Detection of Gravitational Waves
with Pulsar Timing
R. N. Manchester
Australia Telescope National Facility, CSIRO
Sydney Australia
• Brief review of pulsar properties and timing
• Detection of gravitational waves
• Pulsar Timing Array (PTA) projects
• Current status and future prospects
Spin-Powered Pulsars: A Census
• Currently1886 known
(published) pulsars
• 1674 rotation-powered
disk pulsars
• 179 in binary systems
• 192 millisecond pulsars
• 108 in globular clusters*
• 13 AXP/SGR
• 20 extra-galactic pulsars
* Total known: 140 in 26 clusters
(Paulo Freire’s web page)
Data from ATNF Pulsar Catalogue, V1.36
(www.atnf.csiro.au/research/pulsar/psrcat; Manchester et al. 2005)
Pulsar Origins
Pulsars are believed to be rotating neutron stars
– two main classes:
Normal Pulsars:
• Formed in supernova
• Periods between 0.03 and 10 s
• Relatively young (< 107 years)
• Mostly single (non-binary)
Millisecond Pulsars (MSPs):
• MSPs are very old (~109 years).
• Mostly binary
• They have been ‘recycled’ by accretion
from an evolving binary companion.
• This accretion spins up the neutron star to
millisecond periods.
• During the accretion phase the system may
be detectable as an X-ray binary system.
Pulsars as Clocks
• Neutron stars are tiny (about 25 km across) but have a mass
of about 1.4 times that of the Sun
• They are incredibly dense and have gravity 1012 times as
strong as that of the Earth
• Because of this large mass and small radius, their spin rates and hence pulsar periods - are incredibly stable
e.g., PSR J0437-4715 had a period of :
5.757451831072007  0.000000000000008 ms
• Although pulsar periods are very stable, they are not constant.
Pulsars lose energy and slow down
• Typical slowdown rates are less than a microsecond per year
The P – P Diagram
P = Pulsar period
P = dP/dt = slow-down rate
• For most pulsars P ~ 10-15
• MSPs have P smaller by
about 5 orders of magnitude
• Most MSPs are binary, but
few normal pulsars are
• P/(2P) is an indicator of
pulsar age
• Surface dipole magnetic field
~ (PP)1/2
Great diversity in the
pulsar population!
Galactic Disk pulsars
The First Binary Pulsar
• Discovered at Arecibo Observatory
by Russell Hulse & Joe Taylor in 1975
• Pulsar period 59 ms, a recycled
• Doppler shift in observed period due
to orbital motion
• Orbital period only 7 hr 45 min
• Maximum orbital velocity 0.1% of
velocity of light
Relativistic effects detectable!
PSR B1913+16
Orbital Decay in PSR B1913+16
• Rapid orbital motion of two stars in
PSR B1913+16 generates gravitational
PSR B1913+16
Orbit Decay
• Energy loss causes slow decrease of
orbital period
• Can predict rate of orbit decay from
known orbital parameters and masses of
the two stars using general relativity
• Ratio of measured value to predicted
value = 1.0013  0.0021
Confirmation of general
First observational evidence
for gravitational waves!
(Weisberg & Taylor 2005)
Detection of
Gravitational Waves
• Prediction of general relativity and other theories of gravity
• Generated by acceleration of massive object(s)
• Astrophysical sources:
 Inflation era fluctuations
 Cosmic strings
 BH formation in early Universe
 Binary black holes in galaxies
 Coalescing neutron-star binaries
 Compact X-ray binaries
(K. Thorne, T. Carnahan, LISA Gallery)
Detection of Gravitational Waves
• Generated by acceleration of massive objects in Universe, e.g. binary black holes
• Huge efforts over more than four decades to detect gravitational waves
• Initial efforts used bar detectors pioneered by Weber
• More recent efforts use laser interferometer systems, e.g., LIGO, VIRGO, LISA
• Two sites in USA
• Perpendicular 4-km arms
• Spectral range 10 – 500 Hz
• Initial phase now operating
• Advanced LIGO ~ 2014
• Orbits Sun, 20o behind the Earth
• Three spacecraft in triangle
• Arm length 5 million km
• Spectral range 10-4 – 10-1 Hz
• Planned launch ~2020
Limiting the GW Background with Pulsars
• Observed pulsar periods are modulated by gravitational waves in
• With observations of just a few pulsars, can only put a limit on
strength of the stochastic GW background
• Best limits are obtained for GW frequencies ~ 1/T where T is length
of data span
• Analysis of 8-year sequence of Arecibo observations of PSR
B1855+09 gives Wg = rGW/rc < 10-7 (Kaspi et al. 1994, McHugh et al.1996)
Timing residuals for PSR B1855+09
A Pulsar Timing Array (PTA)
• With observations of many pulsars widely distributed on the sky
can in principle detect a stochastic gravitational wave background
• Gravitational waves passing over the pulsars are uncorrelated
• Gravitational waves passing over Earth produce a correlated signal
in the TOA residuals for all pulsars
• Requires observations of ~20 MSPs over 5 – 10 years; could give
the first direct detection of gravitational waves!
