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C. Dickinson

Publications and source records attributed to C. Dickinson.

At least 91 records · Page 5Linked to original sources

Planck intermediate results. XXV. The Andromeda Galaxy as seen by Planck

The Andromeda Galaxy (M31) is one of a few galaxies that has sufficient angular size on the sky to be resolved by the Planck satellite. Planck has detected M31 in all of its frequency bands, and has mapped out the dust emission with the High Frequency Instrument, clearly resolving multiple spiral arms and sub-features. We examine the morphology of this long-wavelength dust emission as seen by Planck, including a study of its outermost spiral arms, and investigate the dust heating mechanism across M31. We find that dust dominating the longer wavelength emission ($\gtrsim 0.3\,$mm) is heated by the diffuse stellar population (as traced by 3.6$\,μ$m emission), with the dust dominating the shorter wavelength emission heated by a mix of the old stellar population and star-forming regions (as traced by 24$\,μ$m emission). We also fit spectral energy distributions (SEDs) for individual 5' pixels and quantify the dust properties across the galaxy, taking into account these different heating mechanisms, finding that there is a linear decrease in temperature with galactocentric distance for dust heated by the old stellar population, as would be expected, with temperatures ranging from around 22$\,$K in the nucleus to 14$\,$K outside of the 10$\,$kpc ring. Finally, we measure the integrated spectrum of the whole galaxy, which we find to be well-fitted with a global dust temperature of ($18.2\pm1.0$)$\,$K with a spectral index of $1.62\pm0.11$ (assuming a single modified blackbody), and a significant amount of free-free emission at intermediate frequencies of 20-60$\,$GHz, which corresponds to a star formation rate of around $0.12$M$_\odot\,$yr$^{-1}$. We find a $2.3\,σ$ detection of the presence of spinning dust emission, with a 30$\,$GHz amplitude of $0.7\pm0.3\,$Jy, which is in line with expectations from our Galaxy.

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Planck intermediate results. XXXV. Probing the role of the magnetic field in the formation of structure in molecular clouds

Within ten nearby (d < 450 pc) Gould Belt molecular clouds we evaluate statistically the relative orientation between the magnetic field projected on the plane of sky, inferred from the polarized thermal emission of Galactic dust observed by Planck at 353 GHz, and the gas column density structures, quantified by the gradient of the column density, $N_H$. The selected regions, covering several degrees in size, are analyzed at an effective angular resolution of 10' FWHM, thus sampling physical scales from 0.4 to 40 pc in the nearest cloud. The column densities in the selected regions range from $N_H \approx 10^{21}$ to $10^{23}$ cm$^{-2}$, and hence they correspond to the bulk of the molecular clouds. The relative orientation is evaluated pixel by pixel and analyzed in bins of column density using the novel statistical tool called "Histogram of Relative Orientations". Throughout this study, we assume that the polarized emission observed by Planck at 353 GHz is representative of the projected morphology of the magnetic field in each region, i.e., we assume a constant dust grain alignment efficiency, independent of the local environment. Within most clouds we find that the relative orientation changes progressively with increasing $N_H$, from preferentially parallel or having no preferred orientation to preferentially perpendicular. In simulations of magnetohydrodynamic turbulence in molecular clouds this trend in relative orientation is a signature of Alfvénic or sub-Alfvénic turbulence, implying that the magnetic field is significant for the gas dynamics at the scales probed by Planck. We compare the deduced magnetic field strength with estimates we obtain from other methods and discuss the implications of the Planck observations for the general picture of molecular cloud formation and evolution.

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Planck intermediate results. XXXIX. The Planck list of high-redshift source candidates

