The international pulsar timing array project: using pulsars as a gravitational wave detector

Abstract

The International Pulsar Timing Array project combines observations of pulsars from both Northern and Southern hemisphere observatories with the main aim of detecting ultra-low frequency (~10^-9 to 10^-8 Hz) gravitational waves. Here we introduce the project, review the methods used to search for gravitational waves emitted from coalescing supermassive binary black-hole systems in the centres of merging galaxies and discuss the status of the project. Comment: accepted by Classical and Quantum Gravity. Review talk for the Amaldi8 conference series

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arXiv:0911.5206v1 [astro-ph.SR] 27 Nov 2009
The international pulsar timing array project: using
pulsars as a gravitational wave detector
G. Hobbs1, A. Archibald2, Z. Arzoumanian3, D. Backer4, M.
Bailes5, N. D. R. Bhat5, M. Burgay6, S. Burke-Spolaor1,5, D.
Champion1,11, I. Cognard7, W. Coles8, J. Cordes9, P.
Demorest10, G. Desvignes7, R. D. Ferdman7, L. Finn24, P.
Freire11, M. Gonzalez12, J. Hessels13, A. Hotan14, G. Janssen20,
F. Jenet15, A. Jessner11, C. Jordan20, V. Kaspi2, M. Kramer11,20,
V. Kondratiev16, J. Lazio21, K. Lazaridis11, K. J. Lee17, Y.
Levin18, A. Lommen19, D. Lorimer16, R. Lynch22, A. Lyne20, R.
Manchester1, M. McLaughlin16, D. Nice23, S. Oslowski1,5, M.
Pilia6, A. Possenti6, M. Purver20, S. Ransom10, J. Reynolds1, S.
Sanidas20, J. Sarkissian1, A. Sesana24, R. Shannon9, X.
Siemens26, I. Stairs12, B. Stappers20, D. Stinebring25, G.
Theureau7, R. van Haasteren18, W. van Straten5, J. P. W.
Verbiest16, D. R. B. Yardley1,27, X. P. You28
1Australia Telescope National Facility, CSIRO, P.O. Box 76, Epping, NSW 1710
Australia
2Department of Physics, McGill University, Montreal, PQ, H3A 2T8, Canada
3CRESST/USRA, NASA Goddard Space Flight Center, Code 662, Greenbelt, MD
20771, USA
4Astronomy department and radio astronomy laboratory, University of California,
Berkeley, CA 94720-3411, USA
5Centre for Astrophysics and Supercomputing, Swinburne University of Technology,
P.O. Box 218, Hawthorn VIC 3122, Australia
6Universit` a di Cagliari, Dipartimento di Fisica, SP Monserrato-Sestu km 0.7, 09042
Monserrato (CA), Italy
7Station de Radioastronomie de Nanay, Observatoire de Paris, 18330 Nan¸ cay, France
8Electrical and Computer Engineering, University of California at San Diego, La
Jolla, California, USA
9Astronomy Department, Cornell University, Ithaca, NY 14853, USA
10National Radio Astronomy Observatory (NRAO), Charlottesville, VA 22903, USA
11Max-Planck-Institut f¨ ur Radioastronomie, Auf Dem H¨ ugel 69, 53121, Bonn,
Germany
12Department of Physics and Astronomy, University of British Columbia, 6224
Agricultural Road, Vancouver, BC V6T 1Z1, Canada
13Astronomical Institute Anton Pannekoek, University of Amsterdam, Kruislaan
403, 1098 SJ Amsterdam, The Netherlands
14Department of Imaging and Applied Physics, Curtin University, Bentley, WA,
Australia
15Center for Gravitational Wave Astronomy, University of Texas at Brownsville, 80

