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We measure the two point correlation function (CF) of 1357 galaxy clusters with a mass of $\log_{10}{M_{200}}\geq 13.6$~\hm~and at a redshift of $z \leq 0.125$. This work differs from previous analyses in that it utilizes a spectroscopic cluster catalogue, $\mathtt{SDSS-GalWCat}$, to measure the CF and detect the baryon acoustic oscillation (BAO) signal. Unlike previous studies which use statistical techniques, we compute covariance errors directly by generating a set of 1086 galaxy cluster lightcones from the GLAM $N$-body simulation. Fitting the CF with a power-law model of the form $\xi(s) = (s/s_0)^{-\gamma}$, we determine the best-fit correlation length and power-law index at three mass thresholds. We find that the correlation length increases with increasing the mass threshold while the power-law index is almost constant. For $\log_{10}{M_{200}}\geq 13.6$~\hm, we find $s_0 = 14.54\pm0.87$~\h~and $\gamma=1.97\pm0.11$. We detect the BAO signal at $s = 100$~\h~with a significance of $1.60 \sigma$. Fitting the CF with a $\Lambda$CDM model, we find $D_\mathrm{V}(z = 0.089)\mathrm{r}^{fid}_d/\mathrm{r}_d = 267.62 \pm 26$ \h, consistent with Planck 2015 cosmology. We present a set of 108 high-fidelity simulated galaxy cluster lightcones from the high-resolution \U~N-body simulation, employed for methodological validation. We find $D_\mathrm{V}(z = 0.089)/r_d = 2.666 \pm 0.129$, indicating that our method does not introduce any bias in the parameter estimation for this small sample of galaxy clusters., Comment: 7 pages, 5 figures

The cluster mass-richness relation (MRR) is an observationally efficient and potentially powerful cosmological tool for constraining the mean matter density of the universe and the amplitude of fluctuations using the cluster abundance technique. We derive the MRR relation using GalWCat19, a publicly available galaxy cluster catalog we created from the Sloan Digital Sky Survey-DR13 spectroscopic dataset. The MRR shows a tail at the low-richness end. Using the Illustris-TNG and mini-Uchuu cosmological numerical simulations, we demonstrate that this tail is caused by systematical uncertainties. We show that, by means of a judicious cut, identified by the use of the Hinge function, it is possible to determine a richness threshold above which the MRR is linear i.e., where cluster mass scales with richness as logM_200 = alpha + beta logN_200. We derive the MRR and show it is consistent with both sets of simulations with a slope of beta ~ 1. We use our MRR to estimate cluster masses from the GalWCat19 catalog which we then use to set constraints on omega_m and sigma_8. Utilizing the all-member MRR, we obtain constraints of omega_m = 0.31 (+0.04-0.03) and sigma_8 = 0.82 (+0.05-0.04), and utilizing the red-member MRR, we obtain omega_m = 0.31 (+0.04-0.03) and sigma_8 = 0.81 (+0.05-0.04). Our constraints on omega_m and sigma_8 are consistent and very competitive with the Planck 2018 results.

We present the public data release of the Uchuu-UM galaxy catalogues by applying the UniverseMachine algorithm to assign galaxies to the dark matter halos in the Uchuu $N$-body cosmological simulation. It includes a variety of baryonic properties for all galaxies down to $\sim 5\times10^8 M_{\odot}$ with halos in a mass range of $10^{10}

We report the discovery of MAGAZ3NE J095924+022537, a spectroscopically-confirmed protocluster at $z = 3.3665^{+0.0009}_{-0.0012}$ around a spectroscopically-confirmed $UVJ$-quiescent ultra-massive galaxy (UMG; $M_{\star}=2.34^{+0.23}_{-0.34}\times10^{11} {\rm M}_\odot$) in the COSMOS UltraVISTA field. We present a total of 38 protocluster members (14 spectroscopic and 24 photometric), including the UMG. Notably, and in marked contrast to protoclusters previously reported at this epoch which have been found to contain predominantly star-forming members, we measure an elevated fraction of quiescent galaxies relative to the coeval field ($73.3^{+26.7}_{-16.9}\%$ versus $11.6^{+7.1}_{-4.9}\%$ for galaxies with stellar mass $M_{\star} \geq 10^{11} {\rm M}_\odot$). This high quenched fraction provides a striking and important counterexample to the seeming ubiquitousness of star-forming galaxies in protoclusters at $z>2$ and suggests, rather, that protoclusters exist in a diversity of evolutionary states in the early Universe. We discuss the possibility that we might be observing either "early mass quenching" or non-classical "environmental quenching." We also present the discovery of MAGAZ3NE J100028+023349, a second spectroscopically-confirmed protocluster, at a very similar redshift of $z = 3.3801^{+0.0213}_{-0.0281}$. We present a total of 20 protocluster members, 12 of which are photometric and 8 spectroscopic including a post-starburst UMG ($M_{\star}=2.95^{+0.21}_{-0.20}\times10^{11} {\rm M}_\odot$). Protoclusters MAGAZ3NE J0959 and MAGAZ3NE J1000 are separated by 18 arcminutes on the sky (35 comoving Mpc), in good agreement with predictions from simulations for the size of "Coma"-type cluster progenitors at this epoch. It is highly likely that the two UMGs are the progenitors of Brightest Cluster Galaxies (BCGs) seen in massive virialized clusters at lower redshift., Comment: 19 pages, 6 figures, 3 tables. Accepted for publication in ApJ

