Gravitational waves: Generation and Detection

Transcription

1 Gravitational waves: Generation and Detection Joseph Bayley Supervisor: Prof. Stewart Boogert November 6, 2015 Abstract After the first indirect observation of gravitational waves from the Hulse-Taylor binary system in 1975, many groups have set out to try and directly detect them. These groups use a range of methods of detection, each of these detectors have advanced substantially since the initial work on the experimental detection of gravitational waves, carried out by Joseph Weber. One of the leading methods in the detection of gravitational waves is interferometry; the most recent upgrades to the laser interferometry gravitational observatory (LIGO) provides a high probability of detection. The interferometric experiments operate in the high frequency range where the coalescence of binary neutron stars generate gravitational waves, the most recent upgrades are expected to be able to detect up to 40 of these coalescences per year. Other experiments such as pulsar timing arrays focus on a lower frequency range, where they hope to detect sources of the gravitational wave background from supermassive black holes. Each of the experiments sensitivity is determined by its signal to noise ratio, therefore a lot of the recent developments in the search for gravitational waves have been in the reduction of noise in the detectors. This review focusses on the generation and detection on gravitational waves, particularly on the interferometry experiments methods of noise reduction and results. 1

2 Contents 1 Introduction Gravitational Waves and their properties Sources of Gravitational Waves Bursts Binary mergers Core collapse Chirp signals Continuous signals Stochastic background Cosmological gravitational wave background Astrophysical gravitational wave background Detectors Observations of the cosmic microwave background Pulsar Timing Arrays Resonant Mass Detectors Interferometers Shot noise Thermal noise Seismic noise Results Future searches for GW 29 5 Conclusion 31 2

3 1 Introduction Gravitational waves (GW) were first predicted by Einstein as a consequence of his theory of general relativity and were theorised to transfer energy in the form of gravitational radiation [1]. Since this prediction many groups have attempted to detect GW. Despite the fact that to date no signals have been detected, the recent upgrades to the laser interferometry gravitational observatory (LIGO), and advances in other detectors provide a promising outlook for their detection. Other than for the discovery itself, there are many motivations for finding GWs. Due to gravity being such a weak force, the GW are not absorbed by clouds of interstellar dust like electromagnetic radiation (EMR), this allows an unobstructed view of the universe. Other motivations for finding GW include the fact that they are emitted by some of the most energetic events in the universe. These events include the formation of black holes from compact binary coalescences and core collapse supernova (CCSN). GW from these sources would allow the study of black hole progenitors and their formation. As well as the observational benefits that GW offer, they also provide a way to test general relativity itself. After the prediction of GW from Einstein, it was not until 1975 that physical evidence of GW were found [2]. The first indirect observation of GW was from the famous Hulse-Taylor binary system, or pulsar B , which was the first binary pulsar system to be discovered [2]. This binary orbit was studied for 30 years and the radius of its orbit was found to decrease with time, this means the system must be losing energy and can be accounted for somewhere. The loss in energy from the orbit matched incredibly well with the prediction from general relativity, therefore the loss in energy is assumed to be from the emission of GW. Figure 1 from Ref. [2] shows how well the prediction matched with the observation. The result from the study of the Hulse-Taylor binary system gave a promising outlook for the existence of gravitational waves and led to the construction of many of the experiments that exist today. Although GW have not been directly detected, many groups and experiments are currently looking to do this. These experiments have to be incredibly sensitive; for example if two stellar mass black holes were close to coalescence at a distance of 1 Mpc, the LIGO experiment will have to detect a strain of m across its 4 km arms [3]. There are a number of different methods that are used to try to detect the displacement caused by a GW. The first experiment was a resonant mass bar designed by Joseph Weber [4], this uses a solid aluminium bar with a particular resonant frequency. If a passing GW is of a similar frequency then it will cause the bar to resonate, this resonance can then be measured. Although many of the bars have been decommissioned there are more recent resonant mass experiments such as MINIGrail [5] which use spherical masses for detection. However the resonant masses have a limited sensitivity, therefore a different type of experiment was developed using interferometry. The largest interferometric experiment is the laser interferometry gravitational observatory (LIGO) [6], this is expected to be the first to directly detect GW, especially after its most recent upgrade. Other more indirect methods include pulsar timing arrays (PTAs), which exploit the regularity of millisecond pulsars [7], and experiments that look at patterns within the cosmic microwave background (CMB). Future detectors that are planned include the laser interferometry space antenna (LISA) [8], this uses a similar technique to LIGO however operates over a distance of km [8] in space. The future detectors therefore hope to be able to reduce their sensitivity to a level that allows for the direct detection of a GW. 1.1 Gravitational Waves and their properties In Einstein s theory of general relativity, gravity is caused by distortions in spacetime, which are created by a mass or energy. The larger the mass of an object is, the more it will distort 3

4 Cumulative shift of periastron time /s General Relativity prediction Year Figure 1: This plot shows the shift in periastron time, which is the change in time of when the stars are closet together, plotted against the time it was observed. It shows how the orbit of pulsar B decayed over the course of 30 years and how well it matched the general relativity prediction [2]. 4

5 spacetime. Figure. 2 shows how spacetime is distorted by three different sized masses. Infor- Figure 2: This is an illustration of how three different masses distort spacetime. The smallest mass on the left to the largest on the right [9]. mation about the curvature of spacetime that these masses create is contained in a parameter called the metric tensor, g µν. The relationship between matter and the curvature of spacetime is contained within Einstein s field equation, this is written as R µν 1 2 Rg µν + Λg µν = 8πG c 4 T µν, (1) where R µν is the Ricci curvature tensor, R is the scalar curvature, g µν is the metric tensor, Λ is the cosmological constant, G is the gravitational constant, c is the speed of light and T µν is the stress-energy tensor. By expanding Einstein s equations around flat space time η µν, it is possible to find the wave equation for gravitational waves. For flat space-time η µν = , (2) where η µν is the Minkowski metric tensor in the coordinate system of (t, x, y, z). By perturbing the metric tensor g µν by h µν, it can be written as g µν = η µν + h µν. (3) The expansion of the equations of motion to linear order h µν is then called linearised theory [1]. The linearised equations of motion can be written more simply by defining h µν = h µν η µνh, (4) where h = η µν h µν [1]. By adopting the Lorentz gauge in which ν hµν = 0, (5) the linearisation of Einstein s equation can be written as a set of wave equations h µν = 16πG c 4 T µν, (6) where = (1/c 2 ) 2 t + 2 [1]. This shows that the gravitational radiation takes energy away from the source in the form of 5

