arXiv subjects

D. L. Clements

Publications and source records attributed to D. L. Clements.

At least 73 records · Page 4Linked to original sources

arXiv2016

Planck intermediate results. XLI. A map of lensing-induced B-modes

The secondary cosmic microwave background (CMB) $B$-modes stem from the post-decoupling distortion of the polarization $E$-modes due to the gravitational lensing effect of large-scale structures. These lensing-induced $B$-modes constitute both a valuable probe of the dark matter distribution and an important contaminant for the extraction of the primary CMB $B$-modes from inflation. Planck provides accurate nearly all-sky measurements of both the polarization $E$-modes and the integrated mass distribution via the reconstruction of the CMB lensing potential. By combining these two data products, we have produced an all-sky template map of the lensing-induced $B$-modes using a real-space algorithm that minimizes the impact of sky masks. The cross-correlation of this template with an observed (primordial and secondary) $B$-mode map can be used to measure the lensing $B$-mode power spectrum at multipoles up to $2000$. In particular, when cross-correlating with the $B$-mode contribution directly derived from the Planck polarization maps, we obtain lensing-induced $B$-mode power spectrum measurement at a significance level of $12\,σ$, which agrees with the theoretical expectation derived from the Planck best-fit $Λ$CDM model. This unique nearly all-sky secondary $B$-mode template, which includes the lensing-induced information from intermediate to small ($10\lesssim \ell\lesssim 1000$) angular scales, is delivered as part of the Planck 2015 public data release. It will be particularly useful for experiments searching for primordial $B$-modes, such as BICEP2/Keck Array or LiteBIRD, since it will enable an estimate to be made of the lensing-induced contribution to the measured total CMB $B$-modes.

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arXiv2016

Planck 2015 results. XV. Gravitational lensing

We present the most significant measurement of the cosmic microwave background (CMB) lensing potential to date (at a level of 40 sigma), using temperature and polarization data from the Planck 2015 full-mission release. Using a polarization-only estimator we detect lensing at a significance of 5 sigma. We cross-check the accuracy of our measurement using the wide frequency coverage and complementarity of the temperature and polarization measurements. Public products based on this measurement include an estimate of the lensing potential over approximately 70% of the sky, an estimate of the lensing potential power spectrum in bandpowers for the multipole range 40<L<400 and an associated likelihood for cosmological parameter constraints. We find good agreement between our measurement of the lensing potential power spectrum and that found in the best-fitting LCDM model based on the Planck temperature and polarization power spectra. Using the lensing likelihood alone we obtain a percent-level measurement of the parameter combination $σ_8 Ω_m^{0.25} = 0.591\pm 0.021$. We combine our determination of the lensing potential with the E-mode polarization also measured by Planck to generate an estimate of the lensing B-mode. We show that this lensing B-mode estimate is correlated with the B-modes observed directly by Planck at the expected level and with a statistical significance of 10 sigma, confirming Planck's sensitivity to this known sky signal. We also correlate our lensing potential estimate with the large-scale temperature anisotropies, detecting a cross-correlation at the 3 sigma level, as expected due to dark energy in the concordance LCDM model.

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arXiv2016

ALMA observations of Lyman-alpha Blob 1: halo sub-structure illuminated from within

