arXiv subjects

P. de Bernardis

Publications and source records attributed to P. de Bernardis.

At least 91 records · Page 5Linked to original sources

arXiv2019

Strong evidence of Anomalous Microwave Emission from the flux density spectrum of M31

We have observed the Andromeda galaxy, Messier 31 (M31), at 6.7GHz with the Sardinia Radio Telescope. We mapped the radio emission in the C-band, re-analyzed WMAP and Planck maps, as well as other ancillary data, and we have derived an overall integrated flux density spectrum from the radio to the infrared. This allowed us to estimate the emission budget from M31. Integrating over the whole galaxy, we found strong and highly significant evidence for anomalous microwave emission (AME), at the level of (1.45+0.17-0.19)Jy at the peaking frequency of ~25GHz. Decomposing the spectrum into known emission mechanisms such as free-free, synchrotron, thermal dust, and AME arising from electric dipole emission from rapidly rotating dust grains, we found that the overall emission from M31 is dominated, at frequencies below 10GHz, by synchrotron emission with a spectral index of -1.10+0.10-0.08, with subdominant free-free emission. At frequencies >10GHz, AME has a similar intensity to that of synchrotron and free-free emission, overtaking them between 20GHz and 50GHz, whereas thermal dust emission dominates the emission budget at frequencies above 60GHz, as expected.

astro-ph.GA↗

arXiv2019

Systematic effects induced by Half Wave Plate precession into Cosmic Microwave Background polarization measurements

The most accessible method to measure polarization features of the CMB radiation is by means of a Stokes Polarimeter based on the rotation of an Half Wave Plate. The current observational cosmology is starting to be limited by the presence of systematic effects. The Stokes polarimeter with a rotating Half Wave Plate (HWP) has the advantage of mitigating a long list of potential systematics, by modulation of the linearly polarized component of the radiation, but the presence of the rotating HWP can by itself introduce new systematic effects, which must be under control, representing one of the most critical part in the design of a B-Modes experiment. In this paper we present, simulate and analyse the spurious signal arising from the precession of a rotating HWP. We first find an analytical formula for the impact of the systematic effect induced by the HWP precession on the propagating radiation, using the 3D generalization of the Muller formalism. We then perform several numerical simulations, showing the effect induced on the Stokes parameters by this systematic. We also derive and discuss the impact into B-modes measured by a satellite experiment. We find the analytical formula for the Stokes parameters from a Stokes polarimeter where the HWP follows a precessional motion with an angle $θ_0$. We show the result depending on the HWP inertia tensor, spinning speed and on $θ_0$. The result of numerical simulations is reported as a simple timeline of the electric fields. Finally, assuming to observe all the sky with a satellite mission, we analyze the effect on B-modes measurements. The effect is not negligible giving the current B-modes experiments sensitivity, therefore it is a systematic which needs to be carefully considered for future experiments.

astro-ph.IM↗

arXiv2019

Planck 2018 results. IX. Constraints on primordial non-Gaussianity

We analyse the Planck full-mission cosmic microwave background (CMB) temperature and E-mode polarization maps to obtain constraints on primordial non-Gaussianity (NG). We compare estimates obtained from separable template-fitting, binned, and modal bispectrum estimators, finding consistent values for the local, equilateral, and orthogonal bispectrum amplitudes. Our combined temperature and polarization analysis produces the following results: f_NL^local = -0.9 +\- 5.1; f_NL^equil = -26 +\- 47; and f_NL^ortho = - 38 +\- 24 (68%CL, statistical). These results include the low-multipole (4 <= l < 40) polarization data, not included in our previous analysis, pass an extensive battery of tests, and are stable with respect to our 2015 measurements. Polarization bispectra display a significant improvement in robustness; they can now be used independently to set NG constraints. We consider a large number of additional cases, e.g. scale-dependent feature and resonance bispectra, isocurvature primordial NG, and parity-breaking models, where we also place tight constraints but do not detect any signal. The non-primordial lensing bispectrum is detected with an improved significance compared to 2015, excluding the null hypothesis at 3.5 sigma. We present model-independent reconstructions and analyses of the CMB bispectrum. Our final constraint on the local trispectrum shape is g_NLl^local = (-5.8 +\-6.5) x 10^4 (68%CL, statistical), while constraints for other trispectra are also determined. We constrain the parameter space of different early-Universe scenarios, including general single-field models of inflation, multi-field and axion field parity-breaking models. Our results provide a high-precision test for structure-formation scenarios, in complete agreement with the basic picture of the LambdaCDM cosmology regarding the statistics of the initial conditions (abridged).

