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Register a new userSpherically Averaging Ellipsoidal Galaxy Clusters in X-Ray and Sunyaev-Zeldovich Studies: II. Biases
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This is the second of two papers investigating the spherical averaging of ellipsoidal galaxy clusters in the context of X-ray and Sunyaev-Zeldovich (SZ) observations. In the present study we quantify the orientation-average bias and scatter in observables that result from spherically averaging clusters described by ellipsoidal generalizations of the NFW profile or a nearly scale-free logarithmic potential. Although the mean biases are small and mostly <1%, the flattest cluster models generally have a significant mean bias; i.e., averaging over all orientations does not always eliminate projection biases. Substantial biases can result from different viewing orientations, where the integrated Compton-y parameter (Y_SZ) and the concentration have the largest scatter (as large as sigma ~10% for Y_SZ), and the emission-weighted temperature (T_X) has the smallest (sigma < ~0.5%). The very small scatter for T_X leads to Y_X and M_gas having virtually the same orientation biases. Substantial scatter is expected for individual clusters (up to sigma ~8%) in the correlation between Y_SZ and Y_X in comparison to the small mean bias (sigma < ~1%) applicable to a random sample of clusters of sufficient size. For ellipsoidal NFW models we show that the orientation bias for the total cluster mass attains a minimum near the radius r_2500 so that the spherically averaged mass computed at this radius is always within ~0.5% of the true value for any orientation. Finally, to facilitate the accounting for orientation bias in X-ray and SZ cluster studies, we provide cubic polynomial approximations to the mean orientation bias and 1-sigma scatter for each cluster observable as a function of axial ratio for the ellipsoidal NFW models.
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This is the first of two papers investigating the deprojection and spherical averaging of ellipsoidal galaxy clusters. We specifically consider applications to hydrostatic X-ray and Sunyaev-Zeldovich (SZ) studies, though many of the results also apply to isotropic dispersion-supported stellar dynamical systems. Here we present analytical formulas for galaxy clusters described by a gravitational potential that is a triaxial ellipsoid of constant shape and orientation. For this model type we show that the mass bias due to spherically averaging X-ray observations is independent of the temperature profile, and for the special case of a scale-free logarithmic potential, there is exactly zero mass bias for any shape, orientation, and temperature profile. The ratio of spherically averaged intracluster medium (ICM) pressures obtained from SZ and X-ray measurements depends only on the ICM intrinsic shape, projection orientation, and H_0, which provides another illustration of how cluster geometry can be recovered through a combination of X-ray and SZ measurements. We also demonstrate that Y_SZ and Y_X have different biases owing to spherical averaging, which leads to an offset in the spherically averaged Y_SZ - Y_X relation. A potentially useful application of the analytical formulas presented is to assess the error range of an observable (e.g., mass, Y_SZ) accounting for deviations from assumed spherical symmetry, without having to perform the ellipsoidal deprojection explicitly. Finally, for dedicated ellipsoidal studies, we also generalize the spherical onion peeling method to the triaxial case for a given shape and orientation.
Galaxy clusters, the most massive collapsed structures, have been routinely used to determine cosmological parameters. When using clusters for cosmology, the crucial assumption is that they are relaxed. However, subarcminute resolution Sunyaev-Zeldovich (SZ) effect images compared with high resolution X-ray images of some clusters show significant offsets between the two peaks. We have carried out self-consistent N-body/hydrodynamical simulations of merging galaxy clusters using FLASH to study these offsets quantitatively. We have found that significant displacements result between the SZ and X-ray peaks for large relative velocities for all masses used in our simulations as long as the impact parameters were about 100-250 kpc. Our results suggest that the SZ peak coincides with the peak in the pressure times the line-of-sight characteristic length and not the pressure maximum (as it would for clusters in equilibrium). The peak in the X-ray emission, as expected, coincides with the density maximum of the main cluster. As a consequence, the morphology of the SZ signal and therefore the offset between the SZ and X-ray peaks change with viewing angle. As an application, we compare the morphologies of our simulated images to observed SZ and X-ray images and mass surface densities derived from weak lensing observations of the merging galaxy cluster CL0152-1357. We find that a large relative velocity of 4800 km/s is necessary to explain these observations. We conclude that an analysis of the morphologies of multi-frequency observations of merging clusters can be used to put meaningful constraints on the initial parameters of the progenitors.
