Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow

We compute the sum of the positive Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow. The computation is based on the analytic Riemann-Roch Theorem and uses a comparison of determinants of flat and hyperbolic Laplacians when the underlying Riemann surface degenerates.Comment: Minor corrections. To appear in Publications mathematiques de l'IHE

Measuring cluster peculiar velocities with the Sunyaev-Zeldovich effects: scaling relations and systematics

The fluctuations in the Cosmic Microwave Background (CMB) intensity due to the Sunyaev-Zeldovich (SZ) effect are the sum of a thermal and a kinetic contribution. Separating the two components to measure the peculiar velocity of galaxy clusters requires radio and microwave observations at three or more frequencies, and knowledge of the temperature T_e of the intracluster medium weighted by the electron number density. To quantify the systematics of this procedure, we extract a sample of 117 massive clusters at redshift z=0 from an N-body hydrodynamical simulation, with 2x480^3 particles, of a cosmological volume 192 Mpc/h on a side of a flat Cold Dark Matter model with Omega_0=0.3 and Lambda=0.7. Our simulation includes radiative cooling, star formation and the effect of feedback and galactic winds from supernovae. We find that (1) our simulated clusters reproduce the observed scaling relations between X-ray and SZ properties; (2) bulk flows internal to the intracluster medium affect the velocity estimate by less than 200 km/s in 93 per cent of the cases; (3) using the X-ray emission weighted temperature, as an estimate of T_e, can overestimate the peculiar velocity by 20-50 per cent, if the microwave observations do not spatially resolve the cluster. For spatially resolved clusters, the assumptions on the spatial distribution of the ICM, required to separate the two SZ components, still produce a velocity overestimate of 10-20 per cent, even with an unbiased measure of T_e. Thanks to the large size of our cluster samples, these results set a robust lower limit of 200 km/s to the systematic errors that will affect upcoming measures of cluster peculiar velocities with the SZ effect.Comment: 14 pages, 12 figures, MNRAS, in press. Figures 3 and 4 now contain more recent observational data. Other minor revisions according to referee's comment

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.Comment: Final version that has appeared in A&

Planck 2015 results. XXIII. The thermal Sunyaev-Zeldovich effect--cosmic infrared background correlation

We use Planck data to detect the cross-correlation between the thermal Sunyaev-Zeldovich (tSZ) effect and the infrared emission from the galaxies that make up the the cosmic infrared background (CIB). We first perform a stacking analysis towards Planck-confirmed galaxy clusters. We detect infrared emission produced by dusty galaxies inside these clusters and demonstrate that the infrared emission is about 50% more extended than the tSZ effect. Modelling the emission with a Navarro--Frenk--White profile, we find that the radial profile concentration parameter is $c_{500} = 1.00^{+0.18}_{-0.15}$. This indicates that infrared galaxies in the outskirts of clusters have higher infrared flux than cluster-core galaxies. We also study the cross-correlation between tSZ and CIB anisotropies, following three alternative approaches based on power spectrum analyses: (i) using a catalogue of confirmed clusters detected in Planck data; (ii) using an all-sky tSZ map built from Planck frequency maps; and (iii) using cross-spectra between Planck frequency maps. With the three different methods, we detect the tSZ-CIB cross-power spectrum at significance levels of (i) 6 $\sigma$, (ii) 3 $\sigma$, and (iii) 4 $\sigma$. We model the tSZ-CIB cross-correlation signature and compare predictions with the measurements. The amplitude of the cross-correlation relative to the fiducial model is $A_{\rm tSZ-CIB}= 1.2\pm0.3$. This result is consistent with predictions for the tSZ-CIB cross-correlation assuming the best-fit cosmological model from Planck 2015 results along with the tSZ and CIB scaling relations.Comment: 18 pages, 16 figure

