The data used in this thesis were taken from LIGO’s6thscience run (S6) and Virgo’s2ndand3rdscience
runs (VSR2 and VSR3). By this time, the performance of the detectors was near optimal, given the design of the instruments.
The performance of a LIGO or Virgo detector, in terms of CBC searches, is defined by the horizon distance, which is the distance out to which it can see an optimally oriented binary (ι= 0) with an average SNR ofρ=8, given by hρi= s 4 Z fhigh flow |˜h(f)|2 Sn(f) df , (2.23)
whereflow is the low-frequency cutoff determined by the detector, 40 Hz for LIGO detectors during S6
and 30 Hz for Virgo during VSR2 and VSR3;fhigh is determined by the sampling rate of the data, whose
Nyquist frequency is 1024 Hz, and the expected waveform,˜h(f); andSn(f)is the power spectral density of the detector, which is a measure of the mean square noise fluctuations [4]. It is the square of the strain amplitude sensitivity, shown for the different detectors in Figure 2.17 and Figure 2.18.
By inserting Equation (2.19) and Equation (2.20) into Equation (2.23), settinghρi= 8(a good approx- imation to the single-detector SNR threshold for confident detection), we can solve forr =D, the horizon
distance (for an inspiral only waveform, under the quadrupole approximation):
D= 1 8 5π 24c3 1/2 (GM)5/6π−7/6 s 4 Z fhigh flow f−7/3 Sn(f) df , (2.24)
which shows how the sensitivity is dependent on the chirp massMof the system. However, it is important to note that this calculation has only taken the inspiral portion of the waveform into consideration. The merger and ringdown can comprise a significant fraction of the power output of a GW for high-mass systems; see how much higher above the noise the merger and ringdown are for the 100 totalMsystem in Figure 2.12 as
compared to the 25 totalMsystem in Figure 2.11. But it is difficult to show the horizon distance analytically
for IMR waveforms because they have complicated parameterizations, numerical solutions to differential equations, or numerical solutions to the full GR equations. Figure 2.19 uses full IMR waveforms and a numerical analysis to illustrate how the detectors are sensitive to higher mass systems to larger distances [4].
The sensitivity of a detector is related to the horizon distance by
sensitivity (range)=D/2.26, (2.25)
since the horizon distance was calculated for a binary with optimal orientation and sky location. The factor of 2.26 comes from integrating over sky location and inclination angles that would give an SNR of 8 (see
Section 3.2 for the definition of these angles with respect to a detector).
Figure 2.17: Representative curves for the strain amplitude sensitivity for LIGO Livingston (L1), in solid red, and LIGO Hanford (H1), in green, during S6 as compared to S5 (dotted lines). Note that S6 performance exceeded the Science Requirements Document (SRD) for Initial LIGO, due to enhancements made between S5 and S6. The distances in the legend are the horizon distance for an optimally oriented NS+NS inspiral. Image courtesy of John Zweizig.
The characterization of Virgo data and its impact on gravitational-wave searches.
13
Figure 2.
(a) Typical sensitivity vs. frequency curves for the first three Virgo
science runs: VSR1 (2007), VSR2 (2009) and VSR3 (2010). (b) The measured VSR2
sensitivity curve is compared to the predicted noise budget [44].
The agreement
between the measured and the predicted sensitivity was the best for VSR2. For
VSR1&3 the agreement was not as good, especially at low frequency.
disturbances coupling through the mirror magnets. At high frequencies (above 300 Hz)
the sensitivity is primarily limited by the shot noise of the main laser beam and by
laser frequency noise. The frequency noise originates from the shot noise of the sensor
delivering the error signal used in the laser frequency stabilization. For intermediate
frequencies (between 100 Hz and 300 Hz), both thermal noise and shot noise limit the
sensitivity. Noise structures around 165 Hz and 210 Hz are suspected to originate from
scattered light (see section 4.2.6).
