THE POSSIBILITIES OF THE “CLUSTER CARTOGRAPHY” TOOL FOR THE STUDY OF THE INNER STRUCTURES OF GALAXY CLUSTERS

We describe the possibilities of the “Cluster Cartography” tool which was created for detailed study of the 2D distribution of galaxies in the clusters. The main tasks of the “Cluster Cartography” tool were the detailed study of the morphologyof galaxy clusters using the statistically significant numerical criteria as well as to detect their regular peculiarities. The tool allows to create the 2D map with positions of galaxies in the cluster field and show for each cluster member its shape and orientation as a best-fit ellipse using input catalogue data. The size of symbols for galaxies correspond to input data.It may reflect the galaxy image in arcseconds from catalogue in the map 4000×4000arcsec. Another way connects the size of the symbol with the magnitude of the galaxy. Tool is able to build the map in four modes: the symbols are dots; the symbols are circles with diameters reflected the magnitudes of galaxies; the symbols are ellipses with size reflected the magnitudesand both ellipticities and orientation from the input catalogue; the symbols illustrate the shape of galaxies in projection to the celestial sphere. The “Cluster Cartography” algorithms allow to detect the standard cases in galaxy distribution, suchas the degree of concentration to the cluster center and/or to some line on a statistically significant level using the numerical criteria. Also “Cluster Cartography” allows to detect other features, such as crosses, semi-crosses, complex crosses and short compact chains, as well as to export the list of galaxies forming the peculiarities for the futurestudy. The final version of the “Cluster Cartography” allows to realize the modern scheme for detailed morphological classification of galaxy clusters. The “Cluster Cartography” is powerful and perspective tool for study of features of galaxy clusters.

Holographic symmetry algebras for gauge theory and gravity

All 4D gauge and gravitational theories in asymptotically flat spacetimes contain an infinite number of non-trivial symmetries. They can be succinctly characterized by generalized 2D currents acting on the celestial sphere. A complete classification of these symmetries and their algebras is an open problem. Here we construct two towers of such 2D currents from positive-helicity photons, gluons, or gravitons with integer conformal weights. These generate the symmetries associated to an infinite tower of conformally soft theorems. The current algebra commutators are explicitly derived from the poles in the OPE coefficients, and found to comprise a rich closed subalgebra of the complete symmetry algebra.

Analysis of modern observations of meteor showers based on PTM methods

The work is focused on the analysis of modern observations of meteoroids included in the data bank formed by both professional researchers and amateur astronomers. Based on the modern physical theory of meteoroids (PTM), a new method for analyzing measurements developed, which provides the accuracy comparable with the results of radar observations. Due to the fact that the accuracy of the new method for analyzing meteoroids observations has increased significantly, it became possible to process observations of the Perseid and Leonid showers over a period of 120 years. The use of PTM made it possible for the first time to explain the distribution of meteor echo signals observed at an altitude of 2 MHz, at which the upper part of this distribution refers to an altitude of 140 km. In the process of work, a database of orbital characteristics of meteoroids was created. A method has been developed for modeling the probability of hitting a certain area of a meteor particle with a mass greater than a certain specified value and determining the density of a meteor shower from radio observations as well as a new “tomography” method for calculating the density distribution of sporadic meteors in the sky using radar observations of meteors at the same station with a goniometer. The method allows calculating the density of a meteor shower on the celestial sphere with an angular resolution of 2°. The use of these methods served as a proof that the distribution density of meteoroid showers on the celestial sphere has two planes of symmetry: the first coincides with the plane of the ecliptic, passing through the poles of the Earth, the other one is perpendicular to the plane of the ecliptic.

Zwanziger’s pairwise little group on the celestial sphere

We generalize Zwanziger’s pairwise little group to include a boost subgroup. We do so by working in the celestial sphere representation of scattering amplitudes. We propose that due to late time soft photon and graviton exchanges, matter particles in the asymptotic states in massless QED and gravity transform under the Poincaré group with an additional pair of pairwise celestial representations for each pair of matter particles. We demonstrate that the massless abelian and gravitational exponentiation theorems are consistent with the proposed pairwise Poincaré transformation properties. For massless QED we demonstrate that our results are consistent with the effects of the Faddeev-Kulish dressing and the abelian exponentiation theorem for celestial amplitudes found in arXiv:2012.04208. We discuss electric and magnetic charges simultaneously as it is especially natural to do so in this formalism.

The Grassmannian for celestial superamplitudes

Recently, scattering amplitudes in four-dimensional Minkowski spacetime have been interpreted as conformal correlation functions on the two-dimensional celestial sphere, the so-called celestial amplitudes. In this note we consider tree-level scattering amplitudes in $$ \mathcal{N} $$ N = 4 super Yang-Mills theory and present a Grassmannian formulation of their celestial counterparts. This result paves the way towards a geometric picture for celestial superamplitudes, in the spirit of positive geometries.

Order and Disorder in Sangam Poems: On the Basics of Paanar-Puluvar Tradition

The theory of law, which deals with supernatural powers, shaped the myth of the celestial sphere. Religions that justify birth and gender segregation and produce slave bodies to adapt to the prevailing social conditions. Orders created to protect the power and interests of the rulers are influential in the name of rules from time to time. When one insists on order, disorder automatically reigns. When laying down rules as to what should be strictly followed, what should be excluded is defined as irregularity. In the Sangam Age Tamils insisted on the rules to be followed in practical life, contrary to the rules of good and bad. Such orders, in turn, were called virtues. At the same time the notion that disorder is anti-social as a whole was emphasized. Rules and exemptions are widely used to emphasize order and disorder in the interests of those who economically dominate society. The order and disorder recorded by the Sangam literary works have become the social document of ancient Tamils.

MHV gluon scattering amplitudes from celestial current algebras

We show that the Mellin transform of an n-point tree level MHV gluon scattering amplitude, also known as the celestial amplitude in pure Yang-Mills theory, satisfies a system of (n−2) linear first order partial differential equations corresponding to (n−2) positive helicity gluons. Although these equations closely resemble Knizhnik-Zamoldochikov equations for SU(N) current algebra there is also an additional “correction” term coming from the subleading soft gluon current algebra. These equations can be used to compute the leading term in the gluon-gluon OPE on the celestial sphere. Similar equations can also be written down for the momentum space tree level MHV scattering amplitudes. We also propose a way to deal with the non closure of subleading current algebra generators under commutation. This is then used to compute some subleading terms in the mixed helicity gluon OPE.