The core fundamental plane of B2 radio galaxies

The photometric, structural and kinematical properties of the centers of elliptical galaxies, harbor important information of the formation history of the galaxies. In the case of non active elliptical galaxies these properties are linked in a way that surface brightness, break radius and velocity dispersion of the core lie on a fundamental plane similar to that found for their global properties. We construct the Core Fundamental Plane (CFP) for a sizeable sample of low redshift radio galaxies and compare it with that of non radio ellipticals. To pursue this aim we combine data obtained from high resolution HST images with medium resolution optical spectroscopy to derive the photometric and kinematic properties of ~40 low redshift radio galaxies. We find that the CFPs of radio galaxies is indistinguishable from that defined by non radio elliptical galaxies of similar luminosity. The characteristics of the CFP of radio galaxies are also consistent (same slope) with those of the Fundamental Plane (FP) derived from the global properties of radio (and non radio) elliptical galaxies. The similarity of CFP and FP for radio and non radio ellipticals suggests that the active phase of these galaxies has minimal effects for the structure of the galaxies.Comment: 8 pages, 4 figures, accepted for publication in Astronomy and Astrophysic

Technical Note—Dual Approach for Two-Stage Robust Nonlinear Optimization

Adjustable robust minimization problems where the objective or constraints depend in a convex way on the adjustable variables are generally difficult to solve. In this paper, we reformulate the original adjustable robust nonlinear problem with a polyhedral uncertainty set into an equivalent adjustable robust linear problem, for which all existing approaches for adjustable robust linear problems can be used. The reformulation is obtained by first dualizing over the adjustable variables and then over the uncertain parameters. The polyhedral structure of the uncertainty set then appears in the linear constraints of the dualized problem, and the nonlinear functions of the adjustable variables in the original problem appear in the uncertainty set of the dualized problem. We show how to recover linear decision rules to the original primal problem and how to generate bounds on its optimal objective value