Pulsars and Gravity R. N. Manchester Australia Telescope National Facility, CSIRO Sydney Australia Summary Introduction to pulsars and pulsar timing Parkes pulsar surveys – the double pulsar Tests of gravitational theories using pulsars The Parkes Pulsar Timing Array project

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

Spin-Powered Pulsars: A Census 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 Data from ATNF Pulsar Catalogue, V1.32 ( Manchester et al. 2005) * Total known: 137 in 25 clusters (Paulo Freire’s web page)

Pulsars as clocks Pulsar periods are incredibly stable and can be measured precisely, e.g. on Jan 16, 1999, PSR J had a period of :  ms Although pulsar periods are stable, they are not constant. Pulsars lose energy and slow down: dP/dt is typically for normal pulsars and 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

Sources of Pulsar Timing “Noise”  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  Receiver noise  Instrumental errors Radio-frequency interference and receiver non-linearities Digitisation artifacts or errors Calibration errors and signal processing artifacts and errors

 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! PSR B : The First Binary Pulsar

Post-Keplerian Parameters: PSR B Periastron advance: (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: (14) x  m p m c M -1/3 Given the Keplerian orbital parameters and assuming general relativity: First two measurements determine m p and m c. Third measurement checks consistency with adopted theory. (Weisberg & Taylor 2005) M p =  M sun M c =  M sun Both neutron stars!

PSR B Orbit Decay 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) =  (Weisberg & Taylor 2005) First observational evidence for gravitational waves!

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 Nobel Prize for Taylor & Hulse in 1993 The Hulse-Taylor Binary Pulsar PSR B

The Parkes radio telescope has found more than twice as many pulsars as the rest of the world’s telescopes put together.

Parkes Multibeam Pulsar Survey Principal papers: 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 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

Parkes Multibeam Surveys: P vs P. J New sample of young, high-B, long- period pulsars Large increase in sample of mildly recycled binary pulsars Three new double- neutron-star systems and one double pulsar! J

The first double pulsar!  Discovered at Parkes in 2003  One of top ten science break- throughs of 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) Highly relativistic binary system! PSR J A/B

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

Binary pulsars and Gravity Tests of Equivalence Principles 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 for Solar-system tests)

PSR J and Nordvedt Effect Long-period binary MSP discovered in Parkes Multibeam Survey P = 4.09 ms, P b = 115 d, Ecc = (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 |  | < 5 x (95% confidence) Comparable to LLR limit but in strong field regime. (Stairs et al. 2005)

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

GR value Measured value Improves as  Periast. adv. (deg/yr)  T 1.5  Grav. Redshift (ms)  T 1.5 P b Orbit decay x (  0.017) x T 2.5 r Shapiro range (  s)  0.3 T 0.5 s Shapiro sin i T 0.5 Measured Post-Keplerian Parameters for PSR J A/B.. GR is OK! Consistent at the 0.05% level! (Kramer et al. 2006) Non-radiative test - distinct from PSR B

PSR J A/B Post-Keplerian Effects R: Mass ratio  : periastron advance  : gravitational redshift r & s: Shapiro delay P b : orbit decay (Kramer et al. 2006).. Six measured parameters Four independent tests Fully consistent with general relativity (0.05%)

Orbit Decay - PSR J A/B Measured P b = (  0.017) x 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 ~ 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 correction at 0.02% level  VLBI measurements should give improved distance.. Will surpass PSR B in ~5 years and improve rapidly!

PSR J : More Post-Keplerian Parameters! Relativistic orbit deformation: e r = e (1 +  r ) e  = 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)

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

Detection of Gravitational Waves Prediction of general relativity and other theories of gravity Generated by acceleration of massive object(s) (K. Thorne, T. Carnahan, LISA Gallery) 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 (NASA GSFC)

Detection of Gravitational Waves 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 ~ 2011 LISALIGO Orbits Sun, 20 o behind the Earth Three spacecraft in triangle Arm length 5 million km Spectral range – Hz Planned launch ~2017

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

Detecting Gravitational Waves with Pulsars 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 B gives  g =  GW /  c < (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 B

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

The Parkes Pulsar Timing Array Project 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 The PPTA Project: Goals 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

Sky Distribution of Millisecond Pulsars P < 20 ms and not in globular clusters

PPTA Pulsars: Recent Results using PDFB2 20 MSPs - all in Galactic disk except J (B ) 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 J (52 ns) and J (97 ns) Highest precision timing results ever obtained! Still not quite good enough though!!

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

Current and Future Limits on the Stochastic GW Background (Jenet et al. 2006) 10  s Timing Residuals Arecibo data for PSR B (Kaspi et al. 1994) and recent PPTA data Monte Carlo methods used to determine detection limit for stochastic background described by h c = A(f/1 yr )  ( where  = -2/3 for SMBH, ~ -1 for relic radiation, ~ -7/6 for cosmic strings)  Current limit:  gw (1/8 yr ) ~ 2   For full PPTA (100ns, 5 yr) : ~ 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)

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

The Gravitational Wave Spectrum

 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 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! Summary

Pulsar Model (Bennet Link) Rotating neutron star Light cylinder R LC = c/  = 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 and/or charge acceleration:  = -K  -3 Characteristic age:  c = P/(2P) Surface dipole magnetic field: B s ~ (PP) 1/2...

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

Geodetic Precession in PSR J Relatively young 394-ms pulsar in 4.7-h binary orbit (Kaspi et al. 2000) From timing, companion mass / M sun : white dwarf (Bailes et al. 2003) Relativistic precession of periastron observed 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)

PSR J Geodetic Precession: Polarisation evolution and beam model

Model timing residuals Period:  P = 5 x s dP/dt:  P = 4 x Position:  = 1 mas Proper motion:  = 5 mas/yr Parallax:  = 10 mas.

Maximum Spin Frequency 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 (  I/I ~ ) results in GW emission (e.g., Bildsten 1998)  r-mode instability in NS leads to viscous damping & GW emission (e.g., Ho & Lai 2000) MSPs and Gravity: (Arras 2004)

Neutron-star masses: PSR (Diagram from C.M. Will, 2001) Periastron advance Grav. Redshift Orbit decay Mp =  M sun Mc =  M sun Both neutron stars! (Weisberg & Taylor 2005)

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

Geodetic Precession - PSR J A Precession period ~ 75 yr Expect changes in pulse profile as line-of- sight cut moves across beam (observed in PSR B , B , J ) Difference profiles over 1.5 years (Manchester et al. 2005) (Kramer 1998,2003; Weisberg & Taylor 2002) Not observed in PSR J A!  Small misalignment angle?  Small natal kick?  Light NS, low velocity, small eccentricity  Different NS formation mechanism? (Piran & Shaviv 2005) PSR B

Orbital Modulation of PSR J B 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! Measurement of pulsar periods

Periastron Precession - higher order terms 1PN 2PN Spin ASpin B GeometryNS Structure If geometry can be understood, measurement of variation in rate of periastron precession can be used to estimate NS moment of inertia (Damour & Schaefer 1988) 1PN: 16.9 o /yr 2PN: o /yr Spin: o /yr Current:  o /yr Since mass known, strong limit on EOS! (Morrison et al. 2004; Lattimer & Schutz 2005) Not Easy! S/N ~ T 1.5

The PPTA Project: Methods 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 week intervals since mid-2004 International collaboration and co-operation to obtain improved data sampling including pulsars at northern declinations

Dispersion Measure Variations  DM from 10/50cm or 20/50cm observation pairs Variations observed in most of PPTA pulsars  DM typically a few x 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.)