Spinning compact binary inspiral II: Conservative angular dynamics

We establish the evolution equations of the set of independent variables characterizing the 2PN rigorous conservative dynamics of a spinning compact binary, with the inclusion of the leading order spin-orbit, spin-spin and mass quadrupole - mass monopole effects, for generic (noncircular, nonspherical) orbits. More specifically, we give a closed system of first order ordinary differential equations for the orbital elements of the osculating ellipse and for the angles characterizing the spin orientations with respect to the osculating orbit. We also prove that (i) the relative angle of the spins stays constant for equal mass black holes, irrespective of their orientation, and (ii) the special configuration of equal mass black holes with equal, but antialigned spins, both laying in the plane of motion (leading to the largest recoil found in numerical simulations) is preserved at 2PN level of accuracy, with leading order spin-orbit, spin-spin and mass quadrupolar contributions included.Comment: v2: 19 pages, extended, improved, published versio

The Distances of SNR W41 and overlapping HII regions

New HI images from the VLA Galactic Plane Survey show prominent absorption features associated with the supernovae remnant G23.3-0.3 (SNR W41). We highlight the HI absorption spectra and the $^{13}$CO emission spectra of eight small regions on the face of W41, including four HII regions, three non-thermal emission regions and one unclassified region. The maximum velocity of absorption for W41 is 78$\pm$2 km/s and the CO cloud at radial velocity 95$\pm$5 km/s is behind W41. Because an extended TeV source, a diffuse X-ray enhancement and a large molecular cloud at radial velocity 77$\pm$5 km/s are also projected at the center of W41, these yield the kinematic distance of 3.9 to 4.5 kpc for W41. For HII regions, our analyses reveal that both G23.42-0.21 and G23.07+0.25 are at the far kinematic distances ($\sim$9.9 kpc and $\sim$ 10.6 kpc respectively) of their recombination-line velocities (103$\pm$0.5 km/s and 89.6$\pm$2.1 km/s respectively), G23.07-0.37 is at the near kinematic distance (4.4$\pm$0.3 kpc) of its recombination-line velocity (82.7$\pm$2.0 km/s), and G23.27-0.27 is probably at the near kinematic distance (4.1$\pm$0.3 kpc) of its recombination-line velocity (76.1$\pm$0.6 km/s).Comment: 11 pages, 3 figs., 2 tables, accepted by A

New lambda6cm observations of the Cygnus Loop

Radio continuum and polarization observations of the entire Cygnus Loop at 6cm wavelength were made with the Urumqi 25m telescope. The 6cm map is analysed together with recently published maps from the Effelsberg 100m telescope at 21cm and 11cm. The integrated flux density of the Cygnus Loop at 6cm is 90+/-9Jy, which implies a spectral index of -0.40+/-0.06 being consistent with that of Uyaniker et al. (2004) in the wavelength range up to 11cm. This rules out any global spectral steepening up to 6cm. However, small spectral index variations in some regions of the source are possible, but there are no indications for any spectral curvature. The linear polarization data at 6cm show percentage polarizations up to 35% in some areas of the Cygnus Loop, exceeding those observed at 11cm. The Rotation Measure is around -21rad/m^2 in the southern area, which agrees with previous observations. However, the distribution of Rotation Measures is rather complex in the northern part of the Cygnus Loop, where the 21cm emission is totally depolarized. Rotation Measures based on 11cm and 6cm data are significantly larger than in the southern part. The difference in the polarization characteristic between the northern and southern part supports previous ideas that the Cygnus Loop consists of two supernova remnants.Comment: 11 pages, 10 figures, accepted for publication in A&

Limits of control for quantum systems: kinematical bounds on the optimization of observables and the question of dynamical realizability

