Simultaneous with this development of LIGO I, plans for the more ambitious LIGO II are gaining momentum. The LIGO Scientific Collaboration  has been refining the vision of what technical advances would constitute a significant step forward and forming the research plan which can realize these advances; and the LIGO Laboratory has studied the practicalities of actually fabricating, installing, commissioning, and observing with a new detector. An introduction to this vision of LIGO II is presented in this article. Readers interested in delving further can investigate the LSC White Paper  and the Laboratory Conceptual Plan .
A look at the anticipated sensitivity of LIGO I (seen at right in
Figure 1, top curve) shows three regions; the near-vertical line at
low frequencies, a midrange from 40 to 120 Hz, and a high frequency
region above 120 Hz. Let's look at how the LIGO II design improves the
performance in each of these regions, starting from the high frequency
end. The design we talk about here is a starting point, rather than a
definition of LIGO II; and we have already been alerted to one missing
component in our model, and anticipate greater thermal noise than
indicated in these curves. With that caveat, here are the broad
outlines of what we hope to achieve with LIGO II.
Shot Noise Dominated Region
LIGO I uses 10 W of laser power in a power-recycled Michelson
interferometer with Fabry-Perot arm cavity transducers to sense the
motion of the test masses. The limit to our ability to sense comes
from the ``shot noise limit"-the (Poisson) statistical fluctuation in
the number of photons arriving at our photodetector makes us uncertain
about the exact position of the test masses. Increasing the laser
power decreases the fractional uncertainty, as the square root of the
laser power, and so an obvious improvement in a second-generation
interferometer is to increase the laser power. The Reference Design
for LIGO II, shown in the
LSC White Paper
, carries an increase from 10 to 180 W of input
laser power, and also takes advantage of the best optical polishing
and coating to date to allow a lower-loss optical system (and thus a
higher ``recycling gain"). These changes lead to a better sensing of
the test mass motion, and as seen in Figure 1 a much-improved
high-frequency sensitivity. They also require considerable research
and development in optical components: low-noise laser amplifiers,
phase modulators, Faraday isolators, and the means to compensate for
thermal lensing of the interferometer components.
A series of experiments and detailed models have been underway for some time to both verify the usability of these configurations and to find a suitable practical form. A significant effort in the Ligo Science Collaboration Research and Development will be in the establishment of high-sensitivity prototypes to give confidence in the design and to test engineering solutions.
We need to delve a little deeper to see a complement to the shot
noise, the radiation pressure noise. Figure 3 at right shows the
aforementioned shot noise contribution to the sensitivity; curve 7
shows the effect of momentum transfer from the photons to the test
masses. The mass motion due to this noise source dominates at low
frequencies, until shot noise takes over at about 100 Hz. This
``buffeting" of the masses grows with the laser power (again as
the square root of the power), and so it becomes clear that an optimum
laser power exists-a power such that the sensing noise at high
frequencies is reduced to an acceptable level, but one where the
low-frequency buffeting of the test masses by radiation pressure is
not so great as to impact the low-frequency performance. We call the
LIGO II design ``a quantum limited interferometer" due to the fact that
at all frequencies the LIGO II sensitivity is limited by the quantum
nature of light. Since the buffeting is a force, it makes sense that
this noise source falls as 1/f2 and that the motion
associated with it becomes smaller if the mass is greater. This leads
us to the second significant change from LIGO I: the test masses are
to be 30 kg, rather than LIGO I's 10 kg, to hold down the radiation
pressure noise (and allow a higher laser power).
Over a broad range of frequencies, the sensitivity of LIGO I will be limited by the Brownian motion, and the related noise due to thermoelastic dissipation, of the test masses. The test masses are in thermal equilibrium with the surrounding heat bath (at a carefully regulated 20 degrees Celsius), and thermodynamics tells us that each mechanical mode of the test masses (and their wire loop pendulum suspensions, in the case of LIGO I) has kT of energy (where k is Boltzmann's constant). This energy is expressed as a random motion of the test mass, where the distribution of the motion as a function of frequency is determined by details of the losses which limit the mechanical Q of the system (test mass or suspension). To reduce this noise, one wants to ``gather" the noise into the peak near the mechanical resonances (by choosing materials and processes which maximize the mechanical Q) and place the resonances either below the frequencies of interest (the pendulum suspension modes, around 1 Hz) or well above the frequencies of interest (the test mass internal modes, 10 kHz and higher).