6 a wave, distorting space time as it travels. Equation 6 shows the result of generating a GW in linearised theory, however to see how a GW interacts with test masses, its behaviour outside of the source needs to be found. In Eq. 6, the stress-energy tensor T µν is equal to zero outside of the source[1], therefore Eq. 6 becomes h µν = 2 hµν 1 c 2 h µν = 0. (7) Any wave in three dimensional cartesian coordinates satisfies the equation ( 2 ) u x u y u z 2 2 u t 2 = 2 u 1 2 u v 2 = u = 0, (8) t2 where v is the velocity of the wave and u(t, x, y, z) is the wavefunction [10]. By comparing this to the gravitational wave equation Eq. 7, it is clear that gravitational waves propagate at the speed of light c. To solve Eq. 7 another gauge is adopted called the transverse-traceless (TT) gauge. In this gauge only the spatial components are non zero as h µ0 = 0, and they are transverse to the direction of propagation [1]. Additionally the spatial components are trace free, h i i = 0, and divergence free, i h ij = 0. These conditions lead to h µν = h µν = h TT µν. (9) where h TT µν is the transverse-traceless gauge metric. This then leads to a solution to Eq. 7 for waves travelling in the z direction. The solution is h µν = 0 h xx h xy 0 0 h yx h yy 0 ei(kz ωt), (10) where k is the wavenumber and ω = kc. Due to the symmetric nature of h µν, there are two possible polarisations of the wave, either a plus h +, or cross h polarisation [11]. These are and h + = h xx = h yy, (11) h = h xy = h yx. (12) The amplitude of a GW h, can usually be interpreted as the physical strain in space and can be written as a combination of the plus as cross polarisations of the GW, where h = A + h + + A h ; (13) A + and A are the amplitudes of the plus and cross polarisations of the GW [12]. GW affect matter by a tidal force that stretches and squeezes spacetime. An illustration of a GW acting on a ring of test masses can be seen in Fig. 3, where the GW is travelling along the z axis. When acting on test masses the amplitude h, from Eq. 13, can be written as h = 2 δl l, (14) where δl is the change in separation of two masses with a separation of l [12]. Figure 3 shows a GW with a large strain amplitude, h > 0.1, however the strains that are expected to be detected are closer to the order of h =

7 y h + x Time y hx x Figure 3: This illustration shows how gravitational waves affect matter by causing a strain tidally. The GW is moving from the left to the right in time and is propagating in the z direction. It distorts space-time in two different ways depending if it is plus h + or cross h polarised. Sources in a circular orbit, such as inspiralling neutron stars, will have a GW with a constant amplitude. However, their plane of polarisation changes twice every orbit, therefore their strain is also observed as shown in Fig. 3. If there is any ellipticity in the orbit then the amplitude of the wave will also vary with time, Einstein s quadrupole formula describes this varying amplitude. The quadrupole formula states that the wave amplitude h µν is proportional to the second time derivative of the quadrupole moment, h µν = 2 r G TT Q c4 µν (t r ), (15) c where G is the gravitational constant, c is the speed of light, Q TT µν is the quadrupole moment and t r c is the retarded time [1]. The retarded time is the time at which the field began to propagate from a point to an observer. Equation. 15 shows how GW follow an inverse square law similar to electromagnetic radiation (EMR), this means that the energy density of a GW falls as 1/r 2 and its amplitude reduces as 1/r. 2 Sources of Gravitational Waves There are a range of sources of GW, due to gravity being such an extremely weak force any detectable GW must originate from high mass or energy systems. The sources can be split into roughly four types; two short lived signals, which are bursts and chirps, and two long lived signals, which are continuous signals and the stochastic background. The shortest signals are bursts, these come from systems such as supernova and compact binary mergers. Chirps are slightly longer signals which originate from the inspiral stage compact binary coalescences (CBC); CBCs are a mixture of neutron stars (NS) and black holes (BH) in binary orbits. Continuous signals are constant signals which can come from certain types of rapidly rotating neutron stars (pulsar). Finally stochastic GWs are the background of gravitational waves 7

8 (GWB), these can come from a range of sources, however are thought to be primarily from supermassive BH mergers. Each of these systems operate in different frequency ranges which suit different detectors, these are outlined in Table 1 below. Table 1: This table shows the four frequency bands of GW, the sources that fall into each band and the detectors that are designed to work in each band. M is the mass of the sun [13]. Band Typical sources Detectors Extremely low frequency Hz Very low frequency 1 nhz - 1 mhz Low frequency 1 mhz - 1 Hz High frequency 1 Hz - 10 khz Primordial stochastic background Supermassive black hole binaries (M 10 9 M ); Stochastic background (supermassive black hole binaries) Supermassive black hole binaries(m 10 3 M 10 9 M ); Extreme mass ratio inspirals; Dwarf/ white dwarf binaries; Stochastic background (dwarf binaries, cosmic strings) Neutron star/ black hole binaries(m M ); Supernovae; Pulsars; X-ray binaries; Stochastic background (cosmic strings, binary mergers) Gravitational wave signatures in the CMB Pulsar timing arrays Space based interferometers Ground based interferometers; Resonant mass detectors 2.1 Bursts Burst signals are very short signals that are thought to originate from the same sources as gamma ray bursts (GRBs). The GRBs can be split into two groups classified by length and spectral hardness; short hard GRB last for 2 s, and long soft GRB last for 2 s [14]. Short hard GRB are thought to come from the merging of binary star systems containing a mixture of neutron stars and black holes and long soft GRBs are though to come from the collapse of massive stars with fast rotating cores. These signals are thought to be dominant in the higher GW frequency range, > 500 Hz [15]. The following section will use the information from Ref. [14], Ref. [15] and Ref. [16] Binary mergers Short hard GRB are thought to come from the merger stage of compact binary coalescences (CBC), this stage is also thought to be an emitter of GW. CBC can be split into three stages, the inspiral stage which will be covered in more detail in Sec. 2.2, the merger stage which is when the two compact objects collide and join together, and the ring down stage which is caused by deformations in the formed BH [16]. The merging of two compact objects leads to a BH with an accretion disk. The accretion disk forms as a significant fraction of the stellar material retains enough angular momentum so that it does not immediately cross the BH horizon. If dynamical instabilities develop in either the rotating core or disk, then the core or disk could potentially radiate GW. The instability or deformation in the core or disk can simply be considered as a 8