We present new Atacama Large Millimeter/Submillimeter Array (ALMA) 850um continuum observations of the original Lyman-alpha Blob (LAB) in the SSA22 field at z=3.1 (SSA22-LAB01). The ALMA map resolves the previously identified submillimeter source into three components with total flux density S_850 = 1.68+/-0.06 mJy, corresponding to a star formation rate of ~150 M_sun/yr. The submillimeter sources are associated with several faint (m~27 mag) rest-frame ultraviolet sources identified in Hubble Space Telescope Imaging Spectrograph (STIS) clear filter imaging (~5850A). One of these companions is spectroscopically confirmed with Keck MOSFIRE to lie within 20 projected kpc and 250 km/s of one of the ALMA components. We postulate that some of these STIS sources represent a population of low-mass star-forming satellites surrounding the central submillimeter sources, potentially contributing to their growth and activity through accretion. Using a high resolution cosmological zoom simulation of a 10^13 M_sun halo at z=3, including stellar, dust and Ly-alpha radiative transfer, we can model the ALMA+STIS observations and demonstrate that Ly-alpha photons escaping from the central submillimeter sources are expected to resonantly scatter in neutral hydrogen, the majority of which is predicted to be associated with halo substructure. We show how this process gives rise to extended Ly-alpha emission with similar surface brightness and morphology to observed giant LABs.

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arXiv2016

HerMES: A search for high-redshift dusty galaxies in the HerMES Large Mode Survey - Catalogue, number counts and early results

Selecting sources with rising flux densities towards longer wavelengths from Herschel/SPIRE maps is an efficient way to produce a catalogue rich in high-redshift (z > 4) dusty star-forming galaxies. The effectiveness of this approach has already been confirmed by spectroscopic follow-up observations, but the previously available catalogues made this way are limited by small survey areas. Here we apply a map-based search method to 274 deg$^2$ of the HerMES Large Mode Survey (HeLMS) and create a catalogue of 477 objects with SPIRE flux densities $S_{500} > S_{350} >S_{250}$ and a $5 σ$ cut-off $S_{500} > $ 52 mJy. From this catalogue we determine that the total number of these "red" sources is at least an order of magnitude higher than predicted by galaxy evolution models. These results are in agreement with previous findings in smaller HerMES fields; however, due to our significantly larger sample size we are also able to investigate the shape of the red source counts for the first time. We have obtained spectroscopic redshift measurements for two of our sources using the Atacama Large Millimeter/submillimeter Array (ALMA). The redshifts z = 5.1 and z = 3.8 confirm that with our selection method we can indeed find high-redshift dusty star-forming galaxies.

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arXiv2016

Planck 2015 results. XVII. Constraints on primordial non-Gaussianity

The Planck full mission cosmic microwave background(CMB) temperature and E-mode polarization maps are analysed to obtain constraints on primordial non-Gaussianity(NG). Using three classes of optimal bispectrum estimators - separable template-fitting (KSW), binned, and modal - we obtain consistent values for the local, equilateral, and orthogonal bispectrum amplitudes, quoting as our final result from temperature alone fNL^local=2.5+\-5.7, fNL^equil=-16+\-70 and fNL^ortho=-34+\-33(68%CL). Combining temperature and polarization data we obtain fNL^local=0.8+\-5.0, fNL^equil=-4+\-43 and fNL^ortho=-26+\-21 (68%CL). The results are based on cross-validation of these estimators on simulations, are stable across component separation techniques, pass an extensive suite of tests, and are consistent with Minkowski functionals based measurements. The effect of time-domain de-glitching systematics on the bispectrum is negligible. In spite of these test outcomes we conservatively label the results including polarization data as preliminary, owing to a known mismatch of the noise model in simulations and the data. Beyond fNL estimates, we present model-independent reconstructions of the CMB bispectrum and derive constraints on early universe scenarios that generate NG, including general single-field and axion inflation, initial state modifications, parity-violating tensor bispectra, and directionally dependent vector models. We also present a wide survey of scale-dependent oscillatory bispectra, and we look for isocurvature NG. Our constraint on the local primordial trispectrum amplitude is gNL^local=(-9.0+\-7.7)x10^4 (68%CL), and we perform an analysis of additional trispectrum shapes. The global picture is one of consistency with the premises of the LambdaCDM cosmology, namely that the structure we observe today was sourced by adiabatic, passive, Gaussian, and primordial seed perturbations.[abridged]

