USING THE CALTECH 40 METER GRAVITY WAVE DETECTOR

The Fabry-Perot cavity mirrors are suspended so that they are free to move in response to a gravity wave. The limit this search sets varies with the mass parameter, '7, which is a function of the stars' mass.

List of Tables

Chapter 1

Introduction

What are Gravity Waves?
Scientific Benefits of Detection
Outline of this Thesis
Chapter 2

As a gravitational wave travels, the masses move relative to each other so that one arm of the interferometer gets longer as the other gets shorter, this appears as a phase shift in the light in the two arms. The first interferometric gravitational wave detector was made by Moss, Miller and Forward in 1971.[4] In 1975, work began on the Max Planck interferometer.

Figure 1.1: The effect of a gravity wave on a ring of test particles.

Sources of Gravity Waves

Generation of Gravitational Radiation

The frequency of the stars' orbits is a function of their mass and the time to coalescence. The circles indicate when a tidal disruption is expected for a neutron star binary.[18] The triangles indicate when the speed of the stars is O.lc.

Figure 2.1: The estimated wave strengths for periodic gravitational radiation and the sensitivities for interferometric detectors today and in the proposed LIGO

Chapter 3

The Caltech Detector

The Detector

Theory of Operation
The Test Masses
The Light

The detector is calibrated by moving the far mirror of the first cavity a certain amount. It is also important that the mirrors do not move relative to the center of mass of the test masses.

Figure 3.1: A simplified schematic of the Caltech detector.

Noise Sources

Noise Sources which Affect the Test Masses
Noise Sources Limiting the Measurement Accuracy
Other Noise Sources

Due to the high Q and resonant frequency of our test masses, the thermal noise in the test masses is negligible in our prototype detector. In a Fabry-Perot, B is defined as cr / L, where T is the storage time of the light in the cavity.

Figure 3.4: A close-up of the noise spectrum of the Caltech interferometer, taken with and without the coils by one mass being driven

Chapter 4

Spatial Fluctuations of the Test Masses and Light Source

Effects on the Detector Sensitivity

Change in the Length of the TEM 00 Mode
Transverse Motion of the Mirrors

A third spatial fluctuation in the cavity is caused by the transverse movement of the test mirrors. The angle between the input beam and the TEM00 mode of the cavity is a = f3 +OF.

Reducing Spatial Fluctuations

Reduction of Mass Jitter

Unfortunately, due to thermal drift, it is necessary to leave the air conditioning on when using the detector for long periods of time, otherwise the reliability of the detector is greatly reduced. The fiber's output must be carefully collimated to travel the 80 meters from its output to the mirror and back to the quadrant diode. The residual jitter on the control beam is due to the movement of the tower on which the fiber output coupler is mounted.

The laser beam captures angular noise both due to the movement of the mirror supports and due to air currents. A second reduction factor of 10 was achieved by placing the output coupler of the fiber in a vacuum and placing the output coupler on top of the lead and rubber insulating bundle. As discussed in Chapter 3, the mode sweep cavity will also act as a spatial filter.[32] Mode-cleaning cavities are more difficult to use than optical fibers because they must be held at resonance, while fiber does not require any light frequency requirements.

Currently neither beam jitter nor angular motion of test masses is a limiting factor in detector noise above 200 Hz. Below that detector noise is possibly limited by seismic noise, which can be incorporated by directly moving the test masses along the beam axis and causing angular movement of the masses.

Figure 4.9: The test mass suspension and control.

Chapter 5

Data Analysis

An Algorithm to Search For Coalescing Compact Binaries

The Signal
The Algorithm
Numerical Tests

Analysis of the Data

The Coincidence Run
Data Collection

Arm 2 Photodiode
Arm 1 Photodiode

Vetos

A major problem when searching for coalescing binaries is that there are three unknowns in the waveform (see equation 2.8 or 5.3), the mass parameter f]. Although the voltage is greatest in the last few moments of the binary, when the frequency is greatest, the Fourier transform of the voltage, S(f), does not increase with frequency. Clearly the easiest way to search through many frequencies is to perform a Fourier transform of the detector output.

I min is equal to the minimum frequency of the detector, and (r- tmin) is the time duration from I = f min to fusion). F(S, fo) = J S(x)e-2'"foxdx (5.9) This transformation will follow the gravity wave's frequency, separating it from background noise at other frequencies. The doppler shift due to the earth's motion is neglected, but over an integration period of 100 seconds it causes a fractional change in frequency of about 10-8, which is negligible.) As mentioned earlier (in Section 3.1.1) the gravity wave signal is the feedback signal to the second arm followed by a pair of filters to keep it within the range of our ADC, without introducing digitization error.

The cutoff point was selected by sampling the light level recorded on tape at 40Hz, and examining a histogram of the output. The broadening of the two peaks is caused by fluctuations in the cavity's contrast and the power of the input light.