astro-ph.CO↗

arXiv2019

Spectral Distortions of the CMB as a Probe of Inflation, Recombination, Structure Formation and Particle Physics

Following the pioneering observations with COBE in the early 1990s, studies of the cosmic microwave background (CMB) have focused on temperature and polarization anisotropies. CMB spectral distortions - tiny departures of the CMB energy spectrum from that of a perfect blackbody - provide a second, independent probe of fundamental physics, with a reach deep into the primordial Universe. The theoretical foundation of spectral distortions has seen major advances in recent years, which highlight the immense potential of this emerging field. Spectral distortions probe a fundamental property of the Universe - its thermal history - thereby providing additional insight into processes within the cosmological standard model (CSM) as well as new physics beyond. Spectral distortions are an important tool for understanding inflation and the nature of dark matter. They shed new light on the physics of recombination and reionization, both prominent stages in the evolution of our Universe, and furnish critical information on baryonic feedback processes, in addition to probing primordial correlation functions at scales inaccessible to other tracers. In principle the range of signals is vast: many orders of magnitude of discovery space could be explored by detailed observations of the CMB energy spectrum. Several CSM signals are predicted and provide clear experimental targets, some of which are already observable with present-day technology. Confirmation of these signals would extend the reach of the CSM by orders of magnitude in physical scale as the Universe evolves from the initial stages to its present form. The absence of these signals would pose a huge theoretical challenge, immediately pointing to new physics.

astro-ph.CO↗

arXiv2019

The short wavelength instrument for the polarization explorer balloon-borne experiment: Polarization modulation issues

In this paper we investigate the impact of using a polarization modulator in the Short Wavelenght Instrument for the Polarization Explorer (SWIPE) of the Large Scale Polarization Explorer (LSPE). The experiment is optimized to measure the linear polarization of the Cosmic Microwave Background at large angular scales during a circumpolar long-duration stratospheric balloon mission, and uses multi-mode bolometers cooled at 0.3 K. The 330 detectors cover 3 bands at 140 GHz, 220 GHz and 240 GHz. Polarimetry is achieved by means of a large rotating half-wave plate (HWP) and a single wire-grid polarizer in front of the arrays. The polarization modulator is the first polarization-active component of the optical chain, reducing significantly the effect of instrumental polarization. A trade-off study comparing stepped vs spinning HWPs drives the choice towards the second. Modulating the CMB polarization signal at 4 times the spin frequency moves it away from $1/f$ noise from the detectors and the residual atmosphere. The HWP is cooled at 1.6 K to reduce the background on the detectors. Furthermore its polarized emission combined with the emission of the polarizer produces spurious signals modulated at $2f$ and $4f$. The $4f$ component is synchronous with the signal of interest and has to characterized to be removed from cosmological data.

astro-ph.IM↗

arXiv2019

Kinetic Inductance Detectors for the OLIMPO experiment: design and pre-flight characterization

We designed, fabricated, and characterized four arrays of horn--coupled, lumped element kinetic inductance detectors (LEKIDs), optimized to work in the spectral bands of the balloon-borne OLIMPO experiment. OLIMPO is a 2.6 m aperture telescope, aimed at spectroscopic measurements of the Sunyaev-Zel'dovich (SZ) effect. OLIMPO will also validate the LEKID technology in a representative space environment. The corrected focal plane is filled with diffraction limited horn-coupled KID arrays, with 19, 37, 23, 41 active pixels respectively at 150, 250, 350, and 460$\:$GHz. Here we report on the full electrical and optical characterization performed on these detector arrays before the flight. In a dark laboratory cryostat, we measured the resonator electrical parameters, such as the quality factors and the electrical responsivities, at a base temperature of 300$\:$mK. The measured average resonator $Q$s are 1.7$\times{10^4}$, 7.0$\times{10^4}$, 1.0$\times{10^4}$, and 1.0$\times{10^4}$ for the 150, 250, 350, and 460$\:$GHz arrays, respectively. The average electrical phase responsivities on resonance are 1.4$\:$rad/pW, 1.5$\:$rad/pW, 2.1$\:$rad/pW, and 2.1$\:$rad/pW; the electrical noise equivalent powers are 45$\:\rm{aW/\sqrt{Hz}}$, 160$\:\rm{aW/\sqrt{Hz}}$, 80$\:\rm{aW/\sqrt{Hz}}$, and 140$\:\rm{aW/\sqrt{Hz}}$, at 12 Hz. In the OLIMPO cryostat, we measured the optical properties, such as the noise equivalent temperatures (NET) and the spectral responses. The measured NET$_{\rm RJ}$s are $200\:μ\rm{K\sqrt{s}}$, $240\:μ\rm{K\sqrt{s}}$, $240\:μ\rm{K\sqrt{s}}$, and $\:340μ\rm{K\sqrt{s}}$, at 12 Hz; under 78, 88, 92, and 90 mK Rayleigh-Jeans blackbody load changes respectively for the 150, 250, 350, and 460 GHz arrays. The spectral responses were characterized with the OLIMPO differential Fourier transform spectrometer (DFTS) up to THz frequencies, with a resolution of 1.8 GHz.

