童明雷

中国科学院国家授时中心

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Pulsar timing residuals induced by non-evolving

single GW sources

Outline

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Introduction of pulsar timingThe 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 Fold

Model

p2

SSB / EsRclkobs fDttt

clktDRsE

Observatory clock to TTDM delay ( D=DM/(2.41×10-16)s )Roemer delayShapiro delayEinstein delayParallex delay

Other delay terms including atmospheric delay, Shklovskii effect, relativistic second-order Doppler shift, GWs, etc.

Time transformationTime transformation

P

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Application of pulsar timingEstablish 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

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Introduction of pulsar timingThe 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 inflationCosmic strings

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In vacuum

the solution is the superposition of plane waves:

GWs only have two polarizations

h+ h×

The solution of GWs in Vacuum

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In vacuum

the solution is the superposition of plane waves:

GWs only have two polarizations

h+ h×

The solution of GWs in Vacuum

What is a non-evolving black hole binary?

Elliptical orbit of a binary system

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The kinematic solution

The period of the orbit

The differential equation for the Keplerian motion

The GW solution from a compact star binary

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In the linearized Einstein theory of GWs, the metric purterbations with TT gauge

The quadrupole moment for a binary system is

The coordinate system

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The solution of GWs

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13 Wahlquist, GRG, 1987

The cace of e=0

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Lee K J et al, MNRAS, 2011

Outline

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Introduction of pulsar timingThe 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

n

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The general cases of e≠0

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The setting of some parameters

Taking J0437-4715 as

an example

pn ,0,0,0

pcDp 157

1510H

sP 910 120

e=0

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e=0.3

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e=0.6

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120

e=0.8

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RMS residuals

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e=0

e=0.3

e=0.6

e=0.8

nsR 3.27

nsR 4.22

nsR 2.11

nsR 2.5

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Outline

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Introduction of pulsar timingThe 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

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The effect of Dp

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The effects of

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,

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3.0' eHH

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Thank you!