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The international pulsar timing array project
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Fort Brown, Brownsville, TX 78520, USA
16Department of Physics, West Virginia University, Morgantown, WV 26506, USA
17Department of Astronomy, Peking University, 5 Haidian Lu, Beijing, 100871, China
18Leiden University, Leiden Observatory, PO Box 9513, NL-2300 RA Leiden, the
Netherlands
19Franklin and Marshall College, 415 Harrisburg Pike, Lancaster, PA 17604, USA
20Jodrell Bank Centre for Astrophysics, University of Manchester, Manchester, M13
9PL, UK
21Naval Research Laboratory, 4555 Overlook Avenue, SW, Washington, DC 20375,
USA
22Department of Astronomy, University of Virginia, Charlottesville, VA 229044325,
USA
23Physics Department, Bryn Mawr College, Bryn Mawr, PA 19010, USA
24Center for Gravitational Wave Physics, The Pennsylvania State University,
University Park, PA 16802, USA
25Physics & Astronomy Dept., Oberlin College, Oberlin, OH 44074, USA
26Center for Gravitation and Cosmology, Department of Physics, University of
Wisconsin — Milwaukee, P.O. Box 413, Wisconsin, 53201, USA
27Sydney institute for astronomy, the University of Sydney, NSW, Australia
28School of Physical Science and Technology, Southwest University, 2 Tiansheng
Road, Chongqing 400715, China
E-mail: george.hobbs@csiro.au
Abstract.
pulsars from both Northern and Southern hemisphere observatories with the main
aim of detecting ultra-low frequency (∼ 10−9− 10−8Hz) gravitational waves. Here
we introduce the project, review the methods used to search for gravitational waves
emitted from coalescing supermassive binary black-hole systems in the centres of
merging galaxies and discuss the status of the project.
The International Pulsar Timing Array project combines observations of
1. Introduction
Since their discovery (Hewish et al. 1968), pulsars have been repeatedly monitored
by many large radio telescopes. The characteristic signature of a radio pulsar is
a regular train of pulsed radiation.The intensity, shape and arrival times of the
pulses are determined by the physical phenomena causing the emission, the pulsar’s
magnetosphere, the pulse propagation through the interstellar medium and effects
caused by the detection systems at the observatory.
this paper, encoded into the pulse arrival times will also be information relating to
gravitational-waves (GWs) passing the Earth and/or the pulsar.
Pulsar observations have aided many new discoveries in physics and astronomy. For
instance, the first extra-solar planets were discovered around a pulsar (Wolszczan & Frail
1992), the first observational evidence for gravitational waves was obtained by studying
a pulsar-neutron star binary system (Hulse & Taylor 1975) and the most stringent tests
of general relativity in the strong-field limit come from pulsar observations (Kramer et
al. 2006). These results all relied on a technique known as “pulsar timing”. Details
As emphasised throughout

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The international pulsar timing array project
3
of this technique have been described numerous times in the literature (see Lorimer &
Kramer 2005 for an overview and Edwards, Hobbs & Manchester 2006 for full details of
the method). In brief, the observed pulse times-of-arrival (TOAs) are compared with a
prediction for the arrival times obtained with a model of the spin, astrometric and orbital
parameters of the pulsar and details of the pulse propagation through the interstellar
medium. The deviations between the predicted and the observed TOAs are known as
the pulsar ‘timing residuals’ and indicate unmodelled effects, i.e., Ri= (φi−Ni)/ν where
φidescribes the time evolution of the pulse phase based on the model pulse frequency
(ν) and its derivatives. Niis the nearest integer to φi. GW signals are not included in
a pulsar timing model and, hence, any such waves will induce residuals. Unfortunately,
the expected signal induced by GWs is small, with typical residuals being <100ns.
The TOA precision achievable for the majority of pulsars is ∼ 1ms and most pulsars
show long-term timing irregularities that would make the detection of the expected GW
signal difficult or impossible (e.g. Hobbs, Lyne & Kramer 2006). However, a sub-set of
the pulsar population, the millisecond pulsars, have very high spin rates, much smaller
timing irregularities and can be observed with much greater TOA precision. Recent
observations of PSR J0437−4715 have shown that TOA precisions of ∼ 30ns can be
achieved (see §4) and over 10yr the root-mean-square (rms) timing residuals are 200ns
(Verbiest et al. 2008).
In §2 of this paper we describe the induced timing residuals caused by GWs.
The expected sources of detectable GW signals are given in §3. We summarise the
International Pulsar Timing Array project in §4 and highlight future telescopes and
timing array projects in §5.
2. Induced timing residuals caused by gravitational waves
Sazhin (1978) and Detweiler (1979) first showed that a GW signal causes a fluctuation
in the observed pulse frequency δν/ν which affects the pulsar timing residuals at time
t from the initial observation as
?t
0
ν
The Doppler shift can be shown to have the form
δν
ν
where he
pulsar when the electromagnetic pulse was emitted (typically ∼ 1000yr ago) and Hij
is a geometrical term that depends upon the angle between the Earth, pulsar and GW
source. This equation was derived assuming a plane gravitational wave and is accurate
to first order in hij for all GW wavelengths. Note, this expression holds even if the
wave is not sinusoidal. Full details of the exact form of the induced residuals are given
by Hobbs et al. (2009a). Standard pulsar timing techniques absorb any low-frequency
GWs by fitting for the pulsar’s spin-down and so the time span of the data provides a
R(t) = −
δν(t)
dt. (1)
= Hij(he
ij− hp
ij) (2)
ijis the GW strain at the Earth at the time of observation, hp
ijthe strain at the