9 bar. The strain, h, caused by this bar can be written as 32 G mr 2 ω 2 h = 45 c 4, (16) d where G is the gravitational constant, m is the mass of the bar which has a length l = 2r, ω is the angular frequency and d is the distance of the source from the detector [16]. After the merging of the compact objects, the initially created black hole is deformed. A deformed black hole should emit radiation in the form of a GW until it settles to a Kerr geometry, this is called the ring down stage of the binary coalescence [16] Core collapse Long soft GRBs are thought to come from the core collapse supernova (CCSN) of rapidly rotating massive stars of mass between M ; rotational instabilities in the central engine that drives the GRB are thought to be a source of GWs. The high rotation rate of the core is required to form a disk that is around the central black hole, this is what powers the GRB jet. This high rotation rate may also cause the development of bar or fragmentation instabilities in the collapsing core or disk [16]. The asymmetrically infalling matter from the disk to the BH perturbs the BHs geometry, this causes a ring down phase of the GW emission. The emission of GW from collapsing massive stars can then be estimated in a similar way to the merger and ring down stages of binary coalescences. For more information on GW from core collapse supernova see Ref. [14] and Ref. [16]. 2.2 Chirp signals Chirp signals are short signals of which the frequency and amplitude increase with time. Radiation is typically emitted for 17 minutes at 10 Hz; for the last 2 s radiation is emitted at 100 Hz, and for the last few ms radiation is emitted at 1 khz [1]. The source of these chirp signals are the inspiral stage of CBCs mentioned in Sec There are three types of binary coalescing systems which will be detectable, these are NS/NS, NS/BH and BH/BH binaries [17]. BH/BH binaries have the strongest signal therefore can be detected to the largest distance, however they are found to be the least likely to be detected as their event rate is 1/250 that of NS/NS systems, this is summarised in Table 2 [19]. The NS/NS and NS/BH (hereafter NS-NS/BH) systems can form in two different ways, as primordial or dynamical binaries. Primordial systems must initially have two stars large enough to undergo collapse to a NS or BH, however when the star explodes it must not destroy its companion star, or shed too much mass so that it is no longer in a bound orbit [17]. Dynamical binaries form slightly differently, these will happen within the cores of globular clusters. These systems form when a compact object (NS or BH) captures a non-degenerate star, this binary system then interacts with another compact object, ejecting the non-degenerate star and leaving a compact binary system [17]. The amplitude of a circularly polarised wave, h 0 (t), from a binary system can be found from Eq. 15, the mathematics is covered in more detail in Ref. [1] and Ref. [18]. The amplitude can be found to be h 0 (t) = 1 [ 5G 5 M 5 ] r 2c 11, (17) where r is the distance from the source to the detector, G is the gravitational constant, M is the mass of each component of the binary, which is the same in this case and τ = t coal t, where t is the observer time and t coal is the coalescence time [1]. Equation 17 shows how the amplitude τ 1 4 9

10 of the GW will increase when the mass of the system increases, and also as the time from the coalescence decreases. Also this equation demonstrates the inverse square law of gravitational radiation, showing that the amplitude of the wave falls of as 1/r. There are a few different models which aim to predict the coalescence rate of compact binaries, in the simplest models they are thought to be proportional to the rate of star birth within the galaxy [19]. This can be found by observing the amount of blue light coming from the galaxy, however this method does not include the currently existing compact binaries. Another more accurate way to find the rate is by looking at gamma ray bursts. In Sec. 2.1 the emission of short hard gamma ray bursts from merging CBC was discussed, this allows a way to measure the coalescence rate of CBC. By assuming that these short hard bursts come from mainly NS- BH/NS, an estimate can be made on the event rate of CBCs. These even rates are shown in Table 2 below for all CBCs, they are measured by how many coalescence events happen per Milky Way like galaxy per Myr [19]. There are currently many uncertainties on the number or extragalactic binary coalescences, therefore in Table 2, low, realistic and high estimates have been made for the event rate. These binary systems operate across a range of frequencies, from Table 2: Table showing the predicted event rates for all compact binaries within a Milky Way like galaxy. R low is the low estimate of the event rates, R re is the realistic estimate and R high is the high estimate.[19] Type R low /Myr R re /Myr R high /Myr NS/NS NS/BH BH/BH nhz 10 khz depending on which compact objects make up the binary; the larger the mass of the system the lower the frequency of GW it will emit. Table 1 shows the frequencies that each of the binary systems operate in. Chirp gravitational wave signals from CBC are likely to be most easily detected by the LIGO antenna, this is because these systems emit GWs in a frequency range where the detectors sensitivity operates, which is Hz [20]. Other types of events that will emit chirp signals involve extreme mass ratio inspirals, this is when a smaller body inspirals into a much heavier body. The mass of the smaller body is usually a compact object with a mass in the range m = M, and the larger body has a mass in the range M = M [21]. This give a mass ratio of µ = m/m Extreme mass ratio inspirals are long lasting signals that emit in a frequency range between Hz, this is the operating range of space based interferometers such as LISA [21]. 2.3 Continuous signals Continuous signals are constant signals that last for many years, they are thought to originate from certain types of rapidly rotating neutron stars (pulsar). GWs cannot be produced by a pulsar if it is spherically symmetric, therefore gravitational waves are only emitted if there is an asymmetry between the pulsar and its rotation axis. This can be due to either a strain in the solid parts of the star or magnetic stresses, which is where the magnetic field of the pulsar is not aligned with the rotation axis [22]. The asymmetry can be characterised by the ellipticity of the star. The ellipticity ɛ can be defined as the relation between two perpendicular moments of inertia, I 1,2 and the principle moment of inertia I 3 [1], this is written as ɛ = I 1 I 2 I 3, (18) where I 1,2,3 are the moments of inertia for the three axis if the ellipsoid. This can be simplified as approximately the relation between the radius of the star and the size of its deformation, 10

11 this is written as ɛ r r, (19) where r is the radius of the star and r is the size of the deformation [23]. These pulsars can be located by observing them in the electromagnetic spectrum, specifically in radio, gamma and X-rays. The pulsars that are emitting GW can then be observed to have a spin down, where its rotational speed decreases, therefore it is losing energy. This loss in energy is thought to be due to the emission of gravitational waves. From observations of pulsars spin down, limits have been placed on their ellipticity. The equatorial distortions have a maximum limit at ɛ = 10 5 [24], which is the largest amount of stress that a crust of the pulsar could support. This allows a correlation between the gravitational wave frequency and the rotational frequency of the pulsar to be determined; the gravitational frequency is thought to be twice the rotation frequency [1]. Therefore a pulsar that is non-axisymmetric emits a GW at a frequency of twice its rotation frequency. The frequency space that pulsars operate in is the high frequency range between 1 10 khz, as Table 1 shows above. This means that ground based interferometers are best suited to detect these sources. 2.4 Stochastic background The stochastic background is a background of gravitational waves within the universe which comes from a range of sources. The gravitational wave background (GWB) can be split into two types; the cosmological GWB, which involves processes from times near the beginning of the universe, and the astrophysical GWB, which comes from astrophysical sources such as compact binary coalescences which are too distant to observe individually Cosmological gravitational wave background The cosmological GWB is analogous to the cosmic microwave background (CMB), but for gravitational radiation [25]. The CMB originated from the time of last scattering which was 380, 000 years after the big bang. The cosmological GWB, however, can probe to much earlier times, near the Planck time of s. This is due to the fact that gravity has a much weaker coupling, therefore decoupled with matter at a much earlier times [25]. Most cosmological theories predict a stochastic background of GW, however the strengths vary substantially. A number of the models are shown in Fig. 4, such as the inflationary model and GW from cosmic strings. The strength of the gravitational wave background can be parametrised in terms of its energy density parameter, Ω gw (f). This can be written as Ω gw (f) = 1 ρ c dρ gw (f) d ln(f), (20) where ρ gw is the spectral energy density of GW, f is the frequency and ρ c is the critical density where ρ c = 3H 2 0 c2 /8πG [27]. Inflation is the mechanism that solves many of the problems which came with the discovery of the CMB, including the horizon, monopole and flatness problems. As well as solving these problems inflation explains primordial density perturbations in the universe as quantum fluctuations in the scalar field driving the exponential expansion [28]. A background of GWs is thought to have been generated from the quantisation of the gravitational field, coupled to the exponential expansion in inflation, for more information see Ref. [28]. These GW are analogous to the primordial density perturbations, however are tensor perturbations rather than scalar ones. If the scale of inflation is large enough then the GW could produce measurable effects within the CMB [28]. 11

