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Timing techniques
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PTA and GW detection--- Lecture
K. J. Lee (李柯伽 )
Max-Planck Institute for Radio astronomy
Aug. 2013
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
Timing techniques
Example of PTA data
Verbiest et al. 2009
Millisecond pulsar are stable.
Hartnett & Luiten. 2011
Pulsar timing data are1. Two parts: TOA and parameter2. Non-stationary3. systematics affected
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.
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!
PTA philosophy Each pulsar's noise is not spatially correlated.
Interesting signal are spatially correlated.
Check the correlation, we can detect these interesting signals!
Gravitational wave
GWs
Gws are ripples of space-time. Because they are usually weak, we treat them as the perturbation of Mankowski background:
where
Gws
Filed equation:
Weak field approximation, neglect anything like h^2
Choose a gauge condition
Re-parameterize
In vacuum
Solutions of vacuum field equation
Null wave vector
Transverse wave
Traceless
Extra degree of freedom comes from gauge transformation
Constrains on A
Geometrical interpretation
+ x
Generation of GW
a
R
In GW astronomy, we are detecting h~1/R. Increasing sensitivity by afactor 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 sourceincrease as 100 times.
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.
Effect of GW on pulsar timing signal
Effects of GW on photon propagation
Photon's geodesic:
Time components
Q
P
Effects to pulsar timing
Perfect pulses:
With perturbation
This is THE equation we can useTo calculate the effect of GW on pulsar timing.
T
GW detection – background
Big picture of GW detectionCMB...
Description of stochastic background
Independent polarization assumption
Power Spectra
Spatial cross correlation of timing signal
Hellings and Downs 1983
Gravitational wave propagate from inside of the screen to the outside.
0 90 180
++
-
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
We are not far from detection!
Jenet … Lee...et al. 2005
h=1e-15, 20 pulsar 5 year ----> detect GW!!!
How the timing data looks like?
van Haasteren,et al. 2011
h<6e-15
Astrophysical consequenceCurrent uplimitEPTA 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
GW detection – Single sources
“See” the SMBH
The size make big difference
L > L <
See Hear
PTA as a short-wave detector
L>> L
Detectable population
Lee et al. 2011
SMBH is detectable given:
1. amplitude large enough2. 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.
Hearing SMBH
We can see more clearly
Lee et al. 2011
Performances and sub-Lyr distance ladder
Lee et al. 2011We can determine the GW source position with great precision!
GW distance ladder
Beyond Newtonian motion
M. F. Mingarelli et al. 2012
Also see Tong's talk later for the elliptic orbit.
Test gravity in radiative regimeBy 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
Polarization of GW
Edward, et al. 73 Lee et al. 08
Such tests are independent of GW source properties!!
Single pulsar response function
To understand this back to geodesic equation
Another interesting thing
0 180 are NOT symmetrical?
90 is NOT the most negative correlation
Dispersion / graviton mass
GR case
Lee et al. 09
Current international efforts
And many more...
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
IPTA data challenge
Web site: 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.
Future expectations
Current
1970-19751975-1980
1980-19851985-1990
1990-19951995-2000
2000-20052005-2010
050
100150200250300350
∑ GW detection events ≈ 0
∑ Paper published =786
When we will detect GW
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
Thanks.If there is any questions or suggestions, please do not
hesitate to contact me via
