Pre-Phase A Report - Lisa - Nasa

82 Chapter 4 Measurement Sensitivity
Considering these types of noise and the frequency dependence of the interferometer response
as presented in Figure 4.2, one arrives at a typical sensitivity curve shown in
Figure 4.3 . In the low-frequency range, say below 2 mHz, the noise, and thus the sensi-
gravitational wave amplitude h
10 −20
10 −21
10 −22
10 −23
10 −24
10 −4
acceleration noise
10 −3
position noise
10 −2
frequency [Hz]
Figure 4.3 LISA sensitivity for one year integration time and a signal-tonoise
ratio of 5, averaged over all possible source locations and polarisations.
Also indicated are the position noise (dashed line) and the acceleration noise
(dotted line).
tivity, is determined by the acceleration noise, leading to a decrease in sensitivity towards
lower frequencies roughly propotional to f −2 . Above about 2 mHz the noise is dominated
mainly by the shot noise, whereby the decline of the antenna transfer function above
10 mHz causes a decrease in sensitivity roughly proportional to the frequency.
The following subsections will discuss the most important noise sources, and means to
suppress them. Their remaining influence is given in tabular form, separately for opticalpath
and acceleration noise.
4.2 Noises and error sources
4.2.1 Shot noise
Among the optical-path noise sources, a very fundamental one is shot noise, whichforeach
single passage through an arm of length L leads to a power spectral density of apparent
optical-path fluctuations
SδL(f) :=
2 δL(f)
10 −1
= c
2π
λ
Pavail
10 0
. (4.4)
There are four such single paths, their uncorrelated contributions adding up quadratically
to the final shot noise value δL, the apparent variation of the total path difference L2 −L1
in one LISA interferometer (see also Section 3.1.4).
3-3-1999 9:33 Corrected version 2.08