Australia Telescope National Facility, CSIRO Sydney
Australia
• Introduction to pulsars and pulsar timing
• Parkes pulsar surveys – the double pulsar
• Tests of gravitational theories using pulsars
• The Parkes Pulsar Timing Array project

Pulsars are believed (by most people) to be rotating neutron stars
Normal Pulsars:
• Formed in supernova
• Periods between 0.03 and 10 s
• Relatively young (< 10 7 years)
• Mostly single (non-binary)
Millisecond Pulsars (MSPs):
• MSPs are very old (~10 9 years).
(ESO – VLT)
• 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.

• Number of known pulsars: 1775
• Number of millisecond pulsars: 172
• Number of binary pulsars: 134
• Number of AXPs: 13
• Number of pulsars in globular clusters: 99*
• Number of extragalactic pulsars: 20
* Total known: 137 in 25 clusters
(Paulo Freire’s web page)
Data from ATNF Pulsar Catalogue, V1.32
(www.atnf.csiro.au/research/pulsar/psrcat; Manchester et al. 2005)

• Pulsar periods are incredibly stable and can be measured precisely, e.g. on Jan 16, 1999, PSR J0437-4715 had a period of :
5.757451831072007

0.000000000000008 ms
• Although pulsar periods are stable, they are not constant. Pulsars lose energy and slow down: dP/dt is typically 10 -15 for normal pulsars and
10 -20 for MSPs
• Precise pulsar timing parameters are measured by comparing observed pulse times of arrival (TOAs) with predicted TOAs based on a model for the pulsar, then using the timing residuals - deviations from the model - to improve the model parameters and to search for unmodelled effects


Intrinsic noise
• Period fluctuations, glitches
• Pulse shape changes
 Perturbations of the pulsar’s motion
• Gravitational wave background
• Globular cluster accelerations
• Orbital perturbations – planets, 1 st order Doppler, relativistic effects
 Propagation effects
• Wind from binary companion
• Variations in interstellar dispersion
• Scintillation effects
 Perturbations of the Earth’s motion
• Gravitational wave background
• Errors in the Solar-system ephemeris

Clock errors
• Timescale errors
• Errors in time transfer
 Instrumental errors
• Radio-frequency interference and receiver non-linearities
• Digitisation artifacts or errors
• Calibration errors and signal processing artifacts and errors
 Receiver noise

 Discovered at Arecibo Observatory by Russell Hulse & Joe Taylor in 1975
 Pulsar period 59 ms, a recycled pulsar
 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!

Given the Keplerian orbital parameters and assuming general relativity:
• Periastron advance: 4.226607(7) deg/year
 M = m p
+ m c
• Gravitational redshift + Transverse Doppler: 4.294(1) ms
 m c
(m p
+ 2m c
)M -4/3
• Orbital period decay: -2.4211(14) x 10 -12
 m p m c
M -1/3
First two measurements determine m p and m checks consistency with adopted theory.
c
. Third measurement
M p
= 1.4408

0.0003 M sun
M c
= 1.3873

0.0003 M sun
Both neutron stars!
(Weisberg & Taylor 2005)

• Energy loss to gravitational radiation
• Prediction based on measured
Keplerian parameters and Einstein’s general relativity
• Corrected for acceleration in gravitational field of Galaxy
.
.
• P b
(obs)/P b
(pred) = 1.0013

0.0021
First observational evidence for gravitational waves!
(Weisberg & Taylor 2005)

The Hulse-Taylor Binary Pulsar
• First discovery of a binary pulsar
• First accurate determinations of neutron star masses
• First observational evidence for gravitational waves
• Confirmation of General Relativity as an accurate description of strong-field gravity

• Covers strip along Galactic plane, -100 o < l < 50 o , |b| < 5 o
• Central frequency 1374 MHz, bandwidth 288 MHz, 96 channels/poln/beam
• Sampling interval 250  s, time/pointing 35 min, 3080 pointings
• Survey observations commenced 1997, completed 2003
• Processed on work-station clusters at ATNF, JBO and McGill
• 740 pulsars discovered, 1015 detected
• At least 18 months of timing data obtained for each pulsar
Principal papers:
I: Manchester et al., MNRAS, 328, 17 (2001)
System and survey description, 100 pulsars
II: Morris et al., MNRAS, 335, 275 (2002)
120 pulsars, preliminary population statistics
III: Kramer et al., MNRAS, 342, 1299 (2003)
200 pulsars, young pulsars and

