Gravitational wave research using pulsar timing arrays
aa r X i v : . [ a s t r o - ph . I M ] A p r Gravitational wave research using pulsar timing arrays
George Hobbs & Shi Dai Australia Telescope National Facility, CSIRO, PO Box 76, Epping. NSW 1710, AustraliaA pulsar timing array (PTA) refers to a program of regular, high-precision timing observations of a widely dis-tributed array of millisecond pulsars. Here we review the status of the three primary PTA projects and the jointInternational Pulsar Timing Array project. We discuss current results related to ultra-low-frequency gravitationalwave searches and highlight opportunities for the near future.
Keywords : Pulsars; Gravitational waves; Radio Astronomy
Pulsar observations have been used for numerous astrophysical applications. Not long after the discovery of pulsars,Counselman & Shapiro (1968) [1] described how observations of pulsars could be used to “test general relativity,to study the solar corona, and to determine the earth’s orbit and ephemeris time . . . [and to determine] the averageinterstellar electron density”. Most studies to date have concentrated on analysing observations of specific pulsars.For instance, observations of one pulsar may provide excellent tests of general relativity, whereas another pulsar willbe observed to probe the solar corona.During 1982 the first millisecond pulsar was discovered [2]. A few hundred millisecond pulsars are now known.Their rotation is significantly more stable than the normal pulsars and their pulse arrival times can both be measuredand also predicted with high accuracy. Foster & Backer (1990) [3] showed how a comparison of timing observationsfrom multiple millisecond pulsars (a spatial array of pulsars) could be used to provide a time standard, to detectperturbations of the Earth’s orbit and to search for gravitational waves (GWs). They initiated an observing program(which they termed a “pulsar timing array program”) to observe three pulsars using the National Radio AstronomyObservatory 43 m telescope. During 2004, a much larger pulsar timing array (PTA) project began with the Parkes 64 mtelescope and is known as the Parkes Pulsar Timing Array (PPTA). This project is ongoing (an overview and the firstdata release was described by Manchester et al. (2013) [4]) and now the team undertakes regular observations of 25pulsars in three observing bands. The North American Nanohertz Observatory for Gravitational Waves (NANOGrav)in North America [5] was founded in 2007 and uses the Arecibo and Green Bank telescopes to observe 36 pulsars.Observations are also carried out for 42 pulsars with the Sardinian, E ff elsberg, Nancay, Westerbork and Jodrell Banktelescopes by the European Pulsar Timing Array (EPTA) project team [6, 7], which was also founded in 2007. Thethree project teams combine their expertise and data sets as part of the International Pulsar Timing Array (IPTA) [8, 9].In this review article, we will concentrate on one aspect of pulsar timing array research: searching for GW signals.The first observational evidence for GWs came from observations of a binary pulsar system (PSR B1913 + / Virgo collaboration. During 2015 they detected two bursts of GW emission coming from the coalescence ofstellar mass black holes [11]. This exciting result has opened the field of observational GW astronomy, and pulsartiming array projects provide a complementary view of the gravitational wave sky. Whereas the LIGO / Virgo detectorsallow us to detect high-frequency GWs from stellar mass systems, the pulsar observations will allow us to detectultra-low-frequency GWs from supermassive binary black holes. In contrast to the Hulse & Taylor (1975) work thatprovided evidence for GWs, the PTAs will enable a direct detection of GWs. For completeness we note that space-based detectors (such as the Laser Interferometer Space Antenna; LISA; Amaro-Seoane et al. 2017 [12]) will besensitive to GWs in a frequency range between the PTA experiments and LIGO.In this paper we describe how GWs a ff ect pulsar observations ( § §
