• In order to computeQij, it might seem that all 10 binary parameters (Table 1.2) are needed.
However, the overall orientation of the binary is not absolutely needed, in the following sense:
we can choose an arbitrary frame, say, one in which L is along the z axis andS1 is in the x-z plane atf = 30 Hz, and computeQij — this is already enough, since the arbitrariness in the orientation of this frame will be automatically accounted for by the (Θ, ϕ) and (θ, φ, ψ) parameters. In the end, 7 is the number of relevant parameters, which we call “basic” and
“local parameters” in Table 1.2.
Although 7 is still too large for the dimensionality of the intrinsic parameter space, 3 of them are absent when the spin of one of the two bodies is unimportant, e.g., in NS-BH binaries. A four-dimensional intrinsic-parameter space is needed in this case, which is not extremely big. An exploration of this parameter space (now physical) will not only help clarify conceptually the ori- gin of the high false alarm probability, but for the first time provide a practical way of searching over the physical templates of precessing binaries, which so far has been regarded as non-practical.
Investigation of this approach is currently being made by Pan, Buonanno, Vallisneri and me.
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Chapter 2
Quantum noise in second generation, signal-recycled laser interferometric gravitational-wave detectors
It has long been thought that the sensitivity of laser interferometric gravitational-wave detectors is limited by the free-mass standard quantum limit, unless radical redesigns of the interferometers or modifications of their input/output optics are introduced.
Within a fully quantum-mechanical approach we show that in a second-generation interferometer composed of arm cavities and a signal recycling cavity, e.g., the LIGO- II configuration, (i) quantum shot noise and quantum radiation-pressure-fluctuation noise are dynamically correlated, (ii) the noise curve exhibits two resonant dips, (iii) the Standard Quantum Limit can be beaten by a factor of 2, over a frequency range
∆f /f∼1, but at the price of increasing noise at lower frequencies.
Originally published as A. Buonanno and Y. Chen, Phys. Rev. D64042006 (2001).