Effects of pulse width and coding on radar returns from clear air

In atmospheric radar studies it is desired to obtain maximum information about the atmosphere and to use efficiently the radar transmitter and processing hardware. Large pulse widths are used to increase the signal to noise ratio since clear air returns are generally weak and maximum height coverage is desired. Yet since good height resolution is equally important, pulse compression techniques such as phase coding are employed to optimize the average power of the transmitter. Considerations in implementing a coding scheme and subsequent effects of an impinging pulse on the atmosphere are investigated

Chaos and Fractals around Black Holes

Fractal basin boundaries provide an important means of characterizing chaotic systems. We apply these ideas to general relativity, where other properties such as Lyapunov exponents are difficult to define in an observer independent manner. Here we discuss the difficulties in describing chaotic systems in general relativity and investigate the motion of particles in two- and three-black-hole spacetimes. We show that the dynamics is chaotic by exhibiting the basins of attraction of the black holes which have fractal boundaries. Overcoming problems of principle as well as numerical difficulties, we evaluate Lyapunov exponents numerically and find that some trajectories have a positive exponent.Comment: To appear in "Fractals" March issue (World Scientific), 20 figures available by request, also available from SLAC's gr-qc postscript archiv

Detecting Galactic Binaries with LISA

One of the main sources of gravitational waves for the LISA space-borne interferometer are galactic binary systems. The waveforms for these sources are represented by eight parameters, of which four are extrinsic, and four are intrinsic to the system. Geometrically, these signals exist in an 8-d parameter space. By calculating the metric tensor on this space, we calculate the number of templates needed to search for such sources. We show in this study that below a particular monochromatic frequency, we can ignore one of the intrinsic parameters and search over a 7-d space. Beyond this frequency, we have a sudden change in dimensionality of the parameter space from 7 to 8 dimensions, which results in a change in the scaling of the growth of template number as a function of monochromatic frequency.Comment: 7 pages-2 figures. One figure added and typos corrected. Accepted for the proceedings of GWDAW 9, special edition of Classical and Quantum Gravit

Mapping the gravitational wave background

The gravitational wave sky is expected to have isolated bright sources superimposed on a diffuse gravitational wave background. The background radiation has two components: a confusion limited background from unresolved astrophysical sources; and a cosmological component formed during the birth of the universe. A map of the gravitational wave background can be made by sweeping a gravitational wave detector across the sky. The detector output is a complicated convolution of the sky luminosity distribution, the detector response function and the scan pattern. Here we study the general de-convolution problem, and show how LIGO (Laser Interferometric Gravitational Observatory) and LISA (Laser Interferometer Space Antenna) can be used to detect anisotropies in the gravitational wave background.Comment: 16 pages, 6 figures. Submitted to CQ

Use of the VAD technique and measurements of momentum flux in the stratosphere at Aercibo, part 4.3A

The Arecibo 430-MHz radar was used in the velocity-azimuth display (VAD) mode to obtain radial velocity measurements at 16 azimuth directions from which the three-dimensional wind field and momentum flux can be calculated. The radar was operated on a nearly continuous basis for a seven-day period in May of 1982 and the elapsed time between start and finish of a VAD scan was approximately 35 minutes. Radial velocities were measured in the upper troposphere and lower stratosphere (6-24 km) with at height resolution of 150 meters at a zenith angle of 15 deg. Vertical and horizontal velocities are calculated from the sums and differences, respectively, of radial velocity pairs, i.e., at azimuth directions AZ and AZ + 180 degrees. Momentum flux at a particular azimuth is calculated by taking the difference between the square of radial velocities at AZ and AZ + 180 degrees. It should be noted that measurements of radial velocity pairs are not simultaneous but are time delayed by approximately 15-25 minutes. This period, the time required to rotate the antenna feed and take measurements at AZ and AZ + 180 deg, effectively limits sampling of velocities and momentum fluxes to longer period gravity waves and planetary waves

Comment on "Gravity Waves, Chaos, and Spinning Compact Binaries"

In this comment, I argue that chaotic effects in binary black hole inspiral will not strongly impact the detection of gravitational waves from such systems.Comment: 1 page, comment on gr-qc/991004

Forward Modeling of Space-borne Gravitational Wave Detectors

Planning is underway for several space-borne gravitational wave observatories to be built in the next ten to twenty years. Realistic and efficient forward modeling will play a key role in the design and operation of these observatories. Space-borne interferometric gravitational wave detectors operate very differently from their ground based counterparts. Complex orbital motion, virtual interferometry, and finite size effects complicate the description of space-based systems, while nonlinear control systems complicate the description of ground based systems. Here we explore the forward modeling of space-based gravitational wave detectors and introduce an adiabatic approximation to the detector response that significantly extends the range of the standard low frequency approximation. The adiabatic approximation will aid in the development of data analysis techniques, and improve the modeling of astrophysical parameter extraction.Comment: 14 Pages, 14 Figures, RevTex

LISA Source Confusion

The Laser Interferometer Space Antenna (LISA) will detect thousands of gravitational wave sources. Many of these sources will be overlapping in the sense that their signals will have a non-zero cross-correlation. Such overlaps lead to source confusion, which adversely affects how well we can extract information about the individual sources. Here we study how source confusion impacts parameter estimation for galactic compact binaries, with emphasis on the effects of the number of overlaping sources, the time of observation, the gravitational wave frequencies of the sources, and the degree of the signal correlations. Our main findings are that the parameter resolution decays exponentially with the number of overlapping sources, and super-exponentially with the degree of cross-correlation. We also find that an extended mission lifetime is key to disentangling the source confusion as the parameter resolution for overlapping sources improves much faster than the usual square root of the observation time.Comment: 8 pages, 14 figure

LISA data analysis I: Doppler demodulation

The orbital motion of the Laser Interferometer Space Antenna (LISA) produces amplitude, phase and frequency modulation of a gravitational wave signal. The modulations have the effect of spreading a monochromatic gravitational wave signal across a range of frequencies. The modulations encode useful information about the source location and orientation, but they also have the deleterious affect of spreading a signal across a wide bandwidth, thereby reducing the strength of the signal relative to the instrument noise. We describe a simple method for removing the dominant, Doppler, component of the signal modulation. The demodulation reassembles the power from a monochromatic source into a narrow spike, and provides a quick way to determine the sky locations and frequencies of the brightest gravitational wave sources.Comment: 5 pages, 7 figures. References and new comments adde

Detecting the Cosmic Gravitational Wave Background with the Big Bang Observer

The detection of the Cosmic Microwave Background Radiation (CMB) was one of the most important cosmological discoveries of the last century. With the development of interferometric gravitational wave detectors, we may be in a position to detect the gravitational equivalent of the CMB in this century. The Cosmic Gravitational Background (CGB) is likely to be isotropic and stochastic, making it difficult to distinguish from instrument noise. The contribution from the CGB can be isolated by cross-correlating the signals from two or more independent detectors. Here we extend previous studies that considered the cross-correlation of two Michelson channels by calculating the optimal signal to noise ratio that can be achieved by combining the full set of interferometry variables that are available with a six link triangular interferometer. In contrast to the two channel case, we find that the relative orientation of a pair of coplanar detectors does not affect the signal to noise ratio. We apply our results to the detector design described in the Big Bang Observer (BBO) mission concept study and find that BBO could detect a background with $\Omega_{gw} > 2.2 \times 10^{-17}$.Comment: 15 pages, 12 Figure