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Chapter 1 Scientific Objectives If the growth of the massive holes is mainly by coalescence (rather than gas accretion), then the physical event rate will be so high that the more distant events will produce a stochastic background of signals rather like the confusion-limited white-dwarf background. An estimate is as follows: if each massive black hole contains 10 −5 of a galaxy’s baryonic mass (probably a conservative number), if the coalescence events that formed it released 10 % of the original mass in gravitational radiation, and if 10 −3 to 10 −2 of the infalling mass is stellar-mass black holes, then about 10 −9 to 10 −8 of the baryonic mass of the Universe will have been converted into gravitational radiation this way. This corresponds to an energy density greater than 10 −11 to 10 −10 of the closure density, a level probably detectable by LISA (see Section 1.2.3 below). MBH – compact star binary signals. A third possible type of MBH signal is from compact stars and stellar-mass black holes orbiting around MBHs in galactic nuclei [70, 71]. MBHs in active galactic nuclei appear to be fueled partly by accreted gas from ordinary stars that were disrupted by the hole’s tidal forces. But white dwarfs, neutron stars and black holes will not be disrupted, and will instead follow complex orbits near the hole. These orbits are very sensitive to relativistic effects that depend on the spin of the MBH and of the infalling star. If these events are as frequent as current thinking suggests, then they can be used not only to test general relativity but also to survey the MBH population out to redshifts beyond 1. Estimates of the expected number and strength of signals observable by LISA in a one year period have been made by Hils and Bender[71] for the case of roughly solar-mass compact stars. Such events may well be observable if the neutron-star space density in the density cusp around the MBH is of the order of 0.1% of the total stellar density, which is not unexpected. Many more coalescence events occur, but the observable event rate is reduced because these stars have highly eccentric orbits, which are easily perturbed by other stars in the cusp. Thus the compact stars usually plunge in rapidly, and the number of orbits one can observe in order to build up the S/N ratio usually will be small. Also, the confusion noise will obscure many of the more distant events for the higher MBH masses. Recent calculations for 5–10M ⊙ black holes orbiting MBHs indicate that these coalescence events will be more easily detected [72, 73, 42]. The signal is stronger, and the more massive black holes are less susceptible to stellar perturbations. If such black holes make up a fraction 10 −3 of the total stellar numbers near the MBH, as they are very likely to do, then the number of signals from BH-MBH binaries observable at any time may well be substantial, and a number of such systems may coalesce each year. Figure 1.6 shows the expected signal strengths and frequencies for 7M ⊙ black holes orbiting around MBHs with different masses M and at different redshifts z [74]. For each factor-2 range in M and z about the value given, the signal strength and frequency are plotted for the strongest expected source within those ranges. For a given symbol corresponding to a given MBH mass, the plotted points correspond to values of z from the lowest to the highest value given as a label. Curves corresponding to the LISA threshold sensitivity and to the confusion noise estimate for 1 year of observation are included. However, for reasons discussed below, they are given for S/N = 10 instead of S/N = 5. The frequencies are treated as constant over a year, even though they actually will chirp strongly, and in a number of cases coalescence will occur during the year. The signals are likely to be stronger for rapidly rotating Kerr MBHs. The orbits for such BH-MBH binaries will be highly relativistic, and observations would test the predictions of general relativity very accurately in extremely strong fields. The orbital velocity near periapsis is roughly 0.5c, and the period for the relativistic precession of periapsis is similar to the period for radial motion. In addition, if the MBH is rapidly rotating, the orbital plane 13-9-2000 11:47 30 Corrected version 1.04
1.2 Low-frequency sources of gravitational radiation Factor 2 Intervals in MBH Mass M and Redshift z -21.60 0.1% of stars in galactic core are assumed to be 7 M black holes -21.80 z=1/16 LISA h(1 yr), S/N=10 Log Gravitational Wave Amplitude h -22.00 -22.20 -22.40 -22.60 z=1/2 z=2 z=1/16 z=1/8 Binary Confusion Noise Estimate for 1 yr, S/N=10 M=4x10 6 M M=2x10 6 M M=1x10 6 M M=0.5x10 6 M z=1/2 z=4 z=4 -22.80 -23.00 -3.20 -3.00 -2.80 -2.60 -2.40 -2.20 -2.00 Log Frequency (Hz) Figure 1.6 Expected signals from BH-MBH binaries. will rapidly precess. In view of the complexity of the orbits, the number of parameter values to be searched for, and the expected evolution of the orbit parameters, the SNR needed to detect the signals reliably probably will be about 10. If these events are observed, then each one will tell us the mass and spin of the central MBH, as well as its distance and direction. The ensemble of events will give us some indication of the numbers of such black holes out to z ∼ 1, and they will give us useful information about the MBH population, particularly the distribution of masses and spins. 1.2.3 Primordial gravitational waves Just as the cosmic microwave background is left over from the Big Bang, so too should there be a background of gravitational waves. If, just after the Big Bang, gravitational radiation were in thermal equilibrium with the other fields, then today its temperature would have been redshifted to about 0.9 K. This radiation peaks, as does the microwave radiation, at frequencies above 10 10 Hz. At frequencies accessible to LISA, or indeed even to ground-based detectors, this radiation has negligible amplitude. So if LISA sees a primordial background, it will be non-thermal. Unlike electromagnetic waves, gravitational waves do not interact with matter after a few Planck times (10 −45 s) after the Big Bang, so they do not thermalize. Their spectrum today, therefore, is simply a redshifted version of the spectrum they formed with, and non-thermal spectra are probably the rule rather than the exception for processes that produce gravitational waves in the early universe. The conventional dimensionless measure of the spectrum of primordial gravitational waves is the energy density per unit logarithmic frequency, as a fraction of the critical density to close Corrected version 1.04 31 13-9-2000 11:47
