Download - 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
![Page 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/1.jpg)
童明雷
中国科学院国家授时中心
23/4/21
1
Pulsar timing residuals induced by non-evolving
single GW sources
![Page 2: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/2.jpg)
Outline
23/4/21
2
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
![Page 3: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/3.jpg)
TOA (measured using the observatory clock) Residual
Pulsar timing
Fold Fold
Model
![Page 4: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/4.jpg)
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
![Page 5: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/5.jpg)
23/4/215
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
![Page 6: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/6.jpg)
Outline
23/4/21
6
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
![Page 7: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/7.jpg)
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
23/4/21
7
![Page 8: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/8.jpg)
23/4/218
In vacuum
the solution is the superposition of plane waves:
GWs only have two polarizations
h+ h×
The solution of GWs in Vacuum
![Page 9: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/9.jpg)
23/4/219
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?
![Page 10: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/10.jpg)
Elliptical orbit of a binary system
23/4/21
10
The kinematic solution
The period of the orbit
The differential equation for the Keplerian motion
![Page 11: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/11.jpg)
The GW solution from a compact star binary
23/4/21
11
In the linearized Einstein theory of GWs, the metric purterbations with TT gauge
The quadrupole moment for a binary system is
![Page 12: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/12.jpg)
The coordinate system
23/4/21
12
![Page 13: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/13.jpg)
The solution of GWs
23/4/21
13 Wahlquist, GRG, 1987
![Page 14: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/14.jpg)
The cace of e=0
23/4/21
14
Lee K J et al, MNRAS, 2011
![Page 15: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/15.jpg)
Outline
23/4/21
15
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
![Page 16: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/16.jpg)
Single GW sources
Earth
Pulsar
GW source
n
![Page 17: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/17.jpg)
23/4/21
17
![Page 18: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/18.jpg)
The general cases of e≠0
23/4/21
18
The setting of some parameters
Taking J0437-4715 as
an example
pn ,0,0,0
pcDp 157
1510H
sP 910 120
![Page 19: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/19.jpg)
e=0
23/4/21
19
![Page 20: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/20.jpg)
e=0.3
23/4/21
20
![Page 21: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/21.jpg)
e=0.6
23/4/21
21
120
![Page 22: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/22.jpg)
e=0.8
23/4/21
22
![Page 23: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/23.jpg)
RMS residuals
23/4/21
23
e=0
e=0.3
e=0.6
e=0.8
nsR 3.27
nsR 4.22
nsR 2.11
nsR 2.5
![Page 24: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/24.jpg)
23/4/21
24
![Page 25: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/25.jpg)
Outline
23/4/21
25
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
![Page 26: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/26.jpg)
The effect of
23/4/21
26
![Page 27: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/27.jpg)
The effect of Dp
23/4/21
27
![Page 28: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/28.jpg)
The effects of
23/4/21
28
,
![Page 29: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/29.jpg)
23/4/2129
![Page 30: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/30.jpg)
23/4/2130
![Page 31: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/31.jpg)
23/4/21
31
3.0' eHH
![Page 32: 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](https://reader033.vdocuments.us/reader033/viewer/2022061319/56649f3d5503460f94c5d4c2/html5/thumbnails/32.jpg)
23/4/21
32
Thank you!