• A timing array can detect instabilities in terrestrial time standards
– establish a pulsar timescale
• Can improve knowledge of Solar system properties, e.g. masses
and orbits of outer planets and asteroids
Idea first discussed by Hellings & Downs (1983),
Romani (1989) and Foster & Backer (1990)
 Clock errors
All pulsars have the same TOA variations:
monopole signature
 Solar-System ephemeris errors
Dipole signature
 Gravitational waves
Quadrupole signature
Can separate these effects provided there is a
sufficient number of widely distributed pulsars
Detecting a Stochastic GW Background
Hellings & Downs correlation function
Simulation of timingresidual correlations
among 20 pulsars for a
GW background from
binary super-massive
black holes in the cores
of distant galaxies
To detect the expected signal, we need ~weekly observations
of ~20 MSPs over 5-10 years with TOA precisions of ~100
ns for ~10 pulsars and < 1 s for the rest
(Jenet et al. 2005, Hobbs et al. 2009)
Sky positions of all known MSPs
suitable for PTA studies
• In the Galactic disk (i.e. not in globular clusters)
• Short period and relatively strong – circle radius ~ S1400/P
• ~60 MSPs meet criteria, but only ~30 “good” candidates
Major Pulsar Timing Array Projects
 European Pulsar Timing Array (EPTA)
• Radio telescopes at Westerbork, Effelsberg, Nancay, Jodrell Bank, (Cagliari)
• Normally used separately, but can be combined for more sensitivity
• High-quality data (rms residual < 2.5 s) for 9 millisecond pulsars
 North American pulsar timing array (NANOGrav)
• Data from Arecibo and Green Bank Telescope
• High-quality data for 17 millisecond pulsars
 Parkes Pulsar Timing Array (PPTA)
• Data from Parkes 64m radio telescope in Australia
• High-quality data for 20 millisecond pulsars
Observations at two or three frequencies required to remove the effects of
interstellar dispersion
The Parkes Pulsar Timing Array
• Using the Parkes 64-m radio telescope to observe 20 MSPs
• ~25 team members – principal groups: Swinburne University (Melbourne;
Matthew Bailes), University of Texas (Brownsville; Rick Jenet), University of
California (San Diego; Bill Coles), ATNF (Sydney; RNM)
• Observations at 2 – 3 week intervals
at three frequencies: 685 MHz, 1400
MHz and 3100 MHz
• New digital filterbank systems and
baseband recorder system
• Regular observations commenced in
• Timing analysis – PSRCHIVE and
• GW simulations, detection
algorithms and implications, galaxy
evolution studies
The PPTA Pulsars
Best result so far – PSR J0437-4715 at 10cm
• Observations of PSR
J0437-4715 at 3100 MHz
• 1 GHz bandwidth with
digital filterbank system
• 1.2 years data span
• 211 TOAs, each 64 min
observation time
• Weighted fit for nine
parameters using TEMPO2
• No dispersion correction
• Reduced 2 = 2.87
Rms timing residual 56 ns!!
PPTA Pulsars:
1.5 years of PDFB2 data
• Timing data at 2 -3 week intervals
at 10cm or 20cm
• TOAs from 64-min observations
(except J1857+0943, J1939+2134,
J2124-3358, each 32 min)
• Uncorrected for DM variations
• Solve for position, F0, F1, Kepler
parameters if binary
• Four pulsars with rms timing
residuals < 200 ns, eleven < 1 s
• Best results on J0437-4715 (80 ns),
J1909-3744 (110 ns), J1939+2134
Approaching our goal but
not there yet!
Timing Stability
of MSPs
• 10-year data span for 20
• Includes 1-bit f/b, Caltech
FPTM and CPSR2 data
10 s
• sz: frequency stability at
different timescales t
• For “white” timing residuals,
expect sz ~ t-3/2
• Most pulsars roughly
consistent with this out to 10
• Good news for PTA projects!