-ray sources
IV: Hobbs et al., MNRAS, 352, 1439 (2004)
180 pulsars, 281 previously known pulsars
V: Faulkner et al., MNRAS, 355, 147 (2004)
Reprocessing methods, 17 binary/MSPs
VI: Lorimer et al., MNRAS, 372, 777 (2006)
142 pulsars, Galactic population and evolution

• New sample of young, high-B, longperiod pulsars
• Large increase in sample of mildly recycled binary pulsars
• Three new doubleneutron-star systems and one double pulsar!
J0737-3039
J1119-6127

QuickTime™ and a
YUV420 codec decompressor are needed to see this picture.

Discovered at Parkes in 2003

One of top ten science breakthroughs of 2004 - Science

P
A
= 22 ms, P
B
= 2.7 s
 Orbital period 2.4 hours!

Periastron advance 16.9 deg/yr!
(Burgay et al., 2003; Lyne et al. 2004)

• “Double-line binary” gives the mass ratio for the two stars – strong constraint on gravity theories
(Lyne et al., Science, 303, 1153, 2004)
0.2 pulse periods
• MSP blows away most of B magnetosphere - dramatic effect on pulse emission
(Spitkovsky & Arons 2005)

Limits on Parameterised Post-Newtonian (PPN) parameters

Dipolar gravitational radiation – dP b
/dt

Variation of gravitational constant G – dP/dt, dP b
/dt
 Orbit ‘polarisation’ due to external field – orbit circularity
Binary pulsars give limits comparable to or better than
Solar-system tests, but in strong-field conditions
(GM/Rc 2 ~ 0.1 compared to 10 -5 for Solar-system tests)

• Long-period binary MSP discovered in Parkes Multibeam Survey
• P = 4.09 ms, P b
= 115 d, Ecc = 0.00002369(9), Min M comp
= 0.24 M sun
• White dwarf companion
• Test of Strong Equivalence Principle: Differential acceleration in
Galactic gravitational field leads to “forced” eccentricity
(Damour & Schaefer 1991)
• Bayesian analysis with 20 other known low-mass wide binary pulsars
• | D
| < 5 x 10 -3 (95% confidence)
Comparable to LLR limit but in strong field regime.
(Stairs et al. 2005)

• Mass functions: sin i < 1 for A and B
• Mass ratio R = M
A
/M
B
Measured value: 1.0714

0.0011

Independent of theory to 1PN order. Strong constraint!
• Periastron advance 
.
: 16.8995

0.0007 deg/yr
Already gives masses of two stars
(assuming GR) :
M
A
= 1.3381

0.0007 M sun
M
B
= 1.2489

0.0007 M sun
Star B is a very low-mass NS!
(Kramer et al. Science, 314, 97, 2006)
Mass function B
Mass Function A

GR value Measured value Improves as
.

Periast. adv. (deg/yr) 16.8995

0.0007 T 1.5
.

Grav. Redshift (ms) 0.3842 0.386

0.003 T 1.5
P b
Orbit decay -1.248 x 10 -12 (-1.252

0.017) x 10 -12 T 2.5
r Shapiro range (
 s) 6.15 6.2

0.3 T 0.5
s Shapiro sin i
+16
0.99987 0.99974 T 0.5
Non-radiative test - distinct from PSR B1913+16
(Kramer et al. 2006)

R: Mass ratio

.
: periastron advance

: gravitational redshift r & s: Shapiro delay
.
P b
: orbit decay
• Six measured parameters
• Four independent tests
• Fully consistent with general relativity (0.05%)
(Kramer et al. 2006)

.
• Measured P b
= (-1.252

0.017) x 10 -12 in 2.5 years
• Will improve at least as T 2.5
• Not limited by Galactic acceleration!

System is much closer to Sun - uncertainty in P
.
b,Gal
~ 10 -16
•
Main uncertainty is in Shklovskii term due to uncertainty in transverse velocity and distance

Scintillation gives V perp
= 66

15 km s -1

Timing gives V perp
~10 km s -1 -- correction at 0.02% level

VLBI measurements should give improved distance
Will surpass PSR B1913+16 in ~5 years and improve rapidly!