12 Figure 4: This plot shows the normalised GWB density parameter Ω GW plotted against the GW frequency. The contours are shown for various models of the GWB which are labelled. Also shown is the initial LIGO and VIRGO limits as well as the predicted limit for advanced detectors [26]. The BBH and BNS on the plot are the stochastic background caused by binary black holes and binary neutron stars respectively Astrophysical gravitational wave background Astrophysical GW are thought to come from many different sources that are too distant to observe individually, this is because the signals become indistinguishable over the much larger distances. The sources of the astrophysical background include the ones mentioned in Sec. 2, however a large contributor is thought to be supermassive black hole coalescences. This type of stochastic background is investigated by the pulsar timing arrays and will be investigated further in Sec Detectors There are a number of methods that have been developed to try to detect gravitational waves directly. These can be split into four main types, CMB experiments, pulsar timing arrays (PTAs), resonant mass detectors and interferometers. Each of these operate in one of the four main bands of the GW frequency spectrum, either the high, low, very low or ultra-low frequencies. Table 1 above shows which sources fall into each category and which detectors are best suited for their detection. Current detectors do not operate in the low frequency range, therefore the future experiments that operate in this band are covered in Sec. 4, where the 12

13 future spaced based interferometers are investigated. Before each of the detectors methods and results are summarised it is worth mentioning the measured quantities which are equivalent for all the detectors. The output of any GW detector is characterised by a time series s(t), which is comprised of the GW signal h(t), and a noise signal n(t) [3]. This time series can be written as s(t) = F + (t, θ, φ, ψ)h + (t) + F (t, θ, φ, ψ)h (t) + n(t), (21) where F + (t, θ, φ, ψ) and F (t, θ, φ, ψ) are the antenna pattern functions that describe the sensitivity from the cross and plus polarisations from different directions, h + (t) and h (t) are the plus and cross polarisations of h(t) and n(t) is the noise signal in the detector [3]. The time series, s(t), is often represented in the frequency domain in terms of the power spectral density S h (f) = s (t) s(t), where s(t) is the Fourier transform of s(t). The time series is then characterised by a strain amplitude spectrum h(f), where h(f) = S h (f). (22) The noise amplitude spectrum is equivalently given by ñ(f) = S n (f), where S n (f) = ñ (t)ñ(t), and these both have dimensions of 1/ Hz. Another quantity used to measure the sensitivity is the characteristic strain, h c (f), which is a dimensionless quantity written as h c (f) = f h(f) = fs h (f), (23) where f is the frequency [29]. This also has an equivalent characteristic strain for the noise. These quantities are then plotted against the frequency to show the sensitivity of the detector across a range of frequencies. The following sections will cover the methods used by each experiment to detect GW as well as some of the limits that have been placed on this strain amplitude. 3.1 Observations of the cosmic microwave background The cosmic microwave background (CMB) can show traces of GW from different sources which are outlined in Sec The experiments that focus on looking for these patterns in the CMB operate in the ultra low frequency band, and comprise mainly of radio telescopes. Some of the experiments currently in operation are the background imaging of cosmic extragalactic polarisation (BICEP) [30], and the Keck array [30]. The aim of the experiments are to map the polarisations of the CMB, specifically the type called B-mode polarisations, which can be a signature for primordial GW. Perturbations within the early universe caused the CMB to be polarised, this happened when the photons scattered from free electrons. When a photon is scattered from an electron the photon will be polarised perpendicular to the incident direction [31]. Therefore for polarisation to be seen, the photons must have a polarisation separated by 90 degrees, this is called a quadrupole anisotropy. Within the CMB there can be two kinds of polarisation, E-mode and B-mode [32]. These polarisations can be induced by a number of sources, from intergalactic magnetic fields, CMB lensing, scalar perturbations of the second order, rotating dust but most importantly primordial GW [31]. The density perturbations generate only E-mode polarisations however GW have a component of E-mode and B-mode. This can be observed by looking at the CMB and observing the polarisations. The BICEP 2 experiment (upgrade from BICEP) was the first to claim direct observations of the GWB, however these claims were refuted due to an incorrect map of cosmic dust. Once the updated version of this map from the Planck satellite was used, the the polarisations could not be distinguished from the patterns that the cosmic dust leaves [32]. However the BICEP team still remain hopeful that they will find the GW pattern within the CMB. 13

14 3.2 Pulsar Timing Arrays As well as certain types of pulsar emitting their own source of GW, other types can be used to detect them. Pulsar timing arrays (PTAs) are collections of millisecond pulsars (MSPs) that are evenly distributed across the sky, and are monitored by an array of single dish radio telescopes [33]. There are three main PTA groups that collaborate to form the international pulsar timing array (IPTA), these are the North American NanoHertz Observatory (NANOGrav), the European pulsar timing array (EPTA) and the Parkes pulsar timing array (PPTA) located in Australia [33]. MSPs are neutron stars that have low spin down rates and therefore rotational stability. This means that they have regular pulse trains, i.e. their beamed radio emission is very regular. What PTAs look for is an irregularity within the received signal from a MSP, this irregularity may have been caused by a GW. As a GW passes between the detector and MSP the space-time is distorted, this changes the apparent distance to the pulsar and affects the received frequency of rotation. The change in the information from the pulsar is known as its time of arrival (TOA). The radio groups can then observe this frequency change and analyse it to find information about the GW [34]. One of the sources that the PTA groups have focussed on is the GWB from supermassive black holes. They have not detected any GW however have placed limits of the amplitudes of the GWB. The data is initially collected from the network of radio telescopes outlined above, the data is then analysed by following a pipeline, where a series of processes is applied to the data to improve the signal to noise ratio (SNR), for more detail on the analysis see Ref. [34]. The measurements of the GWB are characterised by either the GW energy density parameter Ω GW, mentioned in Eq. 20, or the characteristic strain h c which is defined in [34] as ( ) f α h c = A yr 1, (24) where A is the amplitude of the GW, f is the frequency of the gravitational wave and α is the spectral index of the GWB. The results for the upper limits of the GWB are shown in Fig 5, the two contours show the 1σ and 2σ levels which are the 95% and 65% confidence level contours respectively. For a spectral index of α = 2/3 which corresponds to a background from supermassive black hole binaries, the upper limit was found as h c (1yr) with a 95% confidence level [34]. The current PTAs aim to reach sensitivities of h c = in the future which is over five times as sensitive as the above sensitivity [34]. 3.3 Resonant Mass Detectors There are a number of resonant mass detectors located around the world which use solid, nonfree masses as detectors, they look for patterns within the phonons of the solid mass. This section will use information from the Ref. [4] and Ref. [11]. Resonant mass (RM) detectors were initially proposed by Joseph Weber as a way to detect gravitational waves. His idea was to use the fact that the atoms will try to follow the geodesic that the GW creates. The electrostatic forces that oppose the atoms movement create a measurable force within the mass, which causes an oscillation. A large part of the energy in this oscillation is coupled to the 1st longitudinal mode of the bar, this means that the oscillation is amplified [4]. Electromagnetic transducers are placed at the ends of the bar and have magnetic resonance at same frequency as the bar, these will pick up the oscillations induced in the bar. The transducers amplitude will increase until almost all of the energy from the bar has been transferred to the transducer. The transducer then turns it into an electrical signal, which is then pre-amplified by a low noise cryogenic amp. This signal is then recorded and analysed. The main problem encountered with resonant mass detectors is the size of the signal to noise ratio. For RM detectors, thermal noise is the 14