The Planck mission, thanks to its large frequency range and all-sky coverage, has a unique potential for systematically detecting the brightest, and rarest, submillimetre sources on the sky, including distant objects in the high-redshift Universe traced by their dust emission. A novel method, based on a component-separation procedure using a combination of Planck and IRAS data, has been applied to select the most luminous cold submm sources with spectral energy distributions peaking between 353 and 857GHz at 5' resolution. A total of 2151 Planck high-z source candidates (the PHZ) have been detected in the cleanest 26% of the sky, with flux density at 545GHz above 500mJy. Embedded in the cosmic infrared background close to the confusion limit, these high-z candidates exhibit colder colours than their surroundings, consistent with redshifts z>2, assuming a dust temperature of 35K and a spectral index of 1.5. First follow-up observations obtained from optical to submm have confirmed that this list consists of two distinct populations. A small fraction (around 3%) of the sources have been identified as strongly gravitationally lensed star-forming galaxies, which are amongst the brightest submm lensed objects (with flux density at 545GHz ranging from 350mJy up to 1Jy) at redshift 2 to 4. However, the vast majority of the PHZ sources appear as overdensities of dusty star-forming galaxies, having colours consistent with z>2, and may be considered as proto-cluster candidates. The PHZ provides an original sample, complementary to the Planck Sunyaev-Zeldovich Catalogue; by extending the population of the virialized massive galaxy clusters to a population of sources at z>1.5, the PHZ may contain the progenitors of today's clusters. Hence the PHZ opens a new window on the study of the early ages of structure formation, and the understanding of the intensively star-forming phase at high-z.

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Planck 2013 results. XXXI. Consistency of the Planck data

The Planck design and scanning strategy provide many levels of redundancy that can be exploited to provide tests of internal consistency. One of the most important is the comparison of the 70GHz and 100GHz channels. Based on different instrument technologies, with feeds located differently in the focal plane, analysed independently by different teams using different software, and near the minimum of diffuse foreground emission, these channels are in effect two different experiments. The 143GHz channel has the lowest noise level on Planck, and is near the minimum of unresolved foreground emission. In this paper, we analyse the level of consistency achieved in the 2013 Planck data. We concentrate on comparisons between the 70/100/143GHz channel maps and power spectra, particularly over the angular scales of the first and second acoustic peaks, on maps masked for diffuse Galactic emission and for strong unresolved sources. Difference maps covering angular scales from 8deg-15arcmin are consistent with noise, and show no evidence of cosmic microwave background structure. Including small but important corrections for unresolved-source residuals, we demonstrate agreement between 70 and 100GHz power spectra averaged over 70<l<390 at the 0.8% level, and agreement between 143 and 100GHz power spectra of 0.4% over the same l range. These values are within and consistent with the overall uncertainties in calibration given in the Planck 2013 results. We also present results based on the 2013 likelihood analysis showing consistency at the 0.35% between the 100/143/217GHz power spectra. We analyse calibration procedures and beams to determine what fraction of these differences can be accounted for by known approximations or systematic errors that could be controlled even better in the future, reducing uncertainties still further. Several possible small improvements are described...(abridged)

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The Q/U Imaging ExperimenT: Polarization Measurements of the Galactic Plane at 43 and 95 GHz

We present polarization observations of two Galactic plane fields centered on Galactic coordinates (l,b)=(0 deg,0 deg) and (329 deg, 0 deg) at Q- (43 GHz) and W-band (95 GHz), covering between 301 and 539 square degrees depending on frequency and field. These measurements were made with the QUIET instrument between 2008 October and 2010 December, and include a total of 1263 hours of observations. The resulting maps represent the deepest large-area Galactic polarization observations published to date at the relevant frequencies with instrumental rms noise varying between 1.8 and 2.8 uK deg, 2.3-6 times deeper than corresponding WMAP and Planck maps. The angular resolution is 27.3' and 12.8' FWHM at Q- and W-band, respectively. We find excellent agreement between the QUIET and WMAP maps over the entire fields, and no compelling evidence for significant residual instrumental systematic errors in either experiment, whereas the Planck 44 GHz map deviates from these in a manner consistent with reported systematic uncertainties for this channel. We combine QUIET and WMAP data to compute inverse-variance-weighted average maps, effectively retaining small angular scales from QUIET and large angular scales from WMAP. From these combined maps, we derive constraints on several important astrophysical quantities, including a robust detection of polarized synchrotron spectral index steepening of ~0.2 off the plane, as well as the Faraday rotation measure toward the Galactic center (RM=-4000 +/- 200 rad m^-2), all of which are consistent with previously published results. Both the raw QUIET and the co-added QUIET+WMAP maps are made publicly available together with all necessary ancillary information.

