Characterizing Galaxy Clusters with Gravitational Potential

We propose a simple estimator for the gravitational potential of cluster-size halos using the temperature and density profiles of the intracluster gas based on the assumptions of hydrostatic equilibrium and spherical symmetry. Using high resolution cosmological simulations of galaxy clusters, we show that the scaling relation between this estimator and the gravitational potential has a small intrinsic scatter of ~8%-15%, and it is insensitive to baryon physics outside the cluster core. The slope and the normalization of the scaling relation vary weakly with redshift, and they are relatively independent of the choice of radial range used and the dynamical states of the clusters. The results presented here provide a possible way for using the cluster potential function as an alternative to the cluster mass function in constraining cosmology using galaxy clusters.Comment: 10 pages, 7 figures, 4 tables. Matching the version accepted for publication in the Astrophysical Journa

Trajectories in Logarithmic Potentials

Trajectories in logarithmic potentials are investigated by taking as example the motion of an electron within a cylindrical capacitor. The solution of the equation of motion in plane polar coordinates, (r,{\phi}) is attained by forming a series expansion of r and of 1/r as a function of {\phi}. The terms of the series contain polynomials, the recurrence relation of which is given, together with some further characteristics. By the comparison-theorem of infinite series, the convergence of the solution is demonstraded. The simplest trajectories in logarithmic potentials are represented by rosette type orbits with a period of 4{\pi}/3, and by circular paths.Comment: 17 pages, 5 figure