arXiv subjects

A. Hornstrup

Publications and source records attributed to A. Hornstrup.

At least 253 records · Page 14Linked to original sources

arXiv2016

The NuSTAR Extragalactic Surveys: The Number Counts of Active Galactic Nuclei and the Resolved Fraction of the Cosmic X-ray Background

We present the 3-8 keV and 8-24 keV number counts of active galactic nuclei (AGN) identified in the NuSTAR extragalactic surveys. NuSTAR has now resolved 33-39% of the X-ray background in the 8-24 keV band, directly identifying AGN with obscuring columns up to approximately 1e25 /cm2. In the softer 3-8 keV band the number counts are in general agreement with those measured by XMM-Newton and Chandra over the flux range 5e-15 < S(3 - 8 keV)/(erg/cm2/s) < 1e-12 probed by NuSTAR. In the hard 8-24 keV band NuSTAR probes fluxes over the range 2e-14 < S(8-24 keV)/(erg/cm2/s) < 1e-12, a factor of approximately 100 fainter than previous measurements. The 8-24 keV number counts match predictions from AGN population synthesis models, directly confirming the existence of a population of obscured and/or hard X-ray sources inferred from the shape of the integrated cosmic X-ray background. The measured NuSTAR counts lie significantly above simple extrapolation with a Euclidian slope to low flux of the Swift/BAT 15-55 keV number counts measured at higher fluxes S(15-55 keV) > 1e-11 erg/cm2/s, reflecting the evolution of the AGN population between the Swift/BAT local (z<0.1) sample and NuSTAR's z~1 sample. CXB synthesis models, which account for AGN evolution, lie above the Swift/BAT measurements, suggesting that they do not fully capture the evolution of obscured AGN at low redshifts.

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arXiv2016

First NuSTAR observations of the BL Lac - type blazar PKS~2155-304: constraints on the jet content and distribution of radiating particles

We report the first hard X-ray observations with NuSTAR of the BL Lac type blazar PKS 2155-304, augmented with soft X-ray data from XMM-Newton and gamma-ray data from the Fermi Large Area Telescope, obtained in April 2013 when the source was in a very low flux state. A joint NuSTAR and XMM spectrum, covering the energy range 0.5 - 60 keV, is best described by a model consisting of a log-parabola component with curvature beta = 0.3(+0.2,-0.1) and a (local) photon index 3.04 +/- 0.15 at photon energy of 2 keV, and a hard power-law tail with photon index 2.2 +/- 0.4. The hard X-ray tail can be smoothly joined to the quasi-simultaneous gamma-ray spectrum by a synchrotron self-Compton component produced by an electron distribution with index p = 2.2. Assuming that the power-law electron distribution extends down to the minimum electron Lorentz factor gamma_min = 1 and that there is one proton per electron, an unrealistically high total jet power L_p of roughly 10^47 erg/s is inferred. This can be reduced by two orders of magnitude either by considering a significant presence of electron-positron pairs with lepton-to-proton ratio of at least 30, or by introducing an additional, low-energy break in the electron energy distribution at the electron Lorentz factor gamma_br1 of roughly 100. In either case, the jet composition is expected to be strongly matter-dominated.

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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 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. XXV. Diffuse low-frequency Galactic foregrounds

(abridged) We discuss the Galactic foreground emission between 20 and 100GHz based on observations by Planck/WMAP. The Commander component-separation tool has been used to separate the various astrophysical processes in total intensity. Comparison with RRL templates verifies the recovery of the free-free emission along the Galactic plane. Comparison of the high-latitude Halpha emission with our free-free map shows residuals that correlate with dust optical depth, consistent with a fraction (~30%) of Halpha having been scattered by high-latitude dust. We highlight a number of diffuse spinning dust morphological features at high latitude. There is substantial spatial variation in the spinning dust spectrum, with the emission peak ranging from below 20GHz to more than 50GHz. There is a strong tendency for the spinning dust component near many prominent HII regions to have a higher peak frequency, suggesting that this increase in peak frequency is associated with dust in the photodissociation regions around the nebulae. The emissivity of spinning dust in these diffuse regions is of the same order as previous detections in the literature. Over the entire sky, the commander solution finds more anomalous microwave emission than the WMAP component maps, at the expense of synchrotron and free-free emission. This can be explained by the difficulty in separating multiple broadband components with a limited number of frequency maps. Future surveys (5-20GHz), will greatly improve the separation by constraining the synchrotron spectrum. We combine Planck/WMAP data to make the highest S/N ratio maps yet of the intensity of the all-sky polarized synchrotron emission at frequencies above a few GHz. Most of the high-latitude polarized emission is associated with distinct large-scale loops and spurs, and we re-discuss their structure...