Table 5.1: The length of time the signal will have f > frn~n if no tidal disruption occurs

Whitening the Data
Implementing the Binary Star Filter
Calibration
Chapter 6

When this was excited, there were times it caused the gravity wave signal to exceed the range of the ADC. So the data at the edges of the window was not smoothed in the filter output. The shape of the whitening filter is obtained by averaging many FFTs from the beginning of the data set (340 FFTs 1024 points are evaluated).

The Fourier transform of the output of this filter is shown in Figure 5.8, the data used to make this figure was not the same data averaged to make the filter. The time it took for this filter to analyze the data was increased because of the time it took to create and export this additional information. The conversion of these to rack units depends on the channel of the FFT (which is equivalent to the value of 17), this is discussed in Section 5.3.

The maximum peak output and the FFT channel in which it occurred were recorded. The dependence of the height of the output peak versus the error in r, ~ r, is shown in Table 5.3.

Results and Conclusions

Results

Events Found by the Filter
The "Spikes" in the Gravity Wave Signal
Distribution of the Output
Astrophysical Implications
Relevance to the Detector Development

Many of these may have caused part of the servo loop of the second cavity to saturate. This is due to occasional sources of noise, such as the aforementioned bumps in the light level. Unfortunately, not all non-Gaussian noise in the detector can be related to the auxiliary.

As mentioned in Section 6.1.2, some of the events were caused by shocks at the detector output. Seven of the twenty-one events in Table 6.3 turned out to be due to these points, and not to anything in the de-. Many of the events in the detector output were related to the light level of the second cavity.

Some of the excess noise was probably due to non-Gaussian modes in that cavity. The light level of the second cavity can be related to spurious events via two other effects.

Suggestions for the Future

The live time of this experiment was limited by the dynamic range of the second cavity servo. I would like to suggest that we try to reduce a known cause of non-Gaussian noise, the acoustic sensitivity of the detector. Although acoustic noise can be sensed directly and events due to this can be removed, this results in the loss of a large portion of data.

One thing that became clear as we tried to understand what caused the non-Gaussian events was that we need more information about what else is happening in the laboratory. The only signals that need to be sampled using the full detector bandwidth are the detector output itself and the microphone. When the servo of either cavity is near saturation, the detector output becomes noisy; it is therefore advisable to keep the time this happens to a minimum.

The cavity will stop resonating and the servo will need to lock again; it usually locks in the middle of the servo loop's dynamic range. By more frequently studying histograms of the detector output, we should develop intuition about which other signals are important, and how to increase the fraction of the collected data that is not contaminated by spurious effects.

Appendix A

Calculation of Noise due to Off-Axis Modes

Define the leakage field as the light that has been stored in the cavity and escapes from the entrance mirror, [25,41]. The phase of the leakage field is measured relative to the incident light using the phase modulation technique [22]. Now consider the case where A;nc does not exactly match the TEMoo mode of the cavity, but is "contaminated" by some light that spatially matches the TEM01 mode. A.14) (A.15) (A.16).

Since U0(y) and U1(y) are orthonormal, the cross terms cancel out when one integrates over the entire spot and a signal is left. Demodulating this signal gives one the weighted sum of the phase error for each mode. The phase error for the TEMoo mode is essentially zero, since it is the mode held at resonance.

Appendix B

The Computer Codes

The Prefilter and Veto Routines
The Binary Star Filter
The Codes used to Reduce the Results
The Code for Detection of "Bumps"

By plotting a histogram of the DC light level, it is possible to find a suitable boundary between when the cavity resonated and when it did not. To minimize the number of times a single tape is read, one program, pretable./, both creates a table where the data is "good" and whitewashes the data. To avoid any unnecessary digitization error and to improve the speed of this program, the data is not multiplied by the usual scaling factor (1/16384).

Most of the rest of the program is about manipulating the data so that only "good" data is analyzed. As mentioned in Section 5.2.5, the threshold in filtFbins.f was set very low, and one section of the data could activate many channels. The readlog.f program reads the output of filtFbins.f and assigns each section of the data that was above the filtFbins.f threshold the single event that best matched the coalescence of binary stars.

I f (ochan.lt.ochlow.OR.ochan.gt.ochhogh> goto 29 . del tao=CIBLKSZg*CobiKon-obiKmx))+(Jon+ocount-Jmx-ocntmx>. 5 data channels r~corded>. c NBLKS=number of blocks on monus tape onl?. c lavgsz=numb~r poont used to love the slant. ~no onteger•4 LBLK,foll'dl'scropt.real alpha,bmothrshp,bmpthr~hn common/ bu f /b•J f fer.

Table C.1: The time at which these data were collected.

Bibliography