Volume 547, November 2012
|Number of page(s)||23|
|Section||Interstellar and circumstellar matter|
|Published online||22 October 2012|
In Eq. (3), we have provided a conversion between the frequency dependent dust opacity κd(ν) and the NIR extinction law (Cardelli et al. 1989) in order to be able to compare the behaviour of the scatter-free dust opacities of Ossenkopf & Henning (1994) and the extinction law at NIR wavelengths in Fig. 4. Below, we derive this equation in detail by starting from the relation between the extinction value and the optical depth at a given wavelength: Here, ρ is the density of the material that causes the extinction Aλ with its opacity κλ along the LoS path x. This can be written in terms of a surface density Σg,d that includes both dust and gas. Their properties are being disentangled as follows, where Xg,d is the gas-to-dust ratio, which is assumed to be 150 in this paper (Sodroski et al. 1997): At this point, we have come to a relation between the extinction Aλ and the dust opacity κd(ν) that depends on the column density of hydrogen atoms NH. The conversion between the hydrogen and the mean gas mass is mg/mH = 1.36. When replacing the constants with the corresponding numbers, we get Expressed as a relation for κd(ν), we find In the NIR, the extinction law is insensitive to variations in RV = AV/EB − V. Therefore, we can use Cardelli et al. (1989) to transform the ratios NH/AJ (Vuong et al. 2003) and NH/EJ − K (Martin et al. 2012) to hydrogen column density vs. NIR extinction ratios. If the NH/AV or NH/EB − V ratios are used instead, they implicitly introduce a dependence of RV as follows: \newpageThe ratio Aλ/AV as a function of RV represents the extinction law of Cardelli et al. (1989). Several values for the ratio between the hydrogen column density and the colour excess EB − V can be applied. If, for instance, the ratio of Bohlin et al. (1978) is used, we get For a more recent characterisation of that ratio (Ryter 1996; Güver & Özel 2009; Watson 2011), the numerical value in this conversion is modified by about 18%. To be able to convert the quoted ratio NH/AV to NH/EB − V, we have assumed RV = 3.1 as the mean value for the diffuse ISM, and replaced the corresponding ratio in the equation above:
Mid-infrared spectra at 11 positions across B68 obtained with the Spitzer IRS instrument. The most prominent spectral features are indicated by dashed lines. The flux density is given in mJy. The individual spectra are offset by 10 mJy each. There is no significant variation in the strength of the PAH features.
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Coordinates of the Spitzer IRS observations used to extract the background spectra.
13CO (2–1) spectra extracted at two positions in the corresponding map. The upper spectrum shows a line on the western rim of B68 (RA (J2000) = , Dec (J2000) = −23°49′53′′), while the lower spectrum is taken at the location of the point source mentioned in Sect. 4.2. A Gaussian profile fit was applied to both spectra.
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Radial profiles extracted from the extinction map of Alves et al. (2001a) (upper panel) and the newly calculated extinction map shown in Fig. 2 (lower panel). The small dots represent the data in the maps after regridding them to the same scale; the large dots are the mean values in bins of 20″ each with the error bars indicating the corresponding rms scatter. The mean distributions follow a profile fit similar to Eq. (15) (solid line). The power-law indices are α = 3.3 in the upper panel and α = 3.1 in the lower panel. For comparison, we added the profile of the BES (dashed line) given by Alves et al. (2001b).
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© ESO, 2012
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