PTA and GW
detection
--- Lecture
K. J. Lee (李柯伽)
Max-Planck Institute for
Radio astronomy
kjlee007@gmail.com
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
Millisecond pulsar are
stable.
Pulsar timing data are
1. Two parts: TOA and parameter
2. Non-stationary
3. systematics affected
Verbiest et al. 2009
Hartnett & Luiten. 2011
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
Extra degree of freedom comes from gauge transformation
Traceless
Constrains on A
Geometrical interpretation
+
x
Generation of GW
R
a
In GW astronomy, we are detecting h~1/R. Increasing sensitivity by a
factor 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 source
increase 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
DT
Perfect pulses:
With perturbation
This is THE equation we can use
To calculate the effect of GW on
pulsar timing.
GW detection – background
Big picture of GW detection
CMB...
Description of stochastic
background
Independent polarization assumption
Power Spectra
Spatial cross correlation of timing
signal
Gravitational wave propagate from
inside of the screen to the outside.
+
+
q
0
Hellings and Downs 1983
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
Van hassteren et al. 2010
Jenet et al. 2006
We are not far from detection!
h=1e-15, 20 pulsar 5 year
Jenet … Lee...et al. 2005
----> detect GW!!!
How the timing data looks like?
h<6e-15
van Haasteren,et al. 2011
Astrophysical consequence
Current uplimit
EPTA
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
L < l
Hear
PTA as a short-wave detector
L>> l
q~l/L
Detectable population
SMBH is detectable given:
1. amplitude large enough
2. 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.
Lee et al. 2011
Hearing SMBH
We can see more clearly
Lee et al. 2011
Performances and sub-Lyr
distance ladder
We can determine the GW source position with great precision!
Lee et al. 2011
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 regime
By 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
Solar system test
M/R~1 v<<1
Post Newtonian tests
M/R<<1 v~1
GW tests
M/R~1 v~1
Blackhole merger, Blackhole perturbation
Polarization of GW
Such tests are independent of GW source properties!!
Edward, et al. 73
Lee et al. 08
Single pulsar response function
To understand this back to geodesic equation
Another interesting thing
q
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...
International pulsar timing array
http://www.ipta4gw.org/
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.
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.
44
Future expectations
Current
350
300
250
200
150
100
50
0
∑ Paper published =786
1975-1980
1985-1990
1995-2000
2005-2010
1970-1975
1980-1985
1990-1995
2000-2005
∑ GW detection events ≈ 0
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


Study the astrophysics


Polarization and graviton mass
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
kjlee007@gmail.com