Detection of Gravitational Waves with Pulsar Timing R

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

Spin-Powered Pulsars: A Census • Currently 1886 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 * Total known: 140 in 26 clusters (Paulo Freire’s web page) Data from ATNF Pulsar Catalogue, V 1. 36 (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 incredibly 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

. 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 . • 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

The First Binary Pulsar • 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 1913+16

Orbital Decay in PSR B 1913+16 • Rapid orbital motion of two stars in PSR B 1913+16 generates gravitational waves PSR B 1913+16 Orbit Decay • 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 ØConfirmation of general relativity! ØFirst observational evidence for gravitational waves! (Weisberg & Taylor 2005)

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)

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 LIGO LISA • Two sites in USA • Perpendicular 4 -km arms • Spectral range 10 – 500 Hz • Initial phase now operating • Advanced LIGO ~ 2014 • 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

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 B 1855+09 gives g = r. GW/rc < 10 -7 (Kaspi et al. 1994, Mc. Hugh et al. 1996) Timing residuals for PSR B 1855+09

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)

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 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)

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

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 • High-quality data (rms residual < 2. 5 s) for 9 millisecond pulsars Ø North American pulsar timing array (NANOGrav) • Data from Arecibo and Green Bank Telescope • High-quality data for 17 millisecond pulsars Ø Parkes Pulsar Timing Array (PPTA) • Data from Parkes 64 m 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

The Parkes Pulsar Timing Array • Using the Parkes 64 -m radio telescope to observe 20 MSPs Project • ~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 TEMPO 2 • GW simulations, detection algorithms and implications, galaxy evolution studies

The PPTA Pulsars

Best result so far – PSR J 0437 -4715 at 10 cm • Observations of PSR J 0437 -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 TEMPO 2 • No dispersion correction • Reduced 2 = 2. 87 Rms timing residual 56 ns!!

PPTA Pulsars: 1. 5 years of PDFB 2 data • Timing data at 2 -3 week intervals at 10 cm or 20 cm • TOAs from 64 -min observations (except J 1857+0943, J 1939+2134, J 2124 -3358, each 32 min) • Uncorrected for DM variations • Solve for position, F 0, F 1, Kepler parameters if binary • Four pulsars with rms timing residuals < 200 ns, eleven < 1 s • Best results on J 0437 -4715 (80 ns), J 1909 -3744 (110 ns), J 1939+2134 (170 ns) Approaching our goal but not there yet!

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

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 8 n. Hz 100 n. Hz Expect detectable • Strongest signal from galaxies with z ~ 1 with current PTAs! • BH masses ~ 109 – 1010 M • Range of predictions depending on assumptions about BH mass function etc (Sesana, Vecchio & Colacino 2008)

Current and Future Limits on the Stochastic GW Background • Arecibo data for PSR B 1855+09 (Kaspi et al. 1994) and recent PPTA data • Monte Carlo methods used to determine detection limit for stochastic background described by hc = A(f/1 yr) (where = -2/3 for SMBH, ~ -1 for relic radiation, ~ -7/6 for cosmic strings) (Jenet et al. 2006) Ø Current limit: gw(1/8 yr) ~ 2 Ø For full PPTA (100 ns, 5 yr): ~ 10 -10 • Currently consistent with all SMBH evolutionary models (Jaffe & Backer 2003; Wyithe 10 -8 & 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) Timing Residuals 10 s

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 Pulsar timing can already rule out formation of Black Holes in mass range 102 – 104 M ! (Saito & Yokoyama 2009)

Single-source Detection Sensitivity PPTA Localisation with PPTA SKA Predicted merger rates for 5 x 108 M binaries (Wen et al. 2009, Sesana et al. 2009) PPTA can’t detect individual binary systems - but SKA will! (Anholm et al. 2008) Need better sky distribution of pulsars international PTA collaborations are important!

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 B 1855+09 from Arecibo, Effelsberg & Parkes • Jupiter is best candidate – 11 year orbital period Jupiter mass: Best published value: (9. 547919 ± 8) × 10 -4 Msun IPTA result: (9. 5479197 ± 6) × 10 -4 Msun Unpub. Galileo result: (9. 54791915 ± 11) × 10 -4 Msun (Champion et al. , in prep) More pulsars, more data span, should give best available value!

A Pulsar Timescale • Terrestrial time defined by a weighted average of caesium clocks at time centres around the world • Comparison of TAI with TT(BIPM 03) 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 ( 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)

Summary Ø Precision timing of pulsars is a great tool which has given the first observational evidence for the existence of gravitational waves Ø We are now approaching the level of TOA precision that is required to achieve the main goals of PTA projects Ø Good chance that detection of nano. Hertz GW will be achieved with a further 5 - 10 years of data if current predictions are realistic Ø Major task is to eliminate all sources of systematic error - good progress, but not there yet Ø So far, intrinsic pulsar period irregularities are not a limiting factor Ø Progress toward all goals will be enhanced by international collaboration - more (precise) TOAs and more pulsars are better! Ø Current efforts will form the basis for detailed study of GW and GW sources by future instruments with higher sensitivity, e. g. SKA

The Gravitational Wave Spectrum

Dispersion Corrections • DFB for 10 cm/20 cm • CPSR 2 for 50 cm • About 6 yr data span At 20 cm, DM of 10 -4 cm-3 pc corresponds to t = 210 ns • Will be applied to pipeline processing Algorithm development by Xiaopeng You, George Hobbs and Stefan Oslowski

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