Z. L. Wen

GALAXY CLUSTERS IDENTIFIED FROM THE SDSS DR6 AND THEIR PROPERTIES

Clusters of galaxies in most previous catalogs have redshifts z � 0.3. Using the photometric redshifts of galaxies from the Sloan Digital Sky Survey Data Release 6 (SDSS DR6), we identify 39,668 clusters in the redshift range 0.05 2 � 10 14 M� ) clusters of z � 0.42. The false detection rate is � 5%. We obtain the richness, the summed luminosity, and the gross galaxy number within the determined radius for identified clusters. They are tightly related to the X-ray luminosity and temperature of clusters. Cluster mass is rel ated to the richness and summed luminosity with M200 / R 1.90� 0.04 and M200 / L 1.64� 0.03 r , respectively. In addition, 685 new candidates of X-ray clusters are found by cross-identification of our clusters with the so urce list of the ROSAT X-ray survey. Subject headings:galaxies: clusters: general — galaxies: distances and reds hifts

The Sensitivity of the Parkes Pulsar Timing Array to Individual Sources of Gravitational Waves

ABSTRACT We present the sensitivity of the Parkes Pulsar Timing Array to gravitational wavesemitted by individual super-massive black-hole binary systems in the early phases ofcoalescing at the cores of merged galaxies. Our analysis includes a detailed study of theeffects of fitting a pulsar timing model to non-white timing residuals. Pulsar timingis sensitive at nanoHertz frequencies and hence complementary to LIGO and LISA.We place a sky-averaged constraint on the merger rate of nearby (z<0.6) black-holebinaries in the early phases of coalescence with a chirp mass of 10 10 M ⊙ of less thanone merger every seven years. The prospects for future gravitational-wave astronomyof this type with the proposed Square Kilometre Array telescope are discussed.Key words: gravitational waves – pulsars: general. 1 INTRODUCTIONIn the era of ground- and space-based gravitational-wave(GW) detectors, GW astronomy is becoming increasinglyimportant for the wider astronomy and physics communi-ties. The ability of the current GW community to provide ei-ther limits on, or detections of, GW emission is of enormousimportance in characterising astrophysical sources of inter-est for further investigation. It is possible that GW detectionwill provide the only means to probe some of these sources.The sensitivity of existing and future observatories to indi-vidual GW sources, such as neutron-star binary systems andcoalescing black-hole binary systems, has been calculatedin the ∼kHz and ∼mHz frequency ranges. The sensitiv-ity curves of the Laser Interferometer Gravitational-WaveObservatory (Abbott et al. 2009)

Substructure and dynamical state of 2092 rich clusters of galaxies derived from photometric data

Dynamical state of galaxy clusters is closely related to the ir observational properties in X-ray, optical and radio wavelengths. We develop a method to diagnose the substructure and dynamical state of galaxy clusters by using photometric data of Sl oan Digital Sky Survey (SDSS). To trace mass distribution, the brightness distribution of me mber galaxies is smoothed by using a Gaussian kernel with a weight of their optical luminosities. After deriving the asymmetry, the ridge flatness and the normalized deviation of the smooth ed optical map, we define a relaxation parameter, , to quantify dynamical state of clusters. This method is applied to a test sample of 98 clusters of 0.05 0) and unrelaxed ( 0. We find that the dominance and absolute magnitude of the brigh test cluster galaxies closely correlate with dynamical state of clusters. The emission power of radio halos is quantitatively related to cluster dynamical state, beside the known dependence on the X-ray luminosity.

Mass function of rich galaxy clusters and its constraint on σ8

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 between 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.