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Planck 2015 results. I. Overview of products and scientific results

The European Space Agency's Planck satellite, dedicated to studying the early Universe and its subsequent evolution, was launched 14~May 2009 and scanned the microwave and submillimetre sky continuously between 12~August 2009 and 23~October 2013. In February~2015, ESA and the Planck Collaboration released the second set of cosmology products based on data from the entire Planck mission, including both temperature and polarization, along with a set of scientific and technical papers and a web-based explanatory supplement. This paper gives an overview of the main characteristics of the data and the data products in the release, as well as the associated cosmological and astrophysical science results and papers. The science products include maps of the cosmic microwave background (CMB), the thermal Sunyaev-Zeldovich effect, and diffuse foregrounds in temperature and polarization, catalogues of compact Galactic and extragalactic sources (including separate catalogues of Sunyaev-Zeldovich clusters and Galactic cold clumps), and extensive simulations of signals and noise used in assessing the performance of the analysis methods and assessment of uncertainties. The likelihood code used to assess cosmological models against the Planck data are described, as well as a CMB lensing likelihood. Scientific results include cosmological parameters deriving from CMB power spectra, gravitational lensing, and cluster counts, as well as constraints on inflation, non-Gaussianity, primordial magnetic fields, dark energy, and modified gravity.

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Multi-wavelength constraints on cosmic-ray leptons in the Galaxy

Cosmic rays (CRs) interact with the gas, the radiation field and the magnetic field in the Milky Way, producing diffuse emission from radio to gamma rays. Observations of this diffuse emission and comparison with detailed predictions are powerful tools to unveil the CR properties and to study CR propagation. We present various GALPROP CR propagation scenarios based on current CR measurements. The predicted synchrotron emission is compared to radio surveys, and synchrotron temperature maps from WMAP and Planck, while the predicted interstellar gamma-ray emission is compared to Fermi-LAT observations. We show how multi-wavelength observations of the Galactic diffuse emission can be used to help constrain the CR lepton spectrum and propagation. Finally we discuss how radio and microwave data could be used in understanding the diffuse Galactic gamma-ray emission observed with Fermi-LAT, especially at low energies.

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Simulations for single-dish intensity mapping experiments

HI intensity mapping is an emerging tool to probe dark energy. Observations of the redshifted HI signal will be contaminated by instrumental noise, atmospheric and Galactic foregrounds. The latter is expected to be four orders of magnitude brighter than the HI emission we wish to detect. We present a simulation of single-dish observations including an instrumental noise model with 1/f and white noise, and sky emission with a diffuse Galactic foreground and HI emission. We consider two foreground cleaning methods: spectral parametric fitting and principal component analysis. For a smooth frequency spectrum of the foreground and instrumental effects, we find that the parametric fitting method provides residuals that are still contaminated by foreground and 1/f noise, but the principal component analysis can remove this contamination down to the thermal noise level. This method is robust for a range of different models of foreground and noise, and so constitutes a promising way to recover the HI signal from the data. However, it induces a leakage of the cosmological signal into the subtracted foreground of around 5%. The efficiency of the component separation methods depends heavily on the smoothness of the frequency spectrum of the foreground and the 1/f noise. We find that as, long as the spectral variations over the band are slow compared to the channel width, the foreground cleaning method still works.

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Planck intermediate results. XXXIII. Signature of the magnetic field geometry of interstellar filaments in dust polarization maps

Planck observations at 353GHz provide the first fully-sampled maps of the polarized dust emission towards interstellar filaments and their backgrounds. The polarization data provide insight on the structure of their magnetic field (B). We present the polarization maps of three nearby star forming filament of moderate column density (NH~10^22cm^-2): Musca, B211, and L1506. We use the spatial information to separate Stokes I, Q, and U of the filaments from those of their backgrounds, an essential step to measure the intrinsic polarization fraction (p) and angle (psi) of each emission component. We find that the polarization angles in the three filaments (psi_fil) are coherent along their lengths and not the same as in their backgrounds (psi_bg). The differences between psi_fil and psi_bg are 12deg, 6deg, and 54deg for Musca, B211, and L1506, respectively. These differences for Musca and L1506 are larger than the dispersions of psi, both along the filaments and in their backgrounds. The observed changes of psi are direct evidence for variations of the orientation of the plane of the sky (POS) projection of the B-field. As in previous studies, we find a decrease of several percent of p with NH. We show that the drop in p cannot be explained by random fluctuations of the orientation of B within the filaments because they are too small (sigma_psi<10deg). We recognize the degeneracy between dust alignment efficiency and the structure of B in causing variations in p, but we argue that the decrease of p from the backgrounds to the filaments results in part from depolarization associated with the 3D structure of B: both its orientation in the POS and with respect to the POS. We do not resolve the inner structure of the filaments, but at the smallest scales accessible with Planck (~0.2pc), the observed changes of psi and p hold information on the B-field structure within filaments.

