1. Detection of Gravitational Waves with Pulsar Timing R. N. Manchester Australia Telescope National Facility, CSIRO Sydney Australia Summary Brief review of pulsar properties and timing Detection of gravitational waves Pulsar Timing Array (PTA) projects Current status and future prospects

2. Spin-Powered Pulsars: A Census Data from ATNF Pulsar Catalogue, V1.36 (www.atnf.csiro.au/research/pulsar/psrcat; Manchester et al. 2005) * Total known: 140 in 26 clusters (Paulo Freire’s web page) 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

3. 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 to be rotating neutron stars – two main classes: Millisecond Pulsars (MSPs): (ESO – VLT)

4. 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 10 12 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 Pulsars as Clocks

5. 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 The P – P Diagram..... P = Pulsar period P = dP/dt = slow-down rate. Galactic Disk pulsars Great diversity in the pulsar population!

6. 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 PSR B1913+16 Relativistic effects detectable! The First Binary Pulsar

7. Rapid orbital motion of two stars in PSR B1913+16 generates gravitational waves 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 (Weisberg & Taylor 2005)  Confirmation of general relativity!  First observational evidence for gravitational waves! PSR B1913+16 Orbit Decay Orbital Decay in PSR B1913+16

8. 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 fluctuations  Cosmic strings  BH formation in early Universe  Binary black holes in galaxies  Coalescing neutron-star binaries  Compact X-ray binaries

9. 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 LISALIGO 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 ~2020

10. Limiting the GW Background with Pulsars Observed pulsar periods are modulated by gravitational waves in Galaxy 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  g =  GW /  c < 10 -7 (Kaspi et al. 1994, McHugh et al.1996) Timing residuals for PSR B1855+09

11. 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)

12.  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

13. Detecting a Stochastic GW Background Simulation of timing- residual correlations among 20 pulsars for a GW background from binary super-massive black holes in the cores of distant galaxies Hellings & Downs correlation function 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)

14. 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 ~ S 1400 /P ~60 MSPs meet criteria, but only ~30 “good” candidates

15. 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

16. The Parkes Pulsar Timing Array Project 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 mid-2004 Timing analysis – PSRCHIVE and TEMPO2 GW simulations, detection algorithms and implications, galaxy evolution studies

17. The PPTA Pulsars

18. 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!!

19. 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 (170ns) Approaching our goal but not there yet!

20. Timing Stability of MSPs 10-year data span for 20 PPTA MSPs Includes 1-bit f/b, Caltech FPTM and CPSR2 data  z : frequency stability at different timescales  For “white” timing residuals, expect  z ~  -3/2 Most pulsars roughly consistent with this out to 10 years Good news for PTA projects! (Verbiest et al. 2009) 100 ns 10  s

21. 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 Strongest signal from galaxies with z ~ 1 BH masses ~ 10 9 – 10 10 M  Range of predictions depending on assumptions about BH mass function etc (Sesana, Vecchio & Colacino 2008) Expect detectable signal with current PTAs! 8 nHz 100 nHz

22. Current and Future Limits on the Stochastic GW Background 10  s Timing Residuals 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 h c = A(f/1 yr )  ( where  = -2/3 for SMBH, ~ -1 for relic radiation, ~ -7/6 for cosmic strings) (Jenet et al. 2006)  Current limit:  gw (1/8 yr ) ~ 2  10 -8  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)

23. 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 (Saito & Yokoyama 2009) Pulsar timing can already rule out formation of Black Holes in mass range 10 2 – 10 4 M  !

24. Single-source Detection PPTA SKA Need better sky distribution of pulsars - international PTA collaborations are important! Predicted merger rates for 5 x 10 8 M  binaries (Wen et al. 2009, Sesana et al. 2009) PPTA can’t detect individual binary systems - but SKA will! Localisation with PPTA Sensitivity (Anholm et al. 2008)

25. 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 (Champion et al., in prep) Best published value: (9.547919 ± 8) × 10 -4 M sun IPTA result: (9.5479197 ± 6) × 10 -4 M sun Unpub. Galileo result: (9.54791915 ± 11) × 10 -4 M sun More pulsars, more data span, should give best available value! Jupiter mass:

26. 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

27. Summary  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

28. The Gravitational Wave Spectrum

30. 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 Algorithm development by Xiaopeng You, George Hobbs and Stefan Oslowski Will be applied to pipeline processing

31. 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