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arXiv2016

The SCUBA-2 Cosmology Legacy Survey: 850um maps, catalogues and number counts

We present a catalogue of nearly 3,000 submillimetre sources detected at 850um over ~5 square degrees surveyed as part of the James Clerk Maxwell Telescope (JCMT) SCUBA-2 Cosmology Legacy Survey (S2CLS). This is the largest survey of its kind at 850um, probing a meaningful cosmic volume at the peak of star formation activity and increasing the sample size of submillimetre galaxies selected at 850um by an order of magnitude. We describe the wide 850um survey component of S2CLS, which covers the key extragalactic survey fields: UKIDSS-UDS, COSMOS, Akari-NEP, Extended Groth Strip, Lockman Hole North, SSA22 and GOODS-North. The average 1-sigma depth of S2CLS is 1.2 mJy/beam, approaching the SCUBA-2 850um confusion limit, which we determine to be ~0.8 mJy/beam. We measure the single dish 850um number counts to unprecedented accuracy, reducing the Poisson errors on the differential counts to approximately 4% at S_850~3mJy. With several independent fields, we investigate field-to-field variance, finding that the number counts on 0.5-1 degree scales are generally within 50% of the S2CLS mean for S_850>3mJy, with scatter consistent with the Poisson and estimated cosmic variance uncertainties, although there is a marginal (2-sigma) density enhancement in the GOODS-North field. The observed number counts are in reasonable agreement with recent phenomenological and semi-analytic models. Finally, the large solid angle of S2CLS allows us to measure the bright-end counts: at S_850>10mJy there are approximately ten sources per square degree, and we detect the distinctive up-turn in the number counts indicative of the detection of local sources of 850um emission and strongly lensed high-redshift galaxies. Here we describe the data collection and reduction procedures and present calibrated maps and a catalogue of sources; these are made publicly available.

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arXiv2016

Planck 2015 results. XI. CMB power spectra, likelihoods, and robustness of parameters

This paper presents the Planck 2015 likelihoods, statistical descriptions of the 2-point correlations of CMB data, using the hybrid approach employed previously: pixel-based at $\ell<30$ and a Gaussian approximation to the distribution of spectra at higher $\ell$. The main improvements are the use of more and better processed data and of Planck polarization data, and more detailed foreground and instrumental models, allowing further checks and enhanced immunity to systematics. Progress in foreground modelling enables a larger sky fraction. Improvements in processing and instrumental models further reduce uncertainties. For temperature, we perform an analysis of end-to-end instrumental simulations fed into the data processing pipeline; this does not reveal biases from residual instrumental systematics. The $Λ$CDM cosmological model continues to offer a very good fit to Planck data. The slope of primordial scalar fluctuations, $n_s$, is confirmed smaller than unity at more than 5σ from Planck alone. We further validate robustness against specific extensions to the baseline cosmology. E.g., the effective number of neutrino species remains compatible with the canonical value of 3.046. This first detailed analysis of Planck polarization concentrates on E modes. At low $\ell$ we use temperature at all frequencies and a subset of polarization. The frequency range improves CMB-foreground separation. Within the baseline model this requires a reionization optical depth $τ=0.078\pm0.019$, significantly lower than without high-frequency data for explicit dust monitoring. At high $\ell$ we detect residual errors in E, typically O($μ$K$^2$); we recommend temperature alone as the high-$\ell$ baseline. Nevertheless, Planck high-$\ell$ polarization allows a separate determination of $Λ$CDM parameters consistent with those from temperature alone.

