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

TL;DR

Planck 2015 analyzes Sunyaev–Zeldovich cluster counts from the full Planck mission to constrain $\Omega_{ m m}$ and $\sigma_8$ and to test ΛCDM extensions. It introduces a two‑dimensional likelihood in $(z,q)$ and leverages external mass-calibration priors from galaxy weak lensing and CMB lensing to address the dominant mass-bias systematic $1-b$. Depending on the mass-bias prior, cluster counts show varying tension with Planck primary CMB results, underscoring the need for precise mass calibration to fully adjudicate ΛCDM and neutrino-mass scenarios. The work also explores curvature and dark energy via joint analyses, highlighting the potential and limitations of current cluster cosmology and pointing to future gains from sub-percent mass calibration.

Abstract

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.

Figures (18)

• Figure 1: Mass-redshift distribution of the Planck cosmological samples colour-coded by their signal-to-noise, $q$. The baseline MMF3 2015 cosmological sample is shown as the small filled circles. Objects which were in the MMF3 2013 cosmological sample are marked by crosses, while those in the 2015 intersection sample are shown as open circles. The final samples are defined by $q>6$. The mass $M_{\rm Yz}$ is the Planck mass proxy arnaud2015.
• Figure 2: Cluster mass scale determined by CMB lensing. We show the ratio of cluster lensing mass, $M_{\rm lens}$, to the SZ mass proxy, $M_{\rm Yz}$, as a function of the mass proxy for clusters in the MMF3 2015 cosmology sample. The cluster mass is measured through lensing of CMB temperature anisotropies in the Planck data melin2014. Individual mass measurements have low signal-to-noise, but we determine a mean ratio for the sample of $M_{\rm lens}/M_{\rm Yz} = 1/(1-b) = 0.99\pm0.19$. For clarity, only some of the error bars are plotted (see text).
• Figure 3: Contours at 95% for different signal-to-noise thresholds, $q=8.5$, 7, and 6, applied to the 2015 MMF3 cosmology sample for the SZ+BAO+BBN data set. The contours are compatible with the 2013 constraints planck2013-p15, shown as the filled, light grey ellipses at 68 and 95% (for the BAO and BBN priors of Sect \ref{['sec:extdata']}; see text). The 2015 catalogue thresholded at $q>8.5$ has a similar number of clusters (190) as the 2013 catalogue (189). This comparison is made using the analytical error-function model for completeness and adopts the reference observable-mass scaling relation of the 2013 analysis ($1-b=0.8$, see text). The redshift distributions of the best-fit models are shown in Fig. \ref{['fig:psz2_dndz']}. For this figure and Fig. \ref{['fig:psz2_dndz']}, we use the one-dimensional likelihood over the redshift distribution, $dN/dz$ (Eq. \ref{['eq:dndz']}).
• Figure 4: Comparison of observed counts (points with error bars) with predictions of the best-fit models (solid lines) from the one-dimensional likelihood for three different thresholds applied to the 2015 MMF3 cosmology sample. The mismatch between observed and predicted counts in the second and third lowest redshift bins, already noticed in the 2013 analysis, increases at lower thresholds, $q$. The best-fit models are defined by the constraints shown in Fig. \ref{['fig:psz2_vs_threshold']}. For this figure and Fig. \ref{['fig:psz2_vs_threshold']}, we use our one-dimensional likelihood over the redshift distribution, $dN/dz$ (Eq. \ref{['eq:dndz']}), with the mass biased fixed at $(1-b)=0.8$.
• Figure 5: Comparison of constraints from the one-dimensional ($dN/dz$) and two-dimensional ($dN/dzdq$) likelihoods on cosmological parameters and the scaling relation mass exponent, $\alpha$. This comparison uses the MMF3 catalogue, the CCCP prior on the mass bias and the SZ+BAO+BBN data set. The corresponding best-fit model redshift distributions are shown in Fig. \ref{['fig:psz2_dndz_comp']}.