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Register a new userReconciling Planck cluster counts and cosmology? Chandra/XMM instrumental calibration and hydrostatic mass bias
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Holger Israel
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The mass of galaxy clusters can be inferred from the temperature of their X-ray emitting gas, $T_{mathrm{X}}$. Their masses may be underestimated if it is assumed that the gas is in hydrostatic equilibrium, by an amount $b^{mathrm{hyd}}sim(20pm10)$ % suggested by simulations. We have previously found consistency between a sample of observed textit{Chandra} X-ray masses and independent weak lensing measurements. Unfortunately, uncertainties in the instrumental calibration of {em Chandra} and {em XMM-Newton} observatories mean that they measure different temperatures for the same gas. In this paper, we translate that relative instrumental bias into mass bias, and infer that textit{XMM-Newton} masses of $sim 10^{14},mbox{M}_{odot}$ ($> 5cdot 10^{14} mbox{M}_{odot}$) clusters are unbiased ($sim 35$ % lower) compared to WL masses. For massive clusters, textit{Chandra}s calibration may thus be more accurate. The opposite appears to be true at the low mass end. We observe the mass bias to increase with cluster mass, but presence of Eddington bias precludes firm conclusions at this stage. Nevertheless, the systematic textit{Chandra} -- textit{XMM-Newton} difference is important because {em Planck}s detections of massive clusters via the Sunyaev-Zeldovich (SZ) effect are calibrated via {em XMM-Newton} observations. The number of detected SZ clusters are inconsistent with {em Planck}s cosmological measurements of the primary Cosmic Microwave Background (CMB). Given the textit{Planck} cluster masses, if an (unlikely) uncorrected $sim 20$ % calibration bias existed, this tension would be eased, but not resolved.
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We present constraints on cosmological parameters using number counts as a function of redshift for a sub-sample of 189 galaxy clusters from the Planck SZ (PSZ) catalogue. The PSZ is selected through the signature of the Sunyaev--Zeldovich (SZ) effect, and the sub-sample used here has a signal-to-noise threshold of seven, with each object confirmed as a cluster and all but one with a redshift estimate. We discuss the completeness of the sample and our construction of a likelihood analysis. Using a relation between mass $M$ and SZ signal $Y$ calibrated to X-ray measurements, we derive constraints on the power spectrum amplitude $sigma_8$ and matter density parameter $Omega_{mathrm{m}}$ in a flat $Lambda$CDM model. We test the robustness of our estimates and find that possible biases in the $Y$--$M$ relation and the halo mass function are larger than the statistical uncertainties from the cluster sample. Assuming the X-ray determined mass to be biased low relative to the true mass by between zero and 30%, motivated by comparison of the observed mass scaling relations to those from a set of numerical simulations, we find that $sigma_8=0.75pm 0.03$, $Omega_{mathrm{m}}=0.29pm 0.02$, and $sigma_8(Omega_{mathrm{m}}/0.27)^{0.3} = 0.764 pm 0.025$. The value of $sigma_8$ is degenerate with the mass bias; if the latter is fixed to a value of 20% we find $sigma_8(Omega_{mathrm{m}}/0.27)^{0.3}=0.78pm 0.01$ and a tighter one-dimensional range $sigma_8=0.77pm 0.02$. We find that the larger values of $sigma_8$ and $Omega_{mathrm{m}}$ preferred by Plancks measurements of the primary CMB anisotropies can be accommodated by a mass bias of about 40%. Alternatively, consistency with the primary CMB constraints can be achieved by inclusion of processes that suppress power on small scales relative to the $Lambda$CDM model, such as a component of massive neutrinos (abridged).
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 ($3.7,sigma$) for the largest estimated value. We also examine constraints on extensions to the base flat $Lambda$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 $Lambda$CDM model.
Surveys in the next decade will deliver large samples of galaxy clusters that transform our understanding of their formation. Cluster astrophysics and cosmology studies will become systematics limited with samples of this magnitude. With known properties, hydrodynamical simulations of clusters provide a vital resource for investigating potential systematics. However, this is only realized if we compare simulations to observations in the correct way. Here we introduce the textsc{Mock-X} analysis framework, a multiwavelength tool that generates synthetic images from cosmological simulations and derives halo properties via observational methods. We detail our methods for generating optical, Compton-$y$ and X-ray images. Outlining our synthetic X-ray image analysis method, we demonstrate the capabilities of the framework by exploring hydrostatic mass bias for the IllustrisTNG, BAHAMAS and MACSIS simulations. Using simulation derived profiles we find an approximately constant bias $bapprox0.13$ with cluster mass, independent of hydrodynamical method or subgrid physics. However, the hydrostatic bias derived from synthetic observations is mass-dependent, increasing to $b=0.3$ for the most massive clusters. This result is driven by a single temperature fit to a spectrum produced by gas with a wide temperature distribution in quasi-pressure equilibrium. The spectroscopic temperature and mass estimate are biased low by cooler gas dominating the emission, due to its quadratic density dependence. The bias and the scatter in estimated mass remain independent of the numerical method and subgrid physics. Our results are consistent with current observations and future surveys will contain sufficient samples of massive clusters to confirm the mass dependence of the hydrostatic bias.
In recent years, the amplitude of matter fluctuations inferred from low-redshift probes has been found to be generally lower than the value derived from CMB observations in the $Lambda$CDM model. This tension has been exemplified by Sunyaev-Zeldovich and X-ray cluster counts which, when using their Planck standard cluster mass calibration, yield a value of $sigma_8$ , appreciably lower than estimations based on the latest Planck CMB measurements. In this work we examine whether non-minimal neutrino masses can alleviate this tension substantially. We used the cluster X-ray temperature distribution function derived from a flux-limited sample of local X-ray clusters, combined with Planck CMB measurements. These datasets were compared to $Lambda$CDM predictions based on recent mass function, adapted to account for the effects of massive neutrinos. Treating the clusters mass calibration as a free parameter, we examined whether the data favours neutrino masses appreciably higher than the minimal 0.06 eV value. Using Markov chain Monte Carlo methods, we found no significant correlation between the mass calibration of clusters and the sum of neutrino masses, meaning that massive neutrinos do not noticeably alleviate the above-mentioned Planck CMB--clusters tension. The addition of other datasets (BAO and Ly-$alpha$) reinforces those conclusions. As an alternative possible solution to the tension, we introduced a simple, phenomenological modification of gravity by letting the growth index $gamma$ vary as an additional free parameter. We find that the cluster mass calibration is robustly correlated with the $gamma$ parameter, insensitively to the presence of massive neutrinos or/and additional data used. We conclude that the standard Planck mass calibration of clusters, if consolidated, would represent evidence for new physics beyond $Lambda$CDM with massive neutrinos.
Luminous matter produces very energetic events, such as active galactic nuclei and supernova explosions, that significantly affect the internal regions of galaxy clusters. Although the current uncertainty in the effect of baryonic physics on cluster statistics is subdominant as compared to other systematics, the picture is likely to change soon as the amount of high-quality data is growing fast, urging the community to keep theoretical systematic uncertainties below the ever-growing statistical precision. In this paper, we study the effect of baryons on galaxy clusters, and their impact on the cosmological applications of clusters, using the Magneticum suite of cosmological hydrodynamical simulations. We show that the impact of baryons on the halo mass function can be recast in terms on a variation of the mass of the halos simulated with pure N-body, when baryonic effects are included. The halo mass function and halo bias are only indirectly affected. Finally, we demonstrate that neglecting baryonic effects on halos mass function and bias would significantly alter the inference of cosmological parameters from high-sensitivity next-generations surveys of galaxy clusters.
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