The Star-Forming Dwarf Galaxy Populations of two z ~ 0.4 Clusters: MS1512.4+3647 and Abell 851

We present the results of a deep narrow-band [OII] 3727 \AA emission-line search for faint ($g <$ 27), star-forming galaxies in the field of the $z=0.37$ MS1512.4+3647 cluster. We find no evidence for an over-density of emission-line sources relative to the field at $z \sim$ 0.4 (Hogg et al. 1998), and therefore conclude that the MS1512.4+3647 sample is dominated by field [OII] emission-line galaxies which lie along the $\sim$ 180 Mpc line of sight immediately in front and behind the cluster. This is surprising, given that the previously surveyed $z=0.41$ cluster Abell 851 has 3-4 times the field emission-line galaxy density (Martin et al. 2000). We find that the MS1512.4+3647 sample is deficient in galaxies with intermediate colors (1.0 $< g-i <$ 2.0) and implied star-formation exponential decay timescales $\tau \sim$ 100 Myr - 1 Gyr that dominate the Abell 851 emission-line galaxy population. Instead, the majority of [OII] emission-line galaxies surrounding the MS1512.4+3647 cluster are blue ($g-i \leq 1.0$) and forming stars in bursts with $\tau <$ 100 Myr. In both samples, galaxies with the shortest star-formation timescales are preferentially among the faintest star-forming objects. Their i luminosities are consistent with young stellar populations \sim 10^8 - 10^9 \Msun, although an additional factor of ten in stellar mass could be hiding in underlying old stellar populations. We discuss the implications for the star-formation histories of dwarf galaxies in the field and rich clusters.Comment: 26 pages, including 5 tables and 13 figures; accepted for publication in the Astrophysical Journa

Gravitational Lens Statistics for Generalized NFW Profiles: Parameter Degeneracy and Implications for Self-Interacting Cold Dark Matter

Strong lensing is a powerful probe of the distribution of matter in the cores of clusters of galaxies. Recent studies suggest that the cold dark matter model predicts cores that are denser than those observed in galaxies, groups and clusters. One possible resolution of the discrepancy is that the dark matter has strong interactions (SIDM), which leads to lower central densities. A generalized form of the Navarro, Frenk and White profile (Zhao profile) may be used to describe these halos. In this paper we examine gravitational lensing statistics for this class of model. The optical depth to multiple imaging is a very sensitive function of the profile parameters in the range of interest for SIDM halos around clusters of galaxies. Less concentrated profiles, which result from larger self-interaction cross-sections, can produce many fewer lensed pairs. Lensing statistics provide a powerful test for SIDM. More realistic and observationally oriented calculations remain to be done, however larger self-interaction cross-sections may well be ruled out by the very existence of strong lenses on galaxy cluster scales. The inclusion of centrally dominant cluster galaxies should boost the cross-section to multiple imaging. However our preliminary calculations suggest that the additional multiple imaging rate is small with respect to the differences in multiple imaging rate for different halo profiles. In future statistical studies, it will be important to properly account for the scatter among halo profiles since the optical depth to multiple imaging is dominated by the most concentrated members of a cluster population.Comment: 58 pages, 14 figures. To be published in ApJ. Revised version includes discussion of magnification bias and the effect of a centrally dominant galax

A reanalysis of the luminosities of clusters of galaxies in the EMSS sample with 0.3 < z < 0.6

The X-ray luminosities of the Einstein Extended Medium Sensitivity Survey (EMSS) clusters of galaxies with redshifts 0.3<z<0.6 are remeasured using ROSAT PSPC data. It is found that the new luminosities are on average 1.18 +/- 0.08 times higher than previously measured but that this ratio depends strongly on the X-ray core radii we measure. For the clusters with small core radii, in general we confirm the EMSS luminosities, but for clusters with core radii >250 kpc (the constant value assumed in the EMSS), the new luminosities are 2.2 +/- 0.15 times the previous measurements. The X-ray luminosity function (XLF) at 0.3<z<0.6 is recalculated and is found to be consistent with the local XLF. The constraints on the updated properties of the 0.3<z<0.6 EMSS sample, including a comparison with the number of clusters predicted from local XLFs, indicate that the space density of luminous, massive clusters has either not evolved or has increased by a small factor ~2 since z=0.4. The implications of this result are discussed in terms of constraints on the cosmological parameter Omega_0.Comment: 12 pages, 7 figures. Accepted for publication in MNRA

Probing the Core Structure of Dark Halos with Tangential and Radial Arc Statistics

We study the arc statistics of gravitational lensing generated by dark matter halos in order to probe their density profile. We characterize the halo profile by two parameters, the inner slope of the central cusp $\alpha$, and the median amplitude of the concentration parameter, $c_{\rm norm}$, for a halo of mass $10^{14}h^{-1}M_\odot$ at $z=0$, and compute the numbers of tangential and radial arcs produced by gravitational lensing of galaxy clusters. We find that the number of arcs divided by the number of halos is a good statistic which is sensitive to both $c_{\rm norm}$ and $\alpha$ with very weak dependence on the cosmological parameters. If the arc samples with well-defined selection criteria for the clusters become available, one can strongly constrain both $c_{\rm norm}$ and $\alpha$. While our tentative comparison with the existing observational data indicates that the inner density profile of dark halos is indeed as steep as predicted by recent simulations ($\alpha \sim 1.5$), the homogeneous samples of tangential and radial arcs are required for more quantitative discussions.Comment: 23 pages, 8 figures, accepted for publication in Ap

A combined analysis of cluster mass estimates from strong lensing, X-ray measurement and the universal density profile