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arXiv2016

Planck 2015 results. XIII. Cosmological parameters

We present results based on full-mission Planck observations of temperature and polarization anisotropies of the CMB. These data are consistent with the six-parameter inflationary LCDM cosmology. From the Planck temperature and lensing data, for this cosmology we find a Hubble constant, H0= (67.8 +/- 0.9) km/s/Mpc, a matter density parameter Omega_m = 0.308 +/- 0.012 and a scalar spectral index with n_s = 0.968 +/- 0.006. (We quote 68% errors on measured parameters and 95% limits on other parameters.) Combined with Planck temperature and lensing data, Planck LFI polarization measurements lead to a reionization optical depth of tau = 0.066 +/- 0.016. Combining Planck with other astrophysical data we find N_ eff = 3.15 +/- 0.23 for the effective number of relativistic degrees of freedom and the sum of neutrino masses is constrained to < 0.23 eV. Spatial curvature is found to be |Omega_K| < 0.005. For LCDM we find a limit on the tensor-to-scalar ratio of r <0.11 consistent with the B-mode constraints from an analysis of BICEP2, Keck Array, and Planck (BKP) data. Adding the BKP data leads to a tighter constraint of r < 0.09. We find no evidence for isocurvature perturbations or cosmic defects. The equation of state of dark energy is constrained to w = -1.006 +/- 0.045. Standard big bang nucleosynthesis predictions for the Planck LCDM cosmology are in excellent agreement with observations. We investigate annihilating dark matter and deviations from standard recombination, finding no evidence for new physics. The Planck results for base LCDM are in agreement with BAO data and with the JLA SNe sample. However the amplitude of the fluctuations is found to be higher than inferred from rich cluster counts and weak gravitational lensing. Apart from these tensions, the base LCDM cosmology provides an excellent description of the Planck CMB observations and many other astrophysical data sets.

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arXiv2016

Planck intermediate results. XLV. Radio spectra of northern extragalactic radio sources

Continuum spectra covering centimetre to submillimetre wavelengths are presented for a northern sample of 104 extragalactic radio sources, mainly active galactic nuclei, based on four-epoch Planck data. The nine Planck frequencies, from 30 to 857 GHz, are complemented by a set of simultaneous ground-based radio observations between 1.1 and 37 GHz. The single-survey Planck data confirm that the flattest high-frequency radio spectral indices are close to zero, indicating that the original accelerated electron energy spectrum is much harder than commonly thought, with power-law index around 1.5 instead of the canonical 2.5. The radio spectra peak at high frequencies and exhibit a variety of shapes. For a small set of low-z sources, we find a spectral upturn at high frequencies, indicating the presence of intrinsic cold dust. Variability can generally be approximated by achromatic variations, while sources with clear signatures of evolving shocks appear to be limited to the strongest outbursts.

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arXiv2016

Planck 2015 results. XVIII. Background geometry & topology

Full-sky CMB maps from the 2015 Planck release allow us to detect departures from global isotropy on the largest scales. We present the first searches using CMB polarization for correlations induced by a non-trivial topology with a fundamental domain intersecting, or nearly intersecting, the last scattering surface (at comoving distance $χ_{rec}$). We specialize to flat spaces with toroidal and slab topologies, finding that explicit searches for the latter are sensitive to other topologies with antipodal symmetry. These searches yield no detection of a compact topology at a scale below the diameter of the last scattering surface. The limits on the radius $R_i$ of the largest sphere inscribed in the topological domain (at log-likelihood-ratio $Δ\ln{L}>-5$ relative to a simply-connected flat Planck best-fit model) are $R_i>0.97χ_{rec}$ for the cubic torus and $R_i>0.56χ_{rec}$ for the slab. The limit for the cubic torus from the matched-circles search is numerically equivalent, $R_i>0.97χ_{rec}$ (99% CL) from polarisation data alone. We also perform a Bayesian search for a Bianchi VII$_h$ geometry. In the non-physical setting where the Bianchi cosmology is decoupled from the standard cosmology, Planck temperature data favour the inclusion of a Bianchi component. However, the cosmological parameters generating this pattern are in strong disagreement with those found from CMB anisotropy data alone. Fitting the induced polarization pattern for this model to Planck data requires an amplitude of $-0.1\pm0.04$ compared to +1 if the model were to be correct. In the physical setting where the Bianchi parameters are fit simultaneously with the standard cosmological parameters, we find no evidence for a Bianchi VII$_h$ cosmology and constrain the vorticity of such models to $(ω/H)_0<7.6\times10^{-10}$ (95% CL). [Abridged]