In this paper we investigate the limits of control for mixed-state quantum systems. The constraint of unitary evolution for non-dissipative quantum systems imposes kinematical bounds on the optimization of arbitrary observables. We summarize our previous results on kinematical bounds and show that these bounds are dynamically realizable for completely controllable systems. Moreover, we establish improved bounds for certain partially controllable systems. Finally, the question of dynamical realizability of the bounds for arbitary partially controllable systems is shown to depend on the accessible sets of the associated control system on the unitary group U(N) and the results of a few control computations are discussed briefly.Comment: 5 pages, orginal June 30, 2000, revised September 28, 200

Detecting the harmonics of oscillations with time-variable frequencies

A method is introduced for the spectral analysis of complex noisy signals containing several frequency components. It enables components that are independent to be distinguished from the harmonics of nonsinusoidal oscillatory processes of lower frequency. The method is based on mutual information and surrogate testing combined with the wavelet transform, and it is applicable to relatively short time series containing frequencies that are time variable. Where the fundamental frequency and harmonics of a process can be identified, the characteristic shape of the corresponding oscillation can be determined, enabling adaptive filtering to remove other components and nonoscillatory noise from the signal. Thus the total bandwidth of the signal can be correctly partitioned and the power associated with each component then can be quantified more accurately. The method is first demonstrated on numerical examples. It is then used to identify the higher harmonics of oscillations in human skin blood flow, both spontaneous and associated with periodic iontophoresis of a vasodilatory agent. The method should be equally relevant to all situations where signals of comparable complexity are encountered, including applications in astrophysics, engineering, and electrical circuits, as well as in other areas of physiology and biology

The 74MHz System on the Very Large Array

The Naval Research Laboratory and the National Radio Astronomy Observatory completed implementation of a low frequency capability on the VLA at 73.8 MHz in 1998. This frequency band offers unprecedented sensitivity (~25 mJy/beam) and resolution (~25 arcsec) for low-frequency observations. We review the hardware, the calibration and imaging strategies, comparing them to those at higher frequencies, including aspects of interference excision and wide-field imaging. Ionospheric phase fluctuations pose the major difficulty in calibrating the array. Over restricted fields of view or at times of extremely quiescent ionospheric ``weather'', an angle-invariant calibration strategy can be used. In this approach a single phase correction is devised for each antenna, typically via self-calibration. Over larger fields of view or at times of more normal ionospheric ``weather'' when the ionospheric isoplanatic patch size is smaller than the field of view, we adopt a field-based strategy in which the phase correction depends upon location within the field of view. This second calibration strategy was implemented by modeling the ionosphere above the array using Zernike polynomials. Images of 3C sources of moderate strength are provided as examples of routine, angle-invariant calibration and imaging. Flux density measurements indicate that the 74 MHz flux scale at the VLA is stable to a few percent, and tied to the Baars et al. value of Cygnus A at the 5 percent level. We also present an example of a wide-field image, devoid of bright objects and containing hundreds of weaker sources, constructed from the field-based calibration. We close with a summary of lessons the 74 MHz system offers as a model for new and developing low-frequency telescopes. (Abridged)Comment: 73 pages, 46 jpeg figures, to appear in ApJ

VLBA Polarimetry of Three Powerful Radio Galaxy Cores

We present sensitive, high dynamic range, Very Long Baseline Array (VLBA) polarimetric observations of the cores of three powerful radio galaxies: 3C166, 3C236 and 3C390.3. Significant polarization is detected in one source (3C166) allowing us to map out the Faraday Rotation Measure (RM) distribution and projected magnetic field direction. The inner jet of 3C166 is found to have a rest frame RM of -2300 rad/m**2, similar to those found in quasars cores. No polarized flux was detected from the other two sources, but in both counterjets are seen. The counterjet in 3C236 was previously known, but the detection in 3C390.3 is a new discovery. We suggest that the low fractional polarization in radio galaxy cores is the result of Faraday depolarization by ionized gas associated with the accretion disk. The lower polarization of radio galaxy cores compared to quasars is then naturally explained by unified models as a result of the viewing angle.Comment: Accepted to ApJ, 19 pages including 5 figure