Covariance matrices for halo number counts and correlation functions

We study the mean number counts and two-point correlation functions, along with their covariance matrices, of cosmological surveys such as for clusters. In particular, we consider correlation functions averaged over finite redshift intervals, which are well suited to cluster surveys or populations of rare objects, where one needs to integrate over nonzero redshift bins to accumulate enough statistics. We develop an analytical formalism to obtain explicit expressions of all contributions to these means and covariance matrices, taking into account both shot-noise and sample-variance effects. We compute low-order as well as high-order (including non-Gaussian) terms. We derive expressions for the number counts per redshift bins both for the general case and for the small window approximation. We estimate the range of validity of Limber's approximation and the amount of correlation between different redshift bins. We also obtain explicit expressions for the integrated 3D correlation function and the 2D angular correlation. We compare the relative importance of shot-noise and sample-variance contributions, and of low-order and high-order terms. We check the validity of our analytical results through a comparison with the Horizon full-sky numerical simulations, and we obtain forecasts for several future cluster surveys.Comment: 37 page

Star Formation and Relaxation in 379 Nearby Galaxy Clusters

We investigate the relationship between star formation (SF) and level of relaxation in a sample of 379 galaxy clusters at z < 0.2. We use data from the Sloan Digital Sky Survey to measure cluster membership and level of relaxation, and to select star-forming galaxies based on mid-infrared emission detected with the Wide-Field Infrared Survey Explorer. For galaxies with absolute magnitudes M_r < -19.5, we find an inverse correlation between SF fraction and cluster relaxation: as a cluster becomes less relaxed, its SF fraction increases. Furthermore, in general, the subtracted SF fraction in all unrelaxed clusters (0.117 +/- 0.003) is higher than that in all relaxed clusters (0.097 +/- 0.005). We verify the validity of our SF calculation methods and membership criteria through analysis of previous work. Our results agree with previous findings that a weak correlation exists between cluster SF and dynamical state, possibly because unrelaxed clusters are less evolved relative to relaxed clusters.Comment: 6 pages, 4 figures, accepted for publication in Ap

Relations between spatial correlations of rich clusters of galaxies

The authors express the N-point rich cluster correlation function in terms of the two-point rich cluster correlation function in a model where rich clusters formed wherever suitably averaged primordial energy density fluctuations are unusually large. The validity of the results is not restricted to regions where the connected (reduced) N-point correlation functions are small compared with unity

A correlation-based fuzzy cluster validity index with secondary options detector

The optimal number of clusters is one of the main concerns when applying cluster analysis. Several cluster validity indexes have been introduced to address this problem. However, in some situations, there is more than one option that can be chosen as the final number of clusters. This aspect has been overlooked by most of the existing works in this area. In this study, we introduce a correlation-based fuzzy cluster validity index known as the Wiroonsri-Preedasawakul (WP) index. This index is defined based on the correlation between the actual distance between a pair of data points and the distance between adjusted centroids with respect to that pair. We evaluate and compare the performance of our index with several existing indexes, including Xie-Beni, Pakhira-Bandyopadhyay-Maulik, Tang, Wu-Li, generalized C, and Kwon2. We conduct this evaluation on four types of datasets: artificial datasets, real-world datasets, simulated datasets with ranks, and image datasets, using the fuzzy c-means algorithm. Overall, the WP index outperforms most, if not all, of these indexes in terms of accurately detecting the optimal number of clusters and providing accurate secondary options. Moreover, our index remains effective even when the fuzziness parameter $m$ is set to a large value. Our R package called WPfuzzyCVIs used in this work is also available in https://github.com/nwiroonsri/WPfuzzyCVIs.Comment: 19 page

Clustering performance analysis using a new correlation-based cluster validity index

There are various cluster validity indices used for evaluating clustering results. One of the main objectives of using these indices is to seek the optimal unknown number of clusters. Some indices work well for clusters with different densities, sizes, and shapes. Yet, one shared weakness of those validity indices is that they often provide only one optimal number of clusters. That number is unknown in real-world problems, and there might be more than one possible option. We develop a new cluster validity index based on a correlation between an actual distance between a pair of data points and a centroid distance of clusters that the two points occupy. Our proposed index constantly yields several local peaks and overcomes the previously stated weakness. Several experiments in different scenarios, including UCI real-world data sets, have been conducted to compare the proposed validity index with several well-known ones. An R package related to this new index called NCvalid is available at https://github.com/nwiroonsri/NCvalid.Comment: 19 page