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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

Planck intermediate results. XLII. Large-scale Galactic magnetic fields

Recent models for the large-scale Galactic magnetic fields in the literature have been largely constrained by synchrotron emission and Faraday rotation measures. We use three different but representative models to compare their predicted polarized synchrotron and dust emission with that measured by the Planck satellite. We first update these models to match the Planck synchrotron products using a common model for the cosmic-ray leptons. We discuss the impact on this analysis of the ongoing problems of component separation in the Planck microwave bands and of the uncertain cosmic-ray spectrum. In particular, the inferred degree of ordering in the magnetic fields is sensitive to these systematic uncertainties, and we further show the importance of considering the expected variations in the observables in addition to their mean morphology. We then compare the resulting simulated emission to the observed dust polarization and find that the dust predictions do not match the morphology in the Planck data but underpredict the dust polarization away from the plane. We modify one of the models to roughly match both observables at high latitudes by increasing the field ordering in the thin disc near the observer. Though this specific analysis is dependent on the component separation issues, we present the improved model as a proof of concept for how these studies can be advanced in future using complementary information from ongoing and planned observational projects.

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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 intermediate results. XLIII. The spectral energy distribution of dust in clusters of galaxies

Although infrared (IR) overall dust emission from clusters of galaxies has been statistically detected using data from the Infrared Astronomical Satellite (IRAS), it has not been possible to sample the spectral energy distribution (SED) of this emission over its peak, and thus to break the degeneracy between dust temperature and mass. By complementing the IRAS spectral coverage with Planck satellite data from 100 to 857 GHz, we provide new constraints on the IR spectrum of thermal dust emission in clusters of galaxies. We achieve this by using a stacking approach for a sample of several hundred objects from the Planck cluster sample; this procedure averages out fluctuations from the IR sky, allowing us to reach a significant detection of the faint cluster contribution. We also use the large frequency range probed by Planck, together with component-separation techniques, to remove the contamination from both cosmic microwave background anisotropies and the thermal Sunyaev-Zeldovich effect (tSZ) signal, which dominate below 353 GHz. By excluding dominant spurious signals or systematic effects, averaged detections are reported at frequencies between 353 and 5000 GHz. We confirm the presence of dust in clusters of galaxies at low and intermediate redshifts, yielding an SED with a shape similar to that of the Milky Way. Planck's beam does not allow us to investigate the detailed spatial distribution of this emission (e.g., whether it comes from intergalactic dust or simply the dust content of the cluster galaxies), but the radial distribution of the emission appears to follow that of the stacked SZ signal, and thus the extent of the clusters. The recovered SED allows us to constrain the dust mass responsible for the signal, as well as its temperature. We additionally explore the evolution of the IR emission as a function of cluster mass and redshift.

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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 2015 results. II. Low Frequency Instrument data processing

We present an updated description of the Planck Low Frequency Instrument (LFI) data processing pipeline, associated with the 2015 data release. We point out the places where our results and methods have remained unchanged since the 2013 paper and we highlight the changes made for the 2015 release, describing the products (especially timelines) and the ways in which they were obtained. We demonstrate that the pipeline is self-consistent (principally based on simulations) and report all null tests. For the first time, we present LFI maps in Stokes Q and U polarization. We refer to other related papers where more detailed descriptions of the LFI data processing pipeline may be found if needed.