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Polarised radio filaments outside the Galactic plane

We used data from the \wmap satellite at 23, 33 and 41 GHz to study the diffuse polarised emission over the entire sky. The emission originates mostly from filamentary structures with well-ordered magnetic fields. Some of these structures have been known for decades in radio continuum maps. Their origin is not clear and there are many filaments that are visible for the first time. We have identified and studied 11 filaments. The polarisation fraction of some of them can be as high as 40\%, which is a signature of a well ordered magnetic field. The polarisation spectral indices, averaged over 18 regions in the sky is $β= -3.06 \pm 0.02$, consistent with synchrotron radiation. There are significant variations in $β$ over the sky ($Δβ\approx0.2$). We explore the link between the large-scale filaments and the local ISM, using the model of an expanding shell in the solar vicinity. We compared observed polarisation angles with the predictions from the model and found good agreement. This strongly suggests that many large scale filaments and loops are nearby structures. This is important in the context of the Galactic magnetic field as these structures are normally included in global models, neglecting the fact that they might be local. We also studied the level of contamination added by the diffuse filaments to the CMB polarisation power spectra. We conclude that, even though these filaments present low radio brightness, a careful removal will be necessary for future all-sky CMB polarisation analysis.

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An improved source-subtracted and destriped 408 MHz all-sky map

The all-sky 408 MHz map of Haslam et al. is one the most important total-power radio surveys. It has been widely used to study diffuse synchrotron radiation from our Galaxy and as a template to remove foregrounds in cosmic microwave background data. However, there are a number of issues associated with it that must be dealt with, including large-scale striations and contamination from extragalactic radio sources. We have re-evaluated and re-processed the rawest data available to produce a new and improved 408 MHz all-sky map. We first quantify the positional accuracy ($\approx 7$ arcmin) and effective beam ($56.0\pm1.0$ arcmin) of the four individual surveys from which it was assembled. Large-scale striations associated with $1/f$ noise in the scan direction are reduced to a level $\ll 1$ K using a Fourier-based filtering technique. The most important improvement results from the removal of extragalactic sources. We have used an iterative combination of two techniques -- two-dimensional Gaussian fitting and minimum curvature spline surface inpainting -- to remove the brightest sources ($\gtrsim 2$ Jy), which provides a significant improvement over previous versions of the map. We quantify the impact with power spectra and a template fitting analysis of foregrounds to the WMAP data. The new map is publicly available and is recommended as the template of choice for large-scale diffuse Galactic synchrotron emission. We also provide a higher resolution map with small-scale fluctuations added, assuming a power-law angular power spectrum down to the pixel scale (1.7 arcmin). This should prove useful in simulations used for studying the feasibility of detecting HI fluctuations from the Epoch of Reionization.

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Planck intermediate results. XXIII. Galactic plane emission components derived from Planck with ancillary data

Planck data when combined with ancillary data provide a unique opportunity to separate the diffuse emission components of the inner Galaxy. The purpose of the paper is to elucidate the morphology of the various emission components in the strong star-formation region lying inside the solar radius and to clarify the relationship between the various components. The region of the Galactic plane covered is l=300-0-60deg where star-formation is highest and the emission is strong enough to make meaningful component separation. The latitude widths in this longitude range lie between 1deg and 2deg, which correspond to FWHM z-widths of 100-200pc at a typical distance of 6kpc. The four emission components studied here are synchrotron, free-free, anomalous microwave emission (AME), and thermal (vibrational) dust emission. These components are identified by constructing spectral energy distributions (SEDs) at positions along the Galactic plane using the wide frequency coverage of Planck (28.4-857GHz) in combination with low-frequency radio data at 0.408-2.3GHz plus WMAP data at 23-94GHz, along with far-infrared (FIR) data from DIRBE and IRAS. The free-free component is determined from radio recombination line (RRL) data. AME is found to be comparable in brightness to the free-free emission on the Galactic plane in the frequency range 20-40GHz with a width in latitude similar to that of the thermal dust; it comprises 45+/-1% of the total 28.4GHz emission in the longitude range l=300-0-60deg. The free-free component is the narrowest, reflecting the fact that it is produced by current star-formation as traced by the narrow distribution of OB stars. It is the dominant emission on the plane between 60 and 100GHz. RRLs from this ionized gas are used to assess its distance, leading to a free-free z-width of FWHM ~100pc...(abridged)