• Relativistic orbit deformation: e e
 r
= e (1 +
 r
)
= e (1 +


) ~ T 2.5
Should be measurable in a few years
• Spin orbit coupling:

Geodetic precession - precession of spin axis about total angular momentum
Changes in pulse profile should give misalignment angle

Periastron precession - higher order terms
•
Can give measurement of NS moment of inertia
Aberration: x obs
= a
1 sin i = (1 +

A
)x int
Will change due to geodetic precession
(Damour & Deruelle 1985)

• For J0737-3039A, precession period ~ 75 yr
(Damour & Ruffini 1974, Barker & O’Connell 1975)
Difference profiles over 1.5 years
• Expect changes in pulse profile as line-of-sight cut moves across beam (observed in PSR
B1913+16, B1534+12, J1141-6545)
PSR B1913+16
(Kramer 1998,2003; Weisberg & Taylor 2002)
Not observed in PSR J0737-3039A!

Small misalignment angle?

Small natal kick?
 Light NS, low velocity, small eccentricity

Different NS formation mechanism?
(Piran & Shaviv 2005) (Manchester et al. 2005)

• Prediction of general relativity and other theories of gravity
(NASA GSFC)
• Generated by acceleration of massive object(s)
• Astrophysical sources:
 Inflation era

Cosmic strings
 SN, BH formation in early Universe
 Binary black holes in galaxies
 Coalescing neutron-star binaries
 Compact X-ray binaries
(K. Thorne, T. Carnahan, LISA Gallery)

• 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
LIGO
• Two sites in USA
• Perpendicular 4-km arms
• Spectral range 10 – 500 Hz
• Initial phase now operating
• Advanced LIGO ~ 2011
LISA
• Orbits Sun, 20 o behind the Earth
• Three spacecraft in triangle
• Arm length 5 million km
• Spectral range 10 -4 – 10 -1 Hz
• Planned launch ~2017

• Prime candidate source for ground laser-interferometer systems
• Predicted detection rate dominated by double pulsar!
• Around one thousand systems similar to PSR J0737-3039A/B in
Galaxy
• Galactic merger rate between 80 and 370 per Myr (1 s
)
• Detection rate for initial LIGO between one per 8 years and one per
35 years.
• Factor of seven increase over rates estimated from PSR B1913+16
(Kalogera et al. 2004)

• Observed pulse periods affected by presence of gravitational waves in Galaxy
• With observations of <10 pulsars, can only put limit on strength of 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
W g
= r
GW
/ r c
< 10 -7
(Kaspi et al. 1994, McHugh et al.1996)
• Extended 17-year data set gives better limit, but non-uniformity makes quantitative analysis difficult (Lommen 2001, Damour & Vilenkin 2004)
Timing residuals for PSR B1855+09

• 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)


All pulsars have the same TOA variations: monopole signature

Dipole signature

Quadrupole signature
Can separate these effects provided there is a sufficient number of widely distributed pulsars

Simulation using Parkes Pulsar Timing Array (PPTA) pulsars with
GW background from binary black holes in galaxies
(Hobbs et al., 2008)

Collaborators:

Australia Telescope National Facility, CSIRO, Sydney
Dick Manchester, George Hobbs, David Champion, John Sarkissian, John Reynolds,
Mike Kesteven, Grant Hampson, Andrew Brown, David Smith, Jonathan Khoo,
(Russell Edwards)
 Swinburne University of Technology, Melbourne
Matthew Bailes, Ramesh Bhat, Willem van Straten, Joris Verbiest, Sarah Burke,
Andrew Jameson

University of Texas, Brownsville
Rick Jenet
 University of Sydney, Sydney
Daniel Yardley

National Observatories of China, Beijing
Johnny Wen
 Peking University, Beijing
Kejia Lee
 Southwest University, Chongqing
Xiaopeng You

Curtin University, Perth
Aidan Hotan


To detect gravitational waves of astrophysical origin

To establish a pulsar-based timescale and to investigate irregularities in terrestrial timescales