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 $12\,\sigma$, which agrees with the theoretical expectation derived from the Planck best-fit $\Lambda$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.Comment: 20 pages, 12 figures; Accepted for publication in A&A; The B-mode map is part of the PR2-2015 Cosmology Products; available as Lensing Products in the Planck Legacy Archive http://pla.esac.esa.int/pla/#cosmology; and described in the 'Explanatory Supplement' https://wiki.cosmos.esa.int/planckpla2015/index.php/Specially_processed_maps#2015_Lensing-induced_B-mode_ma

Planck Intermediate Results. IV. The XMM-Newton validation programme for new Planck galaxy clusters

We present the final results from the XMM-Newton validation follow-up of new Planck galaxy cluster candidates. We observed 15 new candidates, detected with signal-to-noise ratios between 4.0 and 6.1 in the 15.5-month nominal Planck survey. The candidates were selected using ancillary data flags derived from the ROSAT All Sky Survey (RASS) and Digitized Sky Survey all-sky maps, with the aim of pushing into the low SZ flux, high-z regime and testing RASS flags as indicators of candidate reliability. 14 new clusters were detected by XMM, including 2 double systems. Redshifts lie in the range 0.2 to 0.9, with 6 clusters at z>0.5. Estimated M500 range from 2.5 10^14 to 8 10^14 Msun. We discuss our results in the context of the full XMM validation programme, in which 51 new clusters have been detected. This includes 4 double and 2 triple systems, some of which are chance projections on the sky of clusters at different z. We find that association with a RASS-BSC source is a robust indicator of the reliability of a candidate, whereas association with a FSC source does not guarantee that the SZ candidate is a bona fide cluster. Nevertheless, most Planck clusters appear in RASS maps, with a significance greater than 2 sigma being a good indication that the candidate is a real cluster. The full sample gives a Planck sensitivity threshold of Y500 ~ 4 10^-4 arcmin^2, with indication for Malmquist bias in the YX-Y500 relation below this level. The corresponding mass threshold depends on z. Systems with M500 > 5 10^14 Msun at z > 0.5 are easily detectable with Planck. The newly-detected clusters follow the YX-Y500 relation derived from X-ray selected samples. Compared to X-ray selected clusters, the new SZ clusters have a lower X-ray luminosity on average for their mass. There is no indication of departure from standard self-similar evolution in the X-ray versus SZ scaling properties. (abridged)Comment: accepted by A&

Planck intermediate results. VIII. Filaments between interacting clusters

About half of the baryons of the Universe are expected to be in the form of filaments of hot and low density intergalactic medium. Most of these baryons remain undetected even by the most advanced X-ray observatories which are limited in sensitivity to the diffuse low density medium. The Planck satellite has provided hundreds of detections of the hot gas in clusters of galaxies via the thermal Sunyaev-Zel'dovich (tSZ) effect and is an ideal instrument for studying extended low density media through the tSZ effect. In this paper we use the Planck data to search for signatures of a fraction of these missing baryons between pairs of galaxy clusters. Cluster pairs are good candidates for searching for the hotter and denser phase of the intergalactic medium (which is more easily observed through the SZ effect). Using an X-ray catalogue of clusters and the Planck data, we select physical pairs of clusters as candidates. Using the Planck data we construct a local map of the tSZ effect centered on each pair of galaxy clusters. ROSAT data is used to construct X-ray maps of these pairs. After having modelled and subtracted the tSZ effect and X-ray emission for each cluster in the pair we study the residuals on both the SZ and X-ray maps. For the merging cluster pair A399-A401 we observe a significant tSZ effect signal in the intercluster region beyond the virial radii of the clusters. A joint X-ray SZ analysis allows us to constrain the temperature and density of this intercluster medium. We obtain a temperature of kT = 7.1 +- 0.9, keV (consistent with previous estimates) and a baryon density of (3.7 +- 0.2)x10^-4, cm^-3. The Planck satellite mission has provided the first SZ detection of the hot and diffuse intercluster gas.Comment: Accepted by A&

Planck 2015 results. XXVII. The Second Planck Catalogue of Sunyaev-Zeldovich Sources