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arXiv2016

H-ATLAS: A Candidate High Redshift Cluster/Protocluster of Star-Forming Galaxies

We investigate the region around the Planck-detected z=3.26 gravitationally lensed galaxy HATLAS J114637.9-001132 (hereinafter HATLAS12-00) using both archival Herschel data from the H-ATLAS survey and using submm data obtained with both LABOCA and SCUBA2. The lensed source is found to be surrounded by a strong overdensity of both Herschel-SPIRE sources and submm sources. We detect 17 bright (S_870 >~7 mJy) sources at >4sigma closer than 5 arcmin to the lensed object at 850/870 microns. Ten of these sources have good cross-identifications with objects detected by Herschel-SPIRE which have redder colours than other sources in the field, with 350 micron flux > 250 micron flux, suggesting that they lie at high redshift. Submillimeter Array (SMA) observations localise one of these companions to ~1 arcsecond, allowing unambiguous cross identification with a 3.6 and 4.5 micron Spitzer source. The optical/near-IR spectral energy distribution (SED) of this source is measured by further observations and found to be consistent with z>2, but incompatible with lower redshifts. We conclude that this system may be a galaxy cluster/protocluster or larger scale structure that contains a number of galaxies undergoing starbursts at the same time.

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arXiv2016

Planck 2015 results. XIV. Dark energy and modified gravity

We study the implications of Planck data for models of dark energy (DE) and modified gravity (MG), beyond the cosmological constant scenario. We start with cases where the DE only directly affects the background evolution, considering Taylor expansions of the equation of state, principal component analysis and parameterizations related to the potential of a minimally coupled DE scalar field. When estimating the density of DE at early times, we significantly improve present constraints. We then move to general parameterizations of the DE or MG perturbations that encompass both effective field theories and the phenomenology of gravitational potentials in MG models. Lastly, we test a range of specific models, such as k-essence, f(R) theories and coupled DE. In addition to the latest Planck data, for our main analyses we use baryonic acoustic oscillations, type-Ia supernovae and local measurements of the Hubble constant. We further show the impact of measurements of the cosmological perturbations, such as redshift-space distortions and weak gravitational lensing. These additional probes are important tools for testing MG models and for breaking degeneracies that are still present in the combination of Planck and background data sets. All results that include only background parameterizations are in agreement with LCDM. When testing models that also change perturbations (even when the background is fixed to LCDM), some tensions appear in a few scenarios: the maximum one found is \sim 2 sigma for Planck TT+lowP when parameterizing observables related to the gravitational potentials with a chosen time dependence; the tension increases to at most 3 sigma when external data sets are included. It however disappears when including CMB lensing.