3) and the techniques being applied to hunt for the signals ( § § § § § ff ect pulsar observations? Various authors [13, 14] determined how GWs a ff ect an electromagnetic signal propagating from an emitting objectto a detector. Such calculations were applied to pulse arrival times from pulsars by Sazhin (1978) [15] and Detweiler11979) [16]. A GW induces a fluctuation in the observed pulse frequency, δν/ν , of: δνν = − H i j h h i j ( t e , x ie ) − h i j ( t e − D / c , x ip ) i (1)where H i j is a geometrical term that depends on the position of the GW source, the Earth and the pulsar (at distance D from the Earth). The GW strain, h i j ( t , x ), is evaluated at the Earth (at time t e and position x e ) and at the pulsar (at thetime the GW signal passed the pulsar, t p , and at position x p ). The shift of the pulse frequency is not directly measured.Instead pulse times-of-arrival (ToAs) are determined. These ToAs are then compared with predictions for the arrivaltimes based on a pulsar timing model. The di ff erences between the predictions and the measurements are known asthe pulsar “timing residuals”. A GW signal will induce timing residuals at time t from the initial observation of R ( t ) = − Z t δνν dt . (2)The theory of general relativity predicts two polarisation states, A + and A × , for GWs (see Lee, Jenet & Price2008 [17] for non-GR predictions). We can therefore re-write the Earth term as (note that the pulsar term is the same,but with an extra phase): R e ( t ) = Z t P + A + ( t ) + P × A × ( t )2(1 − γ ) dt (3)in which P + and P × are geometrical terms and γ is the GW-Earth-pulsar angle. For a non-evolving, continuous wavesource (i.e., from a non-evolving, supermassive, binary black hole system), the A + , × will oscillate with an angularfrequency of the GWs being ω g . For a supermassive, circular, binary, black hole system the GWs will be emitted attwice the orbital frequency. Eccentric binaries radiate GWs over a spectrum of harmonics of the orbital frequency.An estimation of the amplitude of the induced timing residuals caused by a binary system can be determinedfrom [18]: ∆ t ∼ d ! M M ⊙ ! / − Hz f ! / (4)where d is the luminosity distance to the system which has a total mass of M / (1 + z ) (where z is the redshift) and theGW frequency is f . More details are provided in Rosado et al. (2016) [19] who considered the detectability of binarysystems at high redshift. They showed that very high mass ( > M ⊙ ) binary systems could be detected by currentPTAs at arbitrarily high redshifts.Of course, our universe will contain a large number of supermassive, binary black hole systems. To determinethe total GW signal from these systems we therefore need to sum Equation 1 over all the sources. This resultsin a background of GW signals. For an isotropic, stochastic, unpolarised background signal, Hellings & Downs(1983) [20] showed that the timing residuals for each pulsar pair will be correlated as: c ( θ ) = x ln x − x + + δ ( x ) (5)where x = [1 − cos θ ] / θ on the sky between two pulsars and δ ( x ) is the Dirac delta function . Thisanalytic expression is plotted in Figure 1 and is commonly referred to as the Hellings-and-Downs curve . Whensearching for a background of GWs, the PTA teams therefore determine how correlated the timing residuals are foreach pulsar pair. A convincing detection of the GW background will be made if those correlations are shown to followthe Hellings-and-Downs curve.Typically pulsars are observed every few weeks and the longest data spans are now a few decades (millisecondpulsars were discovered in 1982). This implies that PTA data sets are sensitive to GWs with wavelengths from weeksto years. These correspond to ultra-low-frequency (10 − –10 − Hz) GWs . As described by Zhu (2015) [21] this function is a factor of 3 / ff erentscaling factors. Many publications parameterise the curve in di ff erent ways; see Jenet & Romano (2015) [22] for a pedagogical discussion ofthe curve. Ravi et al. (2012) [23] showed how the curve would change for a relatively small number of sources and Lee, Jenet & Price (2008) [17]determined the expected correlations for general theories of gravity. Kopeikin (1997) showed that binary pulsars could potentially be used to detect even lower frequency GWs (10 − –10 − Hz) and Dolch etal. (2016) [24] showed that specific observing campaigns can be carried out to search for GWs in the 10 − –10 − Hz regimes. However, almostall of the work carried out so far has been in the ultra-low-frequency regime.
20 40 60 80 100 120 140 160 180
Angular Separation (deg) -0.100.10.20.30.40.5 C o rr e l a t i o n Hellings & Downs curvePPTA (24 pulsars)IPTA (49 pulsars)
Figure 1: The Hellings-and-Downs curve. The red dots indicate the angular separations of the pulsars in the PPTAproject. The blue dots indicate the angular separations for the pulsars in the IPTA project. Note that the IPTA providescoverage at all angular scales.
