The frequency of the emitted gravitational waves need not be the natural frequency, of course, even if the mechanism is an oscillation with that frequency. In many cases, such as binary systems, the radiation comes out at twice the oscillation frequency. But since, at this point, we are not trying to be more accurate than a few factors, we will ignore this distinction here. In later sections, with specific source models, we will get the factors right.

The mean density and hence the frequency are determined by the size and mass of the source, taking . For a neutron star of mass and radius 10 km, the natural frequency is . For a black hole of mass and radius , it is . And for a large black hole of mass , such as the one at the center of our galaxy, this goes down in inverse proportion to the mass to . In general, the characteristic frequency of the radiation of a compact object of mass and radius is

Figure 2 shows the mass-radius diagram for likely sources of gravitational waves. Three lines of constant
natural frequency are plotted: , , and . These are interesting
frequencies from the point of view of observing techniques: gravitational waves between 1 and 10^{4} Hz are
in principle accessible to ground-based detectors, while lower frequencies are observable only
from space. Also shown is the line marking the black-hole boundary. This has the equation
. There are no objects below this line, because they would be smaller than the horizon
size for their mass. This line cuts through the ground-based frequency band in such a way
as to restrict ground-based instruments to looking at stellar-mass objects. No system with a
mass above about can produce quadrupole radiation in the ground-based frequency
band.

A number of typical relativistic objects are placed in the diagram: a neutron star, a pair of
neutron stars that spiral together as they orbit, some black holes. Two other interesting lines
are drawn. The lower (dashed) line is the 1-year coalescence line, where the orbital shrinking
timescale due to gravitational radiation backreaction (cf. Equation (28)) is less than one year.
The upper (solid) line is the 1-year chirp line: if a binary lies below this line, then its orbit
will shrink enough to make its orbital frequency increase by a measurable amount in one year.
(In a one-year observation one can, in principle, measure changes in frequency of 1 yr^{–1}, or
3 × 10^{–8} Hz.)

It is clear from the Figure that any binary system that is observed from the ground will coalesce within
an observing time of one year. Since pulsar binary statistics suggest that neutron-star–binary coalescences
happen less often than once every 10^{5} years in our galaxy, ground-based detectors must be
able to register these events in a volume of space containing at least 10^{6} galaxies in order to
have a hope of seeing occasional coalescences. That corresponds to a volume of radius roughly
100 Mpc. For comparison, first-generation ground-based interferometric detectors have a reach of
around 20 Mpc for such binaries, while advanced interferometers should extend that to about
200 Mpc.

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