Pre-Phase A Report - Lisa - Nasa

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114 Chapter 4 Measurement Sensitivity Results for monochromatic sources. In terms of sheer numbers, stellar-mass binaries will undoubtedly be the dominant LISA source. There are so many white dwarf binaries in the galaxy that they effectively form a stochastic background. In this section we consider measurements of a binary that is sufficiently close that it can be detected individually; i.e., its signal stands up above the detector noise and above the background from other binaries. Binaries with small eccentricity are essentially monochromatic sources. To see this, note first that because the binary orbit is periodic, in Fourier space its gravitational radiation is made up of discrete lines at f =2/P, 4/P, 6/P ,etc.,wherePis the orbital period. (The sequence is multiples of 2/P instead of 1/P because the dominant radiation is quadrupolar.) For eccentricity e
4.4 Data analysis 115 box (in steradians) in source position, ∆ΩL the error box for the binary’s orientation, and ∆A/A is the relative accuracy of the amplitude measurement. Cases A, B, and C refer to three representative choices of the four angles (µ, φ, µL, φL). These angles are: (0.3, 5.0, −0.2, 4.0) for A; (−0.3, 1.0, −0.2, 4.0) for B; and (−0.3, 1.0, 0.8, 0.0) for C. Each case is illustrated for three gravitational wave frequencies: f =10 −4 , 10 −3 , 10 −2 Hz. The subscript ‘I’ on ∆I indicates that the measurement corresponds to detection by interferometer I alone. ∆ without a subscript indicates the result is for a combined measurement by interferometers I and II. f [Hz] Case ∆IΩ [sr] ∆IΩL [sr] ∆IA/A ∆Ω [sr] ∆ΩL [sr] ∆A/A A 2.15×10 −1 3.81×10 −1 3.22×10 −1 8.27×10 −2 1.99×10 −1 2.04×10 −1 10 −4 B 2.23×10 −1 2.81×10 −1 2.38×10 −1 7.89×10 −2 9.78×10 −2 1.53×10 −1 C 1.23×10 −1 8.48×10 −2 1.57×10 −1 7.11×10 −2 4.00×10 −2 1.02×10 −1 A 1.07×10 −1 3.38×10 −1 3.21×10 −1 3.98×10 −2 1.69×10 −1 2.04×10 −1 10 −3 B 1.03×10 −1 1.62×10 −1 2.21×10 −1 3.83×10 −2 7.34×10 −2 1.53×10 −1 C 6.51×10 −2 6.88×10 −2 1.56×10 −1 3.14×10 −2 3.44×10 −2 1.03×10 −1 A 2.57×10 −3 3.50×10 −1 3.12×10 −1 1.08×10 −3 1.53×10 −1 2.04×10 −1 10 −2 B 2.90×10 −3 1.26×10 −1 2.21×10 −1 1.15×10 −3 5.78×10 −2 1.53×10 −1 C 1.95×10 −3 4.22×10 −2 1.54×10 −1 7.66×10 −4 1.94×10 −2 1.02×10 −1 Table 4.5 LISA’s measurement accuracy for monochromatic sources, for a few representative choices of angles and gravitational wave frequency. Results are normalized to a combined S/N =10. Cases A, B, and C refer to source direction and orientation angles, and are defined in the text. Error boxes ∆Ω (for source position) and ∆ΩL (for source orientation) are in steradians. Results for interferometer I alone have subscript ‘I’; other results are for the pair of outputs I and II. Table 4.5 shows that for monochromatic sources, having two independent outputs improves the position and polarisation resolution, ∆Ω and ∆ΩL by a factor of only ∼ 2; i.e., just the improvement that comes from the increased signal-to-noise. This basically tells us that the rotation of the detector over a one year observation time does indeed allow interferometer I alone to measure both polarisations rather effectively. LISA’s ∆Ω for monochromatic sources at f =10 −3 Hz is typically ∼ 10 −3 –10 −2 sr ; LISA’s angular resolution improves at higher frequencies due to the increased impact of the Doppler shift. LISA’s polarisation resolution for these sources is typically ∆ΩL ∼ 0.1sr, and ∆A/A ∼0.1 − 0.2 . Here, too, if only a single interferometric output is available, the degradation in measurement accuracy comes mostly just from the loss in total signal-tonoise. 4.4.4 Results for MBH coalescence Coalescences of MBH binaries, if they occur at sufficient rates to be observable, will be an exceptionally strong LISA source, with signal-to-noise ratios of 10 3 −10 4 . Clearly, detecting Corrected version 2.08 3-3-1999 9:33
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LISA Laser Interferometer Space Ant
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LISA Laser Interferometer Space Ant
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Foreword The first mission concept
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The result of the Team-X study was
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Contents Foreword iii Executive Sum
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Contents ix 4.2.3 Acceleration nois
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Contents xi 9 Science and Mission O
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Executive Summary 1 Executive Summa
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Executive Summary 3 Complementarity
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Mission Summary 5 LISA Mission Summ
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Chapter 1 Scientific Objectives By
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1.1 Theory of gravitational radiati
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1.2 Low-frequency sources of gravit
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Chapter 2 Different Ways of Detecti
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2.2 Ground-based detectors 39 2.2 G
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2.2 Ground-based detectors 41 Count
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2.4 Spacecraft tracking 43 2.4 Spac
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2.7 Heliocentric versus geocentric
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2.8 The LISA concept 47 telescopes
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2.8 The LISA concept 49 Figure 2.6
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2.8 The LISA concept 51 seem rather
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Chapter 3 Experiment Description 3.
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3.1 The interferometer 55 Fiber to
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3.1 The interferometer 57 3.1.4 Sys
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3.1 The interferometer 59 Figure 3.
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3.1 The interferometer 61 3.1.6 Las
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Page 93 and 94: Chapter 4 Measurement Sensitivity 4
Page 95 and 96: 4.1 Sensitivity 81 averaged transfe
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Page 127: 4.4 Data analysis 113 density Sn(f)
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Page 133 and 134: Chapter 5 Payload Design 5.1 Payloa
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Page 139 and 140: 5.4 Mass estimates 125 5.4 Mass est
Page 141 and 142: 5.7 Thermal analysis 127 the Y-shap
Page 143 and 144: 5.8 Telescope assembly 129 surface
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Page 149 and 150: Chapter 6 Mission Analysis 6.1 Orbi
Page 151 and 152: 6.3 Injection into final orbits 137
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Page 159 and 160: 7.1 System configuration 145 2220 m
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8.3 ELITE Technologies 165 8.2.2 Co
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8.4 ELITE Satellite design 167 inco
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Chapter 9 Science and Mission Opera
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9.2 Mission operations 171 9.2 Miss
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9.3 Operating modes 173 Power savin
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Chapter 10 International Collaborat
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10.3 Schedule 177 The ESA Project M
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References [1] C.W. Misner, K.S. Th
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References 181 [35] C. Cutler, T.A.
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References 183 [77] J.E. Faller and
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References 185 [104] E. Grun, H.A.
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List of Acronyms - and other abbrev
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List of Acronyms 189 LHC Large Hadr
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Rear cover figure : This Report has
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