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Register a new userEstimation of high-resolution dust column density maps: Empirical model fits
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M. Juvela
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Sub-millimetre dust emission is an important tracer of density N of dense interstellar clouds. One has to combine surface brightness information at different spatial resolutions, and specific methods are needed to derive N at a resolution higher than the lowest resolution of the observations. Some methods have been discussed in the literature, including a method (in the following, method B) that constructs the N estimate in stages, where the smallest spatial scales being derived only use the shortest wavelength maps. We propose simple model fitting as a flexible way to estimate high-resolution column density maps. Our goal is to evaluate the accuracy of this procedure and to determine whether it is a viable alternative for making these maps. The new method consists of model maps of column density (or intensity at a reference wavelength) and colour temperature. The model is fitted using Markov chain Monte Carlo (MCMC) methods, comparing model predictions with observations at their native resolution. We analyse simulated surface brightness maps and compare its accuracy with method B and the results that would be obtained using high-resolution observations without noise. The new method is able to produce reliable column density estimates at a resolution significantly higher than the lowest resolution of the input maps. Compared to method B, it is relatively resilient against the effects of noise. The method is computationally more demanding, but is feasible even in the analysis of large Herschel maps. The proposed empirical modelling method E is demonstrated to be a good alternative for calculating high-resolution column density maps, even with considerable super-resolution. Both methods E and B include the potential for further improvements, e.g., in the form of better a priori constraints.
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Sub-millimetre dust emission is often used to derive the column density N of dense interstellar clouds. The observations consist of data at several wavelengths but of variable resolution. We examine two procedures that been proposed for the estimation of high resolution N maps. Method A uses a low-resolution temperature map combined with higher resolution intensity data while Method B combines N estimates from different wavelength ranges. Our aim is to determine the accuracy of the methods relative to the true column densities and the estimates obtainable with radiative transfer modelling. We use magnetohydrodynamical (MHD) simulations and radiative transfer calculations to simulate sub-millimetre observations at the wavelengths of the Herschel Space Observatory. The observations are analysed with the methods and the results compared to the true values and to the results from radiative transfer modelling of observations. Both methods A and B give relatively reliable column density estimates at the resolution of 250um data while also making use of the longer wavelengths. For high signal-to-noise data, the results of Method B are better correlated with the true column density, while Method A is less sensitive to noise. When the cloud has internal heating, results of Method B are consistent with those that would be obtained with high-resolution data. Because of line-of-sight temperature variations, these underestimate the true column density and, because of a favourable cancellation of errors, Method A can sometimes give more correct values. Radiative transfer modelling, even with very simple 3D cloud models, can provide better results. However, the complexity of the models required for improvements increases rapidly with the complexity and opacity of the clouds.
We present optical depth and temperature maps of the Perseus molecular cloud, obtained combining dust emission data from the Herschel and Planck satellites and 2MASS/NIR dust extinction maps. The maps have a resolution of 36 arcsec in the Herschel regions, and of 5 arcmin elsewhere. The dynamic range of the optical depth map ranges from $1times10^{-2}, mathrm{mag}$ up to $20 ,mathrm{mag}$ in the equivalent K band extinction. We also evaluate the ratio between the $2.2 ,mathrm{mu m}$ extinction coefficient and the $850 ,mathrm{mu m}$ opacity. The value we obtain is close to the one found in the Orion B molecular cloud. We show that the cumulative and the differential area function of the data (which is proportional to the probability distribution function of the cloud column density) follow power laws with index respectively $simeq -2$, and $simeq -3$. We use WISE data to improve current YSO catalogues based mostly on emph{Spitzer} data and we build an up-to-date selection of Class~I/0 objects. Using this selection, we evaluate the local Schmidt law, $Sigma_{mathrm{YSO}} propto Sigma_{mathrm{gas}}^{beta}$, showing that $beta=2.4 pm 0.6$. Finally, we show that the area-extinction relation is important for determining the star formation rate in the cloud, which is in agreement with other recent works.