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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

Planck 2015 results. III. LFI systematic uncertainties

We present the current accounting of systematic effect uncertainties for the Low Frequency Instrument (LFI) that are relevant to the 2015 release of the Planck cosmological results, showing the robustness and consistency of our data set, especially for polarization analysis. We use two complementary approaches: (i) simulations based on measured data and physical models of the known systematic effects; and (ii) analysis of difference maps containing the same sky signal ("null-maps"). The LFI temperature data are limited by instrumental noise. At large angular scales the systematic effects are below the cosmic microwave background (CMB) temperature power spectrum by several orders of magnitude. In polarization the systematic uncertainties are dominated by calibration uncertainties and compete with the CMB $E$-modes in the multipole range 10--20. Based on our model of all known systematic effects, we show that these effects introduce a slight bias of around $0.2\,σ$ on the reionization optical depth derived from the 70\,GHz $EE$ spectrum using the 30 and 353\,GHz channels as foreground templates. At 30\,GHz the systematic effects are smaller than the Galactic foreground at all scales in temperature and polarization, which allows us to consider this channel as a reliable template of synchrotron emission. We assess the residual uncertainties due to LFI effects on CMB maps and power spectra after component separation and show that these effects are smaller than the CMB amplitude at all scales. We also assess the impact on non-Gaussianity studies and find it to be negligible. Some residuals still appear in null maps from particular sky survey pairs, particularly at 30 GHz, suggesting possible straylight contamination due to an imperfect knowledge of the beam far sidelobes.

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arXiv2015

Multiwavelength Study of Quiescent States of Mrk 421 with Unprecedented Hard X-Ray Coverage Provided by NuSTAR in 2013

We present coordinated multiwavelength observations of the bright, nearby BL Lac object Mrk 421 taken in 2013 January-March, involving GASP-WEBT, Swift, NuSTAR, Fermi-LAT, MAGIC, VERITAS, and other collaborations and instruments, providing data from radio to very-high-energy (VHE) gamma-ray bands. NuSTAR yielded previously unattainable sensitivity in the 3-79 keV range, revealing that the spectrum softens when the source is dimmer until the X-ray spectral shape saturates into a steep power law with a photon index of approximately 3, with no evidence for an exponential cutoff or additional hard components up to about 80 keV. For the first time, we observed both the synchrotron and the inverse-Compton peaks of the spectral energy distribution (SED) simultaneously shifted to frequencies below the typical quiescent state by an order of magnitude. The fractional variability as a function of photon energy shows a double-bump structure which relates to the two bumps of the broadband SED. In each bump, the variability increases with energy which, in the framework of the synchrotron self-Compton model, implies that the electrons with higher energies are more variable. The measured multi-band variability, the significant X-ray-to-VHE correlation down to some of the lowest fluxes ever observed in both bands, the lack of correlation between optical/UV and X-ray flux, the low degree of polarization and its significant (random) variations, the short estimated electron cooling time, and the significantly longer variability timescale observed in the NuSTAR light curves point toward in-situ electron acceleration, and suggest that there are multiple compact regions contributing to the broadband emission of Mrk 421 during low-activity states.

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arXiv2015

Planck 2015 results. V. LFI calibration

We present a description of the pipeline used to calibrate the Planck Low Frequency Instrument (LFI) timelines into thermodynamic temperatures for the Planck 2015 data release, covering four years of uninterrupted operations. As in the 2013 data release, our calibrator is provided by the spin-synchronous modulation of the cosmic microwave background dipole, but we now use the orbital component, rather than adopting the Wilkinson Microwave Anisotropy Probe (WMAP) solar dipole. This allows our 2015 LFI analysis to provide an independent Solar dipole estimate, which is in excellent agreement with that of HFI and within $1σ$ (0.3% in amplitude) of the WMAP value. This 0.3% shift in the peak-to-peak dipole temperature from WMAP and a global overhaul of the iterative calibration code increases the overall level of the LFI maps by 0.45% (30 GHz), 0.64% (44 GHz), and 0.82% (70 GHz) in temperature with respect to the 2013 Planck data release, thus reducing the discrepancy with the power spectrum measured by WMAP. We estimate that the LFI calibration uncertainty is now at the level of 0.20% for the 70 GHz map, 0.26% for the 44 GHz map, and 0.35% for the 30 GHz map. We provide a detailed description of the impact of all the changes implemented in the calibration since the previous data release.

