The probability distribution of cluster formation times and implied Einstein Radii

We provide a quantitative assessment of the probability distribution function of the concentration parameter of galaxy clusters. We do so by using the probability distribution function of halo formation times, calculated by means of the excursion set formalism, and a formation redshift-concentration scaling derived from results of N-body simulations. Our results suggest that the observed high concentrations of several clusters are quite unlikely in the standard Lambda CDM cosmological model, but that due to various inherent uncertainties, the statistical range of the predicted distribution may be significantly wider than commonly acknowledged. In addition, the probability distribution function of the Einstein radius of A1689 is evaluated, confirming that the observed value of ~45" +/- 5" is very improbable in the currently favoured cosmological model. If, however, a variance of ~20% in the theoretically predicted value of the virial radius is assumed, than the discrepancy is much weaker. The measurement of similarly large Einstein radii in several other clusters would pose a difficulty to the standard model. If so, earlier formation of the large scale structure would be required, in accord with predictions of some quintessence models. We have indeed verified that in a viable early dark energy model large Einstein radii are predicted in as many as a few tens of high-mass clusters.Comment: 9 pages, 6 figures, submitted to MNRA

Sunyaev-Zeldovich Cluster Counts as a Probe of Intra-Supercluster Gas

X-ray background surveys indicate the likely presence of diffuse warm gas in the Local Super Cluster (LSC), in accord with expectations from hydrodynamical simulations. We assess several other manifestations of warm LSC gas; these include anisotropy in the spatial pattern of cluster Sunyaev-Zeldovich (S-Z) counts, its impact on the CMB temperature power spectrum at the lowest multipoles, and implications on measurements of the S-Z effect in and around the Virgo cluster.Comment: 14 pages, 6 figures, draft versio

The Largest Gravitational Lens: MACS J0717.5+3745 (z=0.546)

We identify 13 sets of multiply-lensed galaxies around MACS J0717.5+3745 ($z=0.546$), outlining a very large tangential critical curve of major axis \sim2.8\arcmin, filling the field of HST/ACS. The equivalent circular Einstein radius is \theta_{e}= 55 \pm 3\arcsec (at an estimated source redshift of $z_{s}\sim2.5$), corresponding to $r_e\simeq 350\pm 20 kpc$ at the cluster redshift, nearly three times greater than that of A1689 ($r_e\simeq 140 kpc$ for $z_{s}=2.5$). The mass enclosed by this critical curve is very large, $7.4\pm 0.5 \times 10^{14}M_{\odot}$ and only weakly model dependent, with a relatively shallow mass profile within $r<250 kpc$, reflecting the unrelaxed appearance of this cluster. This shallow profile generates a much higher level of magnification than the well known relaxed lensing clusters of higher concentration, so that the area of sky exceeding a magnification of $>10\times$, is \simeq 3.5\sq\arcmin for sources with $z\simeq 8$, making MACS J0717.5+3745 a compelling target for accessing faint objects at high redshift. We calculate that only one such cluster, with \theta_{e}\ge 55\arcsec, is predicted within $\sim 10^7$ Universes with $z\ge 0.55$, corresponding to a virial mass $\ge 3\times 10^{15} M_{\odot}$, for the standard $\Lambda CDM$ (WMAP5 parameters with $2\sigma$ uncertainties).Comment: 5 pages, 5 figures, accepted to the ApJ Letters; title modified; minor change

CMB Comptonization in Clusters: Spectral and Angular Power from Evolving Polytropic Gas

The angular power spectrum of the Sunyaev-Zeldovich (SZ) effect is calculated in the $\Lambda$CDM cosmological model with the aim of investigating its detailed dependence on the cluster population, gas morphology, and gas evolution. We calculate the power spectrum for three different mass functions, compute it within the framework of isothermal and polytropic gas distributions, and explore the effect of gas evolution on the magnitude and shape of the power spectrum. We show that it is indeed possible to explain the `excess' power measured by the CBI experiment on small angular scales as originating from the SZ effect without (arbitrary) rescaling the value of $\sigma_8$, the mass variance parameter. The need for a self-consistent choice of the basic parameters characterizing the cluster population is emphasized. In particular, we stress the need for a consistent choice of the value of $\sigma_8$ extracted from fitting theoretical models for the mass function to the observed cluster X-ray temperature function, such that it agrees with the mass-temperature relation used to evaluate the cluster Comptonization parameter. Our treatment includes the explicit spectral dependence of the thermal component of the effect, which we calculate at various frequencies. We find appreciable differences between the non-relativistic and relativistic predictions for the power spectrum even for this superposed contribution from clusters at the full range of gas temperatures.Comment: Accepted for publication in N

Cluster abundances and S-Z power spectra: effects of non-Gaussianity and early dark energy

In the standard Lambda CDM cosmological model with a Gaussian primordial density fluctuation field, the relatively low value of the mass variance parameter (sigma_8=0.74{+0.05}{-0.06}, obtained from the WMAP 3-year data) results in a reduced likelihood that the measured level of CMB anisotropy on the scales of clusters is due to the Sunyaev-Zeldovich (S-Z) effect. To assess the feasibility of producing higher levels of S-Z power, we explore two alternative models which predict higher cluster abundance. In the first model the primordial density field has a chi^2_1 distribution, whereas in the second an early dark energy component gives rise to the desired higher cluster abundance. We carry out the necessary detailed calculations of the levels of S-Z power spectra, cluster number counts, and angular 2-point correlation function of clusters, and compare (in a self-consistent way) their predicted redshift distributions. Our results provide a sufficient basis upon which the viability of the three models may be tested by future high quality measurements.Comment: 12 pages, 5 figures, accepted for publication in MNRA