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The international pulsar timing array project
4
Figure 1. The expected correlation in the timing residuals of pairs of pulsars as a
function of angular separation for an isotropic GW background.
lower bound on the GW frequencies that are detectable (currently > 10−9Hz). Pulsars
are typically only observed once every few weeks and so the data sampling limits the
maximum detectable GW frequency to ∼ 10−7Hz.
It is not possible to determine the exact origin of the timing residuals with a single
pulsar data set. For instance, residuals may be caused by irregularities in terrestrial
time standards, errors in the planetary ephemeris, irregular spin-down of the pulsar,
calibration effects or GWs. These different effects may be distinguished by searching
for correlations in the residuals of many pulsars. Residuals caused by the irregular
spin-down of one pulsar will be uncorrelated with the residuals observed for a different
pulsar. If there are irregularities in terrestrial time standards then the residuals for
all pulsars will be correlated. For an isotropic, stochastic GW background, the GW
strain at each pulsar will be uncorrelated, but the GW strain at the Earth provides a
common signal. The expected correlation as a function of angular separation between
two pulsars was determined by Hellings & Downs (1983) and is shown in Figure 1. Note,
this figure shows the expected function for GWs described by general relativity. Lee,
Jenet & Price (2008) produced similar angular correlation functions for more general
theories of gravity.
3. Expected sources of gravitational waves
Expected sources of GWs in the pulsar frequency band can be divided into 1) single
persistent sources, 2) individual burst sources and 3) stochastic GW backgrounds. Here
we will only consider the GW emission from coalescing supermassive binary black-hole
systems in the centres of merging galaxies. Details on the GW emission from other
sources such as cosmic strings or from the inflationary era can be found in Maggiore
(2000).
Sudou et al. (2003) obtained observational evidence for a coalescing supermassive

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The international pulsar timing array project
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Figure 2. Simulation of the induced timing residuals for PSR B1855+09 caused by a
postulated supermassive binary black hole system in the radio galaxy 3C66B.
black-hole binary system at the centre of the radio galaxy 3C66B. Jenet et al. (2004)
calculated the expected induced timing residuals from such a system (see Figure 2) and,
by comparison with actual pulsar data (Kaspi et al. 1994), were able to rule out the
existence of the postulated system with 95% confidence. Similarly, the blazar OJ287 has
an observed periodicity of ∼ 12yr which can be modelled as a binary black-hole system
(e.g. Valtonen et al. 2009). The most recent model parameters for this system suggest
that the induced timing residuals will lie around ∼ 1 − 10ns and would therefore be
undetectable in existing data sets.
Using models of black-hole masses and merging rates, Sesana, Vecchio & Colacino
(2008) and Sesana, Vecchio & Volonteri (2009) studied theoretically the detectability of
GW signals from coalescing black-hole systems. They showed that it is unlikely that an
individual source of GWs would be detectable at current PTA sensitivities (rms timing
residuals ∼ 10ns are required to detect such individual sources), but that the amplitude
of a stochastic background created by massive (109M⊙) black-hole binary systems in
distant (z ∼ 2) galaxies could be just below current observational limits.
The current best limit (Jenet et al. 2006) used observations from the Parkes and
Arecibo observatories. The characteristic strain spectrum of an isotropic, stochastic
background as‡ can be written as hc(f) = A(f/f1yr)−2/3. The most recent limit gave
A < 10−14(where f1yr= 1/[1yr]). New techniques to obtain limits (e.g. van Haasteren
et al. 2009, Anholm et al. 2008) and new data sets (see below) should significantly
improve on this limit in the near future.
4. Status of the IPTA project
The International Pulsar Timing Array (IPTA) project is a collaboration between three
individual projects.The European project (EPTA; Janssen et al. 2008) currently
‡ see Sesana et al. (2008) for a more accurate model

