1. Pulsar Timing and the Detection of Gravitational Waves R. N. Manchester CSIRO Astronomy and Space Science Sydney Australia Summary Review of pulsar properties and timing Binary pulsars and GR tests 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, V1.46 (www.atnf.csiro.au/research/pulsar/psrcat) (Manchester et al. 2005) Currently 2213 known (published) pulsars 2050 rotation-powered disk pulsars 213 in binary systems 302 millisecond pulsars 142 in globular clusters 8 X-ray isolated neutron stars 20 AXP/SGR 21 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 extremely 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. Start observation at a known time and average 10 3 - 10 5 pulses to form a 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 Transfer ToAs to an inertial frame – the solar system barycentre Compare barycentric ToAs with predicted values from a model for the pulsar – the 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

6. 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  c = 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. Great diversity in the pulsar population! Galactic Disk pulsars

7. 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 Pulsars are powerful probes of a wide range of astrophysical phenomena

8.  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 B1913+16: The First Binary Pulsar

9. Post-Keplerian Parameters: PSR B1913+16 Periastron advance: 4.226598(5) deg/year  M = m p + m c Gravitational redshift + Transverse Doppler: 4.2992(8) ms  m c (m p + 2m c )M -4/3 Orbital period decay: -2.423(1) x 10 -12  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, Nice & Taylor 2010) M p = 1.4398  0.0002 M sun M c = 1.3886  0.0002 M sun Both neutron stars!

10. Orbital motion of two stars generates gravitational waves Energy loss causes slow decrease of orbital period Predict rate of orbit decay from known orbital parameters and masses of the two stars using GR Ratio of measured value to predicted value = 0.997 +/- 0.002 (Weisberg, Nice & Taylor 2010)  Confirmation of general relativity!  First observational evidence for gravitational waves! PSR B1913+16 Orbit Decay Orbital Decay in PSR B1913+16

11. The first double pulsar!  Discovered at Parkes in 2003  One of top ten science break- throughs 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) Highly relativistic binary system! PSR J0730-3039A/B

12. 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 0.99987 0.99974 T 0.5 Measured Post-Keplerian Parameters for PSR J0737-3039A/B.. GR is OK! Consistent at the 0.05% level! (Kramer et al. 2006) Non-radiative test - distinct from PSR B1913+16 +16 -39

13. The Double Pulsar: Update PSR J0737-3039B has disappeared! Beam has moved away due to orbital precession Expected to return in 5 – 10 years (Kramer et al. 2013) Continued timing at Parkes and GBT has refined relativistic parameters Now limits deviations from GR to 0.02% Good prospects for detection of relativistic orbit deformation and measurement of pulsar moment of inertia

14. 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

15. 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 ~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)

16.  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

17. 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 ~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)

18. 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 Timing 27 millisecond pulsars, 5 with  ToA < 2  s, data spans 5 - 18 years  North American pulsar timing array (NANOGrav) Data from Arecibo and Green Bank Telescope Timing 17 millisecond pulsars, 16 with  ToA < 2  s, data spans ~ 5 years  Parkes Pulsar Timing Array (PPTA) Data from Parkes 64m radio telescope in Australia Timing 22 millisecond pulsars, 16 with  ToA < 2  s, data spans 3 – 19 years Observations at two or three frequencies required to remove the effects of interstellar dispersion

19. The Parkes Pulsar Timing Array Collaboration  CSIRO Astronomy and Space Science, Sydney Dick Manchester, George Hobbs, Ryan Shannon, Mike Keith, Sarah Burke-Spolaor, Aidan Hotan, John Sarkissian, John Reynolds, Mike Kesteven, Warwick Wilson, Grant Hampson, Andrew Brown, (Jonathan Khoo), (Russell Edwards)  Swinburne University of Technology, Melbourne Matthew Bailes, Willem van Straten, Andrew Jameson, (Stefan Oslowski)  Monash University, Melbourne Yuri Levin  University of Melbourne Vikram Ravi (Stuart Wyithe)  University of Western Australia, Perth Linqing Wen, Xingjiang Zhu  Curtin University, Perth Ramesh Bhat  University of California, San Diego Bill Coles  MPIfR, Bonn (David Champion), (Joris Verbiest), (KJ Lee)  National Space Science Center, Beijing Xinping Deng  Xinjiang Astronomical Observatory, Urumqi Jingbo Wang  Southwest University, Chongqing Xiaopeng You

20. The PPTA Project Using the Parkes 64-m radio telescope at three frequencies, 700 MHz, 1400 MHz and 3100 MHz, to observe 21 MSPs Observations at 2 - 3 week intervals Regular observations commenced in mid-2004 Digital filterbanks and baseband recording systems used to remove dispersive delays Database and processing pipeline - PSRCHIVE programs Timing analysis - TEMPO2 Studying detection algorithms for different types of GW sources (stochastic background, individual SMBHB, GW burst sources, etc.) Simulating GW signals and studying implications for galaxy evolution models Establishing a pulsar-based timescale and investigating Solar system properties Using PPTA data sets to investigate individual pulsar properties, e.g., pulse polarisation, binary evolution, astrometry etc. Manchester et al. (2013) www.atnf.csiro.au/research/pulsar/ppta

