Electromagnetic Energy, Momentum, and Angular Momentum in an Inhomogeneous Linear Dielectric

In a previous work, Optics Communications 284 (2011) 2460--2465, we considered a dielectric medium with an anti-reflection coating and a spatially uniform index of refraction illuminated at normal incidence by a quasimonochromatic field. Using the continuity equations for the electromagnetic energy density and the Gordon momentum density, we constructed a traceless, symmetric energy--momentum tensor for the closed system. In this work, we relax the condition of a uniform index of refraction and consider a dielectric medium with a spatially varying index of refraction that is independent of time, which essentially represents a mechanically rigid dielectric medium due to external constraints. Using continuity equations for energy density and for Gordon momentum density, we construct a symmetric energy--momentum matrix, whose four-divergence is equal to a generalized Helmholtz force density four-vector. Assuming that the energy-momentum matrix has tensor transformation properties under a symmetry group of space-time coordinate transformations, we derive the global conservation laws for the total energy, momentum, and angular momentum.Comment: added publication informatio

Resolved Spectroscopy of the Narrow-Line Region in NGC 1068: Kinematics of the Ionized Gas

We have determined the radial velocities of the [O III] emitting gas in the inner narrow-line region (NLR) of the Seyfert 2 galaxy NGC 1068, along a slit at position angle of 202 degrees, from STIS observations at a spatial resolution of 0.1 arcsec and a spectral resolving power of approximately 1000. We use these data to investigate the kinematics of the NLR within 6 arcsec (430 pc) of the nucleus. The emission-line knots show evidence for radial acceleration, to a projected angular distance of 1.7 arcsec in most cases, followed by deceleration that approaches the systemic velocity at a projected distance of about 4 arcsec. We find that a simple kinematic model of biconical radial outflow can match the general trend of observed radial velocities. In this model, the emitting material is evacuated along the bicone axis, and the axis is inclined 5 degrees out of the plane of the sky. The acceleration of the emission-line clouds provides support for dynamical models that invoke radiation and/or wind pressure. We suggest that the deceleration of the clouds is due to their collision with a patchy and anistropically distributed ambient medium.Comment: 18 pages, Latex, includes 3 figures in postscript, to appear in the Astrophysical Journal Letter

HST Observations of the Double-Peaked Emission Lines in the Seyfert Galaxy Markarian 78: Mass Outflows from a Single AGN

Previous ground based observations of the Seyfert 2 galaxy Mrk 78 revealed a double set of emission lines, similar to those seen in several AGN from recent surveys. Are the double lines due to two AGN with different radial velocities in the same galaxy, or are they due to mass outflows from a single AGN?We present a study of the outflowing ionized gas in the resolved narrow-line region (NLR) of Mrk 78 using observations from Space Telescope Imaging Spectrograph (STIS) and Faint Object Camera (FOC) aboard the Hubble Space Telescope(HST) as part of an ongoing project to determine the kinematics and geometries of active galactic nuclei (AGN) outflows. From the spectroscopic information, we deter- mined the fundamental geometry of the outflow via our kinematics modeling program by recreating radial velocities to fit those seen in four different STIS slit positions. We determined that the double emission lines seen in ground-based spectra are due to an asymmetric distribution of outflowing gas in the NLR. By successfully fitting a model for a single AGN to Mrk 78, we show that it is possible to explain double emission lines with radial velocity offsets seen in AGN similar to Mrk 78 without requiring dual supermassive black holes.Comment: 22 pages, 7 figures (2 color), accepted for publication in The Astrophysical Journa