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The international pulsar timing array project
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Figure 3. Detection significance of a GW background with given amplitude for data
spanning five years for different pulsar timing arrays. Also shown is the expected
detection significance for the IPTA project after 10 years. The detection significance
is defined in the appendix of Verbiest et al. (2009).
combines data from four European telescopes (Effelsberg, Jodrell Bank, Nan¸ cay and
Westerbork – a new telescope in Sardinia is currently being commissoned). The North
American project (NANOGrav; Jenet et al. 2009) observes with the Arecibo and Green
Bank telescopes. The Parkes project (PPTA; e.g. Hobbs et al. 2009b) uses the Parkes
radio telescope. Basic parameters of the pulsars observed are listed in Table 1.
Some of our most precise timing residuals have been obtained for PSR J0437−4715.
The rms timing residuals over ∼1yr obtained with the Parkes radio telescope at an
observing frequency of ∼ 3GHz is ∼ 60ns and some individual TOA uncertainties
are ∼ 30ns. However, it is not yet clear whether the low rms of the residuals will
continue with longer data spans. Verbiest et al.
this pulsar over the previous 10yr and detected the presence of low-frequency timing
irregularities. These irregularities may limit the rms achievable over many years. More
recently Verbiest et al. (2009) studied the timing stability for a sample of 20 millisecond
pulsars over time scales of up to 10yr. Even though PSR J1939+2134 showed significant
unmodelled residuals that may make this pulsar unusable for long-term GW detection
experiments, the timing of most of the other pulsars was shown to be stable enough for
GW detection over decadal time scales.
For the pulsars in Table 1 we have used typical, current signal-to-noise (S/N)
measurements of pulse profiles obtained at each of the IPTA observatories to calculate
the best possible timing precision given the period of the pulsar and its pulse shape. We
emphasise that the actual rms timing residuals currently being obtained are usually
significantly worse. Out of 37 pulsars, thirteen have expected TOA uncertainties
< 250ns, seven between 250 and 500ns, a further nine between 500ns and 1µs, five
between 1 and 2µs and the remaining three > 2µs. For the case of a stochastic GW
background created by coalescing supermassive black-hole systems, we have calculated
(2008) presented observations of

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The international pulsar timing array project
7
the signal-to-noise ratio of a measurement of the GWB amplitude for the various PTAs.
Our analysis is based on that presented by Verbiest et al. (2009) who use the term
”detection significance” for this signal-to-noise ratio. The results are plotted in Figure
3. Here we have assumed that 1) each project obtains approximately one observation
every three weeks over five years and 2) the timing residuals (with no simulated GWs
signals present) are white (i.e., they have a flat spectrum) with an rms given by the
expected TOA uncertainties (i.e., all timing noise, ISM effects and calibration errors
are assumed to be negligible). We know that some of the pulsars in Table 1 exhibit
non-white timing noise which would degrade the sensitivity on a 5yr scale significantly
and would be even more detrimental on a 10yr scale. However, we do not have this
information for all of the pulsars in Table 1, so we cannot uniformly improve the analysis.
Our result represents “the best we could do with current systems”. There is some reason
to hope that timing noise can be modeled and corrected (Lyne et al. in preparation).
If the background amplitude is just below current upper bounds (Jenet et al. 2006)
then such a five-year data set would produce a signal-to-noise ratio of ∼ 6. However,
if the amplitude is closer to A = 10−15then the background will be barely detectable.
For similar data sets, but with data spanning 10yr, a background with A = 10−15will
still only have a signal-to-noise ratio of ∼ 5 (triangle symbols). Also shown on this plot
are the detection significance obtained using the PPTA, NANOGrav and EPTA data
individually. Clearly, a detection of the GW background will require the combination
of these data sets. Finally, the thin solid line (marked ‘cPTA’) indicates a canonical
timing array where 20 pulsars are each timed for 100ns over 5yr with weekly sampling.
In Figure 4, we show the sensitivity of the IPTA project to single, persistent sources
of GWs (Yardley et al., in preparation). This figure indicates that sources similar to the
postulated binary system in the radio galaxy 3C66B would be clearly detectable with
any polarisation and at any position in the sky.
A significant reduction in the required time to detect GWs would be made if the rms
timing residuals could be further reduced. Techniques that may achieve such a reduction
include 1) observing at higher frequencies§, 2) discovering new millisecond pulsars, 3)
obtaining pulse TOAs through use of polarisation information (van Straten 2006), 4)
increasing bandwidth and/or observing time and 5) observing only during periods when
the pulsar is bright because of scintillation. Also note that the simulations described
above assume no previous data on each pulsar. Most of these pulsars have been observed
for years to decades with various observing systems. The use of these earlier data sets
will improve our sensitivity to GW signals.
§ Note that for some pulsars improved TOA uncertainties can be obtained from low frequency
observations. However, compared with higher frequency data such observations are more affected
by interstellar medium propagation delays which add uncorrelated timing noise.