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arXiv2015

Planck intermediate results. XXXVII. Evidence of unbound gas from the kinetic Sunyaev-Zeldovich effect

By looking at the kinetic Sunyaev-Zeldovich effect (kSZ) in Planck nominal mission data, we present a significant detection of baryons participating in large-scale bulk flows around central galaxies (CGs) at redshift $z\approx 0.1$. We estimate the pairwise momentum of the kSZ temperature fluctuations at the positions of the CGC (Central Galaxy Catalogue) samples extracted from Sloan Digital Sky Survey (DR7) data. For the foreground-cleaned maps, we find $1.8$-$2.5σ$ detections of the kSZ signal, which are consistent with the kSZ evidence found in individual Planck raw frequency maps, although lower than found in the WMAP-9yr W band ($3.3σ$). We further reconstruct the peculiar velocity field from the CG density field, and compute for the first time the cross-correlation function between kSZ temperature fluctuations and estimates of CG radial peculiar velocities. This correlation function yields a $3.0$-$3.7$$σ$ detection of the peculiar motion of extended gas on Mpc scales, in flows correlated up to distances of 80-100 $h^{-1}$ Mpc. Both the pairwise momentum estimates and kSZ temperature-velocity field correlation find evidence for kSZ signatures out to apertures of 8 arcmin and beyond, corresponding to a physical radius of $> 1$ Mpc, more than twice the mean virial radius of halos. This is consistent with the predictions from hydro simulations that most of the baryons are outside the virialized halos. We fit a simple model, in which the temperature-velocity cross-correlation is proportional to the signal seen in a semi-analytic model built upon N-body simulations, and interpret the proportionality constant as an "effective" optical depth to Thomson scattering. We find $τ_T=(1.4\pm0.5)\times 10^{-4}$; the simplest interpretation of this measurement is that much of the gas is in a diffuse phase, which contributes little signal to X-ray or thermal SZ observations.

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arXiv2015

Planck intermediate results. XL. The Sunyaev-Zeldovich signal from the Virgo cluster

The Virgo cluster is the largest Sunyaev-Zeldovich (SZ) source in the sky, both in terms of angular size and total integrated flux. Planck's wide angular scale and frequency coverage, together with its high sensitivity, allow a detailed study of this large object through the SZ effect. Virgo is well resolved by Planck, showing an elongated structure, which correlates well with the morphology observed from X-rays, but extends beyond the observed X-ray signal. We find a good agreement between the SZ signal (or Compton paranmeter, y_c) observed by Planck and the expected signal inferred from X-ray observations and simple analytical models. Due to its proximity to us, the gas beyond the virial radius can be studied with unprecedented sensitivity by integrating the SZ signal over tens of square degrees. We study the signal in the outskirts of Virgo and compare it with analytical models and a constrained simulation of the environment of Virgo. Planck data suggest that significant amounts of low-density plasma surround Virgo out to twice the virial radius. We find the SZ signal in the outskirts of Virgo to be consistent with a simple model that extrapolates the inferred pressure at lower radii while assuming that the temperature stays in the keV range beyond the virial radius. The observed signal is also consistent with simulations and points to a shallow pressure profile in the outskirts of the cluster. This reservoir of gas at large radii can be linked with the hottest phase of the elusive warm/hot intergalactic medium. Taking the lack of symmetry of Virgo into account, we find that a prolate model is favoured by the combination of SZ and X-ray data, in agreement with predictions.

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arXiv2015

Planck 2015 results. IV. Low Frequency Instrument beams and window functions

This paper presents the characterization of the in-flight beams, the beam window functions, and the associated uncertainties for the Planck Low Frequency Instrument (LFI). The structure of the paper is similar to that presented in the 2013 Planck release; the main differences concern the beam normalization and the delivery of the window functions to be used for polarization analysis. The in-flight assessment of the LFI main beams relies on measurements performed during observations of Jupiter. By stacking data from seven Jupiter transits, the main beam profiles are measured down to -25 dB at 30 and 44 GHz, and down to -30 dB at 70 GHz. It has been confirmed that the agreement between the simulated beams and the measured beams is better than 1% at each LFI frequency band (within the 20 dB contour from the peak, the rms values are 0.1% at 30 and 70 GHz; 0.2% at 44 GHz). Simulated polarized beams are used for the computation of the effective beam window functions. The error budget for the window functions is estimated from both main beam and sidelobe contributions, and accounts for the radiometer band shapes. The total uncertainties in the effective beam window functions are 0.7% and 1% at 30 and 44 GHz, respectively (at $\ell \approx 600$); and 0.5% at 70 GHz (at $\ell \approx 1000$).

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