Transcript KJLee Jul. 2009 NAOC

Pulsar, Gravitational wave,
Gravitational wave polarization
K.J.Lee
Jul. 2009
NAOC
Outline
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Gravity theory, Spacetime geometry
Gravitational Wave and its polarization
Pulsar, Pulsar timing signal
Detect G-wave using pulsar
Present uplimit
Can we say GR is correct?
Gravity theory, Spacetime geometry
Gravity theory, geometry of
spacetime
• Gravity theory must be a geometrical
theory, even from Newton times.
GmM
F  ma 
r2
2
ar  GM
ar  Geometry
2
ar 2 [ L] [ L]2
2


[
L
]
 Curvature
3
2
3
r
[ L] [ L]
M  Gravity
M E
 3  Energy density
3
r
r
Curvature  Energy density
Gravitational wave
Gravitation = Geometry
Gravitational wave = Geometrical wave
A little bit math
In the vacuum
curvature : h  h  0
2
•You get the wave. But things are more
complex than this.
•One important issues is the gauge
G-wave, a toy of Einstein
• The idea appears very soon after the GR is
found
• Another very serious mistake of Einstein
The TT gauge for GR
The meaning of TT gauge is when wave transmit
along Z direction we solution looks like
How G-wave plays ball (test particles)?
Non-Einsteinian theories?
Ap
At
Ab
Ae
Al
1972, Eardley et al.
G-wave is G-wave
y
x
y
x
Some ground based and space
base efforts.
Pulsar, Pulsar timing signal
What is pulsar
• Here, you can just regard pulsar as an exremely
accurate clock radiating photons (radio wave)
according to the accurate timing.
• The photons are broad band
Thompson et al.
Pulsar spin is slowing down
1
t  t0  pn  pn 2  Earth motion+Solar motion+gravitational redshift+plasma effects+noise
2
2
1
8
3.5
x 10
5
4.5
3
4
Time of pulse arrival
2.5
3.5
3
2
2.5
1.5
2
1.5
1
1
0.5
0.5
3
0
0
0.5
1
1.5
2
number of pulse
2.5
3
3.5
8
x 10
4
0
0.5
1
1.5
2
2.5
3
3.5
8
x 10
-6
1
0
-7
x 10
1
x 10
0.9
0
0.8
-1
0.7
0.6
-2
0.5
-3
0.4
0.3
-4
0.2
-5
0.1
-6
0
0.5
1
1.5
2
2.5
3
3.5
8
x 10
0
0
0.5
1
1.5
2
2.5
3
3.5
8
x 10
In reality...
In fact TOA is more complex than I have illustrated
We have so many accurate clock
•
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•
We can set up time standard
We can check NIST atomic clock
We can check solar system dynamics
We can do deep space guiding system
We can....
Gravitational wave detection using pulsar timing
The optical theory in curved space
time
Geometric optic
a
T
b
0
,0
hij
i
aT
d
1
d
2
1
2
k k
g
kg i k p i
j
i
j
0
k k hi j q
g
p
hi j p
Timing formula
R t
R t
dt
A
G T Psr
g
G
1 Pi Pj Hi j
2 1
Pg k P k
T Ear
The First Possibility
• As
R t
A
G T Psr
T Ear
g
• So we can test whether there is some
gravitational wave structure.
• We can not discreminate noise vs signal
• People have already done something like
that (similar to doppler sitellite tracking....)
Single pulsar response function
Longitudinal?!!
To understand this back to geodesic equation
Something like Landau-damping
Uplimits for non-Einsteinian
modes
We find the link formula
Uplimts for a lazy
man
Just use the link formula to convert
GR uplimit (Jenet et al. 2006) to nonEinsteinian modes.
Lee et al. 2009 b
2nd Possibility
• Correlation function
– Correlate the two R(t)
– Define C=<R(t,P1) R(t,P2)>
• Why?
A
R t
G T Psr
T Ear
g
R t R t
A
2
G P1 T Psr
g
A
g
2
G P1 G p1 T Ear2
Cor
T Ear
P1 G p1
T Psr
T Ear
P2
Pulsar correlation and
gravitational wave
HD function
Gravitational wave detection
• We can check the existence for angular
dependent correlation to make sure we
detect gravitational wave.
• The details statistics are complex.
• Non-Einsteinian modes?
Mode dependent polarization
GR
Shear
B
Longitudinal
Lee et al. 2009a
Celestial object
Detection procedure
Receiver
TEMPO
.
.
.
.
.
Compare
The detection significance
The ability to discriminate them
Neyman-Person type detection
Example:
Radar detect enemy’s intrusion
The Probability
Intrusion
No intrusion
Alarm
√
X False alarm rate (pf)
No Alarm
X Missing rate
(Pm)
√
Given a false alarm (1e-3) rate we calculate the missing rate to check the quality
of discriminating processes. It clearly that if the missing rate is 50%, we have
average ability to give 3-sigma detection, if noise is Gaussian.
The ability to discriminate them 1
20 yr
10 yr
30ns
5 yr
20 yr
10 yr
100ns
5 yr
L
S
B
L
S
B
The ability to discriminate them 2
20 yr
10 yr
30ns
5 yr
20 yr
100ns
10 yr
5 yr
L
S
B
L
S
B
The ability to discriminate them 3
20 yr
10 yr
30ns
5 yr
20 yr
10 yr
100ns
5 yr
L
S
B
Why we do this?
• General relativity is just one of theories.
• We have more than one hundred theories
of gravity.
• Which one is correct?
What we will achieve?
• We develop the mathematical presentation for the
polarization of GW for general metric theory
• We figure out how the pulsar timing response to GW with
different polarization modes
• We build up the detection algorithm
• We evaluate the detector’s quality
• With 40 pulsars we can detect GW stronger than hc~1e14, 1e-14 for GR and B modes; With 60 pulsars, shear
and longitudinal modes stronger than hc~1e-16 and 3e17 can be detected.
• With 40, 100, and 300 pulsars, we can discriminate the
modes with 90% probability given false alarm rate 0.001.
• Test gravity theory via gravitational wave observation
directly.
Why we need wave-type test?
• Classical Test (h<<1, v/c<<1)
– Weak field and low speed
• Relativistic Binary Pulsar Test (v/c<<!)
– strong field and low speed
• Wave field test (h<<1)
– Weak field and high speed
Why Wave field test?
• One wrong idea: Post Newtonian test is
everything.
• But if you want to use PN test to
investigate gravitational wave or graviton
spin, you will need expansion to infinite
order, because the PN is expansion
respected to (v/c).
• Thus G-wave test is independent from PN.
Conclusion
• Gravitational wave polarization are
physically interesting
• Pulsar timing is a good tool to measure Gwave polarization.
• Pulsar timing is better than LISA for
longitudinal modes.
• Gravitational wave pulsar timing signal
processing techniques are important for
many application (time scale, navigation,
solar system dynamics et al.).
Thanks!
BTW, wake up the guy beside you.