1. PTA and GW detection --- Lecture K. J. Lee ( 李柯伽 ) Max-Planck Institute for Radio astronomy kjlee007@gmail.com Aug. 2013

2. Outline Pulsar timing array Basic physics about GW Pulsar timing response to GW Detect GW background Detect single source Practical aspects of pulsar timing array Current status of PTA projects IPTA data challenge Outlook

3. Timing techniques

4. Example of PTA data Verbiest et al. 2009 Millisecond pulsar are stable. Hartnett & Luiten. 2011 Pulsar timing data are 1. Two parts: TOA and parameter 2. Non-stationary 3. systematics affected

5. Pulsar timing residual Count the pulse Model the frequency with polynomial Residual describe how data deviates from the pulsar rotation model. Residual includes GW signal, clock noise and other interesting signals.

6. Pulsar timing array and pulsar timing – review Pulsar timing array is the observation and data analysis projects involving multiple pulsars. It is not a telescope array!

7. PTA philosophy Each pulsar's noise is not spatially correlated. Interesting signal are spatially correlated. Check the correlation, we can detect these interesting signals!

8. Gravitational wave

9. GWs Gws are ripples of space-time. Because they are usually weak, we treat them as the perturbation of Mankowski background: where

10. Gws Filed equation: Weak field approximation, neglect anything like h^2 Choose a gauge condition Re-parameterize In vacuum

11. Solutions of vacuum field equation Null wave vector Transverse wave Traceless Extra degree of freedom comes from gauge transformation

12. Constrains on A

13. Geometrical interpretation + x

14. Generation of GW a R In GW astronomy, we are detecting h~1/R. Increasing sensitivity by a factor of 10, the number of source is 1000 times. For other detector, they depend on energy flux, which goes as 1/R^2, number of source increase as 100 times.

15. In history For GR, only two polarization modes exist. Einstein derive the wave equation soon after formulated the GR. However, in 1916, he made mistake and state that there are three polarization modes. The mistake was corrected in 1918.

16. Effect of GW on pulsar timing signal

17. Effects of GW on photon propagation Photon's geodesic: Time components Q P

18. Effects to pulsar timing Perfect pulses: With perturbation This is THE equation we can use To calculate the effect of GW on pulsar timing.  T

19. GW detection – background

20. Big picture of GW detection CMB...

21. Description of stochastic background Independent polarization assumption Power Spectra

22. Spatial cross correlation of timing signal  Hellings and Downs 1983 Gravitational wave propagate from inside of the screen to the outside. 0 90 180 + + -

23. Detection algorithm Gravitational wave detection is to extract the statistics of GW signal from the pulsar timing signals. In simple way, we can check the correlation of pulsar timing signal to get the GW data. Maximal likelihood approach Freqnentist approach Jenet et al. 2006 Van hassteren et al. 2010

24. We are not far from detection! Jenet … Lee...et al. 2005 h=1e-15, 20 pulsar 5 year ----> detect GW!!!

25. How the timing data looks like? van Haasteren,et al. 2011 h<6e-15

26. Astrophysical consequence Current uplimit EPTA A<6E-15 (Van Haasteren et al. 2011) NANOGrav A<7.2E-15 (Demorest et al. 2012) PPTA A<2.4E-15 (Shannon et al. In prep.) Kocsis & Sesana 2012

27. GW detection – Single sources

28. “See” the SMBH The size make big difference L > L < See Hear

29. PTA as a short-wave detector L>>  L

30. Detectable population Lee et al. 2011 SMBH is detectable given: 1. amplitude large enough 2. frequency is in band Due to the fact that we have both the pulsar and earth term, We can see the evolution of GW sources over several thousand years.

31. Hearing SMBH

32. We can see more clearly Lee et al. 2011

33. Performances and sub-Lyr distance ladder Lee et al. 2011 We can determine the GW source position with great precision!

34. GW distance ladder

35. Beyond Newtonian motion M. F. Mingarelli et al. 2012 Also see Tong's talk later for the elliptic orbit.

36. Test gravity in radiative regime By far, general relativity is still the most success theory to describe the gravitational processes in the low energy regime. It is beautiful, but we had a singularity at the center of black hole. We know it must be the effective theory to THE theory. Can we see any evidence of deviation? M/R<<1 v<<1 M/R<<1 v~1 M/R~1 v<<1 M/R~1 v~1 Solar system test Post Newtonian tests GW tests Blackhole merger, Blackhole perturbation

37. Polarization of GW Edward, et al. 73 Lee et al. 08 Such tests are independent of GW source properties!!

38. Single pulsar response function To understand this back to geodesic equation

39. Another interesting thing  0 180 are NOT symmetrical? 90 is NOT the most negative correlation

40. Dispersion / graviton mass GR case Lee et al. 09

41. Current international efforts And many more...

42. International pulsar timing array http://www.ipta4gw.org/

43. IPTA Aim: detect GW Share resources, 30+ MSPs are observed. 200+ persons, stuffs+students ~10 largest radio telescope involves Observers+ data analysts+ astrophysicists Sensitivity improves by nearly an order of magnitude in last 10 years In the SKA era, the pulsar timing community may collaborate as the IPTA.

44. 44 IPTA data challenge Web site: http://www.ipta4gw.org/?page_id=89 http://www.ipta4gw.org/?page_id=89 We simulate fake data, you do the analysis and report your results. Good test data for all types of detection algorithm. The challenge is nearly once per year. We will soon have the second data challenge.

45. Future expectations

46. Current ∑ GW detection events ≈ 0 ∑ Paper published =786

47. When we will detect GW

48. Summary In this lecture, we covered the basics of GW physics We studied the effects of GW on pulsar timing signal We discussed the detection method We may detect gravitational wave in the near future using PTA and after the detection, we can  Study gravity theories Polarization and graviton mass  Study the astrophysics BH merger processes, mass function, cosmic structural formation  Locate the GW source and do other type of follow ups Multi-messenger astronomy

49. Thanks. If there is any questions or suggestions, please do not hesitate to contact me via kjlee007@gmail.com