Pulsar Timing and the Detection of Gravitational Waves

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

Spin-Powered Pulsars: A Census • 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 Data from ATNF Pulsar Catalogue, V 1. 46 (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) (ESO – VLT) 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 extremely stable e. g. , PSR J 0437 -4715 had a period of : 5. 757451831072007 0. 00000008 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

Measurement of pulsar periods • Start observation at a known time and average 103 - 105 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 (To. A) • Measure a series of To. As over days – weeks – months – years • Transfer To. As to an inertial frame – the solar system barycentre • Compare barycentric To. As 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!

. The P – P Diagram P = Pulsar period P = d. P/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 . • tc = P/(2 P) is an indicator of pulsar age • Surface. 1/2 dipole magnetic field ~ (PP) Great diversity in the pulsar population! Galactic Disk pulsars

Sources of Pulsar Timing “Noise” Ø Intrinsic noise • Period fluctuations, glitches • Pulse shape changes Ø Perturbations of the pulsar’s motion • Gravitational wave background • Globular cluster accelerations • Orbital perturbations – planets, 1 st order Doppler, relativistic effects e d i w a f o • Wind from binary companion s e b o r a • Variations in interstellar dispersion ful p n e r m o n • Scintillation effects powe e h p e r l a a c s Ø Perturbations of the Earth’s motion i r s a y s l h p o P • u. Gravitational wavef background r t s a • Errors in the Solar-system ephemeris o e g n a Ø Clockrerrors Ø Propagation effects • Timescale errors • Errors in time transfer Ø Instrumental errors • Radio-frequency interference and receiver non-linearities • Digitisation artifacts or errors • Calibration errors and signal processing artifacts and errors Ø Receiver noise

PSR B 1913+16: The First Binary Pulsar Ø Discovered at Arecibo Observatory by Russell Hulse & Joe Taylor in 1975 Ø Pulsar period 59 ms, a recycled pulsar Ø Doppler shift in observed period due to orbital motion Ø Orbital period only 7 hr 45 min Ø Maximum orbital velocity 0. 1% of velocity of light Relativistic effects detectable!

Post-Keplerian Parameters: PSR B 1913+16 Given the Keplerian orbital parameters and assuming general relativity: • Periastron advance: 4. 226598(5) deg/year Ø M = mp + mc • Gravitational redshift + Transverse Doppler: 4. 2992(8) ms Ø mc(mp + 2 mc)M-4/3 • Orbital period decay: -2. 423(1) x 10 -12 Ø mp mc M-1/3 First two measurements determine mp and mc. Third measurement checks consistency with adopted theory. Mp = 1. 4398 0. 0002 Msun Mc = 1. 3886 0. 0002 Msun Both neutron stars! (Weisberg, Nice & Taylor 2010)

Orbital Decay in PSR B 1913+16 • Orbital motion of two stars generates gravitational waves PSR B 1913+16 Orbit Decay • 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 ØConfirmation of general relativity! ØFirst observational evidence for gravitational waves! (Weisberg , Nice & Taylor 2010)

PSR J 0730 -3039 A/B The first double pulsar! Ø Discovered at Parkes in 2003 Ø One of top ten science breakthroughs of 2004 - Science Ø PA = 22 ms, PB = 2. 7 s Ø Orbital period 2. 4 hours! Ø Periastron advance 16. 9 deg/yr! (Burgay et al. , 2003; Lyne et al. 2004) Highly relativistic binary system!