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arXiv2016

Planck 2015 results. XIX. Constraints on primordial magnetic fields

We compute and investigate four types of imprint of a stochastic background of primordial magnetic fields (PMFs) on the cosmic microwave background (CMB) anisotropies: the impact of PMFs on the CMB spectra; the effect on CMB polarization induced by Faraday rotation; the impact of PMFs on the ionization history; magnetically-induced non-Gaussianities; and the magnetically-induced breaking of statistical isotropy. Overall, Planck data constrain the amplitude of PMFs to less than a few nanogauss. In particular, individual limits coming from the analysis of the CMB angular power spectra, using the Planck likelihood, are $B_{1\,\mathrm{Mpc}}< 4.4$ nG (where $B_{1\,\mathrm{Mpc}}$ is the comoving field amplitude at a scale of 1 Mpc) at 95% confidence level, assuming zero helicity, and $B_{1\,\mathrm{Mpc}}< 5.6$ nG for a maximally helical field.For nearly scale-invariant PMFs we obtain $B_{1\,\mathrm{Mpc}}<2.0$ nG and $B_{1\,\mathrm{Mpc}}<0.9$ nG if the impact of PMFs on the ionization history of the Universe is included. From the analysis of magnetically-induced non-Gaussianity we obtain three different values, corresponding to three applied methods, all below 5 nG. The constraint from the magnetically-induced passive-tensor bispectrum is $B_{1\,\mathrm{Mpc}}< 2.8$ nG. A search for preferred directions in the magnetically-induced passive bispectrum yields $B_{1\,\mathrm{Mpc}}< 4.5$ nG, whereas the the compensated-scalar bispectrum gives $B_{1\,\mathrm{Mpc}}< 3$ nG. The analysis of the Faraday rotation of CMB polarization by PMFs uses the Planck power spectra in $EE$ and $BB$ at 70 GHz and gives $B_{1\,\mathrm{Mpc}}< 1380$ nG. In our final analysis, we consider the harmonic-space correlations produced by Alfvén waves, finding no significant evidence for the presence of these waves. Together, these results comprise a comprehensive set of constraints on possible PMFs with Planck data.

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arXiv2016

Planck intermediate results. XXIX. All-sky dust modelling with Planck, IRAS, and WISE observations

We present all-sky modelling of the high resolution Planck, IRAS, and WISE infrared (IR) observations using the physical dust model presented by Draine and Li in 2007 (DL). We study the performance and results of this model, and discuss implications for future dust modelling. The present work extends the DL dust modelling carried out on nearby galaxies using Herschel and Spitzer data to Galactic dust emission. We employ the DL dust model to generate maps of the dust mass surface density, the optical extinction Av, and the starlight intensity parametrized by Umin. The DL model reproduces the observed spectral energy distribution (SED) satisfactorily over most of the sky, with small deviations in the inner Galactic disk and in low ecliptic latitude areas. We compare the DL optical extinction Av for the diffuse interstellar medium with optical estimates for 2 10^5 quasi-stellar objects (QSOs) observed in the Sloan digital sky survey. The DL Av estimates are larger than those determined towards QSOs by a factor of about 2, which depends on Umin. The DL fitting parameter Umin, effectively determined by the wavelength where the SED peaks, appears to trace variations in the far-IR opacity of the dust grains per unit Av, and not only in the starlight intensity. To circumvent the model deficiency, we propose an empirical renormalization of the DL Av estimate, dependent of Umin, which compensates for the systematic differences found with QSO observations. This renormalization also brings into agreement the DL Av estimates with those derived for molecular clouds from the near-IR colours of stars in the 2 micron all sky survey. The DL model and the QSOs data are used to compress the spectral information in the Planck and IRAS observations for the diffuse ISM to a family of 20 SEDs normalized per Av, parameterized by Umin, which may be used to test and empirically calibrate dust models.

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arXiv2016

Planck 2015 results. XXVI. The Second Planck Catalogue of Compact Sources

The Second Planck Catalogue of Compact Sources is a catalogue of sources detected in single-frequency maps from the full duration of the Planck mission and supersedes previous versions of the Planck compact source catalogues. It consists of compact sources, both Galactic and extragalactic, detected over the entire sky. Compact sources detected in the lower frequency channels are assigned to the PCCS2, while at higher frequencies they are assigned to one of two sub-catalogues, the PCCS2 or PCCS2E, depending on their location on the sky. The first of these catalogues covers most of the sky and allows the user to produce subsamples at higher reliabilities than the target 80% integral reliability of the catalogue. The PCCS2E contains sources detected in sky regions where the diffuse emission makes it difficult to quantify the reliability of the detections. Both the PCCS2 and PCCS2E include polarization measurements, in the form of polarized flux densities, or upper limits, and orientation angles for all seven polarization-sensitive Planck channels. The improved data-processing of the full-mission maps and their reduced noise levels allow us to increase the number of objects in the catalogue, improving its completeness for the target 80 % reliability as compared with the previous versions, the PCCS and ERCSC catalogues.