Multiwavelength analysis of the young open cluster NGC 2362

We present a multiwavelength analysis of the young open cluster NGC 2362. UBVRcIc CCD photometric observations, together with available data in the Chandra data base, near infrared data from the Two Micron All Sky Survey (2MASS), and recently published Halpha spectroscopy were used to get information about the evolutionary stage of the cluster and the main physical properties of its stellar content. Cluster membership is estimated for every individual star by means of ZAMS and isochrone fitting. The cluster is confirmed to host a richly populated pre-main sequence (PMS), and to contain a large amount of X-ray emitting stars, which reach from the PMS members of GK spectral type, up to the most luminous OB type main sequence (MS) members. The PMS cluster members show no significant age spread, and the comparison to both PMS and post-MS isochrones suggests a younger age for the more massive MS than for lower mass PMS members. The analysis allows to asses the validity of currently used pre-main sequence evolutionary models, and supports the suggestion of a well defined positive correlation of the X-ray emission from PMS stars with their bolometric luminosity. Clear differences are found on the other hand, between the X-ray activity properties of MS and PMS cluster members, both in the relation between X-ray luminosity and bolometric luminosity, and in spectral properties as well.Comment: 1 gzipped file: 1 tex file with 9 pages text. 5 ps files with figures. Submitted to Astrophysical Journa

The ACS survey of globular clusters. XIII. Photometric calibration in comparison with Stetson standards

In this study we compare the photometric data of 34 Milky Way globular clusters, observed within the ACS Treasury Program (PI: Ata Sarajedini) with the corresponding ground-based data, provided by the Photometric Standard Field Catalogs of Stetson (2000, 2005). We focus on the transformation between the HST/ACS F606W to V-band and F814W to I-band only. The goal is to assess the validity of the filter transformation equations by Sirianni et al.(2005) with respect to their dependence on metallicity, Horizontal Branch morphology, mass and integrated (V-I) colour of the various globular clusters. Such a dependence is expected due to the fact that the transformation equations are based on the observations of only one globular cluster, i.e., NGC 2419. Surprisingly, the correlation between offset and metallicity is found to be weak, with a low level significance. The correlation between offset and Horizontal Branch structure, as well as total cluster mass is still weaker. Based on the available data we do not find the photometric offset to be linked to multiple stellar populations, e.g., as found in NGC 0288, NGC 1851, and NGC 5139. The results of this study show that there are small systematic offsets between the transformed ACS- and observed ground based photometry, and that these are only weakly correlated, if at all, with various cluster parameters and their underlying stellar populations. As a result, investigators wishing to transform globular cluster photometry from the Sirianni et al.(2005) ground-based V, I system onto the Stetson (2000) system simply need to add 0.040 (+/-0.012) to the V-band magnitudes and 0.047 (+/-0.011) to the I-band magnitudes. This in turn means that the transformed ACS (V-I) colours match the ground-based values from Stetson (2000) to within ~0.01 mag.Comment: 28 pages, 14 figures, accepted for publication in ApJ

A numerical and analytical study of two holes doped into the 2D t--J model

Exact diagonalization numerical results are presented for a 32-site square cluster, with two holes propagating in an antiferromagnetic background described by the t-J model. We characterize the wave function of the lowest energy bound state found in this calculation, which has d_{x^2-y^2} symmetry. Analytical work is presented, based on a Lang-Firsov-type canonical transformation derived quasiparticle Hamiltonian, that accurately agrees with numerically determined values for the electron momentum distribution function and the pair correlation function. We interpret this agreement as strong support for the validity of this description of the hole quasiparticles.Comment: 3 pages, REVTeX, to appear in the proceedings of the Fifth International Conference on Spectroscopies in Novel Superconductors, September 14-18, 1997, Cape Cod, Massachusett