We derive cosmological constraints on the matter density, \om, and the amplitude of fluctuations, \sig, using $\mathtt{GalWCat19}$, a catalog of 1800 galaxy clusters we identified in the Sloan Digital Sky Survey-DR13 spectroscopic data set using our GalWeight technique to determine cluster membership \citep{Abdullah18,Abdullah19}. By analyzing a subsample of 756 clusters in a redshift range of $0.045\leq z \leq 0.125$ and virial masses of $M\geq 0.8\times10^{14}$ \hm ~with mean redshift of $z = 0.085$, we obtain \om ~$=0.310^{+0.023}_{-0.027} \pm 0.041$ (systematic) and \sig ~$=0.810^{+0.031}_{-0.036}\pm 0.035$ (systematic), with a cluster normalization relation of $\sigma_8= 0.43 \Omega_m^{-0.55}$. There are several unique aspects to our approach: we use the largest spectroscopic data set currently available, and we assign membership using the GalWeight technique which we have shown to be very effective at simultaneously maximizing the number of {\it{bona fide}} cluster members while minimizing the number of contaminating interlopers. Moreover, rather than employing scaling relations, we calculate cluster masses individually using the virial mass estimator. Since $\mathtt{GalWCat19}$ is a low-redshift cluster catalog we do not need to make any assumptions about evolution either in cosmological parameters or in the properties of the clusters themselves. Our constraints on \om ~and \sig ~are consistent and very competitive with those obtained from non-cluster abundance cosmological probes such as Cosmic Microwave Background (CMB), Baryonic Acoustic Oscillation (BAO), and supernovae (SNe). The joint analysis of our cluster data with Planck18+BAO+Pantheon gives \om ~$=0.315^{+0.013}_{-0.011}$ and \sig ~$=0.810^{+0.011}_{-0.010}$., Comment: 14 pages, 10 figures, accepted for publication in the ApJ

Utilizing the SDSS-DR13 spectroscopic dataset, we create a new publicly-available catalog of 1,800 galaxy clusters (GalWeight cluster catalog, $\mathtt{GalWCat19}$) and a corresponding catalog of 34,471 identified member galaxies. The clusters are identified from overdensities in redshift-phase space. The GalWeight technique introduced in Abdullah, Wilson and Klypin (AWK18) is then applied to identify cluster members. The completeness of the cluster catalog ($\mathtt{GalWCat19}$) and the procedure followed to determine cluster mass are tested on the Bolshoi N-body simulations. The 1,800 $\mathtt{GalWCat19}$ clusters range in redshift between $0.01 - 0.2$ and in mass between $(0.4 - 14) \times 10^{14}h^{-1}M_{\odot}$. The cluster catalog provides a large number of cluster parameters including sky position, redshift, membership, velocity dispersion, and mass at overdensities $\Delta = 500, 200, 100, 5.5$. The 34,471 member galaxies are identified within the radius at which the density is 200 times the critical density of the Universe. The galaxy catalog provides the coordinates of each galaxy and the ID of the cluster that the galaxy belongs to. The cluster velocity dispersion scales with mass as $\log(\sigma_{200})=\log(946\pm52~ \mbox{km} ~ \mbox{s}^{-1}) +(0.349\pm0.142)\log\left[h(z) ~ M_{200}/10^{15}M_\odot\right]$ with scatter of $\delta_{\log\sigma} = 0.06$. The catalogs are publicly available at the following website\footnote{\url{https://mohamed-elhashash-94.webself.net/galwcat/}}., Comment: 15 pages, 6 figures