The afterglows of gamma-ray bursts (GRBs) have more soft X-ray absorption than expected from the foreground gas column in the Galaxy. While the redshift of the absorption can in general not be constrained from current X-ray observations, it has been assumed that the absorption is due to metals in the host galaxy of the GRB. The large sample of X-ray afterglows and redshifts now available allows the construction of statistically meaningful distributions of the metal column densities. We construct such a sample and show, as found in previous studies, that the typical absorbing column density (N_HX) increases substantially with redshift, with few high column density objects found at low to moderate redshifts. We show, however, that when highly extinguished bursts are included in the sample, using redshifts from their host galaxies, high column density sources are also found at low to moderate redshift. We infer from individual objects in the sample and from observations of blazars, that the increase in column density with redshift is unlikely to be related to metals in the intergalactic medium or intervening absorbers. Instead we show that the origin of the apparent increase with redshift is primarily due to dust extinction bias: GRBs with high X-ray absorption column densities found at $zlesssim4$ typically have very high dust extinction column densities, while those found at the highest redshifts do not. It is unclear how such a strongly evolving N_HX/A_V ratio would arise, and based on current data, remains a puzzle.
We present high-resolution, high dynamic range column-density and color-temperature maps of the Orion complex using a combination of Planck dust-emission maps, Herschel dust-emission maps, and 2MASS NIR dust-extinction maps. The column-density maps combine the robustness of the 2MASS NIR extinction maps with the resolution and coverage of the Herschel and Planck dust-emission maps and constitute the highest dynamic range column-density maps ever constructed for the entire Orion complex, covering $0.01 , mathrm{mag} < A_K < 30 ,mathrm{mag}$, or $2 times 10^{20} , mathrm{cm}^{-2} < N < 5 times 10^{23} ,mathrm{cm}^{-2}$. We determined the ratio of the 2.2 microns extinction coefficient to the 850 microns opacity and found that the values obtained for both Orion A and B are significantly lower than the predictions of standard dust models, but agree with newer models that incorporate icy silicate-graphite conglomerates for the grain population. We show that the cloud projected pdf, over a large range of column densities, can be well fitted by a simple power law. Moreover, we considered the local Schmidt-law for star formation, and confirm earlier results, showing that the protostar surface density $Sigma_*$ follows a simple law $Sigma_* propto Sigma_{gas}^beta$, with $beta sim 2$.
The analysis of the Planck polarization E and B mode power spectra of interstellar dust emission at 353 GHz recently raised new questions on the impact of Galactic foregrounds to the detection of the polarization of the Cosmic Microwave Background (CMB) and on the physical properties of the interstellar medium (ISM). In the diffuse ISM a clear E-B asymmetry is observed, with twice as much power in E modes than in B modes; as well as a positive correlation between the total power, T, and both E and B modes, presently interpreted in terms of the link between the structure of interstellar matter and that of the Galactic magnetic field. In this paper we aim at extending the Planck analysis of the high-latitude sky to low Galactic latitude, investigating the correlation between the TEB power spectra with the gas column density from the diffuse ISM to molecular clouds. We divide the sky between Galactic latitude |b|>5 deg and |b|<60 deg in 552 circular patches and we study the cross-correlations between the TEB power spectra and the column density of each patch using the latest release of the Planck polarization data. We find that the B-to-E power ratio (BB/EE) and the TE correlation ratio (rTE) depend on column density. While the former increases going from the diffuse ISM to molecular clouds in the Gould Belt, the latter decreases. This systematic variation must be related to actual changes in ISM properties. The data show significant scatter about this mean trend. The variations of BB/EE and rTE are observed to be anti-correlated for all column densities. In the diffuse ISM, the variance of these two ratios is consistent with a stochastic non-Gaussian model in which the values of BB/EE and rTE are fixed. We finally discuss the dependencies of TB and EB with column density, which are however hampered by instrumental noise.
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