List of Footnotes

1 In the case of an inspiraling binary, the root mean square of the two polarization amplitudes in a direction orthogonal to the orbital plane will be a factor √- 2 2 larger than in the plane.
2 In Sections 5.1 we will use parameters called chirp times, instead of the masses, to characterize a binary. The timescale defined here is closely related to the chirp times.
3 How large the SNR should be to presume that there is no bias in the estimation of parameters depends on the number of parameter-space dimensions and strictly speaking the statement is true only in the limit as SNR → ∞.
4 Working with analytic signals h (t) = a(t)eĻ•(t)+iĻ•0, where a(t) and Ļ•(t) are the time-varying amplitude and phase of the signal, respectively, we see that the initial phase Ļ• 0 of the signal simply factors out as a constant phase in the Fourier domain and we can maximize over this initial phase by simply taking the absolute value of the scalar product of a template with a signal.
5 Even though we deal with normed signals (which amounts to fixing D), astrophysical gravitational wave signals are characterized by this additional parameter.
6 We have followed the definition of the metric as is conventional in parameter estimation theory (see, e.g., [159Jump To The Next Citation Point, 161Jump To The Next Citation Point, 115Jump To The Next Citation Point, 67Jump To The Next Citation Point]), which differs from that used in template placement algorithms (see, e.g., [278]) by a factor of two. This difference will impact the relationship between the metric and the match, as will be apparent in what follows.
7 In what follows we shall use an over-line to distinguish the measured parameters from the true parameters pα.
8 A Bayesian interpretation of š’« (Δp α) is the probability of having the true signal parameters lie somewhere inside the ellipsoidal volume centered at the Maximum Likelihood point - pα.
9 A black hole can, in principle, carry an electric charge in addition to mass and spin angular momentum. However, astrophysical black holes are believed to be electrically neutral
10 Note that a black hole of physical mass M at a redshift of z will appear as a black hole of mass Mz = (1+ z)M. This shifts the frequency of the QNM to the lower end of the spectrum. Assuming a frequency cutoff of 10–4 Hz for LISA, this means that only black holes of intrinsic mass M < 1.2× 108M āŠ™āˆ•(1+ z) can be observed at a redshift z.
11 By large spins we mean values that are close to the maximum value allowed by general relativity. If J is the magnitude of the spin angular momentum then general relativity requires that |J| ≤ M 2
12 In Newton’s theory a two-body problem can be reduced to a one-body problem, in which a body of reduced mass μ moves in an effective potential. The parameter v is the velocity of the reduced mass, if the orbit is circular. In the extreme mass ratio limit ν → 0, v is the velocity of the smaller mass.
13 QUaD stands for QUEST (Q and U Extragalactic Survey Telescope) at DASI (Degree Angular Scale Interferometer).