Lensing Sunyaev-Zel'dovich Clusters

Full-sky microwave surveys like the upcoming Planck satellite mission will detect of order 10^4 galaxy clusters through their thermal Sunyaev-Zel'dovich effect. I investigate the properties of the gravitationally lensing subsample of these clusters. The main results are: (1) The combined sample comprises >~70% of the complete sample. (2) It is confined to redshifts 0.2+-0.1, and to masses (5+-3) x 10^14 solar masses. (3) Using a particular measure for the weak lensing effect, viz. the aperture mass, cluster masses can be determined with a relative accuracy of ~20% if their density profile is known. Consequently, the mass function of the combined sample can accurately be measured. (4) For low-density universes, I predict a sharp peak in the measured (aperture) mass function near 5 x 10^14 solar masses and explain its origin, showing that the peak will be absent in high-density universes. (5) The location of the peak and the exponential decrease of the mass function on its high-mass side will allow the determination of the amplitude of the dark-matter power spectrum on the cluster scale and the baryon fraction in clusters, and constrain the thermal history of the intracluster gas.Comment: submitted to Astronomy & Astrophysic

On the spin parameter of dark-matter haloes

The study by White (1984) on the growth of angular momentum in dark haloes is extended towards a more detailed investigation of the spin parameter $\lambda\equiv L\sqrt{E}/{G M^{2.5}}$. Starting from the Zel'dovich approximation to structure formation, a dark halo is approximated by a homogeneous ellipsoid with the inertial tensor of the (highly irregular) Lagrangian region $\Upsilon$ from which the dark halo forms. Within this approximation, an expression for the spin parameter can be derived, which depends on the geometry of $\Upsilon$, the cosmological density parameter $\Omega_0$, the overdensity of the dark halo, and the tidal torque exerted on it. For Gaussian random fields, this expression can be evaluated statistically. As a result, we derive a probability distribution of the spin parameter which gives $\lambda\simeq0.07^{+0.04}_{-0.05}$, consistent with numerical investigations. This probability distribution steeply rises with increasing spin parameter, reaching its maximum at $\lambda\simeq0.025$. The 10 (50,90) percentile values are $\lambda=0.02$ (0.05,0.11, respectively). There is a weak anticorrelation of the spin parameter with the peak height $\nu$ of the density fluctuation field $\lambda\propto \nu^{-0.29}$. The dependence on $\Omega_0$ and the variance $\sigma$ of the density-contrast field is very weak; there is only a marginal tendency for the spin parameter to be slightly larger for late-forming objects in an open universe. Due to the weak dependence on $\sigma$, our results should be quite generally applicable and independent onComment: 16 pages, preprint MPA 79

A Comparison of X-ray and Strong Lensing Properties of Simulated X-ray Clusters

We use gas-dynamical simulations of galaxy clusters to compare their X-ray and strong lensing properties. Special emphasis is laid on mass estimates. The cluster masses range between 6 x 10^14 solar masses and 4 x 10^15 solar masses, and they are examined at redshifts between 1 and 0. We compute the X-ray emission of the intracluster gas by thermal bremsstrahlung, add background contamination, and mimic imaging and spectral observations with current X-ray telescopes. Although the beta model routinely provides excellent fits to the X-ray emission profiles, the derived masses are typically biased low because of the restricted range of radii within which the fit can be done. For beta values of ~ 2/3, which is the average in our numerically simulated sample, the mass is typically underestimated by ~ 40 per cent. The masses of clusters which exhibit pronounced substructure are often substantially underestimated. We suggest that the ratio between peak temperature and emission-weighted average cluster temperature may provide a good indicator for ongoing merging and, therefore, for unreliable mass estimates. X-ray mass estimates are substantially improved if we fit a King density profile rather than the beta model to the X-ray emission, thereby dropping the degree of freedom associated with beta. Clusters selected for their strong lensing properties are typically dynamically more active than typical clusters. Bulk flows in the intracluster gas contain a larger than average fraction of the internal energy of the gas in such objects, hence the measured gas temperatures are biased low. The bulk of the optical depth for arc formation is contributed by clusters with intermediate rather than high X-ray luminosity. Arcs occur predominantly in clusters which exhibit substructure and are not in an equilibrium state. Finally we explain why theComment: 22 pages including figures, submitted to MNRA

Triaxial collapse and virialisation of dark-matter haloes

We reconsider the ellipsoidal-collapse model and extend it in two ways: We modify the treatment of the external gravitational shear field, introducing a hybrid model in between linear and non-linear evolution, and we introduce a virialisation criterion derived from the tensor virial theorem to replace the ad-hoc criterion employed so far. We compute the collapse parameters delta_c and Delta_v and find that they increase with ellipticity e and decrease with prolaticity p. We marginalise them over the appropriate distribution of e and p and show the marginalised results as functions of halo mass and virialisation redshift. While the hybrid model for the external shear gives results very similar to those obtained from the non-linear model, ellipsoidal collapse changes the collapse parameters typically by (20...50)%, in a way increasing with decreasing halo mass and decreasing virialisation redshift. We qualitatively confirm the dependence on mass and virialisation redshift of a fitting formula for delta_c, but find noticeable quantitative differences in particular at low mass and high redshift. The derived mass function is in good agreement with mass functions recently proposed in the literature.Comment: 9 pages, 9 figures, published in Astronomy and Astrophysics; slight modifications to match the published versio