Constraining the coalescence rate of supermassive black-hole binaries using pulsar timing

Pulsar timing observations are used to place constraints on the rate of coalescence of supermassive black-hole (SMBH) binaries as a function of mass and redshift. In contrast to the indirect constraints obtained from other techniques, pulsar timing observations provide a direct constraint on the black-hole merger rate. This is possible since pulsar timing is sensitive to the gravitational waves (GWs) emitted by these sources in the final stages of their evolution. We find that upper bounds calculated from the recently published Parkes Pulsar Timing Array data are just above theoretical predictions for redshifts below 10. In the future, with improved timing precision and longer data spans, we show that a non-detection of GWs will rule out some of the available parameter space in a particular class of SMBH binary merger models. We also show that if we can time a set of pulsars to 10 ns timing accuracy, for example, using the proposed Square Kilometre Array, it should be possible to detect one or more individual SMBH binary systems.

Mergers of Luminous Early-Type Galaxies in the Local Universe and Gravitational Wave Background

Supermassive black hole (SMBH) coalescence in galaxy mergers is believed to be one of the primary sources of very low frequency gravitational waves (GWs). Significant contribution of the GWs comes from mergers of massive galaxies with redshifts z < 2. Very few previous studies gave the merger rate of massive galaxies. We selected a large sample (1209) of close pairs of galaxies with projected separations 7 < rp < 50 kpc from 87,889 luminous early-type galaxies (Mr < –21.5) from the Sloan Digital Sky Survey Data Release 6. These pairs constitute a complete volume-limited sample in the local universe (z < 0.12). Using our newly developed technique, 249 mergers have been identified by searching for interaction features. From them, we found that the merger fraction of luminous early-type galaxies is 0.8%, and the merger rate in the local universe is R g ~ (1.0 ± 0.4) × 10–5 Mpc–3 Gyr–1 with an uncertainty mainly depending on the merging timescale. We estimated the masses of SMBHs in the centers of merging galaxies based on their luminosities. We found that the chirp mass distribution of the SMBH binaries follows a power law with an index of –3.0 ± 0.5 in the range 5 × 108-5 × 109 M ☉. Using the SMBH population in the mergers and assuming that the SMBHs can be efficiently driven into the GW regime, we investigated the stochastic GW background in the frequency range 10–9-10–7 Hz. We obtained the spectrum of the GW background of hc (f) ~ 10–15(f/yr–1)–2/3, which is one magnitude higher than that obtained by Jaffe & Backer in 2003, but consistent with those calculated from galaxy-formation models.

THE CORRELATION FUNCTION OF GALAXY CLUSTERS AND DETECTION OF BARYON ACOUSTIC OSCILLATIONS

We calculate the correlation function of 13,904 galaxy clusters of z ≤ 0.4 selected from the cluster catalog of Wen et al. The correlation function can be fitted with a power-law model ξ(r) = (r/R 0)–γ on the scales of 10 h –1 Mpc ≤ r ≤ 50 h –1 Mpc, with a larger correlation length of R 0 = 18.84 ± 0.27 h –1 Mpc for clusters with a richness of R ≥ 15 and a smaller length of R 0 = 16.15 ± 0.13 h –1 Mpc for clusters with a richness of R ≥ 5. The power-law index of γ = 2.1 is found to be almost the same for all cluster subsamples. A pronounced baryon acoustic oscillations (BAO) peak is detected at r ~ 110 h –1 Mpc with a significance of ~1.9σ. By analyzing the correlation function in the range of 20 h –1 Mpc ≤ r ≤ 200 h –1 Mpc, we find that the constraints on distance parameters are Dv (zm = 0.276) = 1077 ± 55(1σ) Mpc and h = 0.73 ± 0.039(1σ), which are consistent with the cosmology derived from Wilkinson Microwave Anisotropy Probe (WMAP) seven-year data. However, the BAO signal from the cluster sample is stronger than expected and leads to a rather low matter density Ω m h 2 = 0.093 ± 0.0077(1σ), which deviates from the WMAP7 result by more than 3σ. The correlation function of the GMBCG cluster sample is also calculated and our detection of the BAO feature is confirmed.