To improve on the Solar System ephemeris used for barycentric correction
To achieve these goals we need ~weekly observations of
~20 MSPs over at least five years with TOA precisions of
~100 ns for ~10 pulsars and < 1
 s for rest
• Modelling and detection algorithms for GW signals
• Measurement and correction for interstellar and Solar System propagation effects
• Implementation of radio-frequency interference mitigation techniques

P < 20 ms and not in globular clusters

Recent Results using PDFB2
• 20 MSPs - all in Galactic disk except
J1824-2452 (B1821-24) in M28
• ~200 days of timing data at 2 -3 week intervals at 10cm and 20cm
• Uncorrected for DM variations
• Two pulsars with rms timing residuals < 100 ns, seven < 500 ns, eleven < 1
 s, all < 2.6
 s
• Best results on J0437-4715 (52 ns) and J1909-3744 (97 ns)
Highest precision timing results ever obtained!
Still not quite good enough though!!

• 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 removed
• Revisions of TT(BIPM) show variations of ~50 ns
• Pulsar timescale is not absolute, but can reveal irregularities in TAI and other terrestrial timescales
• Current best pulsars give a 10-year stability
( s z
) 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 better
(Petit 2004)

• Arecibo data for PSR B1855+09
Timing Residuals
(Kaspi et al. 1994) and recent PPTA data
• Monte Carlo methods used to determine detection limit for stochastic background described by h = A(f/ 1 yr )
 c
( where

= -2/3 for SMBH, ~ -1 for relic radiation, ~
-7/6 for cosmic strings)
 Current limit:
W gw
(1/8 yr
) ~ 2

10 -8
 For full PPTA (100ns, 5 yr) : ~ 10 -10
• Currently consistent with all SMBH evolutionary models (e.g., Jaffe & Backer
2003; Wyithe & Loeb 2003, Enoki et al. 2004)
• 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)
10
 s
(Jenet et al. 2006)

Single source detection
Stochastic GW Background
PPTA
SKA 5 years, 100 ns
Predicted merger rates for 5 x 10 8 M
 binaries (Wen & Jenet 2008)
PPTA can’t detect individual binary systems - but SKA will!
Range of predicted amplitudes
(Jaffe & Backer 2003; Wyithe & Loeb 2003)
Difficult to get sufficient observations with PPTA alone - international collaborations important!


Pulsars are extraordinarily good clocks and provide highly sensitive probes of a range of gravitational effects
 Parkes multibeam pulsar surveys have been extremely successful, more than doubling the number of known pulsars
 First-known double-pulsar system detected! Makes possible additional independent tests of relativistic gravity

Direct detection of gravitational waves (GW) is a major goal of current astrophysics - it will open a new window on the Universe
 A pulsar timing array can detect GW from astrophysical sources (or rule out most current models)

Parkes Pulsar Timing Array (PPTA) timing 20 MSPs since mid-2004. Goal is
~100 ns rms residuals on at least half of sample; currently have two with rms residuals < 100 ns and seven less 500 ns

A pulsar-based timescale will have better long-term stability than current best terrestrial timescales
 SKA will herald a new era in the study of gravitation using pulsars!

• Rotating neutron star
• Light cylinder R
LC
= c/
W
= 5 x 10 4 P(s) km
• Charge flow along open field lines
• Radio beam from magnetic pole (in most cases)
• High-energy emission from outer magnetosphere
• Rotation braked by reaction to magnetic-dipole radiation
.
W
= -K
W
-3
• Characteristic age:  c
.
= P/(2P)
B s
~ (PP) 1/2
(Bennet Link)

• Formed in Type II supernova explosion core collapse of massive star
• Diameter 20 - 30 km
• Mass ~ 1.4 Msun
(MT77)
(Stairs 2004)
(Lattimer & Prakash 2004)

• Relatively young 394-ms pulsar in 4.7-h binary orbit
(Kaspi et al. 2000)
• From timing, companion mass 0.99 +/- 0.02 M sun
• Relativistic precession of periastron observed
: white dwarf (Bailes et al. 2003)
• Expected rate of geodetic precession 1.36 deg/yr - precession period 265 yr
• Dramatic evolution of pulse profile observed! (7-yr data span)
(Manchester et al. (2007)