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Planck intermediate results. XXII. Frequency dependence of thermal emission from Galactic dust in intensity and polarization

Planck has mapped the intensity and polarization of the sky at microwave frequencies with unprecedented sensitivity. We make use of the Planck 353 GHz I, Q, and U Stokes maps as dust templates, and cross-correlate them with the Planck and WMAP data at 12 frequencies from 23 to 353 GHz, over circular patches with 10 degree radius. The cross-correlation analysis is performed for both intensity and polarization data in a consistent manner. We use a mask that focuses our analysis on the diffuse interstellar medium at intermediate Galactic latitudes. We determine the spectral indices of dust emission in intensity and polarization between 100 and 353 GHz, for each sky-patch. The mean values, $1.59\pm0.02$ for polarization and $1.51\pm0.01$ for intensity, for a mean dust temperature of 19.6 K, are close, but significantly different ($3.6\,σ$). We determine the mean spectral energy distribution (SED) of the microwave emission, correlated with the 353 GHz dust templates, by averaging the results of the correlation over all sky-patches. We find that the mean SED increases for decreasing frequencies at $ν< 60$ GHz, for both intensity and polarization. The rise of the polarization SED towards low frequencies may be accounted for by a synchrotron component correlated with dust, with no need for any polarization of the anomalous microwave emission. We use a spectral model to separate the synchrotron and dust polarization and to characterize the spectral dependence of the dust polarization fraction. The polarization fraction ($p$) of the dust emission decreases by $(21\pm6)$ % from 353 to 70 GHz. The decrease of $p$ could indicate differences in polarization efficiency among components of interstellar dust (e.g., carbon versus silicate grains). Our observational results provide inputs to quantify and optimize the separation between Galactic and cosmological polarization.

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The QUIJOTE experiment: project overview and first results

QUIJOTE (Q-U-I JOint TEnerife) is a new polarimeter aimed to characterize the polarization of the Cosmic Microwave Background and other Galactic and extragalactic signals at medium and large angular scales in the frequency range 10-40 GHz. The multi-frequency (10-20~GHz) instrument, mounted on the first QUIJOTE telescope, saw first light on November 2012 from the Teide Observatory (2400~m a.s.l). During 2014 the second telescope has been installed at this observatory. A second instrument at 30~GHz will be ready for commissioning at this telescope during summer 2015, and a third additional instrument at 40~GHz is now being developed. These instruments will have nominal sensitivities to detect the B-mode polarization due to the primordial gravitational-wave component if the tensor-to-scalar ratio is larger than r=0.05.

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A Joint Analysis of BICEP2/Keck Array and Planck Data

We report the results of a joint analysis of data from BICEP2/Keck Array and Planck. BICEP2 and Keck Array have observed the same approximately 400 deg$^2$ patch of sky centered on RA 0h, Dec. $-57.5°$. The combined maps reach a depth of 57 nK deg in Stokes $Q$ and $U$ in a band centered at 150 GHz. Planck has observed the full sky in polarization at seven frequencies from 30 to 353 GHz, but much less deeply in any given region (1.2 $μ$K deg in $Q$ and $U$ at 143 GHz). We detect 150$\times$353 cross-correlation in $B$-modes at high significance. We fit the single- and cross-frequency power spectra at frequencies $\geq 150$ GHz to a lensed-$Λ$CDM model that includes dust and a possible contribution from inflationary gravitational waves (as parameterized by the tensor-to-scalar ratio $r$), using a prior on the frequency spectral behavior of polarized dust emission from previous \planck\ analysis of other regions of the sky. We find strong evidence for dust and no statistically significant evidence for tensor modes. We probe various model variations and extensions, including adding a synchrotron component in combination with lower frequency data, and find that these make little difference to the $r$ constraint. Finally we present an alternative analysis which is similar to a map-based cleaning of the dust contribution, and show that this gives similar constraints. The final result is expressed as a likelihood curve for $r$, and yields an upper limit $r_{0.05}<0.12$ at 95% confidence. Marginalizing over dust and $r$, lensing $B$-modes are detected at $7.0\,σ$ significance.