15 Joint GWB (α,h c ) distribution -13 GWB Amplitude log( h c (1yr -1 ) ) σ 2 σ van Haasteren et al. (2011) Expected α for GWB from SMBHBs GWB normalised energy density log( h 0 ΩGW (1yr -1 ) ) GWB Index α -11 Figure 5: This plot shows the log scales of both the characteristic strain h c (yr 1 ) and the normalised GW energy density parameter Ω GW (yr 1 ) potted against the GW spectral index. The contours show the 1σ (95% confidence) and 2σ (65% confidence) limits that have been places on the GWB by the EPTA joint analysis by Haasteren et al. in [34]. The vertical line on the plot shows α = 2/3 which is the spectral index for supermassive black hole binaries. 15

16 dominating source of noise. Weber decided to choose a material with a high quality factor, this allowed the signal to be more easily distinguished from the background. The quality factor Q is defined by Q = ω 0m, (25) b where ω 0 = 2πf 0, f 0 is the resonant frequency of the bar, m is the mass of each test mass and b is the dissipation factor [4]. Webers first RM detector was a cylindrical bar made with 1.2 tonnes of aluminium, it was 1.5m long and 61cm diameter. This was then suspended in a vacuum on acoustic filters to try to dampen any seismic backgrounds [4]. Once Weber had an array of detectors (i.e. > 1), he claimed to see coincidence events between them. However subsequent detectors that were more sensitive could not replicate any of his results, therefore they were assumed to be incorrect. Nevertheless his findings did spark an interest in the experimental discovery for GW and led the way for many more GW antenna. The next generation of RM detectors, including the groups at Stanford and Louisiana state university (LSU), started to develop cryogenic resonant mass detectors (CRM) [4]. CRM detectors are cooled to temperatures around 100 mk or lower with liquid helium, and have many advantages to the previous room temperature devices [11]. The main advantage being that the thermal noise is reduced as well as an increase in the quality factor of the material. This increases the sensitivity of the device, therefore increases the distance it can observe to. The international gravitational event collaboration (IGEC) have two main sets of data called IGEC1 and IGEC2, they use a network of five and four detectors respectively. The four in use for IGEC2 are ALLEGRO, EXPLORER, NAUTILUS and AURIGA [35]. The strain sensitivity of the four detectors are compared in Fig. 6 below. Figure 6 shows how the RM detectors are Figure 6: This plot shows the strain amplitude spectrum of the four detectors for IGEC2 as marked in the legend [35]. 16

17 a narrowband search of the sky, this is because their sensitivity has a bandwidth of 100 Hz. The IGEC can then only search for specific sources within a certain bandwidth, mainly binary coalescences and supernova. The ICEG2 collaboration combined the four detectors in Fig. 6, this allowed checks to be made of the number of coincidence events between the operating detectors, however no significant events have been observed yet. The latest resonant mass detectors such as MiniGRAIL [36] and Mario Schenberg [5] are spherical masses, which has the added benefit of having the same sensitivity in all directions, plus they will be more sensitive than its bar counterparts. These two detectors are 1.3 ton spheres made of CuAl alloy (6%) [5]. The detectors weigh 1400 kg and 1159 kg respectively with an operation temperature of 5 mk and resonant frequencies at 3 khz. Figure 7 shows the strain sensitivity of the MiniGRAIL experiment. The bandwidth of this detector is larger than the ICEG counterparts however it does not currently detect to a higher sensitivity due to only one transducer readout. Figure 7, however, shows what the current sensitivity is at 50 mk and the future MINIgrail II experiments proposed sensitivity. Figure 7: This plot shows the measured strain sensitivity or strain amplitude spectrum of the MiniGRAIL experiment alongside the predicted strain sensitivities of future detectors. The second from bottom dotted line (MiniGRAIL II) shows the sensitivity that is achievable with current technology, and the lowest dotted line shows the sensitivity of a quantum limited detector [37]. Resonant mass detectors operate in a similar frequency band to interferometers, however, despite being cheaper to build, operate at a lower sensitivity with a smaller bandwidth. For this reason most efforts are going into upgrading interferometry experiments, as they are more likely to achieve detection. 17

18 3.4 Interferometers Interferometers are the most promising experiments under-way to directly detect GW, therefore will be investigated in more detail than other GW detectors. There are a number of GW detectors which focus on using interferometry to directly detect gravitational waves. The network of GW interferometers include the laser interferometry gravitational observatory (LIGO) in the USA, VIRGO in Italy, GEO 600 in Germany and TAMA 300 in Japan [18]. All these experiments collaborate with the LIGO scientific collaboration. All of these are based around a similar laboratory experiment, the Michelson interferometer, however they have many more sophisticated components and operate on a much larger scale ( 4 km). The Michelson interferometer works by taking a laser beam and splitting the beam down two perpendicular arms. This light is then reflected from a mirror at the end of the arm back to where the beam split and the two beams recombine; a detector can then read any interference between the two beams. Figure 8 shows the setup of a basic interferometer. The phase of the light between each beam may Screen or detector Laser Beam Splitter L2 Mirror 2 L1 Mirror 1 Figure 8: This image shows the basic setup of a Michelson interferometer. A laser source is aimed at a beam splitter which sends a beam down each arm. The beams are then reflected back and recombined for the detector to read any interference. change due to a difference in length of the arms or some other effect, this can then be measured as a phase shift φ. This phase shift affects whether the light constructively or destructively 18