Morphological Dependence of Star Formation Properties for the Galaxies in the Merging Galaxy Cluster A2255

The merging cluster of galaxies A2255 is covered by the Sloan Digital Sky Survey (SDSS) survey. The physical parameters of 184 bright member galaxies derived from the SDSS data analyses by Brinchmann et al. allow a detailed study of the star formation properties of galaxies within a merging cluster at intermediate redshift. In this paper we perform a morphological classification on the basis of the SDSS imaging and spectral data and investigate the morphological dependence of the star formation rates (SFRs) for these member galaxies. As we expect, a tight correlation between the SFR normalized by stellar mass (SFR/M*) and the Hα equivalent width is found for the late-type galaxies in A2255. The correlation of SFR/M* with the continuum break strength at 4000 A is also confirmed. A SFR/M*-M* correlation is found for both early- and late-type galaxies, indicating that the star formation activity tends to be suppressed when the assembled stellar mass (M*) increases, and this correlation is tighter and steeper for the late-type cluster galaxies. Compared with the mass range of field spiral galaxies, only two massive late-type galaxies with M* > 1011 M⊙ have survived in A2255, suggesting that the gas disks of massive spiral galaxies could have been tidally stripped during cluster formation. In addition, the SFR variation with the projected radial distance is found to be heavily dependent on galaxy morphology: the early-type galaxies have a very weak inner decrease in SFR/M*, while the inner late-type galaxies tend to have higher SFR/M* values than the outer late-type galaxies. This may suggest that the galaxy-scale turbulence stimulated by the merging of subclusters might have played different roles in early- and late-type galaxies, which leads to a suppression of the star formation activity for E/S0 galaxies and an SFR enhancement for spiral and irregular galaxies.

THE SCALING RELATIONS AND THE FUNDAMENTAL PLANE FOR RADIO HALOS AND RELICS OF GALAXY CLUSTERS

Diffuse radio emission in galaxy clusters is known to be related to cluster mass and cluster dynamical state. We collect the observed fluxes of radio halos, relics, and mini-halos for a sample of galaxy clusters from the literature, and calculate their radio powers. We then obtain the values of cluster mass or mass proxies from previous observations, and also obtain the various dynamical parameters of these galaxy clusters from optical and X-ray data. The radio powers of relics, halos, and mini-halos are correlated with the cluster masses or mass proxies, as found by previous authors, with the correlations concerning giant radio halos being, in general, the strongest ones. We found that the inclusion of dynamical parameters as the third dimension can significantly reduce the data scatter for the scaling relations, especially for radio halos. We therefore conclude that the substructures in X-ray images of galaxy clusters and the irregular distributions of optical brightness of member galaxies can be used to quantitatively characterize the shock waves and turbulence in the intracluster medium responsible for re-accelerating particles to generate the observed diffuse radio emission. The power of radio halos and relics is correlated with cluster mass proxies and dynamical parameters in the form of a fundamental plane.

ERRATUM: “GALAXY CLUSTERS IDENTIFIED FROM THE SLOAN DIGITAL SKY SURVEY DR6 AND THEIR PROPERTIES” (2009, ApJS, 183, 197)

We were alerted by Dr. Heinz Andernach that the online version of Table 1 contains 15 repeated entries, which was caused by using a very early version of a code with a known bug. Furthermore, Table 2 contains some known X-ray clusters in the NASA/IPAC Extragalactic Database (NED). We therefore revised the online Tables 1 and 2. Detail of changes are as follows. Table 1. 48 entries are removed. BCG positions of 296 clusters are corrected. The unit for Column 10 is added. Table 2. All 912 clusters with projected separation rp < 0.3 Mpc between the ROSAT sources and BCGs of clusters are listed. The 227 X-ray clusters known from the NED are marked in Column 8. After these changes, the total number of identified clusters is now 39,668, and the total number of new X-ray cluster candidates is now 685. However, the results and conclusions in the paper do not change except for these numbers.