In addition to achieving a good sensitivity, it is also important to maintain the
detector in operation as long as possible in order to maximize the live-time (or duty
cycle). A lock acquisition scheme [42, 43] was designed to bring and maintain the Virgo
detector to its working point. The Virgo locking procedure has proved to be very efficient
and robust. The lock can last for several hours or days at a time (see table 1). If lock
is lost, it can be recovered in a few minutes. When locked, the detector is manually
set in science mode when a stable state is reached. When in science mode, no external
input or detector tuning is allowed. Science mode ends when decided by the detector
operator (for maintenance or tuning) or whenever an instability causes loss of lock of
the interferometer. The beginning and the end of a lock segment are considered unsafe
in terms of data quality. Thus, the first 300 seconds after the end of locking procedure
and the 10 seconds of data before the loss of lock are,
a priori, rejected and not used
for science analysis.
The first Virgo science run, VSR1, took place between May and October 2007,
in coincidence with the LIGO detectors. The second run, VSR2, started in July 2009
after a commissioning period devoted to detector upgrades. These upgrades included:
more powerful and less noisy read-out and control electronics, a new laser amplifier
that provided an increase of the laser power from 17 to 25 W at the input port of
Figure 2.18: Representative curves for the strain amplitude sensitivity for Virgo during Virgo science run(VSR) 1, 2, and 3 [5]. Note that VSR1 was during S5, while VSR2 and VSR3 were during S6.
30 40 50 60 70 80 90 100
Binary total mass (M
)
0 100 200 300 400 500 600 700 800Horizon
distance
(Mp
c)
S6, H1 S6, L1 VSR2, V1 VSR3, V1Figure 2.19: Horizon distances for non-spinning equal-mass IMR signals in the LIGO and Virgo detectors, using EOBNRv2 waveforms, which are explained in Section 2.2.1.1 as the signal model, averaged over periods of data when the detector sensitivities were near optimal for S6 and VSR2/3, respectively [4]. Note that above 100M, the horizon distance drops abruptly, as the number of cycles in the detectors’ sensitive
Chapter 3
Ground-based interferometric GW
detection
Initial LIGO and Virgo (V1) operated between 1999 and 2010 and collected data in a series of observa- tional science runs, delimited by commissioning breaks and hardware upgrades. Initial LIGO science data sets are labeled science run 1 (S1), S2, S3, S4, S5, and S6; initial Virgo’s are labeled VSR1, VSR2, and VSR3. From S1 to S5, there were three LIGO detectors, a 4-kilometer arm detector in Livingston (L1) (see Figure 3.1), a 4-kilometer arm detector in Hanford (H1), and a 2-kilometer arm detector (H2) sharing the same vacuum system as H1 (see Figure 3.2). H1 and L1 were upgraded for S6 [51], also known asenhanced LIGO, to include DC readout [10], a higher powered laser, a substantially upgraded thermal compensation system (TCS) [52] [53], and, most notably, improved sensitivity with respect to S5 for signals above 300 Hz [54]; H2 was not in use during S6. S5 (during which LIGO reached its design sensitivity [42]) and S6 have the longest stretches of science data for LIGO detectors. Some of the many papers published on the search for CBCs from this data (and in some cases Virgo data) are References [55], [56], [23], [57], [58], and [17]. No GWs were found, but this was not unexpected.
Currently, the H1 and L1 detectors are being replaced by their advanced versions, as is Virgo (the sites and vacuum enclosures remain the same, but the detectors themselves are completely redesigned) [59]. We can also look forward to LIGO-India, which will employ the base hardware from H2, and Japan’s Kamioka Gravitational Wave Detector (KAGRA) [60], which will be underground and have cryogenically cooled test masses.
This thesis is based mainly on the data during LIGO’s S6 and Virgo’s VSR2 and VSR3 data sets. In the following sections I will explain the basic elements of the detectors that are required to understand the results presented in this thesis.
Figure 3.1: An arial view of LIGO Livingston (L1) showing the full y-arm, part of the x-arm and the exterior building around the control room and laser and vacuum equipment area. Image taken from www.ligo.org.
