Opening angles, Lorentz factors and confinement of X-ray binary jets

We present a collation of the available data on the opening angles of jets in X-ray binaries, which in most cases are small (≲10°). Under the assumption of no confinement, we calculate the Lorentz factors required to produce such small opening angles via the transverse relativistic Doppler effect. The derived Lorentz factors, which are in most cases lower limits, are found to be large, with a mean >10, comparable to those estimated for active galactic nuclei (AGN) and much higher than the commonly assumed values for X-ray binaries of 2–5. Jet power constraints do not, in most cases, rule out such high Lorentz factors. The upper limits on the opening angles show no evidence for smaller Lorentz factors in the steady jets of Cygnus X-1 and GRS 1915+105. In those sources in which deceleration has been observed (notably  XTE J1550−564  and Cygnus X-3), some confinement of the jets must be occurring, and we briefly discuss possible confinement mechanisms. It is however possible that all the jets could be confined, in which case the requirement for high bulk Lorentz factors can be relaxed.     

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.     

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.     

On The Concept Of Periapsis In Hill’s Problem

The concept of closest approach is analyzed in Hill’s problem, resulting in a partitioning of the position space. The different behavior between the direct and retrograde motion is explained analytically, resulting in a simple estimate of the variation of Hill’s periodic and quasi-circular orbits as a function of the Jacobi constant. The local behavior of the orbits on the zero velocity surfaces and an analytical definition of local escape and capture in Hill’s problem are also given.     

Optical monitoring of the quasar 4C 38.41

The results of a photometric monitoring of the quasar 4C 38.41, performed at the optical R and B bands in 2002 February–March, are presented. With a 60/90 cm Schmidt telescope at the Xinglong station of the National Astronomical Observatories of China, we observed the source exhibiting amplitude variations of up to 0.78 mag in both bands during the whole campaign. Intraday and even intranight variations are detected as well. A typical variability time-scale of about 36 d is derived from our 2-month observations at the optical bands, which is identical to that found at a radio wavelength of 92 cm, suggesting a common origin for the variations in 4C 38.41 from optical to radio bands.