Clusters of galaxies have a huge mass which can act as gravitational lenses. Galaxies behind clusters can be distorted to form arcs in images by the lenses. Herein a search was done for giant lensed arcs by galaxy clusters using the SDSS data. By vis
ually inspecting SDSS images of newly identified clusters in the SDSS DR8 and Stripe 82 data, we discover 8 strong lensing clusters together with additional 3 probable and 6 possible cases. The lensed arcs show bluer colors than the member galaxies of clusters. The masses and optical luminosities of galaxy clusters interior to the arcs are calculated, and the mass-to-light ratios are found to be in the range of a few tens of M_Solar/L_Solar, consistent with the distribution of previously known lensing clusters.
Using the photometric redshifts of galaxies from the Sloan Digital Sky Survey III (SDSS-III), we identify 132,684 clusters in the redshift range of 0.05<z<0.8. Monte Carlo simulations show that the false detection rate is less than 6% for the whole s
ample. The completeness is more than 95% for clusters with a mass of M_{200}>1.0*10^{14} M_{odot} in the redshift range of 0.05<z<0.42, while clusters of z>0.42 are less complete and have a biased smaller richness than the real one due to incompleteness of member galaxies. We compare our sample with other cluster samples, and find that more than 90% of previously known rich clusters of 0.05<z<0.42 are matched with clusters in our sample. Richer clusters tend to have more luminous brightest cluster galaxies (BCGs). Correlating with X-ray and the Planck data, we show that the cluster richness is closely related to the X-ray luminosity, temperature and Sunyaev-Zeldovich measurements. Comparison of the BCGs with the SDSS luminous red galaxy (LRG) sample shows that 25% of LRGs are BCGs of our clusters and 36% of LRGs are cluster member galaxies. In our cluster sample, 63% of BCGs of r_{petro}<19.5 satisfy the SDSS LRG selection criteria.
The mass function of galaxy clusters is a powerful tool to constrain cosmological parameters, e.g., the mass fluctuation on the scale of 8 h^{-1} Mpc, sigma_8, and the abundance of total matter, Omega_m. We first determine the scaling relations betwe
en cluster mass and cluster richness, summed r-band luminosity and the global galaxy number within a cluster radius. These relations are then used to two complete volume-limited rich cluster samples which we obtained from the Sloan Digital Sky Survey (SDSS). We estimate the masses of these clusters and determine the cluster mass function. Fitting the data with a theoretical expression, we get the cosmological parameter constraints in the form of sigma_8(Omega_m/0.3)^{alpha}=beta and find out the parameters of alpha=0.40-0.50 and beta=0.8-0.9, so that sigma_8=0.8-0.9 if Omega_m=0.3. Our sigma_8 value is slightly higher than recent estimates from the mass function of X-ray clusters and the Wilkinson Microwave Anisotropy Probe (WMAP) data, but consistent with the weak lensing statistics.
We have made a careful selection of a large complete volume-limited sample (1209) of projected close pairs (7<r_p<50 kpc) of luminous early-type galaxies (M_r<-21.5) in the local universe (z<0.12) from the SDSS data. 249 (21%) of them show interactio
n features, which suggests that about 0.8% of the galaxies are merging. We derived a comoving volume merger rate of ~(1.0+/-0.4)times 10^{-5} Mpc^{-3} Gyr^{-1} for luminous early-type galaxies. This is a direct observational determination of the merger rate of luminous galaxies in the local universe. We also obtained the chirp mass distribution of supermassive black hole (SMBH) binary following log[Phi(log M /M_{odot})]=(21.7+/-4.2)-(3.0+/-0.5)log M/M_{odot}. With less assumptions than previous works, we estimated the strain amplitude of the gravitational wave (GW) background from coalescence of SMBH binaries at frequency 10^{-9}-10^{-7} Hz.
We report the discovery of 4 strong gravitational lensing systems by visual inspections of the Sloan Digital Sky Survey images of galaxy clusters in Data Release 6 (SDSS DR6). Two of the four systems show Einstein rings while the others show tangenti
al giant arcs. These arcs or rings have large angular separations (>8) from the bright central galaxies and show bluer color compared with the red cluster galaxies. In addition, we found 5 probable and 4 possible lenses by galaxy clusters.