Figure 3.2: An arial view of LIGO Hanford (H1 and H2) showing the full y-arm, part of the x-arm and the exterior building around the control room and laser and vacuum equipment area. Image taken from www.ligo.org.
3.1
The operating principles of ground-based interferometric GW de-
tectors
As hinted at in Section 2.2.1, in order to detect GWs you need an instrument that measures differential strain. Strain is equal to the change in length over length,
h=δL/L, (3.1)
whereLis the length of your measuring device. A gravitational wave from a 50+50Msystem at 100 Mpc
will impart a strain on the order of10−20around merger (see Figure 2.12, noting that the y-axis is the strain
scaled by the square root of the x-axis). Therefore, we need an instrument that can measure very small ratios of change in length to length.
The designers of the LIGO and Virgo detectors chose a Michelson interferometer as the basic structure for the instrument, since it can measure small length changesδLto very high precision. In a classic Michelson, coherent incident light is directed at a beam splitter, which sends half of the light down the x-axis and half of the light down the y-axis. There are mirrors at the end of each arm that send the light back toward the beam splitter (see Figure 3.3); depending on the difference in arm lengths, when this light recombines it will either head back toward the laser (symmetric port) or toward a photodetector (anti-symmetric port). If the arms are exactly the same length, no light hits the photodetector and thus the anti-symmetric port has earned the nickname “the dark port”. If a GW passes through the detector, it changes the relative positions of the mirrors, allowing a pattern of light to reach the anti-symmetric port’s photodetector — this can be calibrated into the likely GW strain signal.
In reality, the LIGO and Virgo detectors are much more than Michelsons. The full optical configuration is sometimes referred to as a power-recycled Fabry-Perot Michelson interferometer (PRFPMI) [61]. Fabry- Perot and power-recycling optical cavities increase the laser power in the arms, effectively increasing L
because the light bounces back and forth hundreds of times before exiting to the anti-symmetric port, thus improving the sensitivity at relevant frequencies by two orders of magnitude [62]. However, this signal is still very tiny — only quadratically proportional to the small GW signal we are trying to detect. Therefore, LIGO detectors employ either heterodyne detection(S1 - S5) or a specialized form ofhomodyne detection (S6) known asDC readout. DC readout adds a local oscillator field at the same frequency as the input laser. When a GW signal modulates the phase of the input laser, it will interfere with the local oscillator to produce power variations on the anti-symmetric port’s photodetector that are linearly proportional to the GW signal [10]. Homodyne detection benefits from a local oscillator field that has been filtered by the Fabry-Perot arms, and an output mode cleaner (between the beam splitter and the anti-symmetric port) which removes “junk” light that may be resonating in the power-recycling cavity [10]. Virgo does the same thing [63].
LIGO Detector Characterization in S6 3 ! "# $# %&#
Figure 1: Optical layout of the LIGO interferometers during S6 [21]. The layout differs
from that used in S5 with the addition of the output mode cleaner.
components for the aLIGO laser system [26]. In order to correct for the higher thermal lensing of the test masses [27], a improved CO2-laser thermal-compensation system
was installed [28,29] and used to heat the outer annulus of the input test masses to counteract excessive lensing from the main beam.
An alternative GW detection system was installed, replacing the initial heterodyne readout scheme [30]. A special form of homodyne detection, known asDC readout, was implemented, whereby a local oscillator field is introduced at the same frequency as the main laser beam [31]. In this system, GW-induced phase modulations interfere with this field to produce power variations on the output photodiode, without the need for demodulating the output signal. In order to improve the quality of the light incident on the output photodiode in this new readout system, an output mode cleaner (OMC) cavity was installed to filter out the higher-order mode content of the output beam [32]. The OMC was required to be in-vacuum, but also highly stable, and so a new single-stage seismic isolation system was designed and installed for the output optical platform [33], from which the OMC was suspended .
Futhermore, controls for seismic feed-forward to a hydraulic actuation system were implemented at LLO to combat the higher level of seismic noise at that site [34]. This system, to be installed on all chambers at both sites for aLIGO, uses signals from seismometers at the Michelson vertex, and at ends of each of the arms, to suppress the effect of low-frequency (below∼10 Hz) seismic motion on the instrument.
