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

Outline 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

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

Observatory clock to TT DM delay ( D=DM/(2.41× )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

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

Outline 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

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

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

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?

Elliptical orbit of a binary system The kinematic solution The period of the orbit The differential equation for the Keplerian motion

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

The coordinate system

The solution of GWs Wahlquist, GRG, 1987

The cace of e= Lee K J et al, MNRAS, 2011

Outline 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

Single GW sources Earth Pulsar GW source

The general cases of e≠ The setting of some parameters Taking J as an example

e=

e=

e=

e=

RMS residuals e=0 e=0.3 e=0.6 e=0.8

Outline 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

The effect of

The effect of D p

The effects of

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