We present results on the rest-frame $H$-band luminosity functions (LF) of red sequence galaxies in seven clusters at 1.0 < z < 1.3 from the Gemini Observations of Galaxies in Rich Early Environments Survey (GOGREEN). Using deep GMOS-z' and IRAC $3.6 \mu$m imaging, we identify red sequence galaxies and measure their LFs down to $M_{H} \sim M_{H}^{*} + (2.0 - 3.0)$. By stacking the entire sample, we derive a shallow faint end slope of $ \alpha \sim -0.35^{+0.15}_{-0.15} $ and $ M_{H}^{*} \sim -23.52^{+0.15}_{-0.17} $, suggesting that there is a deficit of faint red sequence galaxies in clusters at high redshift. By comparing the stacked red sequence LF of our sample with a sample of clusters at z~0.6, we find an evolution in the faint end of the red sequence over the ~2.6 Gyr between the two samples, with the mean faint end red sequence luminosity growing by more than a factor of two. The faint-to-luminous ratio of our sample ($0.78^{+0.19}_{-0.15}$) is consistent with the trend of decreasing ratio with increasing redshift as proposed in previous studies. A comparison with the field shows that the faint-to-luminous ratios in clusters are consistent with the field at z~1.15 and exhibit a stronger redshift dependence. Our results support the picture that the build up of the faint red sequence galaxies occurs gradually over time and suggest that faint cluster galaxies, similar to bright cluster galaxies, experience the quenching effect induced by environment already at z~1.15., Comment: Accepted for publication in ApJ. 24 pages, 13 figures

We introduce GalWeight, a new technique for assigning galaxy cluster membership. This technique is specifically designed to simultaneously maximize the number of bona fide cluster members while minimizing the number of contaminating interlopers. The GalWeight technique can be applied to both massive galaxy clusters and poor galaxy groups. Moreover, it is effective in identifying members in both the virial and infall regions with high efficiency. We apply the GalWeight technique to MDPL2 \& Bolshoi N-body simulations, and find that it is $> 98\%$ accurate in correctly assigning cluster membership. We show that GalWeight compares very favorably against four well-known existing cluster membership techniques (shifting gapper, den Hartog, caustic, SIM). We also apply the GalWeight technique to a sample of twelve Abell clusters (including the Coma cluster) using observations from the Sloan Digital Sky Survey. We end by discussing GalWeight's potential for other astrophysical applications., Comment: Accepted for publication in APJ

We show that spherical infall models (SIMs) can better describe some galaxy clusters in redshift slice space than in traditional axially-convolved projection space. This is because in SIM, the presence of transverse motion between cluster and observer, and/or shear flow about the cluster (such as rotation), causes the infall artifact to tilt, obscuring the characteristic two-trumpet profile; and some clusters resemble such tilted artifacts. We illustrate the disadvantages of applying SIM to convolved data and, as an alternative, introduce a method fitting a tilted 2D envelope to determine a 3D envelope. We also introduce a fitting algorithm and test it on toy SIM simulations as well as three clusters (Virgo, A1459, and A1066). We derive relations useful for using the tilt and width-to-length ratio of the fitted envelopes to analyze peculiar velocities. We apply them to our three clusters as a demonstration. We find that transverse motion between cluster and observer can be ruled out as sole cause of the observed tilts, and that a multi-cluster study could be a feasible way to find our infall toward Virgo cluster.

Using SDSS-DR7, we construct a sample of 42382 galaxies with redshifts in the region of 20 galaxy clusters. Using two successive iterative methods, the adaptive kernel method and the spherical infall model, we obtained 3396 galaxies as members belonging to the studied sample. The 2D projected map for the distribution of the clusters members is introduced using the 2D adaptive kernel method to get the clusters centers. The cumulative surface number density profile for each cluster is fitted well with the generalized King model. The core radii of the clusters' sample are found to vary from 0.18 Mpc $\mbox{h}^{-1}$ (A1459) to 0.47 Mpc $\mbox{h}^{-1}$ (A2670) with mean value of 0.295 Mpc $\mbox{h}^{-1}$. The infall velocity profile is determined using two different models, Yahil approximation and Praton model. Yahil approximation is matched with the distribution of galaxies only in the outskirts (infall regions) of many clusters of the sample, while it is not matched with the distribution within the inner core of the clusters. Both Yahil approximation and Praton model are matched together in the infall region for about 9 clusters in the sample but they are completely unmatched for the clusters characterized by high central density. For these cluster, Yahil approximation is not matched with the distribution of galaxies, while Praton model can describe well the infall pattern of such clusters., Comment: 16 pages, 8 figures