astro-ph.IM↗

arXiv2019

Kinetic Inductance Detectors and readout electronics for the OLIMPO experiment

Kinetic Inductance Detectors (KIDs) are superconductive low$-$temperature detectors useful for astrophysics and particle physics. We have developed arrays of lumped elements KIDs (LEKIDs) sensitive to microwave photons, optimized for the four horn-coupled focal planes of the OLIMPO balloon-borne telescope, working in the spectral bands centered at 150 GHz, 250 GHz, 350 GHz, and 460 GHz. This is aimed at measuring the spectrum of the Sunyaev-Zel'dovich effect for a number of galaxy clusters, and will validate LEKIDs technology in a space-like environment. Our detectors are optimized for an intermediate background level, due to the presence of residual atmosphere and room--temperature optical system and they operate at a temperature of 0.3 K. The LEKID planar superconducting circuits are designed to resonate between 100 and 600 MHz, and to match the impedance of the feeding waveguides; the measured quality factors of the resonators are in the $10^{4}-10^{5}$ range, and they have been tuned to obtain the needed dynamic range. The readout electronics is composed of a $cold$ $part$, which includes a low noise amplifier, a dc$-$block, coaxial cables, and power attenuators; and a $room-temperature$ $part$, FPGA$-$based, including up and down-conversion microwave components (IQ modulator, IQ demodulator, amplifiers, bias tees, attenuators). In this contribution, we describe the optimization, fabrication, characterization and validation of the OLIMPO detector system.

astro-ph.IM↗

arXiv2019

Planck 2018 results. XII. Galactic astrophysics using polarized dust emission

We present 353 GHz full-sky maps of the polarization fraction $p$, angle $ψ$, and dispersion of angles $S$ of Galactic dust thermal emission produced from the 2018 release of Planck data. We confirm that the mean and maximum of $p$ decrease with increasing $N_H$. The uncertainty on the maximum polarization fraction, $p_\mathrm{max}=22.0$% at 80 arcmin resolution, is dominated by the uncertainty on the zero level in total intensity. The observed inverse behaviour between $p$ and $S$ is interpreted with models of the polarized sky that include effects from only the topology of the turbulent Galactic magnetic field. Thus, the statistical properties of $p$, $ψ$, and $S$ mostly reflect the structure of the magnetic field. Nevertheless, we search for potential signatures of varying grain alignment and dust properties. First, we analyse the product map $S \times p$, looking for residual trends. While $p$ decreases by a factor of 3--4 between $N_H=10^{20}$ cm$^{-2}$ and $N_H=2\times 10^{22}$ cm$^{-2}$, $S \times p$ decreases by only about 25%, a systematic trend observed in both the diffuse ISM and molecular clouds. Second, we find no systematic trend of $S \times p$ with the dust temperature, even though in the diffuse ISM lines of sight with high $p$ and low $S$ tend to have colder dust. We also compare Planck data with starlight polarization in the visible at high latitudes. The agreement in polarization angles is remarkable. Two polarization emission-to-extinction ratios that characterize dust optical properties depend only weakly on $N_H$ and converge towards the values previously determined for translucent lines of sight. We determine an upper limit for the polarization fraction in extinction of 13%, compatible with the $p_\mathrm{max}$ observed in emission. These results provide strong constraints for models of Galactic dust in diffuse gas.

astro-ph.GA↗

arXiv2019

Kinetic Inductance Detectors for the OLIMPO experiment: in--flight operation and performance

