Pre-Phase A Report - Lisa - Nasa

18 Chapter 1 Scientific Objectives
radius R (m)
10 13
10 12
10 11
10 10
10 9
10 8
10 7
10 6
10 5
10 4
10 3
10 -1
10 2
Sun
close NS-NS binary
10 0
10 1
f = 10 -4 Hz
LISA band Binary lifetime = 1 yr
Black hole line
10 2
10 3
10 4
10 5
mass M (solar masses)
f = 1 Hz
Binary chirp line
10 6
10 6 M o BH binary
10 6 M o BH burst
Figure 1.2 Gravitational dynamics. This diagram shows the wide range of
masses and radii of sources whose natural dynamical frequency is in the LISA
band. The two heavy lines delineate the outer limits of sources accessible from
space, at gravitational wave frequencies of 10 −4 Hz and 1Hz. They follow the
formula f GW =(GM/R 3 ) 1/2 /π.
The “black hole line” follows R =2GM/c 2 ; if general relativity is correct, there
are no systems below it. The “chirp line” shows the upper limit on binary
systems whose orbital frequencies change (due to gravitational-wave energy
emission) by a measurable amount (3×10 −8 Hz) in one year: any circular
binary of total mass M and orbital separation R that lies below this line
will “chirp” in LISA’s observations, allowing LISA to determine its distance.
(See text.) The curve labelled “binary lifetime = 1 yr” is the upper limit on
binaries that chirp so strongly that they coalesce during a LISA observation.
Any binaries formed of black holes above 10 6 M⊙ that are in the LISA band
will coalesce as LISA observes them.
At the lower-mass end of LISA’s range we show the Sun and the shortest-period
close neutron-star binary we expect LISA to see, which is on the chirp line but
not the 1-year lifetime line. Near the upper mass limit we illustrate a 10 6 M⊙
black hole formation burst and a 10 6 M⊙ black hole binary chirp (vertical line).
Ground-based detectors operate only in the mass range between the f =1Hz
line and the black-hole line.
1.1.4 Other theories of gravity
When using gravitational wave observations to test general relativity, it is important to
have an idea of what alternative predictions are possible. While general relativity has
successfully passed every experimental and observational test so far [5, 9], it is clear that
3-3-1999 9:33 Corrected version 2.08
10 7
10 8