19 interferes. For an area of constructive interference and for an area of destructive interference Φ = 2πm, (26) Φ = (2m + 1)π, (27) where m = ±1, ±2, ±3,... [38]. The total optical path difference (OPD) in the interferometer is then OPD = (2 L1 2 L2) = 2 L, where L1 and L2 are the length of the respective arms. The phase difference Φ over the two arms can then be written as Φ = 2π λ 2 L, (28) where λ is the wavelength of the light and L is the difference in length of the arms [38]. This interference pattern can then be observed at the output of the Michelson interferometer. The design of a GW interferometer follows the same principle as the Michelson interferometer mentioned above, where the lengths of the arms are thought to be distorted by a passing GW. A GW interferometer however does not look at the whole interference pattern but focusses on a dark fringe. Also a gravitational wave interferometer has many different components. The LIGO antenna has undergone three major upgrades in its history, starting at initial LIGO, then improving its sensitivity to enhanced LIGO and most recently has begun operation with advanced LIGO. Throughout these upgrades LIGO has housed 3 interferometers, 2 of which have 4 km arms and one has 2 km arms [39]. These are located in Hanford, Washington and Livingston, Louisiana, with a separation in distance of 3002 km [40]. As the two locations are isolated it allows a check for coincidence events, improving the accuracy of a GW detection. As well as this, the two isolated locations means that the antenna has directionality, therefore the location of the source can be found. Compared to the basic design the Michelson interferometer, the GW interferometers have additional components which allow it to measure to a much higher sensitivity. A diagram of the most recent upgrades for the S6 run can be seen in Fig. 9. Many of the components shown in Fig. 9 are designed to reduce the amount of noise within the system, this is because the amount of noise within a detector determines its sensitivity. By increasing the sensitivity of the detector it is possible for it to see to a greater distance. This is because the gravitational radiation follows the inverse square law, therefore weaker signals from more distant sources would be detectable. Gravitational waves are measured by a strain over the interferometer arms, the biggest factor that affects how accurately the antenna can measure this strain, is the noise strain amplitude that clouds the GW signal. There are a range of sources of noise, Fig. 10 shows some of the noise sources and how they affect different frequency ranges. Figure 10 shows that the dominating noise sources at the LIGO, Hanford observatory is from seismic noise at the lower frequencies, thermal noise at the intermediate frequencies and the shot noise at higher frequencies. Below is a summary of each of these noise sources and the systems that are in place to reduce them Shot noise Shot noise is due to the fact that photons come quantised wavepackets, the uncertainty arises from the statistical fluctuations in the number of photons [1]. Shot noise is dominant at high frequencies > 100 Hz, as Fig. 10 shows. The photons in the laser follow Poisson statistics, 19

20 ERM ETM Input Mode Cleaner 4 km Laser 125 W T= 3% PRM PR2 5.2 kw ITM BS CP ITM 750 kw ETM PR3 SR2 T=1.4% ERM SRM SR3 PD GW readout Output Mode Cleaner Figure 9: The layout and components of the Advanced LIGO detector, ETM: End test mass, ERM: End reaction mass, ITM: Input test mass, CP: compensation plate, BS: Beam splitter, PRM: Power recycling mirror, SRM: signal recycling miror, PD: photodetector. The power of the laser in each section is also labelled and can been seen to increase through each section [41]. therefore there is an error in the number of incident photons σ N, and an error in the phase of the photons σ φ. The error in the number of incident photons is σ N = N γ, (29) where N γ is the number of incident photons [46]. Heisenberg s uncertainty principle states that σ N σ φ = 1, (30) where σ φ is the error in the phase. Therefore by combining Eq. 29 and 30 one can find the uncertainty in the phase is σ φ = 1 Nγ. (31) The power P γ of a laser is related to the number of photons by P γ = N γ E γ, (32) where E γ is the energy of a wavepacket [46]. This means that the error in the phase, i.e the shot noise, is σ φ 1 Pγ, (33) therefore by increasing the power of the laser the shot noise is reduced. The laser that is used is a neodymium-doped yttrium aluminium garnet (Nd:YAG) laser, with wavelength of 1064nm 20

21 Figure 10: This plot shows the primary noise contributors to the signal at LIGO (H1). The black line at the top is the measured strain for the detector, the cyan curve is the root square sum of all the contributors of noise. Each of the individual noise components are marked on the plot. The peaks in the measured strain are well identified and have been marked as p - power line harmonic, s - suspension wire vibrational mode and m - mirror test mass vibrational mode [44]. 21

22 and a power of up to 180W [41]. It is then put through an input mode cleaner, this stabilises the beam in position and mode content as well as providing a high quality laser frequency reference [41]. There are a few additional components that are installed in the interferometer to increase the power and reduce shot noise, these are Fabry-Perot arms, power recycling mirrors and signal recycling mirrors. Each of the arms of the interferometer are Fabry-Peirot cavities and are characterised by a parameter called finesse, LIGO operates at a finesse of 450 [41]. A Fabry-Perot cavity consists of two highly reflecting mirrors, between these light is trapped and reflected multiple times. The finesse of a Fabry-Perot cavity is the ratio of the free spectral range and the full width half maximum of its resonant peaks. The finesse can then be defined as F = λ δλ, (34) where F is the finesse, λ is the free spectral range, which is the frequency spacing of its resonator modes [42] and δλ is the full width half maximum of the resonance [42]. A Fabry- Perot cavity with a high and low finesse is shown in Fig. 11. This high finesse of the cavity allows for a higher accuracy and sensitivity in the measurement F =0.5 F =2 F =10 Transmission, T Wavelength, λ Figure 11: This image shows the transmission of the mirrors in a Fabry-Perot cavity, plotted against the wavelength for different finesse values [42]. This plot also shows the free spectral range λ and the full width half maximum of the resonances δλ. The power recycling mirror is located between the laser and the Fabry-Perot Michelson Interferometer (FPMI) as shown in Fig. 9. A power recycling mirror is a partially reflective mirror that recycles waste light back into the interferometer, this increases the effective power of the laser [47]. By increasing the power of the laser the shot noise is reduced as Eq. 33 shows. The shot noise is then reduced by a factor of G pr, where G pr is the gain of the power recycling mirror. The power recycling gain is defined as ( ) t 2 RM G pr =, (35) 1 r RM r FPMI 22

23 where r RM is the amplitude reflectivity of the power recycling mirror, r FPMI is the amplitude reflectivity of the FPMI and t RM is the time spent in the power recycling cavity [47]. A signal recycling mirror is located at the dark port of the interferometer and forms a signal tuned cavity [48]. The signal recycling mirror can be tuned for different types of operation, either signal recycling or broadband. For broadband operation the cavity is tuned to effectively reduce the finesse of the arm cavities at the signal side bands, this increases the bandwidth. For signal recycling the cavity is tuned to a specific frequency of the source that is being searched for, this allows a narrow band search with a higher sensitivity [48] Thermal noise Thermal noise induces vibrations in both the suspensions of the test masses and the test masses themselves, this noise is dominant in the intermediate frequencies between Hz [43]. For a GW to be detected the test masses need to be free masses, as they are connected through the earth they are not completely free, however by suspending the masses it means that they are free to move in the plane of the interferometer, therefore can be treated as free masses. Within the suspensions, thermal noise can affect it in three different ways: pendulum thermal fluctuations, which induce swinging in the suspensions, vertical thermal fluctuations, which cause vertical movement in the suspensions, and violin modes, which are fluctuations in the normal modes of the suspensions [1]. The suspension thermal noise has been reduced substantially due to the input of silica fibres as opposed to the steel wires previously used to suspend the test masses. The test mass thermal noise, similarly, can be split into three categories: Brownian motion of the mirrors, thermo-elastic fluctuations and thermo-refractive fluctuations [1]. Brownian motion of the mirrors is due to the fact that the mirrors have a temperature T, the atoms in the mirror then have some kinetic energy causing movement within the mirror. Thermo-elastic fluctuations are due to the fact that in a finite volume, V, the temperature fluctuates with a variance (δt ) 2 = k BT 2 ρc V V, (36) where C V is the specific heat, k B is Boltzmann s constant, T is the temperature and ρ is the density of the material [1]. This generates expansion in the mirror and its coatings, causing thermal noise. Finally, thermo-refractive fluctuations are due to the fact that the mirror coatings refractive index is temperature dependant, therefore fluctuations in temperature change the refraction index of the mirrors, causing noise [1]. The thermo-refractive fluctuations can be reduced as the noise scales inversely with the beam size. Therefore the size of the beam is made as large as practically possible so that the thermal noise is averaged over as much of the mirrors surface as possible [45]. For advanced LIGO the mirror has been upgraded to an ultra-high purity fused silica mirror with dimensions of 34 cm diameter and 20 cm depth, from the 25 cm diameter and 10 cm thick fused silica mirrors of initial LIGO [45]. The beam size has increased from 3.7 cm and 4.3 cm (for the input and end mirrors respectively) to 6 cm for both mirrors [43], this means that the thermo-refractive fluctuations are reduced. The mass of the mirror has also increased from 11 kg to 40 kg, which reduces the amount of radiation pressure noise on the mirror [45] Seismic noise Seismic noise is the noise generated by vibrations in the earths surface, and begins to dominate at lower frequencies < 100 Hz [49]. This can be seen in Fig 10, where the seismic noise is shown by the brown line at lower frequencies. The two main sources of seismic noise are microseismic 23