We report on the performance of lumped--elements Kinetic Inductance Detector (KID) arrays for mm and sub--mm wavelengths, operated at 0.3K during the stratospheric flight of the OLIMPO payload, at an altitude of 37.8 km. We find that the detectors can be tuned in-flight, and their performance is robust against radiative background changes due to varying telescope elevation. We also find that the noise equivalent power of the detectors in flight is significantly reduced with respect to the one measured in the laboratory, and close to photon-noise limited performance. The effect of primary cosmic rays crossing the detector is found to be consistent with the expected ionization energy loss with phonon-mediated energy transfer from the ionization sites to the resonators. In the OLIMPO detector arrays, at float, cosmic ray events affect less than 4% of the detector samplings for all the pixels of all the arrays, and less than 1% of the samplings for most of the pixels. These results are also representative of what one can expect from primary cosmic rays in a satellite mission with similar KIDs and instrument environment.

astro-ph.IM↗

arXiv2019

The geometry of the magnetic field in the Central Molecular Zone measured by PILOT

We present the first far infrared (FIR) dust emission polarization map covering the full extent Milky Way's Central molecular zone (CMZ). The data, obtained with the PILOT balloon-borne experiment, covers the Galactic Center region $-2\,^\circ<l<2\,^\circ$, $-4\,^\circ<b<3\,^\circ$ at a wavelength of 240 $μ$m and an angular resolution $2.2\,'$. From our measured dust polarization angles, we infer a magnetic field orientation projected onto the plane of the sky that is remarkably ordered over the full extent of the CMZ, with an average tilt angle of $\simeq 22\,^\circ$ clockwise with respect to the Galactic plane. Our results confirm previous claims that the field traced by dust polarized emission is oriented nearly orthogonal to the field traced by GHz radio synchrotron emission in the Galactic Center region. The observed field structure is globally compatible with the latest Planck polarization data at 353 GHz and 217 GHz. Upon subtraction of the extended emission in our data, the mean field orientation that we obtain shows good agreement with the mean field orientation measured at higher angular resolution by the JCMT within the 20 km/s and 50 km/s molecular clouds. We find no evidence that the magnetic field orientation is related to the 100 pc twisted ring structure within the CMZ. We propose that the low polarization fraction in the Galactic Center region and the highly ordered projected field orientation can be reconciled if the field is strong, with a 3D geometry that is is mostly oriented $\simeq 15\,^\circ$ with respect to the line-of-sight towards the Galactic center. Assuming equipartition between the magnetic pressure and ram pressure, we obtain magnetic field strengths estimates as high as a few mG for several CMZ molecular clouds.

astro-ph.GA↗

arXiv2018

Planck 2018 results. XI. Polarized dust foregrounds

The study of polarized dust emission has become entwined with the analysis of the cosmic microwave background (CMB) polarization. We use new Planck maps to characterize Galactic dust emission as a foreground to the CMB polarization. We present Planck EE, BB, and TE power spectra of dust polarization at 353 GHz for six nested sky regions covering from 24 to 71 % of the sky. We present power-law fits to the angular power spectra, yielding evidence for statistically significant variations of the exponents over sky regions and a difference between the values for the EE and BB spectra. The TE correlation and E/B power asymmetry extend to low multipoles that were not included in earlier Planck polarization papers. We also report evidence for a positive TB dust signal. Combining data from Planck and WMAP, we determine the amplitudes and spectral energy distributions (SEDs) of polarized foregrounds, including the correlation between dust and synchrotron polarized emission, for the six sky regions as a function of multipole. This quantifies the challenge of the component separation procedure required for detecting the reionization and recombination peaks of primordial CMB B modes. The SED of polarized dust emission is fit well by a single-temperature modified blackbody emission law from 353 GHz to below 70 GHz. For a dust temperature of 19.6 K, the mean spectral index for dust polarization is $β_{\rm d}^{P} = 1.53\pm0.02 $. By fitting multi-frequency cross-spectra, we examine the correlation of the dust polarization maps across frequency. We find no evidence for decorrelation. If the Planck limit for the largest sky region applies to the smaller sky regions observed by sub-orbital experiments, then decorrelation might not be a problem for CMB experiments aiming at a primordial B-mode detection limit on the tensor-to-scalar ratio $r\simeq0.01$ at the recombination peak.

astro-ph.GA↗

arXiv2018

Thermal architecture for the QUBIC cryogenic receiver

QUBIC, the QU Bolometric Interferometer for Cosmology, is a novel forthcoming instrument to measure the B-mode polarization anisotropy of the Cosmic Microwave Background. The detection of the B-mode signal will be extremely challenging; QUBIC has been designed to address this with a novel approach, namely bolometric interferometry. The receiver cryostat is exceptionally large and cools complex optical and detector stages to 40 K, 4 K, 1 K and 350 mK using two pulse tube coolers, a novel 4He sorption cooler and a double-stage 3He/4He sorption cooler. We discuss the thermal and mechanical design of the cryostat, modelling and thermal analysis, and laboratory cryogenic testing.