Figure 3.3: A basic illustration of a LIGO detector and its main components during S6 [6].
is extremely stable and that scattering is minimized. The beam path and optical components are enclosed in a vacuum (10−9-10−8torr for LIGO detectors) [62] so that the laser beam experiences minimal random phase
fluctuations due to residual gas fluctuations in the beampipe. Also, high vacuum ensures the mirrors do not get dusty; dust not only causes scatter but also causes the optics to heat up unevenly [64]. The mirrors, often referred to as test masses, are coated with dielectric and polished to have very low absorption (a few parts- per-million (ppm)) and scattering (60−70ppm)) [62]. Scattering not only leads to loss in laser power where it is needed, but to photons with the wrong frequency sneaking into the anti-symmetric port’s photodiode.
In order for Earthly motions to not influence the test masses and mimic GWs, seismic isolation systems are used. For Initial LIGO, a passive form of isolation for components inside the vacuum is achieved by a stack of masses and springs, providing vertical isolation at frequencies above a few Hz. This is essentially a cascade of harmonic oscillators [65], which are natural passive mechanical low-pass filters. In addition, the mirrors are suspended with thin wires as pendula, which further provide passive isolation in the horizontal (beam path) direction from seismic noise as well as thermal noise coming from the passive isolation stack [65].
There are also active isolation measures taken to isolate motions in the direction of the laser beam [66]. Because Livingston experiences more seismic disturbance than Hanford (logging and other anthropogenic activity prevented science data from being taken for most of the daytime hours prior to S4 [67] [68]), hydraulic external pre-isolators (HEPI) that were planned as an upgrade for Advanced LIGO were added to L1 between S3 and S4 to actively suppress vibrations [9]. In the middle of S6, the performance of HEPI was greatly improved by adding feed-forward control; this can be seen by contrasting the sporadicity of the green dots in Figure 3.4 from about 80 days to 156 days to the density of green dots from 156 days onward, indicating that the detector was able to stay in lock for longer [6]. The feed-forward system “damps low-frequency
36
noise by using signals from the onsite seismometers to control movement of the vacuum chambers for the end test masses” [66]. Hanford has been using a piezoelectric pre-isolation (PEPI) system since S2, but will be upgraded to HEPI for Advanced LIGO [66].
102 103
Frequency (Hz)
10−23 10−22 10−21 10−20 10−19Strain
amplitude
sp
ectral
densit
y
(1
/
√
Hz)
H1L1Figure 3: Representative strain amplitude sensitivity of the LIGO detectors during S6.
0 100 200 300 400
Time (days) since the start of S6
4 6 8 10 12 14 16 18 20 22Inspiral
detection
range
(Mp
c)
H1 L1Figure 4: The inspiral detection range of the LIGO detectors throughout S6 to an
optimally oriented and located binary neutron star merger. The rapid
improvements between epochs can be attributed to hardware and control changes implemented during commissioning periods.
Figure 3.4: The range (See Equation (2.25) to which the LIGO detectors are sensitive to a binary neutron star inspiral signal, shown to illustrate the changing sensitivity as various hardware or software upgrades are made throughout the course of the run [6].
A very important part of the detectors’ proper function areservos, also known as control loops. These stabilize the laser amplitude and frequency at the pre-stabilized laser table (PSL), damp the pendulum motion of the suspended optics, control the lengths of various cavities and the angular positions of the optics, and more. For example, the lengths of the two Fabry-Perot cavities in the arms and the power-recycling cavity are kept at an integer number of wavelengths so that new light that enters interferes constructively with the light already resonant in the cavities. There is also a servo that controls the Michelson phase so that the anti-symmetric port stays at the dark fringe [62]. The detector strain signal is derived from the sensing and actuation signals of the differential arm motion control loop — see Section 3.3 below.
Virgo detectors operate in a similar fashion; see Reference [63].