→ Back to LISA and GWs
Explores the angular resolution of space-based detectors of gravitational waves. In the long-wavelength approximation (similar to Cutler's, but for a single interferometric combination), using a "least-squares" approach that is essentially the Fisher formalism.
Discusses the detection of simple monochromatic sources as peaks in power after Doppler demodulation (but no amplitude demodulation), which is obtained in the frequency domain by a simple approximate mapping between Fourier coefficients (this mapping depends on source frequency, though). Shows effect of demodulating with the wrong sky position, and of overlapping-source interference. Cutler LISA response is assumed.
→ R. W. Hellings, "LISA data analysis: the detection and initial guess problems for monochromatic binaries", Class. Quantum Grav. 20, 1019 (2003). CQG
Discusses providing initial monochromatic-signal parameters as input to "least-squares" (essentially, maximum likelihood, a la Moore and Hellings) parameter-estimation procedure, by way of peak finding after Doppler demodulation, which is achieved in the time domain.
→ N. J. Cornish and L. J. Rubbo, "LISA response function", Phys. Rev. D 67, 022001 (2003). PRD
Derives the LISA response by integrating the GW strain along the photon trajectories, using a hybrid time-frequency approach that emphasizes the transfer function. Obtains also static (stationary LISA s/c) and long-wavelength limits of the expression. Describes the Keplerian orbits used in the LISA Simulator and in pseudo-LISA.
→ N. J. Cornish and S. L. Larson, "LISA data analysis: Source identification and subtraction", Phys. Rev. D 67, 103001 (2003). PRD
Lays out gCLEAN, a method to identify and remove overlapping sources in a LISA data stream. The method is template-based, and templates for monochromatic signals are computed in the Fourier domain by a "total modulation" sum over AM and FM sidebands. Also studies the Doppler (Owen-Sathyaprakash) metric induced by the FM modulations, and uses it to place templates in banks. The gCLEAN method is generalized from CLEAN, used in optical astronomy. Basically, one looks for the strongest match w.r.t. the template bank, and subtracts a small fraction of it, repeating until no strong match is apparent anymore; then one reconstructs sources by pooling partial subtracted sources of nearby parameters. The method is easily confused by close overlapping binaries at low frequencies.
→ N. J. Cornish, "Rapid LISA Astronomy", gr-qc/0312042 (2003).
Writes the LISA TDI responses (first and second gen.) to moderately chirping signals as analytic expressions, exact in the case of rigid LISA orbits. The expression lend themselves to write an F statistic that is automatically maximized over the initial signal phase, signal polarization, and (essentially) hp/hc ratio. Shows a simple test of this F statistic.
→ M. Tinto and S. L. Larson, "LISA time-delay interferometry zero-signal solution: Geometrical properties", Phys. Rev. D 70, 062002 (2004). PRD
Generalizing work by Gursel and Tinto for ground-based interferometer networks, derives a "zero-signal solution" TDI combination that has null response for sources at specific sky directions. Shows response patterns strongly peaked (at least in the high-frequency limit) at the "target" frequency. Shows that in the long-wavelength limit the ZSS limits to the null "zeta" variable. Does not deal with noise.
→ L. J. Rubbo, N. J. Cornish, and O. Poujade, "Forward modeling of space-borne gravitational wave detectors", Phys. Rev. D 69, 082003 (2004). PRD
Essentially, describes the mathematics behind the LISA Simulator, including eˆ2-accurate LISA orbits and plane wave conventions; introduces a highly-accurate "rigid adiabatic approximation" whereby the detector rotates rigidly, and its motion is neglected within the timescale needed to assemble the TDI combinations. Also reconciles its phase response with the Doppler frequency response of Seto (2004).
Lays out a template-bank based matched-filtering formalism for linearly chirping binaries, using an F statistic that removes the four extrinsic parameters (amplitude, inclination, initial phase, polarization angle). Shows a scaling for the size of the template bank, taking into account the F statistic by way of a projected metric; a steepening in the scaling, corresponding to the fdot parameter becoming meaningful, is evident above 1.5 mHz. In the long-wavelength approximation (from Rubbo, Cornish, Poujade).
→ J. A. Edlund, M. Tinto, A. Krolak, and Gijs Nelemans, "White-dwarf--white-dwarf galactic background in the LISA data", Phys. Rev. D 71, 122003 (2005). PRD
Describes a simulation of the LISA GWDB, where the "KTV" expressions for the TDI observables are rendered as truncated sums in the frequency domain. Handles infinite vs. finite Fourier transforms by assuming windowed data, and using the corresponding frequency-domain kernel. Generalizes the long-wavelength approximation to a series expansion in the parameter x = omega L (with omega the angular frequency of the source). Analyzes the simulated background as a cyclostationary process.
© M. Vallisneri 2012 — last modified on 2010/01/29
Tantum in modicis, quantum in maximis