astro-ph.IM↗

arXiv2018

Planck intermediate results. LIV. The Planck Multi-frequency Catalogue of Non-thermal Sources

This paper presents the Planck Multi-frequency Catalogue of Non-thermal (i.e. synchrotron-dominated) Sources (PCNT) observed between 30 and 857 GHz by the ESA Planck mission. This catalogue was constructed by selecting objects detected in the full mission all-sky temperature maps at 30 and 143 GHz, with a signal-to-noise ratio (S/N)>3 in at least one of the two channels after filtering with a particular Mexican hat wavelet. As a result, 29400 source candidates were selected. Then, a multi-frequency analysis was performed using the Matrix Filters methodology at the position of these objects, and flux densities and errors were calculated for all of them in the nine Planck channels. The present catalogue is the first unbiased, full-sky catalogue of synchrotron-dominated sources published at millimetre and submillimetre wavelengths and constitutes a powerful database for statistical studies of non-thermal extragalactic sources, whose emission is dominated by the central active galactic nucleus. Together with the full multi-frequency catalogue, we also define the Bright Planck Multi-frequency Catalogue of Non-thermal Sources PCNTb, where only those objects with a S/N>4 at both 30 and 143 GHz were selected. In this catalogue 1146 compact sources are detected outside the adopted Planck GAL070 mask; thus, these sources constitute a highly reliable sample of extragalactic radio sources. We also flag the high-significance subsample PCNThs, a subset of 151 sources that are detected with S/N>4 in all nine Planck channels, 75 of which are found outside the Planck mask adopted here. The remaining 76 sources inside the Galactic mask are very likely Galactic objects.

astro-ph.CO↗

arXiv2018

Planck 2018 results. II. Low Frequency Instrument data processing

We present a final description of the data-processing pipeline for the Planck, Low Frequency Instrument (LFI), implemented for the 2018 data release. Several improvements have been made with respect to the previous release, especially in the calibration process and in the correction of instrumental features such as the effects of nonlinearity in the response of the analogue-to-digital converters. We provide a brief pedagogical introduction to the complete pipeline, as well as a detailed description of the important changes implemented. Self-consistency of the pipeline is demonstrated using dedicated simulations and null tests. We present the final version of the LFI full sky maps at 30, 44, and 70 GHz, both in temperature and polarization, together with a refined estimate of the Solar dipole and a final assessment of the main LFI instrumental parameters.

astro-ph.CO↗

arXiv2018

Planck intermediate results. LIII. Detection of velocity dispersion from the kinetic Sunyaev-Zeldovich effect

Using the ${\it Planck}$ full-mission data, we present a detection of the temperature (and therefore velocity) dispersion due to the kinetic Sunyaev-Zeldovich (kSZ) effect from clusters of galaxies. To suppress the primary CMB and instrumental noise we derive a matched filter and then convolve it with the ${\it Planck}$ foreground-cleaned `${\tt 2D-ILC\,}$' maps. By using the Meta Catalogue of X-ray detected Clusters of galaxies (MCXC), we determine the normalized ${\it rms}$ dispersion of the temperature fluctuations at the positions of clusters, finding that this shows excess variance compared with the noise expectation. We then build an unbiased statistical estimator of the signal, determining that the normalized mean temperature dispersion of $1526$ clusters is $\langle \left(ΔT/T \right)^{2} \rangle = (1.64 \pm 0.48) \times 10^{-11}$. However, comparison with analytic calculations and simulations suggest that around $0.7\,σ$ of this result is due to cluster lensing rather than the kSZ effect. By correcting this, the temperature dispersion is measured to be $\langle \left(ΔT/T \right)^{2} \rangle = (1.35 \pm 0.48) \times 10^{-11}$, which gives a detection at the $2.8\,σ$ level. We further convert uniform-weight temperature dispersion into a measurement of the line-of-sight velocity dispersion, by using estimates of the optical depth of each cluster (which introduces additional uncertainty into the estimate). We find that the velocity dispersion is $\langle v^{2} \rangle =(123\,000 \pm 71\,000)\,({\rm km}\,{\rm s}^{-1})^{2}$, which is consistent with findings from other large-scale structure studies, and provides direct evidence of statistical homogeneity on scales of $600\,h^{-1}{\rm Mpc}$. Our study shows the promise of using cross-correlations of the kSZ effect with large-scale structure in order to constrain the growth of structure.