24 noise and anthropogenic noise. Microseismic noise is dominant between Hz, and is due to vibrations in the earth s surface caused by waves of the ocean. Anthropogenic noise is dominant between 1 10 Hz, this is generated primarily by human activity on the ground [50]. These vibrations can prevent the length systems from holding the optics accurately enough, this increases the noise signal and reduces the probability of detecting a GW. Therefore this needs to be minimised for successful GW detection, for the Advanced LIGO system the masses are aimed to be held to a value of less than m [51]. There are two main ways of dealing with seismic noise, passive and active. Passive isolation involves using damping materials which operate without any input, and active systems use actuators and sensors to actively counteract any vibrational movement. The initial LIGO experiment used passive stacks to dampen the seismic noise, however to reach the design sensitivity needed for Advanced LIGO, a combination of passive and active systems are used. There are several stages to the isolation systems at LIGO, an external active hydraulic stage, two types of active internal seismic isolation stages and a passive quadruple pendulum that suspends the mirror [3]. The initial system is the hydraulic external pre-isolator (HEPI), shown in Fig. 12, which is an active isolation platform located outside of the vacuum chamber. Within the vacuum chamber there are internal seismic isolators (ISI) located on the HEPI. There are two different systems that house the ISI, these are called horizontal access modules or (HAM or HAM-ISI), Fig. 13, and basic symmetric chambers (BSC or BSC-ISI), Fig. 14. The HAM-ISI isolate the auxiliary optics of the interferometer from ground motion and the BSC-ISI isolate the core opitics [51]. The quadruple pendulums suspend the 40 kg test masses that are used in the core optics for the interferometer [53]. The actuators for the HEPI system were chosen as they have a bandwidth of 20 Hz, and between 0 10 Hz they operate with a noise of m/ Hz [50], this then provides suitable isolation in this frequency range. The HEPI system has four sensor-actuator assemblies located on each of the four corner support piers. Each sensor-actuator consists of hydraulic actuators, position sensors, geophones and two offload springs. The two offload springs support the weight of the payload and were initially used to position it. The position sensors measure the relative distance of the payload from the ground, and the geophones measure the payloads inertial velocity. The hydraulic actuators are controlled by a central pump, this pumps a viscous fluid to the actuators. The pump controls a differential pressure between two terminals which in turn controls two axially soft bellows, this can then be transferred to the payload [50]. Both the HAM and BSC ISI systems use a similar passive-active system shown in Fig. 13 and Fig. 14 respectively, they both use sets of blades, flexure s and sensor-actuators to isolate any vibrations. The main difference between the BSC and HAM is that the BSC has a two stage isolation system in place as opposesd to the 1 stage that HAM operates with. The blades and flexure s are sets of triangular steel blades, which as well as supporting the mass provide passive isolation. The HAM system can be split into two stages, stage 0 which is supported by the HEPI system, and stage 1 which is supported with sets of blades and flexure s by stage 0, this is shown in Fig. 13. Both seismometers and geophones are used as sensors to detect any movement from the ground; non contact magnetic actuators use the information from the sensors to adjust to any movement, providing active isolation [51]. The BSC system used for the core optics has another stage which is supported by stage 1, shown in Fig. 14, and follows a similar isolations system. The quadruple pendulum consists of four layers of suspension which is shown in Fig. 15. The test mass is the bottom layer which is suspended by silica fibres from an intermediate test mass above. Above these there are three stages of cantilever blades which are suspended as shown in Fig. 15, these are made from maraging steel and provide vertical isolation to the test 24

25 Instruments and springs support structure Vacuum chamber Payload attachment point Support Tubes Springs Feedback instruments (Geophones and relative sensors) Ground Instrument Ground Cross Beam Bellows Quiet hydraulic actuators Figure 12: This diagram shows the layout for the HEPI system, which consists of seismometers, geophones and springs which are all labelled [51] mass [53]. The combined isolation systems for advanced LIGO aim to bring the seismic noise cutoff level down from 40 Hz to 10 Hz [52] Results The LIGO experiment operates in the high frequency range which is between Hz [20], therefore it has the capability to detect many of the sources of gravitational waves. These sources include NS-NS/BH binaries, supernovas, pulsars and the stochastic background, as Table 1 shows. This wide range of sources demonstrates how versatile interferometers are as an instrument in the search for gravitational waves. Although GW have not yet been detected, many limits have been placed on their amplitudes. This section will focus on the results from the S5 and S6 data runs from enhanced LIGO; the results originate from Ref. [54], Ref. [55], Ref. [20] and Ref. [56]. The target sources for LIGO have different signal lengths with a varying knowledge of their waveform. The more that is known about the waveform of the source the easier it is to search for, this is because the signal can be compared to an already predicted model. To analyse data, it is first collected from the network of interferometric detectors, then analysis is completed in different ways depending on which source is being searched for. If one is searching for CBC the waveform is well defined, therefore the detectors strain output can be compared to a theoretical model of the waveforms, this technique is called matched filtering. Any match that occurs with a signal to noise ratio (SNR) above a certain threshold is then investigated further. The background rate of coincidence events between two or more detectors is measured by a method called time shifting. Time shifting is when the triggers from different detectors are shifted in time relative to each other and the analysis is repeated, this will give a different rate of coincidence events which is known not to be a signal. By performing many of these time shifts it is possible to gain a good estimate of the accidental coincidence events that will occur. 25

