effect of the sources depends sensitively on their position along the LOS, their temperature, and the density structures in their immediate vicinity.
Analysis of model surface brightness and optical depth. Panel a) shows the 250 μm surface brightness and the apertures used for flux measurements of sources B-1, B-2, B-3, and B-4. Panel b) shows the ratio of optical depths that are estimated from synthetic surface brightness data and the actual 250 μm optical depth of the model cloud. Panels c) and d) show the residuals between the actual Herschel observations and the model predictions at 160 μm and 350 μm, respectively. Panel e) shows the SEDs derived for the sources using the model-predicted intensities and quotes the results of the MBB fits.
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Figure D.1 shows the final 250 μm surface brightness map (within ~1% of the observed values) as well as the residuals of the 160 μm and 350 μm surface brightness data. The residuals are low at the very positions of the three sources. However, the heating effect of source B-2 is too extended. Because of the constraint on the average colour, the model is correspondingly too cold around the sources B-1 and B-3, leaving positive residuals in the 160 μm map. In the immediate vicinity of B-2 the high residuals are caused by the fact that the source is associated with some extended emission and the peak position changes with wavelength. At 160 μm the relative error is up to ~20% around B-2 and rises to ~30% around the sources B-1 and B-3. Compared with 160 μm, the relative errors are of similar magnitude at 350 μm and 500 μm, but are, of course, in the opposite direction. Because of these inaccuracies, we used the model mainly for qualitative analysis.
Figure D.1e shows the spectra calculated for the four sources using 80″ apertures. Because the effect of point sources appears to be more extended than in Herschel data, we used flux densities in the apertures without further subtracting the surrounding annulus. Thus, the values do not exactly correspond to those derived from Herschel data. The most noticeable fact is that the estimated spectral indices are lower than the opacity spectral index β = 1.8 of the dust grains. The strongest source B-2 has a value of β = 1.63 that is 0.17 units lower than the intrinsic beta value. In the observations, the value was even lower, β = 1.25 (see the right panel of Fig. 10). Nevertheless, the model suggests
that most if not all of the difference to diffuse regions might be caused by temperature variations within the beam.
Figure D.1b compares the optical depth map obtained directly from the model density cube with the optical depth τ(250 μm) derived from the synthetic surface brightness maps at a resolution of 40″. The optical depth was estimated as described in Sect. 4.2, using a fixed value of β = 1.8 when performing least-squares fits of MBB spectra. Because the result depends on the assumed dust opacity, we normalised the results so that the mean optical depth ratio is one in the area where the Herschel column density is between 1 × 1021 cm-2 and 2 × 1021 cm-2. The result shows that at the moderate column densities of L1642, the temperature variations (colour temperature exceeding the mass-averaged temperature) generally leads to no more than an underestimation of ~10% in optical depth. However, the errors increase to ~30% towards the sources B-1 and B-3 and the largest error towards B-2 is larger by a factor of ~3.
© ESO, 2014
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