Re: Is LIGO just observing viscosity of the vacuum?

Ian Parker <ianparker2@xxxxxxxxx> wrote:
There is another question to "What is R(6)?". We have established that
LIGO can only detect harmonics, the baseline is too short for
fundamentals.

Actually, LIGO's sensitivity (signal/noise ratio) depends in a rather
complicated way on the signal frequency. The LIGO noise curve looks
roughly like this:

| *
| *
| *
| *
| * ****
| * ****
| * ****
| * ****
| * ****
| *** ****
| ******
|
+--------------------------------------------

Here the y axis is the noise (log scale), and the x axis is frequency
(log scale). The useful frequency range is very roughly from 50 Hertz
to a few kilohertz.

Since LIGO's arms are 4km long, the peak sensitivity is going to be
(very roughly) a signal which oscillates through O(pi/2) radians in the
round-trip light travel time. LIGO is actually much closer to a
Fabry-Perot interferometer than a Michelson interferometer, with
the light typically bouncing back and forth 100 or so times between
the mirrors. So we can very roughly estimate the frequency where
LIGO has peak sensitivity as (3e5 km/sec) / (100 * 8km) = 375 Hertz.

The question I have is "How do Neutron stars collide?". This question
is vitally important for establishing the fundamental/harmonic ratio.
GTR tells us what happens if (say) we drop something (a point mass)
into a Black Hole. However a neutron star is not a point mass. Before
it finally collides it could become elongated from tidal forces. This
will not affect the fundamental transmission too much but it will
radically reduce the harmonic component, since if we integrate the
retarded potential the harmonics will tend to cancel out.

This could make the LIGO estimates very optimistic.

Fortunately, most of the LIGO signal/noise ratio comes from the
*orbital* motion well before the neutron stars physically collide.
In this regime, the system is pretty close to a pair of point
masses, for which the gravitational-radiation signals are
relatively easy to calculate.

Of course, a big chunk of the interesting astrophysics knowledge we
hope to learn from analysing LIGO signals will come from the signals
during and after the actual collision. These signals are indeed
smaller than the orbital-motion ones just before the collision,
but if they can be measured with good signal/noise ratio, they
should carry a lot of information about the equation of state of
dense nuclear matter (there are all sorts of shock waves running
around!), *and* about the operation of general relativity in a
highly strong-field dynamic regime.

If we consider binary black-hole collisions instead of binary
neutron stars, then the complcated matter-shock-wave effects are
gone, and we are left with "just" strong-field highly dynamic
gravitational fields. This is why BH collisions are such a great
arena for testing general relativity!

ciao,

--
-- "Jonathan Thornburg [remove -animal to reply]" <jthorn@xxxxxxxxxxxxxxxxxxxxxxx>
Dept of Astronomy, Indiana University, Bloomington, Indiana, USA
"C++ is to programming as sex is to reproduction. Better ways might
technically exist but they're not nearly as much fun." -- Nikolai Irgens

.

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