26 Actuator Blade Flexure Geophone Stage 1 Stage 0 Figure 13: This diagram shows the layout for the HAM-ISI system inside the vacuum chamber. This system will be located on the HEPI system in Fig. 12 [51]. Stage 1 Stage 2 Stage 0-1 blade and flexure Stage 0-1 vertical and horizontal actuators Stage 1 vertical and horizontal geophones (L4C) Stage 2 vertical and horizontal geophones (GS13) Stage 0 Stage 1-2 blade and flexure Stage 1 seismometer Stage 1-2 vertical and horizontal actuators Figure 14: This diagram shows the layout for the BSC-ISI system that will house the core optics inside the vacuum chamber. This system will be located on the HEPI system in Fig. 12 [51]. The maximum sensitivity of an interferometric detector is characterised by two quantities, the amount of time spent with two or more detectors in operation, and the distance to which each of the detectors observe to. The S6 data run for the LIGO detectors started on the 7th of July 2009, and ended on the 20th of October 2010, each detector recorded approximately seven months of data in this period. Each of the data runs are split up into smaller segments labelled A,B,C and D, these did not run continuously for the whole time however, as the instrumental stability plays a large role. Each segment that runs continuously is called a science segment, this is when the instruments are stable enough to be able to record data to a significant sensitivity. These data runs are usually ended when the noise is too great for the electronic control systems to control the interferometer. Figure 16 is a histogram showing the length of time for each science run at each of the LIGO sites. The Livingston site can be seen to have a higher event count in the 1 10 s segments, this is due to the lack of stability in the detector in early runs. The mean length of time for a segment at both detectors is approximately 1 hour. The other factor that effects the maximum sensitivity of the detector is the distance that they can detect to, this is called the horizon distance. This horizon distance is different for each 26

27 Front View Side View Cantilever blades Metal masses Intermediate mass Heavy glass Silica fibres Test mass Sapphire Figure 15: This diagram shows the four stages of the quadruple pendulum suspension system, including the cantilever blades and silica fibres. This image shows the front and side view of the system [53]. source as it depends on the amplitude of the emitted GW. For CBC the horizon distance as a function of the total mass of the binary system is shown in Fig. 17. Figure 17 shows how the mean inspiral horizon distance increases with the mass of the binary system, this is due to the fact that the higher mass systems will emit gravitational waves with a larger amplitude. This follows from Eq. 17 in Sec The overall sensitivity of a GW detector is characterised by a strain spectral sensitivity or a characteristic strain as mentioned in Sec. 3, this is determined by a combination of noise components. The strain sensitivity of the LIGO detectors in the S6 data runs is shown in Fig. 18. The black line is the design sensitivity of the the detectors, therefore it can be seen that the sensitivity has surpassed the design at most frequencies. The exception to this is the lower frequency range, this is where the seismic noise dominates. The Livingston (L1) observatory can be seen to have a higher sensitivity in the low frequency range, this is in part due to the installation of the prototype version of the hydraulic isolation system (HEPI) covered in Sec This should be reduced further with the most recent instalment of seismic isolation systems [54]. From the S5 and S6 data runs, upper limits have been placed of the event rates of compact binary coalescences. Table 3 shows the upper limit rates and realistic rates for CBC with a 90% confidence level, these are for a neutron star mass of 1.35 M and black hole mass of 1.5 M. These upper limit rates can be see in Fig. 19 compared to the astrophysically predicted rates for coalescence. 27

28 Figure 16: This histogram shows the length of time spent in each science segment for the Hanford (H1) and Livingston (L1) observatories in their S6 data run [54]. Figure 17: This plot shows the mean horizon distance as a function of mass for the 4 km Hanford and 4 km Livingston interferometers (S6 data run), and the 3 km VIRGO interferometer (V2 and 3 data run) [55]. The error bars are one standard deviation above and below the mean 28

29 Figure 18: This plot shows the strain spectral density against frequency for the S6 run data. L1 is the Livingston observatory and H1 is the Hanford observatory. The black line is the design sensitivity, therefore the seismic noise can be seen to be a large problem at the lower frequencies [49]. Table 3: This table shows the upper limit rates and realistic rates for different types of CBC [20]. The neutron stars in this have a mass of 1.35 M and black holes have a mass of 1.5 M, where M is one solar mass. System NS/NS NS/BH BH/BH Component masses (M ) 1.35/ / /1.5 Upper Limit (Mpc 3 yr 1 ) Realistic rates (Mpc 3 yr 1 ) Future searches for GW There are a number of GW detectors proposed for the future, most of these detectors use interferometry as their method of detection. These experiments will be designed to detect to a much higher sensitivity, spanning a larger portion of the frequency range. The most recent developments in the search for GW have been in the upgrade to Advanced LIGO, this detector has been mentioned throughout the review, however has not yet reached design sensitivity and may not for some time. Once Advanced LIGO has reached its design sensitivity it is expected to be the first to directly detect GW. The predicted number of compact binary coalescences that will be detected by Advanced LIGO can be summarised from Ref. [19]; for NS/NS, NS/BH and BH/BH coalescences the detection rates are predicted to be 40 yr 1, 10 yr 1 and 20 yr 1 respectively [19]. These are large improvements on the 0.02, and respective yearly limits from the initial LIGO experiments [19]. The laser interferometry space antenna (LISA), is the closest third generation detector to begin operation after Advanced LIGO; the pathfinder for this mission is scheduled to be launched in November The space based interferometer will consist of 3 separate test masses which operate over a distance of 10 6 km [8]. As the antenna operates over a large distance, sources 29

30 RateEstimates Mpc 3 yr BNS NSBH BBH Figure 19: This plot show the event rates of the three types of CBC [20]. The light grey regions show the event rates predicted in Ref. [20] in the S5 data run, the dark grey regions show previous upper limit rates and the blue regions show the astrophysically predicted rates. The dotted line shows the realistic rates for CBC. 30

31 in the low frequency range of 0.03 mhz 0.1 Hz can be detected [8]. Also as the antenna operates in space it is isolated from seismic noise, which is dominant in the lower frequency range. This allows observations of many events including the inspirals of massive black holes and extreme mass ratio inspirals. The big bang observer (BBO) is another spaced based interferometry network that will operate on a similar setup to LISA, however will operate over a distance of 50, 000 km. Although the BBO operates over a smaller distance than LISA, it is planned to have 4 separate triangular interferometers which will orbit the sun [57], it is also designed to operate over a frequency band that spans parts of both LIGO and LISAs spectrum as Fig. 20 shows. Other planned ground based interferometers are the Einstein telescope (ET) [58] and the Kamioka gravitational wave detector (KAGRA) [59], the main advantages of these experiments are that they use cryogenics to reduce the thermal noise within the optics and detector. All of the advanced detectors will reduce the noise in the detector by a significant amount and allow for better measurements of GW to be made across a wider frequency range. A plot showing the sensitivities and frequency ranges of most of these experiments can be seen in Fig. 20 [60]. Figure 20: This plot shows the characteristic strain of the labelled detectors which have been mentioned throughout this paper, including the planned strain sensitivities of future detectors [60]. This plot also shows the frequency bands and strains of a number of sources that each experiment should be able to detect. IPTA is the international pulsar timing array, BBO is the big bang observer, LISA is the laser interferometry gravitational observatory and LIGO and aligo are the initial and advanced versions of the laser interferometry gravitational observatory. 5 Conclusion Ever since the first indirect observation of GWs from the Hulse-Taylor binary system, many groups have set out to try to directly detect gravitational waves. Despite the fact that these 31