1. 童明雷 中国科学院国家授时中心 2015-11-26 1 Pulsar timing residuals induced by non-evolving single GW sources

2. Outline 2015-11-26 2 Introduction of pulsar timing The general solution of GWs from a supermassive black hole binary The time properties of timing residuals due to a single GW The effects of all the related parameters on the timing residuals

3. TOA (measured using the observatory clock) Residual Pulsar timing Fold Model

4. Observatory clock to TT DM delay ( D=DM/(2.41×10 -16 )s ) Roemer delay Shapiro delay Einstein delay Parallex delay Other delay terms including atmospheric delay, Shklovskii effect, relativistic second-order Doppler shift, GWs, etc. Time transformation

5. 2015-11-26 5 Application of pulsar timing Establish pulsar time standard similar to atomic time scale Direct detection of GWs Improve knowledge of Solar system properties, e.g. masses and orbits of outer planets and asteroids. Application to spacecraft navigation based on pulsar timing

6. Outline 2015-11-26 6 Introduction of pulsar timing The general solution of GWs from a supermassive black hole binary The time properties of timing residuals due to a single GW The effects of all the related parameters on the timing residuals

7. GW sources  Continuous sources: inspiral of binary compact stars, the rotating isolated neutron stars, and the neutron stars in the x-ray binary star systems.  Instantaneous sources: supernovae and coalescing binary systems  Stochastic background sources: Numbers of compact binary stars (inspiral and merge) Relic GW from inflation Cosmic strings 2015-11-26 7

8. 8 In vacuum the solution is the superposition of plane waves: GWs only have two polarizations h+h+ h×h× The solution of GWs in Vacuum

9. 2015-11-26 9 In vacuum the solution is the superposition of plane waves: GWs only have two polarizations h+h+ h×h× The solution of GWs in Vacuum What is a non- evolving black hole binary?

10. Elliptical orbit of a binary system 2015-11-26 10 The kinematic solution The period of the orbit The differential equation for the Keplerian motion

11. The GW solution from a compact star binary 2015-11-26 11 In the linearized Einstein theory of GWs, the metric purterbations with TT gauge The quadrupole moment for a binary system is

12. The coordinate system 2015-11-26 12

13. The solution of GWs 2015-11-26 13 Wahlquist, GRG, 1987

14. The cace of e=0 2015-11-26 14 Lee K J et al, MNRAS, 2011

15. Outline 2015-11-26 15 Introduction of pulsar timing The general solution of GWs from a supermassive black hole binary The time properties of timing residuals due to a single GW The effects of all the related parameters on the timing residuals

16. Single GW sources Earth Pulsar GW source

17. 2015-11-26 17

18. The general cases of e≠0 2015-11-26 18 The setting of some parameters Taking J0437-4715 as an example

19. e=0 2015-11-26 19

20. e=0.3 2015-11-26 20

21. e=0.6 2015-11-26 21

22. e=0.8 2015-11-26 22

23. RMS residuals 2015-11-26 23 e=0 e=0.3 e=0.6 e=0.8

24. 2015-11-26 24

25. Outline 2015-11-26 25 Introduction of pulsar timing The general solution of GWs from a supermassive black hole binary The time properties of timing residuals due to a single GW The effects of all the related parameters on the timing residuals

26. The effect of 2015-11-26 26

27. The effect of D p 2015-11-26 27

28. The effects of 2015-11-26 28

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32. 2015-11-26 32 Thank you!