The three PTAs carry out regular timing observations of their sample of millisecond pulsars. Details of the observingsystems have been presented in the various data release papers (see Desvignes et al. 2016 [7], Arzoumanian et al.2015 [25] and Manchester et al. 2013). In brief, the data from a given telescope is generally folded online using theknown timing model for the pulsar being observed. The resulting data files are processed to remove radio-frequency-interference and to apply various calibration procedures (such as removing instrumental delays and calibrating thepolarisation and flux density of the signal). Pulse ToAs are determined for each observation by cross-correlating theobserved pulse profile with a template providing a high S / N representation of the expected pulse shape.One of the primary noise sources that a ff ect searches for GWs are variations in electron densities in the interstellarmedium (see, for example, Keith et al. 2013 [26] and Lee et al. 2014 [27]). Such changes can be monitored and (tosome extent) removed or modelled by observing the pulsars over a wide range of frequencies. The PPTA currently usesa dual band receiver providing simultaneous observations in the 10 cm (3 GHz) and 40 cm (700 MHz) observing bandsalong with a 20 cm receiver (1400 MHz). The EPTA uses their large number of telescopes to obtain observations ofeach pulsar at frequencies between ∼
300 MHz with the Westerbork Synthesis Radio telescope and ∼ ff elsberg radio telescope. Data in the 20 cm observing band from five of the European telescopes are also combinedas part of the Large European Array for Pulsars (LEAP) to form a tied-array telescope with an e ff ective apertureequivalent to a 195 m diameter telescope [28]. NANOGrav carries out observations between ∼
300 MHz and 2.4 GHz.Some of the pulsars in the Southern hemisphere can only be observed by the PPTA. The Northern hemispherepulsars are generally observed by a large number of telescopes in both Europe and North America. A few pulsars areobserved by all three PTAs. This has led to some observing campaigns in which a large number of IPTA telescopesobserve the same source. For instance, PSR J1713 + ffi cial members of the IPTA, other telescopes are used to observe millisecond pulsarsand are likely to contribute to PTA research. In China, the Nanshan, Yunnan, Shanghai and Jiamusi telescopes observepulsars at a wide range of observing frequencies. The GMRT in India, LOFAR in Europe and the MWA in Australiaobserve pulsars at low frequencies (10 to 240 MHz and 80 to 300 MHz respectively). Papers related to PTA researchhave also been published using observations from Kalyazin in Russia (e.g., Ilyasov et al. 2004[30]).3able 1: Publically available PTA data setsPTA Access ReferenceIPTA Verbiest et al. (2016) [8]NANOGrav https://data.nanograv.org
Arzoumanian et al. (2015) [25]EPTA
Desvignes et al. (2016) [7]PPTA http://doi.org/10.4225/08/561EFD72D0409
Reardon et al. (2016) [29]
GWs will induce timing residuals. The form of those timing residuals will depend on the nature of the GWs (single,non-evolving sources will induce sinusoidal residuals, a background will induce timing residuals that have a power-law spectrum). The statistical challenge is therefore to first search for statistically significant residuals and then toprove that they arise because of GWs. If no GWs are detected then upper bounds on the GW amplitude can bedetermined.All existing techniques are based on the “pulsar timing method”. Timing software packages (such as tempo , tempo pint ) are used to compare the measured pulse ToAs with predictions for those ToAs based on a modelfor the astrometric, pulse and, interstellar medium and orbital parameters of each pulsar. Both “frequentist” and“Bayesian” methods exist for searching GWs. We summarise these methods in Table 2. The various algorithmsdescribed in the table can be split into routines for specific types of GW signals (such as the find CW and detect
GWBplugins to tempo
2) or more general codes that can search for various GW types. In all these cases, the user provides aset of high precision pulsar observations and defines the type of GW signal to be searched for along with informationon what other noise processes are likely to be present in the data. For instance, the measured timing residuals arenot only induced by GWs as pulse ToAs are a ff ected by many phenomena. Along the line-of-sight to the pulsar theinterstellar medium and the Solar wind can contribute significant delays to the measured ToAs. The measurement ofa ToA is also sensitive to instrumental errors and incomplete polarisation calibration. A GW background produceslow-frequency timing residuals, but so do errors in terrestrial time standards, intrinsic pulsar instabilities and muchmore. A detection of a GW signal therefore requires the confirmation of the expected spatial angular signature (theHellings-Downs curve for a background or a quadrupolar spatial