We present the all-sky Planck catalogue of Sunyaev-Zeldovich (SZ) sources detected from the 29 month full-mission data. The catalogue (PSZ2) is the largest SZ-selected sample of galaxy clusters yet produced and the deepest all-sky catalogue of galaxy clusters. It contains 1653 detections, of which 1203 are confirmed clusters with identified counterparts in external data-sets, and is the first SZ-selected cluster survey containing > $10^3$ confirmed clusters. We present a detailed analysis of the survey selection function in terms of its completeness and statistical reliability, placing a lower limit of 83% on the purity. Using simulations, we find that the Y5R500 estimates are robust to pressure-profile variation and beam systematics, but accurate conversion to Y500 requires. the use of prior information on the cluster extent. We describe the multi-wavelength search for counterparts in ancillary data, which makes use of radio, microwave, infra-red, optical and X-ray data-sets, and which places emphasis on the robustness of the counterpart match. We discuss the physical properties of the new sample and identify a population of low-redshift X-ray under- luminous clusters revealed by SZ selection. These objects appear in optical and SZ surveys with consistent properties for their mass, but are almost absent from ROSAT X-ray selected samples

Planck Intermediate Results II: Comparison of Sunyaev-Zeldovich measurements from Planck and from the Arcminute Microkelvin Imager for 11 galaxy clusters

A comparison is presented of Sunyaev-Zeldovich measurements for 11 galaxy clusters as obtained by Planck and by the ground-based interferometer, the Arcminute Microkelvin Imager. Assuming a universal spherically-symmetric Generalised Navarro, Frenk & White (GNFW) model for the cluster gas pressure profile, we jointly constrain the integrated Compton-Y parameter (Y_500) and the scale radius (theta_500) of each cluster. Our resulting constraints in the Y_500-theta_500 2D parameter space derived from the two instruments overlap significantly for eight of the clusters, although, overall, there is a tendency for AMI to find the Sunyaev-Zeldovich signal to be smaller in angular size and fainter than Planck. Significant discrepancies exist for the three remaining clusters in the sample, namely A1413, A1914, and the newly-discovered Planck cluster PLCKESZ G139.59+24.18. The robustness of the analysis of both the Planck and AMI data is demonstrated through the use of detailed simulations, which also discount confusion from residual point (radio) sources and from diffuse astrophysical foregrounds as possible explanations for the discrepancies found. For a subset of our cluster sample, we have investigated the dependence of our results on the assumed pressure profile by repeating the analysis adopting the best-fitting GNFW profile shape which best matches X-ray observations. Adopting the best-fitting profile shape from the X-ray data does not, in general, resolve the discrepancies found in this subset of five clusters. Though based on a small sample, our results suggest that the adopted GNFW model may not be sufficiently flexible to describe clusters universally.Comment: update to metadata author list onl

Planck intermediate results. III. The relation between galaxy cluster mass and Sunyaev-Zeldovich signal

We examine the relation between the galaxy cluster mass M and Sunyaev-Zeldovich (SZ) effect signal D_A^2 Y for a sample of 19 objects for which weak lensing (WL) mass measurements obtained from Subaru Telescope data are available in the literature. Hydrostatic X-ray masses are derived from XMM-Newton archive data and the SZ effect signal is measured from Planck all-sky survey data. We find an M_WL-D_A^2 Y relation that is consistent in slope and normalisation with previous determinations using weak lensing masses; however, there is a normalisation offset with respect to previous measures based on hydrostatic X-ray mass-proxy relations. We verify that our SZ effect measurements are in excellent agreement with previous determinations from Planck data. For the present sample, the hydrostatic X-ray masses at R_500 are on average ~ 20 per cent larger than the corresponding weak lensing masses, at odds with expectations. We show that the mass discrepancy is driven by a difference in mass concentration as measured by the two methods, and, for the present sample, the mass discrepancy and difference in mass concentration is especially large for disturbed systems. The mass discrepancy is also linked to the offset in centres used by the X-ray and weak lensing analyses, which again is most important in disturbed systems. We outline several approaches that are needed to help achieve convergence in cluster mass measurement with X-ray and weak lensing observations.Comment: 19 pages, 9 figures, matches accepted versio