This introduces two very important changes from LIGO I. First, we are studying the use of sapphire instead of fused quartz for the test mass material. Sapphire has very low mechanical losses, and also a high speed of sound and a high density. These are all advantageous for the thermal noise, and the increased mass is needed for the radiation pressure noise. However, to obtain sapphire in the size required for a LIGO test mass (order of 28 cm diameter, 12 cm thickness) and of an optical quality sufficient for the interferometric sensing, requires a development effort, but will be rewarded with a much reduced thermal noise. (Curve 4, Fig 3 shows an estimate for the thermal noise not including the thermoelastic term, which will increase the level by factors of 3 to 10 depending upon the frequency). For reference, the thermal noise for 30 kg fused silica masses is also shown (curve 5); realizing this alternative test mass material would require physically large test masses and presents different fabrication challenges.
The second change is to use fused quartz instead of steel wire for the
suspension, and to use a ribbon rather than a simple cylindrical
fiber. Fused quartz is a much lower loss material than wire, and
making a ribbon allows the suspension to be very ``soft" along the
optical path (to store little energy in stiffness of the ribbon
itself, and instead to use gravity as a restoring force for the
pendulum motion) and thus to further reduce the thermal noise from the
fiber (curve 3, Fig 3). The suspension and its design, shown in Figure
4 at right, uses multiple masses and multiple fibers, and is a
contribution from our close collaborators of the German-Scots GEO
group; a similar design will be first tried in the GEO-600
The requirement for the attenuation of seismic noise is to make it a negligible contributor to the overall interferometer performance. Thus it must be small at all frequencies where other, more difficult and subtle noise sources (like quantum or thermal noise) are at a level allowing the observation of probable gravitational wave sources. For LIGO I, this led to a ``cutoff" or ``brick wall" frequency of 40 Hz-at all lower frequencies, the thermal noise would have been so great that no reasonable model for gravitational wave sources would predict detectable signals. For LIGO II, due to the much reduced thermal noise and managed radiation pressure noise, a cutoff frequency of 10 Hz is a good choice (curve 2, Fig 3). This puts the seismic noise contribution at 10 Hz close to the background due to the Newtonian background-dynamic changes in the net direction of the gravitational attraction of the test mass to the earth due to compression and rarefaction of the nearby earth as normal seismic motion takes place.
There are two approaches to the seismic attenuation under study. One uses passive isolation, in a design derived from that used by the VIRGO project; the other uses servo control techniques to slave the quiet suspension platform to quiet seismometers. The final design must deliver the required reduction in both the seismic noise near 10 Hz as well as fulfilling the very important role of reducing motion for frequencies 1 Hz and lower as part of the overall control approach.
To verify the mechanical design of the experiment, a prototype allowing tests of the suspension and isolation components of LIGO II is in preparation. The objective, as for the configuration prototypes mentioned above, is to allow a demonstration of the performance levels of LIGO II without disturbing observation underway with LIGO I.
The resulting interferometer (or detector, as interferometers at both the LIGO Livingston, Louisiana and Hanford, Washington observatories will be improved) will offer an enormous increase in the sensitivity to many gravitational wave sources. In one coarse measure, the strain sensitivity to broad-band sources in the region of 100 Hz will increase by a factor of many factors of 10. Because the included volume of space goes as the cube of the distance, this means we include many, many times more candidate sources with LIGO II as compared to LIGO I. Also, the ``tunability" of the response means that, as we learn more about specific sources, we can increase our sensitivity even more dramatically for those sources. Sources which might be observable by LIGO I once per year would be observed many times every day by LIGO II, and the signal-to-noise ratio may allow detailed studies of the waveform for comparison with numerical models, leading to better understanding of both astrophysics and of physics in highly relativistic conditions. The LIGO II detector will be run in cooperation with the other gravitational-wave detectors to form a powerful network, permitting the extraction of position, polarization, and other source parameters from the combined data.
The plan is an ambitious one. We would like to start the replacement of the LIGO I interferometers with the LIGO II design in 2005 and be observing before 2007. This schedule will need exquisite preparation to minimize the ``down time" for observation to a minimum and to assure that the LIGO II interferometer will perform as designed as quickly as possible after installation. Close coordination of the Research and Development leading to a final design is a pre-requisite, and ``all-hands" must be available for the well-rehearsed installation. The results will be very satisfying of course as a technical achievement-but more importantly, they will be extraordinarily rich in astrophysical insights.