signature for a single GW source). When searchingfor GWs it is therefore necessary either to first determine and then remove the non-GW noise processes or to searchfor the GWs whilst simultaneously modelling these other phenomena that a ff ect the pulse arrival times.Bayesian algorithms can be significantly slower than frequentist algorithms and GW searches using large datasets often require high-performance-computing facilities . Frequentist-based methods often require that each noiseprocess is dealt with in turn and, without care, this can lead to correlations between the di ff erent processes beingunaccounted for in the final results. All the available algorithms should be used with care and tested on simulateddata sets that have similar properties to the real data (i.e., di ff erent noise properties, irregular sampling, di ff erent dataspans for di ff erent pulsars, etc.). The IPTA produced a set of simulated data sets with the primary goal of testing andcomparing di ff erent GW detection algorithms. Ultra-low-frequency GWs have not yet been detected. Work has therefore been split between 1) predicting the ex-pected signal and time to detection, 2) making more-and-more sensitive searches for the GWs and 3) understandingthe astrophysical implications of our non-detections. A summary is given in Figure 2 where we show the currentupper-bounds from the three PTAs as dotted lines. A theoretical prediction (from Sesana et al. 2016) for the likelyGW background signal from coalescing supermassive, binary black holes is shown in the shaded region. One possiblerealisation of such a background (made up from numerous individual black hole binaries) is shown as the jagged,solid line. We note that the current PTAs are starting to constrain some models of the GW signal. However, it is likely tempo , tempo pint are accessible from http://tempo.sourceforge.net , https://bitbucket.org/psrsoft/tempo2 and https://github.com/nanograv/PINT respectively. A single step in the Bayesian algorithms may be just as fast as the computation of a frequentist statistic, however, the Bayesian methodssample a large parameter space of signals and noise processes. Available from . Software Access Application ReferenceNX01 http://stevertaylor.github.io/NX01/
Isotropic and anisotropicGW background, bursts withmemory and individual sourcesearches. Taylor (2017)[31]PAL2 https://github.com/jellis18/PAL2
Isotropic and anisotropic GWbackground, bursts with mem-ory, burst events and continuouswaves Ellis & van Haasteren(2017)[32]Piccard https://github.com/vhaasteren/piccard
Isotropic and anisotropic GWbackground, bursts with mem-ory, burst events and continuouswaves van Haasteren(2016)[33]Tempo2 https://bitbucket.org/psrsoft/tempo2
Generic search for GW signalwith arbitrary waveform Madison et al.(2016)[34]Global least squares fitting formemory event Wang et al. (2015)[35]Tempo2plugins Access with tempo2 distribution findCW: search for continuouswave sources Zhu et al. (2014)[36]detectGWB: fast, but simplemethod for GWB detection Tiburzi et al.(2016)[37]Temponest https://github.com/LindleyLentati/TempoNest
Bayesian analysis tools includ-ing GWB searches Lentati et al.(2014)[38]libstempo https://github.com/vallis/mc3pta/tree/master/stempo
Routines for interfacing manyof the software packages abovewith tempo tempo and pint Developed primarily byVallisneri, M.
Figure 2: Current upper bounds (dotted lines) and the theoretical expectation (shaded region and orange, solid curve)for the GW signal. A possible bound that could be reached by the IPTA by 2020 is shown as the dotted line. Figurecourtesy of A. Sesana. 5hat we will require the sensitivity of the entire IPTA project to finally detect the GWs. A bound that potentially couldbe reached by the IPTA within a decade or so is shown as the dotted, black line. A more in-depth analysis of the likelytime to detection has recently been published by Kelley et al. (2017).In the following subsections we describe the results to date for di ff erent types of GW searches. We note (and seee.g., Rosado et al. 2015 [39]) that it is not yet clear whether we will first detect an individual supermassive binaryblack hole system or a background made up from a large number of GW sources. Lommen & Backer (2001) [40] unsuccessfully searched for GW emission from Sagittarius A ∗ that had been proposedto be a binary system. They also searched for continuous GW emission from other nearby galaxies. Sudou et al.