astro-ph.CO↗

arXiv2018

Planck 2018 results. III. High Frequency Instrument data processing and frequency maps

This paper presents the High Frequency Instrument (HFI) data processing procedures for the Planck 2018 release. Major improvements in mapmaking have been achieved since the previous 2015 release. They enabled the first significant measurement of the reionization optical depth parameter using HFI data. This paper presents an extensive analysis of systematic effects, including the use of simulations to facilitate their removal and characterize the residuals. The polarized data, which presented a number of known problems in the 2015 Planck release, are very significantly improved. Calibration, based on the CMB dipole, is now extremely accurate and in the frequency range 100 to 353 GHz reduces intensity-to-polarization leakage caused by calibration mismatch. The Solar dipole direction has been determined in the three lowest HFI frequency channels to within one arc minute, and its amplitude has an absolute uncertainty smaller than $0.35μ$K, an accuracy of order $10^{-4}$. This is a major legacy from the HFI for future CMB experiments. The removal of bandpass leakage has been improved by extracting the bandpass-mismatch coefficients for each detector as part of the mapmaking process; these values in turn improve the intensity maps. This is a major change in the philosophy of "frequency maps", which are now computed from single detector data, all adjusted to the same average bandpass response for the main foregrounds. Simulations reproduce very well the relative gain calibration of detectors, as well as drifts within a frequency induced by the residuals of the main systematic effect. Using these simulations, we measure and correct the small frequency calibration bias induced by this systematic effect at the $10^{-4}$ level. There is no detectable sign of a residual calibration bias between the first and second acoustic peaks in the CMB channels, at the $10^{-3}$ level.

astro-ph.CO↗

arXiv2018

Ultra High Molecular Weight Polyethylene: optical features at millimeter wavelengths

The next generation of experiments for the measurement of the Cosmic Microwave Background (CMB) requires more and more the use of advanced materials, with specific physical and structural properties. An example is the material used for receiver's cryostat windows and internal lenses. The large throughput of current CMB experiments requires a large diameter (of the order of 0.5m) of these parts, resulting in heavy structural and optical requirements on the material to be used. Ultra High Molecular Weight (UHMW) polyethylene (PE) features high resistance to traction and good transmissivity in the frequency range of interest. In this paper, we discuss the possibility of using UHMW PE for windows and lenses in experiments working at millimeter wavelengths, by measuring its optical properties: emissivity, transmission and refraction index. Our measurements show that the material is well suited to this purpose.

astro-ph.IM↗

arXiv2018

Planck 2015 results. XXIV. Cosmology from Sunyaev-Zeldovich cluster counts

We present cluster counts and corresponding cosmological constraints from the Planck full mission data set. Our catalogue consists of 439 clusters detected via their Sunyaev-Zeldovich (SZ) signal down to a signal-to-noise ratio of 6, and is more than a factor of 2 larger than the 2013 Planck cluster cosmology sample. The counts are consistent with those from 2013 and yield compatible constraints under the same modelling assumptions. Taking advantage of the larger catalogue, we extend our analysis to the two-dimensional distribution in redshift and signal-to-noise. We use mass estimates from two recent studies of gravitational lensing of background galaxies by Planck clusters to provide priors on the hydrostatic bias parameter, $(1-b)$. In addition, we use lensing of cosmic microwave background (CMB) temperature fluctuations by Planck clusters as an independent constraint on this parameter. These various calibrations imply constraints on the present-day amplitude of matter fluctuations in varying degrees of tension with those from the Planck analysis of primary fluctuations in the CMB; for the lowest estimated values of $(1-b)$ the tension is mild, only a little over one standard deviation, while it remains substantial ($3.7\,σ$) for the largest estimated value. We also examine constraints on extensions to the base flat $Λ$CDM model by combining the cluster and CMB constraints. The combination appears to favour non-minimal neutrino masses, but this possibility does little to relieve the overall tension because it simultaneously lowers the implied value of the Hubble parameter, thereby exacerbating the discrepancy with most current astrophysical estimates. Improving the precision of cluster mass calibrations from the current 10%-level to 1% would significantly strengthen these combined analyses and provide a stringent test of the base $Λ$CDM model.

astro-ph.CO↗