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 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 . | |
4 | Working with analytic signals , where and are the time-varying amplitude and phase of the signal, respectively, we see that the initial phase 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 ), 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., [159, 161, 115, 67]), 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 . | |
8 | A Bayesian interpretation of is the probability of having the true signal parameters lie somewhere inside the ellipsoidal volume centered at the Maximum Likelihood point . | |
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 at a redshift of will appear as a black hole of mass . 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 can be observed at a redshift . | |
11 | By large spins we mean values that are close to the maximum value allowed by general relativity. If is the magnitude of the spin angular momentum then general relativity requires that | |
12 | In Newton’s theory a two-body problem can be reduced to a one-body problem, in which a body of reduced mass moves in an effective potential. The parameter is the velocity of the reduced mass, if the orbit is circular. In the extreme mass ratio limit , is the velocity of the smaller mass. | |
13 | QUaD stands for QUEST (Q and U Extragalactic Survey Telescope) at DASI (Degree Angular Scale Interferometer). |
http://www.livingreviews.org/lrr-2009-2 |
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