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The international pulsar timing array project
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Figure 4. The sensitivity to individual sources of GWs is shown for the IPTA and a
possible future experiment with the SKA. The expected signals from coalescing black
holes at the cores of 3C66B and OJ287 are shown. The dashed lines indicate the
expected signals from black hole binary systems with chirp masses of 109and 1010M⊙
respectively, situated in the Virgo cluster. For comparison, sensitivity curves of LIGO
and LISA and predicted signal levels are also shown.
Table 1. Pulsars observed as part of the International Pulsar Timing Array project.
The best possible rms values for observations (with current observing systems) from
the PPTA, EPTA and NANOGrav projects are estimated in the final three columns.
PSR BPSR JP
(ms)
4.87
2.32
5.76
3.06
28.85
Pb
(d)
-
2.03
5.74
1.20
8.32
S1400
(mJy)
Array PPTA
(µs)
-
-
0.03
0.71
-
EPTA
(µs)
0.54
-
-
0.45
9.58
NANOGrav
(µs)
0.31
4.81
-
0.50
-
-
-
-
-
J0030+0451
J0218+4232
J0437−4715
J0613−0200
J0621+1002
0.6
0.9
EPTA, NANOGrav
NANOGrav
PPTA
PPTA, EPTA, NANOGrav
EPTA
142.0
1.4
1.9
-
-
-
-
-
J0711−6830
J0751+1807
J0900−3144
J1012+5307
J1022+1001
5.49
3.48
11.1
5.26
16.45
-
0.3
18.7
0.60
7.81
1.6
3.2
3.8
3.0
3.0
PPTA
EPTA
EPTA
EPTA, NANOGrav
PPTA, EPTA
1.32
-
-
-
0.37
-
0.78
1.55
0.32
0.48
-
-
-
0.61
-
-
-
-
-
-
J1024−0719
J1045−4509
J1455−3330
J1600−3053
J1603−7202
5.16
7.47
7.99
3.60
14.84
-
4.08
76.17
14.35
6.31
0.7
3.0
1.2
3.2
3.0
PPTA, EPTA
PPTA
EPTA, NANOGrav
EPTA, PPTA
PPTA
0.43
2.68
-
0.32
0.70
0.25
-
3.83
0.23
-
-
-
1.60
-
-
-
-
-
-
-
J1640+2224
J1643−1224
J1713+0747
J1730−2304
J1732−5049
3.16
4.62
4.57
8.12
5.31
175.46
147.02
67.83
-
5.26
2.0
4.8
8.0
4.0
EPTA, NANOGrav
PPTA, EPTA, NANOGrav
PPTA, EPTA, NANOGrav
PPTA, EPTA
PPTA
-
0.57
0.15
0.83
1.74
0.45
0.56
0.07
1.01
-
0.19
0.53
0.04
-
--
-
-
-
-
B1821−24
J1738+0333
J1741+1351
J1744−1134
J1751−2857
J1824−2452
5.85
3.75
4.08
3.91
3.05
0.35
16.34
-
110.7
-
-
-
NANOGrav
NANOGrav
PPTA, EPTA, NANOGrav
EPTA
PPTA, EPTA
-
-
0.21
-
0.39
-
-
0.14
0.90
0.24
0.24
0.19
0.14
-
-
3.0
0.06
0.2
-
B1855+09
-
-
-
J1853+1303
J1857+0943
J1909−3744
J1910+1256
J1918−0642
4.09
5.37
2.95
4.98
7.65
115.65
12.33
1.53
58.47
10.91
0.4
5.0
3.0
0.5
NANOGrav
PPTA, EPTA, NANOGrav
PPTA, EPTA, NANOGrav
EPTA, NANOGrav
EPTA, NANOGrav
-
0.82
0.19
-
-
-
0.44
0.04
0.99
0.87
0.17
0.25
0.15
0.17
1.08-
B1937+21
B1953+29
-
-
-
J1939+2134
J1955+2908
J2019+2425
J2124−3358
J2129−5721
1.56
6.13
3.94
4.93
3.73
-
117.35
76.51
-
6.63
10.0
1.1
PPTA, EPTA, NANOGrav
NANOGrav
NANOGrav
PPTA
PPTA
0.11
-
-
1.52
0.87
0.02
-
-
-
-
0.03
0.18
0.66
-
-
-
1.6
1.4
-
-
J2145−0750
J2317+1439
16.05
3.44
6.84
2.46
8.0
4.0
PPTA, EPTA, NANOGrav
NANOGrav
0.86
-
0.40
0.81
1.37
0.25