We used optical imaging and spectroscopic data to derive substructure estimates for local Universe ($z < 0.11$) galaxy clusters from two different samples. The first was selected through the Sunyaev-Zeldovich (SZ) effect by the Planck satellite and the second is an X-ray selected sample. In agreement to X-ray substructure estimates we found that the SZ systems have a larger fraction of substructure than the X-ray clusters. We have also found evidence that the higher mass regime of the SZ clusters, compared to the X-ray sample, explains the larger fraction of disturbed objects in the Planck data. Although we detect a redshift evolution in the substructure fraction, it is not sufficient to explain the different results between the higher-z SZ sample and the X-ray one. We have also verified a good agreement ($sim$60$%$) between the optical and X-ray substructure estimates. However, the best level of agreement is given by the substructure classification given by measures based on the brightest cluster galaxy (BCG), either the BCG$-$X-ray centroid offset, or the magnitude gap between the first and second BCGs. We advocate the use of those two parameters as the most reliable and cheap way to assess cluster dynamical state. We recommend an offset cut of $sim$0.01$times$R$_{500}$ to separate relaxed and disturbed clusters. Regarding the magnitude gap the separation can be done at $Delta m_{12} = 1.0$. The central galaxy paradigm (CGP) may not be valid for $sim$20$%$ of relaxed massive clusters. This fraction increases to $sim$60$%$ for disturbed systems.
All-sky data from the Planck survey and the Meta-Catalogue of X-ray detected Clusters of galaxies (MCXC) are combined to investigate the relationship between the thermal Sunyaev-Zeldovich (SZ) signal and X-ray luminosity. The sample comprises ~ 1600 X-ray clusters with redshifts up to ~ 1 and spans a wide range in X-ray luminosity. The SZ signal is extracted for each object individually, and the statistical significance of the measurement is maximised by averaging the SZ signal in bins of X-ray luminosity, total mass, or redshift. The SZ signal is detected at very high significance over more than two decades in X-ray luminosity (10^43 erg/s < L_500 E(z)^-7/3 < 2 X 10^45 erg/s). The relation between intrinsic SZ signal and X-ray luminosity is investigated and the measured SZ signal is compared to values predicted from X-ray data. Planck measurements and X-ray based predictions are found to be in excellent agreement over the whole explored luminosity range. No significant deviation from standard evolution of the scaling relations is detected. For the first time the intrinsic scatter in the scaling relation between SZ signal and X-ray luminosity is measured and found to be consistent with the one in the luminosity -- mass relation from X-ray studies. There is no evidence of any deficit in SZ signal strength in Planck data relative to expectations from the X-ray properties of clusters, underlining the robustness and consistency of our overall view of intra-cluster medium properties.
We present Sunyaev-Zeldovich (SZ) effect observations of a sample of 25 massive relaxed galaxy clusters observed with the Sunyaev-Zeldovich Array (SZA), an 8-element interferometer that is part of the Combined Array for Research in Millimeter-wave Astronomy (CARMA). We perform an analysis of new SZA data and archival Chandra observations of this sample to investigate the integrated pressure -- a proxy for cluster mass -- determined from X-ray and SZ observations, two independent probes of the intra-cluster medium. This analysis makes use of a model for the intra-cluster medium introduced by Bulbul (2010) which can be applied simultaneously to SZ and X-ray data. With this model, we estimate the pressure profile for each cluster using a joint analysis of the SZ and X-ray data, and using the SZ data alone. We find that the integrated pressures measured from X-ray and SZ data are consistent. This conclusion is in agreement with recent results obtained using WMAP and Planck data, confirming that SZ and X-ray observations of massive clusters detect the same amount of thermal pressure from the intra-cluster medium. To test for possible biases introduced by our choice of model, we also fit the SZ data using the universal pressure profile proposed by Arnaud (2010), and find consistency between the two models out to r500 in the pressure profiles and integrated pressures.
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