Polarisation evolution and beam model

• Period:
D
P = 5 x 10 -16 s
• dP/dt: .
D
P = 4 x 10 -23
• Position:
D
= 1 mas
• Proper motion:
D
= 5 mas/yr
• Parallax:
Dp
= 10 mas

• In LMXB systems, long evolution time allows spin-up to > 1 kHz
• Most neutron-star EOSs allow spin at > 1 kHz
• X-ray observations and recent radio observations have little or no observational selection against sub-ms pulsars
• But, maximum observed spin frequency ~ 700 Hz
 Mass asymmetry due to accretion
(
D
I/I ~ 10 -7 ) results in GW emission
(e.g., Bildsten 1998)
 r-mode instability in NS leads to viscous damping & GW emission (e.g.,
Ho & Lai 2000) (Arras 2004)

• Periastron advance
• Grav. Redshift
• Orbit decay
Mp = 1.4408

0.0003 M sun
Mc = 1.3873

0.0003 M sun
Both neutron stars!
(Weisberg & Taylor 2005)
(Diagram from C.M. Will, 2001)

Measured Shapiro delay implies i = 87 o .8 +/- 1 o .2
(Kramer et al. 2005)
Correlated scintillation in A and B: implies i = 90 o .26 +/- 0 o .13
(Coles et al. 2005)

• Precession period ~ 75 yr
• Expect changes in pulse profile as line-ofsight cut moves across beam (observed in
PSR B1913+16, B1534+12, J1141-6545)
PSR B1913+16
Difference profiles over 1.5 years
(Kramer 1998,2003; Weisberg & Taylor 2002)
Not observed in PSR J0737-3039A!

Small misalignment angle?

Small natal kick?
 Light NS, low velocity, small eccentricity

Different NS formation mechanism?
(Piran & Shaviv 2005) (Manchester et al. 2005)

Secular changes are observed!

Mechanism for orbital modulation not fully understood
 Can’t separate effects of periastron precession and geodetic precession
(Burgay et al. 2005)

• Start observation at known time and average 1000 or more pulses to get mean pulse profile.
• Cross-correlate this with a standard template to give the arrival time at the telescope of a fiducial point on profile, usually the pulse peak – the pulse time-of-arrival (TOA).
• Measure a series of TOAs over days – weeks – months – years.
• Compare observed TOAs with predicted values from a model for pulsar using TEMPO - differences are called timing residuals .
• Fit the observed residuals with functions representing errors in the model parameters (pulsar position, period, binary period etc.).
• Remaining residuals may be noise – or may be science!

Spin A Spin B
1PN 2PN
Geometry NS Structure
• If geometry can be understood, measurement of variation
1PN: 16.9 o /yr in rate of periastron precession can be used to estimate NS moment of inertia (Damour & Schaefer 1988) 2PN: 0.0004 o /yr
S/N ~ T 1.5
Spin: 0.0002 o /yr
Current:

0.0007 o /yr
• Since mass known, strong limit on EOS!
(Morrison et al. 2004; Lattimer & Schutz 2005)

• Using the Parkes 64-m telescope at three frequencies (680, 1400 and
3100 MHz)
• Digital filterbank system, 256 MHz bandwidth (1 GHz early 2007),
8-bit sampling, polyphase filter
• CPSR2 baseband system 2 x 64 MHz bandwidth, 2-bit sampling, coherent de-dispersion
• Developing APSR with 512 MHz bandwidth and 8-bit sampling
• Implementing real-time RFI mitigation for 50-cm band
• TEMPO2: New timing analysis program, systematic errors in TOA corrections < 1 ns, graphical interfaces, predictions and simulations
(Hobbs et al. 2006, Edwards et al. 2006)
• Observing 20 MSPs at 2 - 3 week intervals since mid-2004
• International collaboration and co-operation to obtain improved data sampling including pulsars at northern declinations

• D
DM from 10/50cm or 20/50cm observation pairs
• Variations observed in most of PPTA pulsars
• D
DM typically a few x 10 -3 cm -3 pc
• Weak correlation of d(DM)/dt with DM, closer to linear rather than DM 1/2
• Effect of Solar wind observed in pulsars with low ecliptic latitude
(You et al., in prep.)