(Verbiest et al. 2009)
100 ns
The Stochastic GW Background
• Super-massive binary black holes in
the cores of galaxies – formed by
galaxy mergers
• GW in PTA range when orbital period
~10 years
8 nHz
100 nHz
Expect detectable
• Strongest signal
signal from galaxies with z ~ 1
with current
• BH masses
~ 109 – 1010 M
• Range of predictions depending on
assumptions about BH mass function etc
(Sesana, Vecchio & Colacino 2008)
Current and Future Limits on the
Stochastic GW Background
• Arecibo data for PSR B1855+09 (Kaspi et al.
1994) and recent PPTA data
• Monte Carlo methods used to determine
detection limit for stochastic background
described by hc = A(f/1yr) (where  = -2/3 for
SMBH, ~ -1 for relic radiation, ~ -7/6 for cosmic
strings) (Jenet et al. 2006)
 Current limit: Wgw(1/8 yr) ~ 2 
 For full PPTA (100ns, 5 yr): ~ 10-10
• Currently consistent with all SMBH
evolutionary models (Jaffe & Backer 2003; Wyithe
& Loeb 2003, Enoki et al. 2004, Sesana et al. 2008)
• If no detection with full PPTA, all current
models ruled out
• Already limiting EOS of matter in epoch of
inflation (w = p/ > -1.3) and tension in
cosmic strings (Grishchuk 2005; Damour &
Vilenkin 2005)
Timing Residuals
10 s
GW from Formation of Primordial Black-holes
• Black holes of low to intermediate mass can be formed at end of the inflation era
from collapse of primordial density fluctuations
• Intermediate-mass BHs (IMBH) proposed as origin of ultra-luminous X-ray
sources; lower mass BHs may be “dark matter”
• Collapse to BH generates a spectrum of gravitational waves depending on mass
Pulsar timing can already rule out formation of
Black Holes in mass range 102 – 104 M!
(Saito & Yokoyama 2009)
Single-source Detection
Localisation with PPTA
Predicted merger rates for 5 x 108 M
binaries (Wen et al. 2009, Sesana et al. 2009)
PPTA can’t detect individual binary
systems - but SKA will!
(Anholm et al. 2008)
Need better sky distribution of pulsars international PTA collaborations are
IPTA – The International Pulsar Timing Array
• First application: search for
effects of planet-mass errors in
Solar-system ephemeris used
for barycentre correction
• 22 years of TOA data for PSR
B1855+09 from Arecibo,
Effelsberg & Parkes
• Jupiter is best candidate – 11
year orbital period
Jupiter mass:
Best published value: (9.547919 ± 8) × 10-4 Msun
IPTA result:
(9.5479197 ± 6) × 10-4 Msun
Unpub. Galileo result: (9.54791915 ± 11) × 10-4 Msun
(Champion et al., in prep)
More pulsars, more data span, should give best available value!
A Pulsar Timescale
• Terrestrial time defined by a weighted average of
caesium clocks at time centres around the world
• Comparison of TAI with TT(BIPM03) shows
variations of amplitude ~1 s even after trend
• Revisions of TT(BIPM) show variations of ~50 ns
• Pulsar timescale is not absolute, but can reveal
irregularities in TAI and other terrestrial
• Current best pulsars give a 10-year stability
(sz) comparable to TT(NIST) - TT(PTB)
• Full PPTA will define a pulsar timescale with
precision of ~50 ns or better at 2-weekly
intervals and model long-term trends to 5 ns or
(Petit 2004)
 Precision timing of pulsars is a great tool which has given the first
observational evidence for the existence of gravitational waves
 We are now approaching the level of TOA precision that is
required to achieve the main goals of PTA projects
 Good chance that detection of nanoHertz GW will be achieved
with a further 5 - 10 years of data if current predictions are realistic
 Major task is to eliminate all sources of systematic error - good
progress, but not there yet
 So far, intrinsic pulsar period irregularities are not a limiting factor
 Progress toward all goals will be enhanced by international
collaboration - more (precise) TOAs and more pulsars are better!
 Current efforts will form the basis for detailed study of GW and
GW sources by future instruments with higher sensitivity, e.g. SKA
The Gravitational Wave Spectrum
Dispersion Corrections
• DFB for 10cm/20cm
• CPSR2 for 50cm
• About 6 yr data span
At 20cm, DM
of 10-4 cm-3 pc
corresponds to
t = 210 ns
• Will be applied to
pipeline processing
Algorithm development
by Xiaopeng You,
George Hobbs and
Stefan Oslowski
PTA Pulsars: Timing Residuals
• 30 MSPs being timed in PTA projects world-wide
• Circle size ~ (rms residual)-1
• 12 MSPs being timed at more than one observatory