1. Gravitational Wave and Pulsar Timing Xiaopeng You, Jinlin Han, Dick Manchester National Astronomical Observatories, Chinese Academy of Sciences

2. Outline WaveGravitational Wave –Physics of gravitational waves –Gravitational wave detection –Gravitational wave sources Detecting G-wave by Pulsar Timing –Introduction to pulsar timing –PPTA project –Directly detecting gravitational wave Effect of ISM on Pulsar Timing –Dispersion measure change –Scintillation

3. Gravitational Wave: Ripples in Spacetime! Einstein field equation Weak field approximation Gravitational wave equation

4. Properties of G-wave Quadrupole moment Two polarization states “+” “×” Generation of G-waves

5. G-wave Detection Interferometer detector –Basic formula: –LIGO: h~10 -22, L=4 km,  L~10 -17 cm –LISA: h~10 -21, L=5×10 6 km,  L~10 -10 cm Pulsar timing as G-wave detector –See pulsar timing part

6. G-wave Sources High frequency (10 ~ 10 4 Hz, LIGO Band) –Inspiraling compact binaries (NS and BH, M BH  10 3 M ) –Spinning neutron star –Supernovae –Gamma ray bursts –Stochastic background Low frequency (10 -4 ~ 1 Hz, LISA Band) –Galactic binaries –Massive BH binary merger (10 4 M  M BH  10 9 M ) –MBH capture of compact object –Collapse of super massive star –Stochastic background

7. G-wave Sources Very low frequency (10 -9 ~ 10 -7 Hz, pulsar timing) –Processes in the very early universe Big bang Topological defects, cosmic strings First-order phase transitions –Inspiral of super-massive BH (M BH >10 10 M ) Extremely low frequency (10 -18 ~ 10 -15 Hz) –Primordial gravitational fluctuations amplified by the inflation of the universe –Method: imprint on the polarization of CMB radiation

8. Pulsar Timing Pulsars are excellent celestial clocks, especially MSP Basic pulsar timing observation The timing model, inertial observer Correct observed TOA to SSB Series TOAs corrected to SSB: t i Least squares fit time residual

9. Modeling Timing Residual and Timing “Noise” From Hobbs et al. (2005)

10. Source of Timing Noise Receiver noise Clock noise Intrinsic noise Perturbations of pulsar motion –G-wave background –Globular cluster accelerations –Orbital perturbations Propagation effects –Wind from binary companion –Variants in interstellar dispersion –Scintillation effects Perturbations of Earth’s motion –G-wave background –Errors in the Solar-system ephemeris

11. Indirect evidence of G-wave PSR B1913+16 First observational evidence of G-wave Nobel Prize for Taylor & Hulse in 1993 ! From Weisberg & Taylor (2003)

12. Detect G-wave by pulsar timing Observation one pulsar, only put limit on strength of G-wave background New limits on G-wave radiation (Lommen, 2002) Photon Path Pulsar Earth G-wave

13. Direct detection of G-wave Observation of many pulsars Effect of G-wave background –Uncorrelated on individual pulsars –But correlated on the Earth Method: two point correlation Sensitive wave frequency 10 -8 Hz

14. PPTA project Goal: detect G-wave & establish PSR timescale Timing, 20 MSPs, 2-3 week interval, 5 years 3 frequencies: 700 MHz, 1400 MHz and 3100 MHz TOA precision: 100 ns > 10 pulsars, 1  s for others

15. Detect G-wave background Simulation using PPTA pulsars with G-wave background from SMBH (Jenet et al.)

16. Detect G-wave background From Jenet et al. (2005) G-wave from SMBH A) Simple correlation, B) Pre-whiten 20 psrs, 100 ns, 250 obs, 5 years Low-pass filtering 10 psrs, 100 ns, 250 obs, 5 years 10 psrs, 100ns, 10 psrs, 500 ns, 250 obs, 5 years 20 psrs, 100 ns, 250 obs, 5 years 20 psrs, 100 ns, 500 obs, 10 years

17. ISM Effect on Pulsar Timing 1. Dispersion measure variation PSR B0458+46 From Hobbs et al. (2004) What we will do: Calculate DM change for PPTA pulsars, improve the accuracy of pulsar timing Method: Obtain DM from simultaneous multi-frequency observation

18. ISM Effect on Pulsar Timing 2. Scintillation effect Scintillation affects precision of pulsar timing Second dynamic spectrum can deduce the time delay PSR B1737+13 From Stinebring & Hemberger (2005) What we will do: Study scintillation effect on PPTA pulsars, improve the accuracy of pulsar timing

19. Summary Gravitational wave detection is a major goal for current astronomy PPTA project has a chance for directly detecting gravitational wave Lots of works still need to be done to improve the accuracy of pulsar timing