(Abridged)We present a combined analysis of mass estimates in the central cores of galaxy clusters from the strong lensing, the X-ray measurements and the universal density profile (NFW). Special attention is paid to the questions (1)whether the previously claimed mass discrepancy between the strong lensing and X-ray measurements is associated with the presence of cooling/non-cooling flows, (2)whether the cusped NFW density model can provide a consistent cluster mass with the strong lensing result and (3)whether a non-zero cosmological constant can be of any help to reducing the strong lensing - X-ray mass ratios. We analyse a sample of 26 arc-like images among 21 clusters. The X-ray and NFW cluster masses are obtained by assuming that the intracluster gas is isothermal and in hydrostatic equilibrium with the underlying gravitational potential of the clusters. A statistical comparison of these three mass estimates reveals that the mass discrepancies for all the events are well within a factor of 2. We confirm the result of Allen that the larger mass discrepancy is only detected in the intermediate cooling, especially non-cooling flow clusters, thus attributing the mass discrepancy to the local dynamical activities in the central regions. We show that the NFW profile yields a consistent cluster mass with the conventional X-ray measurement, and any difference between these two models must occur at even smaller radii (e.g. within the arc-like images) or at large radii. Finally, a non-zero cosmological constant is able to moderately reduce the mass ratios of m_lens to m_xray.Comment: 10 pages, 3 figures, to appear in MNRAS July issu

Arc Statistics in Triaxial Dark Matter Halos: Testing the Collisionless Cold Dark Matter Paradigm

Statistics of lensed arcs in clusters of galaxies serve as a powerful probe of both the non-sphericity and the inner slope of dark matter halos. We develop a semi-analytic method to compute the number of arcs in triaxial dark matter halos. This combines the lensing cross section from the Monte Carlo ray-tracing simulations, and the probability distribution function (PDF) of the axis ratios evaluated from cosmological N-body simulations. This approach enables one to incorporate both asymmetries in the projected mass density and elongations along the line-of-sight analytically, for the first time in cosmological lensed arc statistics. As expected, triaxial dark matter halos significantly increase the number of arcs relative to spherical models; the difference amounts to more than one order of magnitude while the value of enhancement depends on the specific properties of density profiles. Then we compare our theoretical predictions with the observed number of arcs from 38 X-ray selected clusters. In contrast to the previous claims, our triaxial dark matter halos with inner density profile \rho \propto r^{-1.5} in a Lambda-dominated cold dark matter (CDM) universe reproduces well the observation. Since both the central mass concentration and triaxial axis ratios (minor to major axis ratio ~0.5) required to account for the observed data are consistent with cosmological N-body simulations, our result may be interpreted to lend strong support for the collisionless CDM paradigm at the mass scale of clusters.Comment: 19 pages, 15 figures, 3 tables, error in eq. (47) corrected, conclusion unchange

Cluster strong lensing in the Millennium Simulation: The effect of galaxies and structures along the line-of-sight

We use ray-tracing through the Millennium simulation to study how secondary matter structures along the line-of-sight and the stellar mass in galaxies affect strong cluster lensing, in particular the cross-section for giant arcs. Furthermore, we investigate the distribution of the cluster Einstein radii and the radial distribution of giant arcs. We find that additional structures along the line-of-sight increase the strong-lensing optical depth by ~10-25%, while strong-lensing cross-sections of individual clusters are frequently boosted by as much as ~50%. The enhancement is mainly due to structures that are not correlated with the lens. Cluster galaxies increase the strong-lensing optical depth by up to a factor of 2, while interloping galaxies are not significant. We conclude that these effects need to be taken into account for predictions of the giant arc abundance, but they are not large enough to fully account for the reported discrepancy between predicted and observed abundances. Furthermore, we find that Einstein radii defined via the area enclosed by the critical curve are 10-30% larger than those defined via radial surface mass density profiles. The contributions of radial and tangential arcs to the radial distribution of arcs can be clearly distinguished. The radial distribution of tangential arcs is very broad and extends out to several Einstein radii. Thus, individual arcs are not well suited for constraining Einstein radii.Comment: 13 pages, 10 figures, 1 table, minor revisions, MNRAS accepte

Deep Optical Imaging of A Compact Group of Galaxies, Seyfert's Sextet

In order to investigate the dynamical status of Seyfert's Sextet (SS), we have obtained a deep optical ($VR+I$) image of this group. Our image shows that a faint envelope, down to a surface brightness $\mu_{\rm optical}$(AB) $\simeq 27$ mag arcsec$^{-2}$, surrounds the member galaxies. This envelope is irregular in shape. It is likely that this shape is attributed either to recent-past or to on-going galaxy interactions in SS. If the member galaxies have experienced a number of mutual interactions over a long timescale, the shape of the envelope should be rounder. Therefore, the irregular-shaped morphology suggests that SS is in an early phase of dynamical interaction among the member galaxies. It is interesting to note that the soft X-ray image obtained with ROSAT (Pildis et al. 1995) is significantly similar in morphology. We discuss the possible future evolution of SS briefly.Comment: 7 pages text (emulateapj LaTeX), 8 figures (3 EPS files, 1 PostScript file, and 4 jpeg files) figures, The Astronomical Journal, 120, No. 5 inpres

Gravitational Lensing

Gravitational lensing has developed into one of the most powerful tools for the analysis of the dark universe. This review summarises the theory of gravitational lensing, its main current applications and representative results achieved so far. It has two parts. In the first, starting from the equation of geodesic deviation, the equations of thin and extended gravitational lensing are derived. In the second, gravitational lensing by stars and planets, galaxies, galaxy clusters and large-scale structures is discussed and summarised.Comment: Invited review article to appear in Classical and Quantum Gravity, 85 pages, 15 figure