(2003) [41] presented evidence for a supermassive black hole binary system in the radio galaxy 3C66B. It was shownby Jenet et al. (2004) [42] that such a system would be producing detectable GWs and therefore ruled out the Sudou etal., models with high confidence. Zhu et al. (2014) [36], Arzoumanian et al. (2014) [43] and Babak et al. (2016) [44]have presented recent bounds on individual GW sources over the entire sky or in particular sky directions with arepresentative value being that the GW strain amplitude: h < × − (6)at a frequency of 10 nHz. The exact bound depends upon the sky direction and GW frequency. Such bounds constrainthe local merger rate density of supermassive binary black holes, but the current limits are higher than the theoreticalexpectations (e.g., Sesana 2013 [45] and Ravi et al. 2012 [23]) for such GWs. Even though the first GW detection was a burst signal in the audio band (Abbott et al. 2016), the expectations forburst GW signals are not well developed in the pulsar timing band. To date, the PTA teams have considered burstemission from the formation of supermassive black holes, highly eccentric black hole binaries, close encounters ofmassive objects, cosmic string cusps and memory events.Seto (2009) [46] showed how permanent distortions can occur in spacetime during mergers of supermassive binaryblack holes. Such a “memory event” will lead to a step change in the pulse frequency of all pulsars. Cordes & Jenet(2012) [47] gave an order-of-magnitude estimation of the signal-strength of: h mem ∼ × − µ M ⊙ ! D ! (7)where µ is the reduced mass of the system and D is the distance. Searches for bursts with memory have been carriedout by Arzoumanian et al. (2015) and Wang et al. (2015). No detection was made and the current conclusion is thatGW memory events are unlikely to be detected in the near future. Most PTA research has been related to detecting or bounding the GW background. It is common to define thebackground spectrum as: h c ( f ) = A ff ! α (8)where f = / (1yr). The spectral exponent is thought to be close to α = − / − − / A < − with 95% confidence (e.g., Shannonet al. 2015 [49], Lentati et al. 2015 [50], Arzoumanian et al. 2016 [51], Verbiest et al. 2016 [8]). The amplitude ofthe astrophysical GW background predicted by di ff erent models is based on various physical assumptions (see, e.g.,Sesana 2013 for an overview). Firstly, models for the binary supermassive black hole (SMBH) population rely onmeasurements of the galaxy merger rate. Secondly, it has often been assumed that all galaxy mergers form binarySMBHs that coalesce well before a subsequent galaxy merger. Thirdly, the binary orbital decay has been assumed tobe driven only by losses of energy to GWs when radiating in the pulsar timing frequency band.6he current GW background limits are inconsistent with some of the early theoretical models for the expected GWbackground signal, which suggests that at least one of the physical assumptions underlying such GWB models is likelyto be incorrect. For instance, the galaxy-merger timescales might be longer than we currently expect. This would resultin a lower merger rate and, hence, fewer binary SMBHs. It is also possible that not all large galaxies host SMBHs.SMBH binaries may not e ffi ciently reach the GW emitting stage in our assumed time scale (they “stall”; e.g., Simon &Burke-Spolaor 2016 [52]) and other mechanisms in addition to GW emission drive binaries to coalescence, such as thecoupling of binary SMBHs to their environments (e.g., Kocsis & Sesana 2011 [53]) or orbital eccentricity [54, 55]).Binary SMBHs could lose energy and momentum because of three-body scattering of stars and viscous friction againstcircumbinary gaseous disk. Such coupling mechanisms also bend the GW background spectrum at low frequencies(i.e., large orbital separations). Arzoumanian et al. (2016) checked the consistency of their limit with previouslyreported scaling relations between SMBH mass and galactic bulge mass, using fiducial estimates for galaxy mergerrates and the stellar mass function. Under the assumption of circular GW-driven binaries, they found that the scalingrelations of Kormendy & Ho (2013) [56] and McConnell & Ma (2013) [57] to be inconsistent with their data at the95% and 90% level respectively. They also placed constrains on the strength of environmental coupling e ff ects viaparameterisation of the GW background spectrum that allows for a turn-over frequency (see also Sampson, Cornish& McWilliams 2015 [58]). More recently Kelley et al. (2017) [59] used the iIllustris simulation to make a newprediction for the GW background signal in the pulsar timing band and their models are not ruled out by the currentupper bounds.SMBHB mergers are not the only possible source of a GW background in the pulsar timing band. Quantum fluc-tuations of the gravitational field in the early universe, amplified by an inflationary phase could produce a stochasticrelic GW background (e.g., Grishchuk 1977 [60]). The spectral index of the relic GWs is related to the equation ofstate of the early universe. By extending the power-law background search to generic spectral indices, Arzoumanianet al. (2016) placed limits on the energy density of relic GWs. From this they obtained limits on the Hubble parameterduring inflation. Lasky et al. (2016) [61] discussed the implications of the bounds on the cosmological backgroundover the entire range of GW frequencies. Cosmic strings could