1. Studying the Dynamical Properties of 20 Nearby Galaxy Clusters,

Mohamed H. Abdullah, Gamal B. Ali, Hamed A. Ismail, and M. A. Rassem, 2011, MNRAS, 416, 2027

This was my first published paper. This research focused on studying the dynamics of 20 galaxy clusters obtained from SDSS. Using the binary tree algorithm, the adaptive kernel method and the application of spherical infall models (SIM), I identified cluster locations and obtained the member galaxies of each cluster. Then, under the assumption that the dynamical mass follows galaxy distribution, I determined the mass and mass profile of each cluster using two independent mass estimators; the projected mass and the virial mass methods.

The cumulative surface number density profiles (dots) together with the generalized King model (solid line).

2. Distortion of Infall Regions in Redshift Space-I

Mohamed H. Abdullah, Elizabeth Praton, Gamal B. Ali, 2013, MNRAS, 434, 1989

I also studied the distortion of infall regions of galaxy clusters in the redshift-space. Even though some clusters are well fit by the simple spherical infall model other clusters, such as Virgo, are not. These clusters exhibit tilted structure in the redshift space even though this artifact is not shown in the real-space. With my collaborators, we modified the spherical infall model by taking into account the distortion of galaxy motion due to the line-of-sight and transverse motions of galaxies with respect to the observer, and/or rotational motion of galaxies in the cluster-frame in addition to the pure infall motion of galaxies towards the cluster center. This modified spherical infall model can successfully describe these tilted structures in the clusters.

Virgo. (a) Aitoff projection in supergalactic coordinates of elliptical (big black), dwarf elliptical (open), spiral (grey) and irregular (small black) galaxies with heliocentric velocities <3000 km s−1. Circle is turnaround radius; rectangles outline 63◦ thick fat slice (solid line) and 20◦ thin slice (dashed). (b) Fat slice in redshift space. (c) Thin slice in redshift space, with PSM Sv envelope. (d) Sv envelope in 3D. Members (black) are inside and outliers (grey) outside the envelope. (e) Sp envelope, determined in projection space. Members (black) and outliers (grey) from panel d are shown. False members (red) are outliers inside Sp envelope. (f) Fat slice showing positions of members, outliers and false members from panel e.

3. A New and EffectiveWeighting Technique for Determining Galaxy Cluster and Group Membership

Mohamed H. Abdullah, , Gillian Wilson, Anatoly Klypin, 2018, GalWeight: , ApJ, 861, 22

In 2018, I invented GalWeight, a new tool 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. Because of the presence of interlopers, estimates of cluster masses tend to be biased too high, and estimates of cluster concentrations tend to be biased too low. With its efficiency of ~ 98% in correctly assigning cluster membership, GalWeight allowed us to calculate cluster masses with high accuracy. GalWeight can be applied to both massive clusters and poor groups. The technique is also effective in identifying members in both the virial and infall regions. For the press release: http://astro.ucr.edu/mohamed2018

Membership identification of a simulated cluster taken from Multi dark simulation by applying GalWeight technique. The plot shows the weight of each galaxy in line-of-sight velocity/projected radius phase space (magenta color indicates higher weight).

4. GalWeight Application: A publicly-available catalog of dynamical parameters of 1800galaxy clusters from SDSS-DR13, (GalWCat19)

Mohamed H. Abdullah, Gillian Wilson, Anatoly Klypin, Lyndsay Old, Elizabeth Praton, Gamal B. Ali, 2020b, ApJS, 246, 2

At the beginning of 2020, I introduced a spectroscopic catalog of dynamical properties of 1800 galaxy clusters and a corresponding catalog of 34,471 identified member galaxies (GalWCat19). The catalog is derived from the SDSS-DR13 spectroscopic data set. In this paper, I developed a powerful toolkit (FoG-GalWegiht) for constructing galaxy cluster catalogs and determining cluster dynamical properties from spectroscopic galaxy surveys. The cluster locations were identified using the Finger-of-God effect (distortion of line-of-sight velocities of galaxies due to the cluster potential well). The cluster members were identified using GalWeight and the cluster masses were calculated using the virial mass estimator and NFW mass model.

Aitoff projection in celestial coordinates. The black points represent the distribution of all galaxies in the
sample, while the blue and red points represent the distribution of 1800 cluster members identified by GalWeight that are within virial and turnaround radii, respectively.

5. Cosmological Constraints on Ωm and σ8 from Cluster Abundances using the GalWCat19 Optical-Spectroscopic SDSS Catalog

Mohamed H. Abdullah, Anatoly Klypin, Gillian Wilson, 2020a, ApJ, 901, 90

I also studied the distortion of infall regions of galaxy clusters in the redshift-space (Abdullah et al. 2013). Even though some clusters are well fit by the simple spherical infall model other clusters, such as Virgo, are not. These clusters exhibit tilted structure in the redshift space even though this artifact is not shown in the real-space. With my collaborators, we modified the spherical infall model by taking into account the distortion of galaxy motion due to the line-of-sight and transverse motions of galaxies with respect to the observer, and/or rotational motion of galaxies in the cluster-frame in addition to the pure infall motion of galaxies towards the cluster center. This modified spherical infall model can successfully describe these tilted structures in the clusters.

Constraints on Ωm and σ8 obtained from cluster abundance studies (cluster mass function; CMF). Left: 68% confidence levels (CLs) derived from GalWCat19 (magenta), plus select other optical, X-ray, or SZ-detected cluster catalogs, as shown in the legend. The two dashed lines show the best-fit values derived in this work. Right: uncertainties on Ωm and σ8 for each of the cluster abundance studies.

Constraints on Ωm and σ8 obtained from cluster abundance studies and non-cluster cosmological constraint methods. Left: 68% confidence levels (CLs) derived from GalWCat19 (magenta), WMAP9 (CMB; Hinshaw et al. 2013), Planck18 (CMB; Planck Collaboration et al. 2018), BAO data (Beutler et al. 2011; Ross et al. 2015; Alam et al. 2017), Pantheon sample (SNe; Scolnic et al. 2018), and the surveys KiDS+GAMA (van Uitert et al. 2018) and DES Y1 (Abbott et al. 2018b) which both use the cosmological probes of cosmic shear, galaxy–galaxy lensing, and angular clustering. The constraints on Ωm and σ8 derived from GalWCat19 are consistent with those derived from the non-cluster methods. Joint analysis between our constraints and the results of Planck18+BAO+Pantheon is represented by the red contour line. Right: uncertainties of Ωm and σ8 estimated for the aforementioned probes except for the BAO and SNe probes, which constrain Ωm only.