Page 1: LISA Laser Interferometer Space Ant
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Page 8 and 9: Foreword making the detection of gr
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Chapter 9 Spacecraft Design assembl
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Chapter 10 Mission Analysis launch.
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Chapter 10 Mission Analysis maneuve
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Chapter 10 Mission Analysis separat
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Chapter 10 Mission Analysis Figure
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Chapter 10 Mission Analysis plane,
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Chapter 10 Mission Analysis Earth 5
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Chapter 11 Technology Demonstration
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Chapter 12 Science and Mission Oper
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Collaboration, Management, Schedule
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Appendix LISA averaged Sensitivity
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Appendix stability of straylight pa
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Appendix serve aside from their fun
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Appendix Optical path-lengths: L 12
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Appendix • a fall-back configurat
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Appendix Table A.1 Null space of th
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Appendix • ambiguities exist betw
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Appendix Table A.3 Sensitivity of m
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Appendix ( ) −R ∂M ∂x j · st
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Appendix 0.1 Pathlength Error rad/S
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Appendix size in the phase meter. A
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Appendix Table A.4 Properties of th
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Appendix • Acceleration resulting
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Appendix Table A.7 Pre-Phase A opti
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Appendix effects. • Two types of
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Appendix -8 1. 10 Optical Path Erro
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Appendix A.2.2 Modelling the charge
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Appendix right through). The curve
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Appendix where the first term ( ˙Q
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Appendix The charge build-up will b
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Appendix The integration times give
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Appendix The integral divides natur
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Appendix shorter period than this,
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Appendix + HW HU R G\QH O DV HU L
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Appendix A.4.4 Laser metrology harn
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Appendix beamwidth of the diode las
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Appendix of less then 100 kHz in th
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Appendix The phase noise characteri
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Appendix Table A.14 Experimental re
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Appendix Table A.16 Photodiodes for
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Appendix Figure A.26 Telescope desi
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Appendix • minimise external stra
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Appendix A telescope with a CFRP st
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Appendix • no WFE impact over a -
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Appendix On the basis of the above
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Appendix
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Appendix A.7.4 Location of the cent
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Appendix A.7.4.4 Conclusion Conside
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Appendix The voice-coil solution wo
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Appendix The plots that will be pre
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References [18] V.M. Lipunov, K.A.
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References [59] M.J. Rees: Astrophy
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References [101] L. Morgenroth, LIS
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References [135] B.T.C. Zandbergen,
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Acronyms - and other abbreviations
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Acronyms ETR Extended Tuning Range
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Acronyms NAO National Astronomical
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Acronyms TC TeleCommand TCS Thermal
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