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arXiv2016

Planck Intermediate Results. XXXVI. Optical identification and redshifts of Planck SZ sources with telescopes in the Canary Islands Observatories

We present the results of approximately three years of observations of Planck Sunyaev-Zeldovich (SZ) sources with telescopes at the Canary Islands observatories as part of the general optical follow-up programme undertaken by the Planck collaboration. In total, 78 SZ sources are discussed. Deep-imaging observations were obtained for most of these sources; spectroscopic observations in either in long-slit or multi-object modes were obtained for many. We effectively used 37.5 clear nights. We found optical counterparts for 73 of the 78 candidates. This sample includes 53 spectroscopic redshift determinations, 20 of them obtained with a multi-object spectroscopic mode. The sample contains new redshifts for 27 Planck clusters that were not included in the first Planck SZ source catalogue (PSZ1).

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arXiv2016

Witnessing the birth of the red sequence: ALMA high-resolution imaging of [CII] and dust in two interacting ultra-red starbursts at z = 4.425

Exploiting the sensitivity and spatial resolution of the Atacama Large Millimeter/submillimeter Array (ALMA), we have studied the morphology and the physical scale of the interstellar medium - both gas and dust - in SGP38326, an unlensed pair of interacting starbursts at $z= 4.425$. SGP38326 is the most luminous star bursting system known at $z > 4$ with an IR-derived ${\rm SFR \sim 4300 \,} M_\odot \, {\rm yr}^{-1}$. SGP38326 also contains a molecular gas reservoir among the most massive ever found in the early Universe, and it is the likely progenitor of a massive, red-and-dead elliptical galaxy at $z \sim 3$. Probing scales of $\sim 0.1"$ or $\sim 800 \, {\rm pc}$ we find that the smooth distribution of the continuum emission from cool dust grains contrasts with the more irregular morphology of the gas, as traced by the [CII] fine structure emission. The gas is also extended over larger physical scales than the dust. The velocity information provided by the resolved [CII] emission reveals that the dynamics of the two components of SGP38326 are compatible with disk-like, ordered rotation, but also reveals an ISM which is turbulent and unstable. Our observations support a scenario where at least a subset of the most distant extreme starbursts are highly dissipative mergers of gas-rich galaxies.

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arXiv2016

Planck 2015 results. XVI. Isotropy and statistics of the CMB

We test the statistical isotropy and Gaussianity of the cosmic microwave background (CMB) anisotropies using observations made by the Planck satellite. Our results are based mainly on the full Planck mission for temperature, but also include some polarization measurements. In particular, we consider the CMB anisotropy maps derived from the multi-frequency Planck data by several component-separation methods. For the temperature anisotropies, we find excellent agreement between results based on these sky maps over both a very large fraction of the sky and a broad range of angular scales, establishing that potential foreground residuals do not affect our studies. Tests of skewness, kurtosis, multi-normality, N-point functions, and Minkowski functionals indicate consistency with Gaussianity, while a power deficit at large angular scales is manifested in several ways, for example low map variance. The results of a peak statistics analysis are consistent with the expectations of a Gaussian random field. The "Cold Spot" is detected with several methods, including map kurtosis, peak statistics, and mean temperature profile. We thoroughly probe the large-scale dipolar power asymmetry, detecting it with several independent tests, and address the subject of a posteriori correction. Tests of directionality suggest the presence of angular clustering from large to small scales, but at a significance that is dependent on the details of the approach. We perform the first examination of polarization data, finding the morphology of stacked peaks to be consistent with the expectations of statistically isotropic simulations. Where they overlap, these results are consistent with the Planck 2013 analysis based on the nominal mission data and provide our most thorough view of the statistics of the CMB fluctuations to date.

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