The Mid-Infrared Spectral Energy Distribution, Surface Brightness and Color Profiles in Elliptical Galaxies

We describe photometry at mid-infrared passbands (1.2 - 24 microns) for a sample of 18 elliptical galaxies. All surface brightness distributions resemble de Vaucouleurs profiles, indicating that most of the emission arises from the photospheres or circumstellar regions of red giant stars. The spectral energy distribution peaks near 1.6 microns, but the half-light or effective radius has a pronounced minimum near the K band (2.15 microns). Apart from the 24 micron passband, all sample-averaged radial color profiles have measurable slopes within about twice the (K band) effective radius. Evidently this variation arises because of an increase in stellar metallicity toward the galactic cores. For example, the sampled-averaged color profile (K - 5.8 microns) has a positive slope although no obvious absorption feature is observed in spectra of elliptical galaxies near 5.8 microns. This, and the minimum in the effective radius, suggests that the K band may be anomalously luminous in metal-rich stars in galaxy cores. Unusual radial color profiles involving the 24 micron passband may suggest that some 24 micron emission comes from interstellar not circumstellar dust grains.Comment: 18 pages. Accepted by Ap

The universal expression for the amplitude square in quantum electrodynamics

The universal expression for the amplitude square |u_f M u_i|^2 for any matrix of interaction M is derived. It has obvious covariant form. It allows the avoidance of calculation of products of the Dirac's matrices traces and allows easy calculation of cross-sections of any different processes with polarized and unpolarized particles.Comment: 4 page

Determination of continuous variable entanglement by purity measurements

We classify the entanglement of two--mode Gaussian states according to their degree of total and partial mixedness. We derive exact bounds that determine maximally and minimally entangled states for fixed global and marginal purities. This characterization allows for an experimentally reliable estimate of continuous variable entanglement based on measurements of purity.Comment: 4 pages, 3 EPS figures. Final versio