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ALMA observations of 99 GHz free-free and H40$α$ line emission from star formation in the centre of NGC 253

We present Atacama Large Millimeter/submillimeter Array observations of 99.02 GHz free-free and H40$α$ emission from the centre of the nearby starburst galaxy NGC 253. We calculate electron temperatures of 3700-4500 K for the photoionized gas, which agrees with previous measurements. We measure a photoionizing photon production rate of $(3.2\pm0.2)\times10^{53}$ s$^{-1}$ and a star formation rate of $1.73\pm0.12$ M$_\odot$ yr$^{-1}$ within the central 20$\times$10 arcsec, which fall within the broad range of measurements from previous millimetre and radio observations but which are better constrained. We also demonstrate that the dust opacities are ~3 dex higher than inferred from previous near-infrared data, which illustrates the benefits of using millimetre star formation tracers in very dusty sources.

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Planck intermediate results. XXXII. The relative orientation between the magnetic field and structures traced by interstellar dust

The role of the magnetic field in the formation of the filamentary structures observed in the interstellar medium (ISM) is a debated topic. The Planck all-sky maps of linearly polarized emission from dust at 353GHz provide the required combination of imaging and statistics to study the correlation between the structures of the Galactic magnetic field and of interstellar matter, both in the diffuse ISM and in molecular clouds. The data reveal structures, or ridges, in the intensity map with counterparts in the Stokes Q and/or U maps. We focus on structures at intermediate and high Galactic latitudes with column density from $10^{20}$ to $10^{22}$ cm$^{-2}$. We measure the magnetic field orientation on the plane of the sky from the polarization data, and present an algorithm to estimate the orientation of the ridges from the dust intensity map. We use analytical models to account for projection effects. Comparing polarization angles on and off the structures, we estimate the mean ratio between the strengths of the turbulent and mean components of the magnetic field to be between 0.6 and 1.0, with a preferred value of 0.8. We find that the ridges are preferentially aligned with the magnetic field measured on the structures. This trend becomes more striking for increasing polarization fraction and decreasing column density. We interpret the increase of alignment with polarization fraction as a consequence of projections effects. The decrease of alignment for high column density is not due to a loss of correlation between the structures and the geometry of the magnetic field. In molecular complexes, we observe structures perpendicular to the magnetic field, which cannot be accounted for by projection effects. We discuss our results in the context of models and MHD simulations, which describe the formation of structures in the magnetized ISM.

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Planck intermediate results. XXVIII. Interstellar gas and dust in the Chamaeleon clouds as seen by Fermi LAT and Planck

Shortened abstract: Observations of the nearby Chamaeleon clouds in gamma rays with the Fermi Large Area Telescope and in thermal dust emission with Planck and IRAS have been used with the HI and CO radio data to (i) map the gas column densities in the different phases and at the dark neutral medium (DNM) transition between the HI-bright and CO-bright media; (ii) constrain the CO-to-$H_2$ conversion factor, $X_{CO}$; (iii) probe the dust properties per gas nucleon in each gas phase and spatially across the clouds. We have separated clouds in velocity in HI and CO emission and modelled the 0.4-100 GeV intensity, the dust optical depth at 353 GHz, the thermal radiance of the large grains, and an estimate of the dust extinction empirically corrected for the starlight intensity, $A_{VQ}$. The gamma-ray emissivity spectra confirm that the GeV-TeV cosmic rays uniformly permeate all gas phases up to the CO cores. The dust and cosmic rays reveal large amounts of DNM gas, with comparable spatial distributions and twice as much mass as in the CO-bright clouds. We give constraints on the HI-DNM-CO transitions and CO-dark $H_2$ fractions for separate clouds. The corrected extinction provides the best fit to the total gas traced by the gamma rays, but we find evidence for a rise in $A_{VQ}/N_H$ and a steep rise in opacity, with increasing $N_H$ and $H_2$ fraction, and with decreasing dust temperature. We observe less variations for the specific power of the grains, except for a decline by half in the CO cores. This combined information suggests grain evolution. The gamma rays and dust radiance yield consistent $X_{CO}$ estimates near $0.7\times10^{20}$ cm$^{-2}$ (K km/s)$^{-1}$. The other dust tracers yield biased values because of the grain opacity rise in the CO clouds. These results also confirm a factor of 2 difference between $X_{CO}$ estimates at pc and kpc scales.

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