Statistical description of the radiation field in a homogeneous medium of finite optical thickness

The problem of finding statistical averages which characterize the radiation field in a semi-infinite atmosphere has been discussed by the author in a series of papers. In this paper some of the results obtained there are generalized to media of finite optical thickness. The average number of scattering events undergone by a photon during its random walk in an atmosphere and the average time required for this are determined. Three different types of averages are considered, depending on the photon characteristics over which the averages are taken. Special attention is devoted to the asymptotic behavior of these quantities for media with large optical depths taking the influence of continuum absorption into account. __________ Translated from Astrofizika, Vol. 49, No. 2, pp. 263–275 (May 2006).     

Long-Period Variations of the Eccentricity Vector Valid also for Near Circular Orbits around a Non-Spherical Body

This paper studies the long period variations of the eccentricity vector of the orbit of an artificial satellite, under the influence of the gravity field of a central body. We use modified orbital elements which are non-singular at zero eccentricity. We expand the long periodic part of the corresponding Lagrange equations as power series of the eccentricity. The coefficients characterizing the differential system depend on the zonal coefficients of the geopotential, and on initial semi-major axis, inclination, and eccentricity. The differential equations for the components of the eccentricity vector are then integrated analytically, with a definition of the period of the perigee based on the notion of “free eccentricity”, and which is also valid for circular orbits. The analytical solution is compared to a numerical integration. This study is a generalization of (Cook, Planet. Space Sci., 14, 1966): first, the coefficients involved in the differential equations depend on all zonal coefficients (and not only on the very first ones); second, our method applies to nearly circular orbits as well as to not too eccentric orbits. Except for the critical inclination, our solution is valid for all kinds of long period motions of the perigee, i.e., circulations or librations around an equilibrium point.     

The HNCO ring in the Sgr B2 region

The large-scale structure associated with the 2′N HNCO peak in Sgr B2 [Minh, Y.C., Haikala, L., Hjalmarson, Å., Irvine, W.M., 1998. ApJ 498, 261 (Paper I)] has been investigated. A ring-like morphology of the HNCO emission has been found; this structure may be colliding with the Principal Cloud of Sgr B2. This “HNCO Ring” appears to be centered at (l,b) = (0.7°,−0.07°), with a radius of 5 pc and a total mass of 1.0 × 10⁵ to 1.6 × 10⁶ M. The expansion velocity of the Ring is estimated to be 30–40 km s⁻¹, which gives an expansion time scale of 1.5 × 10⁵ year. The morphology suggests that collision between the Ring and the Principal Cloud may be triggering the massive star formation in the Sgr B2 cloud sequentially, with the latest star formation taking place at the 2′N position. The chemistry related to HNCO is not certain yet, but if it forms mainly via reaction with the evaporated OCN⁻ from icy grain mantles, the observed enhancement of the HNCO abundance can be understood as resulting from shocks associated with the collision between the Principal Cloud and the expanding HNCO Ring.     

Effect of signal contamination in matched-filter detection of the signal on a cluttered background

To derive a matched filter for detecting a weak target signal in a hyperspectral image, an estimate of the band-to-band covariance of the target-free background scene is required. We investigate the effects of including some of the target signal in the background scene. Although the covariance is contaminated by the presence of a target signal (there is increased variance in the direction of the target signature), we find that the matched filter is not necessarily affected. In fact, if the variation in plume strength is strictly uncorrelated with the variation in background spectra, the matched filter and its signal-to-clutter ratio (SCR) performance will not be impaired. While there is little a priori reason to expect significant correlation between the plume and the background, there usually is some residual correlation, and this correlation leads to a suppressing effect that limits the SCR obtainable even for strong plumes. These effects are described and quantified analytically, and the crucial role of this correlation is illustrated with some numerical examples using simulated plumes superimposed on real hyperspectral imagery. In one example, we observe an order-of-magnitude loss in SCR for a matched filter based on the contaminated covariance.