also produce a stochastic background of GWs as wellas individual bursts (e.g., Damour & Vilenkin 2001 [62]). Arzoumanian et al. (2016) placed the most stringent limitsto date on a GW background generated by a network of cosmic strings, which translates into a conservative upper limiton cosmic string tension of G µ < × − (see also Lentati et al. 2015 and Sanidas, Battye & Stappers 2012 [63]). Pulsar timing data processing packages are su ffi ciently advanced to produce pulsar timing residuals at the level neededfor GW detection (the tempo ff ects the propagationof the pulse from the pulsar to the observatory at the 1 ns level; Hobbs et al. 2006 [64]). For instance, the PTA teamsare now achieving sub-100 ns rms timing residuals on a handful of pulsars (this implies that, for at least a few pulsars,calibration errors, radio interference mitigation, interstellar medium propagation e ff ects, orbital motion and manymore phenomena can be accounted for). GW detection codes have also been well tested on both real and simulateddata sets. The primary issue is that we are simply not achieving the necessary precision for a large sample of pulsarsand / or we are not observing enough pulsars. Jenet et al. (2005) [65] demonstrated that at least 20 pulsars are neededto be observed over 5-10 years with an rms timing residual of 100 ns in order to make a low-sigma detection of aGW background. Siemens et al. (2013) [66] considered whether a small number of well timed pulsars or a largernumber of poorly-timed pulsars would be preferable and showed that adding in a su ffi cient number of pulsars withrms residuals of ∼ µ s can significantly increase the sensitivity of the array.In many cases the timing precision is not limited simply by the sensitivity of the observing systems. For the verybrightest pulsars (such as PSR J0437 − ff ects a relatively small number of the PTA pulsars, butthe era of much larger and more sensitive telescopes jitter will become a major limitation for PTA research. On longtime scales many of the pulsars are a ff ected by long-term timing variations known as timing noise (see, e.g., Lentatiet al. 2016 [68], Caballero et al. 2016 [69], Lam et al. 2017 [70]) and two of the PTA pulsars (PSRs J0613 − − ff ects of dispersion and scattering for PTAs.7nsuring an un-ambiguous detection of a GW signal is also non-trivial. Taylor et al. (2016) [75] presented twomethods for assessing the significance of a stochastic GW background signal in a given data set. Zhu et al. (2015) [74]discuss the construction of null streams as a means to provide a consistency check when a single source GW signal isdetected. Tiburzi et al. (2016) showed that, without care, false detections of a GW background could be made even ifno GW signal were present. These false detections can come from incomplete removal (or modelling) of e ff ects suchas errors in terrestrial clocks, the solar wind or in the solar system planetary ephemerides. In particular the planetaryephemerides are currently being actively investigated as the more recent ephemerides seem to induce low-frequencynoise into the timing residuals (that can mimic the signature of a gravitational wave background; Shannon et al.,private communication). The reason for this is not currently understood, but is being explored by all three PTAs andit is clear that the choice of planetary ephemeris has a significant e ff ect on the resulting data sets and sensitivity toGWs. The three main PTA projects have now been ongoing for more than a decade. The data sets produced are the most high-timing-precision data sets yet made. Processing such data has required huge improvements in understanding noiseprocesses and calibration methods. The observations have been used to place stringent constraints on the amplitudeof GWs. The bounds have been used to constrain cosmological and cosmic string models and to rule out models ofGW emission from supermassive binary black holes. The data have also been used to study atomic clocks and thesolar system ephemeris. Unfortunately GWs have not been detected by the PTAs.Determining when we should expect our first detection is non-trivial. The most recent GW models from super-massive binary black holes predict a background with an amplitude A ∼ × − (e.g., Sesana et al. 2016 [76] andKelley et al. 2017), but the uncertainty is still large. Predictions from cosmic strings or the early Universe are evenmore uncertain. Groups have attempted to calculate the time to detection based on estimates of the GW amplitude(see, e.g., Siemens et al. 2013 [66] and Taylor et al. 2016 [77]). The estimated times range from a few years fromnow to a few decades. These calculations are made even more uncertain through the assumptions made about howmany new pulsars will be discovered (and added into PTAs) over the coming years, what the timing precision willbe of those pulsars, whether we will be able to correct for interstellar medium e ff ects at the necessary