Scuola nazionale de Astrofisica Radio Pulsars 4: Precision Timing and GR Outline The double pulsar PSR J A/B Strong-field tests of GR Pulsar Timing Arrays - pulsar timescale and the detection of gravitational radiation

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 John Rowe Animations/ATNF

22.7 ms 1.7 x Myr 6 x 10 9 G 1,080 km 5 x 10 3 G 6 x erg s -1 A: 2.77 s 0.88 x Myr 1.6 x G 1.32 x 10 5 km 0.7 G 1.6 x erg s -1 P  c B S R LC B LC E B: Basic Parameters of PSR J A/B..  A is a standard mildly recycled pulsar  B is a relatively young but slow pulsar whose environment is greatly affected by the presence of A

PSR J B “Double-line binary” gives the mass ratio for the two stars – strong constraint on gravitational theories B pulsar only active for small fraction of the orbital period 0.2 pulse periods Orbital period MSP blows away most of B magnetosphere - dramatic effect on pulse emission (Spitkovsky & Arons 2005)

PSR J A/B Orbit Geometry a 1 +a 2 = 8.8 x 10 5 km i = 88 o.7  0 o.6 Distance = 0.55 kpc We view the orbit almost edge-on At conjunction, pulses from A pass through the B magnetosphere B is bright when on near side of orbit

PSR J A Eclipse For orbit inclination 88.7 deg, impact parameter of A l.o.s. on B ~ 0.15 R LC,B B magnetosphere eclipses A - a unique probe of a pulsar magnetosphere! Eclipse duration only ~25 sec Orbital velocity of A relative to B ~ 630 km s -1 Eclipse width only ~ 16,000 km, ~ 0.12 R LC,B Radius of eclipsing region: 0.06 R LC,B < R eclip < 0.16 R LC,B Eclipsing region only a small part of B magnetosphere!

Eclipse of A is modulated with B rotational phase! Eclipse is deeper when B radio beam is directed toward and away from us Models:  Synchrotron absorption by shock- heated wind in magnetosheath (Arons et al. 2005, Lyutikov 2004)  Synchrotron absorption by relativistic plasma in closed field-line region (Rafikov & Goldreich 2005, Lyutikov & Thompson 2005) (McLaughlin et al. 2004a) All models require plasma density times  GJ

Modulation of B radio emission by A Sequence of ~ 400 individual pulses from B during leading bright phase Individual pulses from A visible in background - varying phase due to relative motion of A & B wrt observer On leading edge of B pulse, “drifting” effect with systematic variation of “subpulse” phase in successive pulses Most clearly seen between 200 o and 210 o (McLaughlin et al. 2004b)

  A B Drift rate of cycles/period interpreted as a beat frequency with B period Ratio of pulsar barycentric periods: P B /P A = Doppler shift from varying separation of A & B - at orbital longitude 205 o, predicted beat frequency ~ cycles/period, exactly as observed! Modulation is at 1/P A ~ 44 Hz Suggests that modulation is due to impact of A’s magnetic-dipole radiation field on B’s magnetosphere, rather than A pulses or wind energy Mechanism not clear - modulation of beam direction or emission intensity? Modulation of B by A (ctd) (McLaughlin et al. 2004b)

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)

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)

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 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 (as is PSR B test)  System is 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 will 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)

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, LISA Two sites in USA Perpendicular 4-km arms Spectral range 10 – 500 Hz Initial phase now commissioning 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

Detecting Gravitational Waves with Pulsars Observed pulse periods affected by presence of gravitational waves in Galaxy For stochastic GW background, effects at pulsar and Earth are uncorrelated With observations of one or two 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 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 (Rick Jenet, George Hobbs)

 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

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)

The Gravitational Wave Spectrum

Pulsars are fascinating objects whose study gives insight into extreme physical states unrealisable on Earth Pulsed, highly polarised and throughout our Galaxy, they are unique probes of the interstellar medium As precision clocks they are powerful tools for investigation of a wide range of problems, especially concerning relativity and gravitation Summary Grazie e Arrivederci

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.)

The Parkes Pulsar Timing Array Project Collaborators:  Australia Telescope National Facility, CSIRO Dick Manchester, George Hobbs, Russell Edwards, John Sarkissian, John Reynolds, Mike Kesteven, Grant Hampson, Andrew Brown  Swinburne University of Technology Matthew Bailes, Ramesh Bhat, Joris Verbiest, Albert Teoh  University of Texas, Brownsville Rick Jenet, Willem van Straten  University of Sydney Steve Ord  National Observatories of China, Beijing Xiaopeng You  Peking University, Beijing Kejia Lee  University of Tasmania Aidan Hotan