21. The PPTA Pulsars All (published) MSPs not in globular clusters

22. PPTA Three-band Timing Residuals 50cm 20cm 10cm

23. PPTA Data Sets Data for 22 pulsars, currently timing 21, two started 3 years ago PPTA data + earlier Parkes data – spans up to 19 years Best 1-year rms timing residuals ~40 ns (J0437-4715, J1909-3744) DM correction is important About half of the sample shows evidence for red noise Rms timing residuals 0.2 – 4  s Not yet applied: full polarisation (MTM) fitting, frequency- dependant templates Still work to do! (Hobbs 2013)

24. PPTA Timing Residuals Timing data for 22 pulsars Data spans to 19 years DM corrections applied where available Low-frequency (red) variations significant in about half of sample – some due to uncorrected DM variations in early data Several of best-timing pulsars nearly white

25. The International Pulsar Timing Array The IPTA is a consortium of consortia, namely existing PTAs from around the world Currently three members: EPTA, NANOGrav and PPTA The aims of the IPTA are to facilitate collaboration between participating PTA groups and to promote progress toward PTA scientific goals There is a Steering Committee which sets policy guidelines for data sharing, publication of results etc. The IPTA organises annual Student Workshops and Science Meetings – 2013 meetings will be in Krabi, Thailand, June 17-28 The IPTA has organised Data Challenges for verification of GW detection algorithms

26. IPTA Website: www.ipta4gw.org

27. IPTA Data Challenge 1 Three types of data set (uniform sampling, white noise; non-uniform sampling, white noise; non-uniform sampling, red+white noise) All data sets have 5-year span Results for Closed Challenge, Data set 3: Open Challenge: details of injected GW signal given. Closed Challenge: blind detection Data Challenge 2 planned – will have more realistic data sets and weaker injected GW signal Organised by Rick Jenet, KJ Lee and Mike Keith

28. IPTA Data Sets: 39 MSPs

29. Detection of the GW Background Pulsar timing arrays are most sensitive to GW signals with frequency f ~ 1/T span ~ few nanoHertz Strongest source of nHz GW waves is background from orbiting super-massive black holes in distant galaxies Number of mergers per comoving volume based on model for galaxy evolution (e.g. Millennium simulation) plus model for formation and evolution of SMBH in galaxies (M = binary chirp mass, q = mass ratio) (Phinney 2001; Jenet et al. 2006; Sesana 2013)

30. Stochastic GW Background: Distribution of SMBBH Most of background from SMBBH in galaxies at z = 1-2 Biggest contribution from largest BH masses: 10 8 – 10 9 M sun Chirp mass = (M 1 M 2 ) 3/5 (M 1 + M 2 ) -1/5 (Sesana et al. 2008)

31. (Sesana 2013; van Haasteren et al. 2011) Predicted Stochastic GW Background Amplitude = h c (1/1yr) 20 psrs, 100 ns 10 years EPTA limit

32. GW Detection Sensitivity (Siemens et al. 2013) Low signal level (< white noise) High signal level (>~ w. noise) Based on correlation analysis – Earth term only  IJ : Hellings-Downs coefficients Simplified model: M pulsars, all same  (rms timing noise) At low signal levels, S/N improves as MT  ~ MT 13/3 At higher signal levels, S/N ~ MT 1/2

33. Likely that many SMBH binary systems are highly eccentric GW spectrum may be dominated by a strong individual source Single Sources First GW detection by PTAs could be a single source with period <~ 1 year! (Sesana 2012)

34. Localisation of GW Sources (Tempo2) Fits quadrupolar signature to arbitrary waveforms for multiple pulsars – good for continuous or burst sources Strong GW source injected into PPTA data sets Grid search over sky to measure detection significance as function of position “Blind” search: independent software for injection and detection (George Hobbs and Ryan Shannon) Source detected at close to correct position

35. Limiting the GW Background Can use auto-correlations – pulsar terms contribute power to ACF Detection statistic: Weights:Spectral model: Observed spectrum Fitted GW signal (A=1.2x10 -15) Expected signal for A 95 M W GW signal: (Shannon et al. 2013) Used six best PPTA pulsars (f PPTA =2.8 nHz) 95% confidence limit on GW signal in data: A 95 < 2.4 x 10 -15 Rel. energy density  GW (f PPTA ) < 1.3 x 10 -9

36. Current PPTA Limit (95% confidence) (Shannon et al. 2013) A 95 = 2.4 x 10 -15 McWilliams et al. 2012 Sesana 2013 Ravi et al. 2012 (Millennium model with new BH mass function)

37. (Sesana 2013, van Haasteren et al. 2011; Shannon et al. 2013) Predicted Stochastic GW Background Amplitude = h c (1/1yr) 20 psrs, 100 ns 10 years EPTA limit PPTA limit

38. Future Prospects Continuing searches will increase number of known pulsars Combination of extended PTA data sets to make IPTA should give a detection of the stochastic GW background (M ~ 35) Very high sensitivity of FAST and SKA should allow timing of 100 – 200 MSPs Sensitivity of a PTA to a stochastic GW background Black: 20 psrs Red: 50 psrs Blue: 200 psrs Plain line: 5 yrs Line with ×: 10 yrs Line with o : 20 yrs (Manchester et al. 2012) (Sesana prediction) 100 ns rms residuals No intrinsic red noise

39. FAST: Guizhou China SKA Mid-Frequency Array: South Africa 2012 2020+ 2017

40. The Gravitational Wave Spectrum