Measured Post-Keplerian Parameters for PSR J 0737 -3039 A/B GR value Measured value . Periast. adv. (deg/yr) . - Grav. Redshift (ms) 0. 3842 Pb Orbit decay r Shapiro range ( s) s Shapiro sin i 16. 8995 0. 0007 0. 386 0. 003 Improves as T 1. 5 -1. 248 x 10 -12 (-1. 252 0. 017) x 10 -12 T 2. 5 6. 15 0. 99987 6. 2 0. 3 0. 99974 +16 -39 T 0. 5 GR is OK! Consistent at the 0. 05% level! Non-radiative test - distinct from PSR B 1913+16 (Kramer et al. 2006)

The Double Pulsar: Update • PSR J 0737 -3039 B has disappeared! • Beam has moved away due to orbital precession • Expected to return in 5 – 10 years c i t s i v i t a l re f o n o i t ec t e f d o t r n o f e s m t re ec u p s s a o r e p m d nd • Continued timing a Goo at n o i t a ia m t r r o e f n e i d f t o i Parkes and GBT has t n orb e m o m pulsar refined relativistic parameters • Now limits deviations from GR to 0. 02% (Kramer et al. 2013)

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

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)

Ø Clock errors All pulsars have the same TOA variations: monopole signature Ø Solar-System ephemeris errors Dipole signature Ø 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 ~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)

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

The Parkes Pulsar Timing Array Collaboration Ø 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) Ø Swinburne University of Technology, Melbourne Matthew Bailes, Willem van Straten, Andrew Jameson, (Stefan Oslowski) Ø Monash University, Melbourne Yuri Levin Ø University of Melbourne Vikram Ravi (Stuart Wyithe) Ø University of Western Australia, Perth Linqing Wen, Xingjiang Zhu ØCurtin University, Perth Ramesh Bhat ØUniversity of California, San Diego Bill Coles Ø MPIf. R, Bonn (David Champion), (Joris Verbiest), (KJ Lee) Ø National Space Science Center, Beijing Xinping Deng Ø Xinjiang Astronomical Observatory, Urumqi Jingbo Wang ØSouthwest University, Chongqing Xiaopeng You

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 - TEMPO 2 • 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

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

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

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 (J 0437 -4715, J 1909 -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, frequencydependant templates Still work to do! (Hobbs 2013)

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

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

IPTA Website: www. ipta 4 gw. org

IPTA Data Challenge 1 • Three types of data set (uniform sampling, white noise; non-uniform sampling, red+white noise) • All data sets have 5 -year span • 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 Results for Closed Challenge, Data set 3: Organised by Rick Jenet, KJ Lee and Mike Keith

IPTA Data Sets: 39 MSPs

Detection of the GW Background • Pulsar timing arrays are most sensitive to GW signals with frequency f ~ 1/Tspan ~ few nano. Hertz • Strongest source of n. Hz 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 formation and evolution of SMBH in galaxies (M = binary chirp mass, q = mass ratio) (Phinney 2001; Jenet et al. 2006; Sesana 2013)

Stochastic GW Background: Distribution of SMBBH • Most of background from SMBBH in galaxies at z = 1 -2 • Biggest contribution from largest BH masses: 108 – 109 Msun Chirp mass = (M 1 M 2)3/5 (M 1 + M 2)-1/5 (Sesana et al. 2008)

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

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

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

Localisation of GW Sources (Tempo 2) • 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 Source detected at close to correct position (George Hobbs and Ryan Shannon)

Limiting the GW Background • Can use auto-correlations – pulsar terms contribute power to ACF • Detection statistic: Weights: Spectral model: GW signal: Expected signal for A 95 • Used six best PPTA pulsars Observed spectrum M (f. PPTA=2. 8 n. Hz) • 95% confidence limit on GW signal in data: A 95 < 2. 4 x 10 -15 Rel. energy density WGW(f. PPTA) < 1. 3 x 10 -9 W Fitted GW signal (A=1. 2 x 10 -15) (Shannon et al. 2013)

Current PPTA Limit (95% confidence) Ravi et al. 2012 (Millennium model with new BH mass function) Sesana 2013 Mc. Williams et al. 2012 A 95 = 2. 4 x 10 -15 (Shannon et al. 2013)

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

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 100 ns rms residuals No intrinsic red noise 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)

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The Gravitational Wave Spectrum