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5. Future data sets
Current pulsar timing array projects have the potential to make a detection of a GW
background or a single GW source. Unfortunately, the predicted S/N of any such
detection is too low for detailed studies of the GW properties. A high S/N detection of
a background would provide a test of general relativity (Lee et al. 2009) and allow a
detailed understanding of the properties of the sources that form the GW background.
Within ∼10yr it is expected that various new telescopes will be able to improve
the existing timing projects.For instance, the Australian Square Kilometre Array
Pathfinder (ASKAP) and the South African Karoo Array Telescope (MeerKAT) will
increase the number of known pulsars and provide a larger number of telescopes
in the Southern Hemisphere for high-precision pulsar timing (Johnston et al. 2007,
http://www.ska.ac.za/). It is also likely that a new 500m diameter telescope (FAST)
will be built in China by 2014 (Nan et al. 2006). This telescope will be an ideal
instrument for pulsar searching and timing and should significantly improve our timing
precision for a large number of pulsars. The EPTA is currently undertaking a plan to
create the Large European Array for Pulsars (LEAP). The LEAP project will coherently
combine the signals from the five major European observatories to create a telescope
that will have a sensitivity similar to that of the illuminated Arecibo telescope.
On a slightly longer timescale, the Square Kilometre Array (SKA) telescope is
planned (current plans are for the full SKA to be completed in 2022, with initial
observations with a 10% SKA to begin in 2018).
telescope implies that it will be able to time many hundreds of pulsars at the level
currently achieved for a few pulsars (Kramer et al. 2004). Such timing data sets will
revolutionise GW detection and analysis projects by enabling high S/N detections of
GW sources.
The huge collecting area of this
6. Outreach
Many of the IPTA projects have components that are being used to train the first
generation of GW astronomers and to discover new pulsars useful for timing array
projects. Arecibo pulsar survey data are currently being obtained and analysed both
by high school students in the USA (through the Arecibo Remote Command Center)
and the public Worldwide as part of the Einstein@Home project?. Students in West
Virginia, U.S.A., are able to search for pulsars using observations taken with the Green
Bank telescope¶. The PULSE@Parkes project (Hollow et al. 2008) allows students in
Australia and overseas to carry out timing observations for the PPTA project (Hobbs et
al. 2009c). The Mid-Atlantic Relativistic Initiative in Education (MARIE) is creating
tools for introducing gravitational waves in high school and college courses+.
? http://arcc.phys.utb.edu/ARCC, http://einstein.phys.uwm.edu/
¶ http://www.pulsarsearchcollaboratory.com
+http://www.fandm.edu/marie

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7. Conclusion
Given current theoretical models, it is likely that ultra-low frequency GWs will be
detected by pulsar timing experiments within 5-10yr. The first detections are expected
to be of an isotropic, stochastic GW background created by coalescing supermassive
binary black-hole systems. It is expected that GW astronomy using pulsars will become
commonplace in the SKA era during which the background will be analysed in detail
and individual binary black-hole systems and burst GW sources will be detectable.
7.1. Acknowledgements
We acknowledge the dedication and skills of the engineers and support staff at the
various observatories without whom the IPTA project could not exist.
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