level, howintrinsically stable the pulsars are and how will new telescopes (that are currently not part of the PTA experiments)contribute.Some pulsars (such as PSRs J0437 − + − ff ects: 1) GW bounds will stop decreasing as they will be dominated by the noise in thesepulsars and 2) even though pulsar astronomers will not be able to state unambiguously that these residuals have beeninduced by GWs, statements such as “if these residuals are induced by GWs then the amplitude and spectral propertiesof those GWs are . . . ” will become possible. Most of the existing telescopes being used for PTA observations will continue to be upgraded. For instance, the Parkestelescope will soon be commissioning a new ultra-wide-bandwidth receiver covering from 700 MHz to ∼ ff els-berg [80], Arecibo (e.g., Cordes et al. 2006 [81]), Green Bank (e.g., Stovall et al. 2014 [82]) and LOFAR (e.g.,Coenen et al. 2014 [83]) telescopes. Traditional pulsar search methods are computationally expensive and this is8 ASTQTT TianmaGMRTMeerKATSKA-mid ASKAPMWASKA-lowParkesLovellWRSTEffelsbergNancaySRT LOFAR KalyazinGBT AreciboVLACHIME
Figure 3: Telescopes currently part of the IPTA and those that are expected to contribute soon. Together thesetelescopes are able to observe pulsars anywhere in the sky and to detect GWs coming from any direction. Telescopeslabelled in blue are existing IPTA telescopes. Those in yellow exist, but are not o ffi cially part of the IPTA yet. Thoselabelled in black are being designed.becoming a limiting factor for surveys on future telescopes. One recent and very successful method is to observeobjects that were identified as gamma-ray emitting sources by the Fermi spacecraft. To date, such surveys have ledto the discovery of more than 75 new millisecond pulsars and many of those are now observed by the PTAs. Variousnovel search techniques are also being considered which may lead to a much larger sample of IPTA pulsars (see, forinstance, Dai et al. 2016, for a description of images of the variance in both time and frequency that can be used todetect pulsars in large-scale continuum surveys) [84]. A large number of new telescopes will soon to be significantly contributing to PTA projects (see Figure 3 for aWorld-map showing current and future PTA telescopes). The most exciting new developments are the Five HundredMetre Aperture Spherical Telescope (FAST; e.g., Li et al. 2013 [85]) that recently opened in China and MeerKAT inSouth Africa (e.g., Foley et al.. 2016 [86]). Both telescopes will contribute to 1) finding new millisecond pulsars, 2)high-precision pulsar timing and 3) studies of pulsar noise processes that can only be probed by a detailed study ofindividual pulses (for instance, jitter noise).On the longer term the Chinese are also planning a large, single-dish, steerable telescope known as the QiTai (orQTT) telescope (see Xu & Wang 2016 [87]). This telescope will operate over a wide range of frequencies and will beable to observe a much larger number of pulsars than is available from FAST. An analysis of how the Qitai and FASTtelescopes will contribute to PTAs was provided in Hobbs et al. (2014) [88]. In the Southern hemisphere, the SquareKilometre Array will be built in Southern Africa and Australia. One of the key science goals for the mid-frequencypart of this telescope is to detect and study ultra-low-frequency GWs using the methods described in this review (see,e.g., Janssen et al. 2015 [89]).Over time more and more telescopes will contribute observations to the global IPTA e ff ort. This means that it willbecome important to optimise which telescopes observe which pulsars. Lee et al. (2012) [90] and Burt, Lommen &Finn (2011) [91] have considered methods for such optimisation. Of course, such optimisation is non-trivial as pulsarobservations are used for so much more than GW detection. Pulsar timing arrays are ongoing with existing telescopes and form key science goals for many of the next generationradio telescopes. PTAs combine observations of pulsars to probe the population of supermassive black holes, the9arly universe and cosmic strings. These are all exciting objects and topics for the general public. Projects such asPULSE@Parkes (Hobbs et al. 2009) [92] in which high school students observe pulsars using the Parkes telescope,the Arecibo Remote Command Center (ARCC) project in which students use the Arecibo telescope to search for newpulsars and the Pulsar Search Collaboratory (Rosen et al. 2010) [93] with Green Bank ensure that the enthusiasm thatthe IPTA members have for this project gets passed down to the next generation of pulsar astronomers.Within decades it is likely that ground-based detectors will be analysing high-frequency GWs in detail, space-based detectors will study mid-frequency GWs and PTAs will be probing ultra-low frequency GWs. Astronomy overthe entire spectrum of GW frequencies will soon become a reality.
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