A method to resolve the nuclear activity in galaxies, as applied to NGC1358

Nuclear regions of galaxies generally host a mixture of components with different exitation, composition, and kinematics. Derivation of emission line ratios and kinematics could then be misleading, if due correction is not made for the limited spatial and spectral resolutions of the observations. The aim of this paper is to demonstrate, with application to a long slit spectrum of the Seyfert2 galaxy NGC1358, how line intensities and velocities, together with modelling and knowledge of the point spread function, may be used to resolve the differing structures. In the situation outlined, the observed kinematics differs for different spectral lines. From the observed intensity and velocity distributions of a number of spectral lines and with some reasonable assumptions to diminish the number of free parameters, the true line ratios and velocity structures may be deduced. A preliminary solution for the nuclear structure of NGC1358 is obtained, involving a nuclear point source and an emerging outflow of high excitation with a post shock cloud, as well as a nuclear emission line disk rotating in the potential of a stellar bulge and expressing a radial exitation gradient. The method results in a likely scenario for the nuclear structure of NGC1358. For definitive results an extrapolation of the method to two dimensions combined with the use of integral field spectroscopy will generally be necessary.Comment: to appear in proceedings for the IAU 277th Symposium, Editors: C. Carignan, F. Combes, K. Freema

A remark on asymptotic completeness for the critical nonlinear Klein-Gordon equation

We give a short proof of asymptotic completeness and global existence for the cubic Nonlinear Klein-Gordon equation in one dimension. Our approach to dealing with the long range behavior of the asymptotic solution is by reducing it, in hyperbolic coordinates to the study of an ODE. Similar arguments extend to higher dimensions and other long range type nonlinear problems.Comment: To appear in Lett. Math. Phy