Pulsar, Gravitational wave, Gravitational wave polarization

K.J.LeeJul. 2009

NAOC

Outline

• 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.

2

GmMF ma

r

2ar GM2ar Geometry M Gravity

2 22

3 2 3

[ ] [ ][ ]

[ ] [ ]

ar L LL Curvature

r L L 3 3

M E

Energy densityr r

Curvature Energy density

Gravitational wave

Gravitation = Geometry

Gravitational wave = Geometrical wave

A little bit math

2: 0curvature h h In the vacuum

•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

Al

Ae

1972, Eardley et al.

G-wave is G-wave

x

y

x

y

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

0 0.5 1 1.5 2 2.5 3 3.5

x 108

0

0.5

1

1.5

2

2.5

3

3.5x 10

8

number of pulse

Tim

e of

pul

se a

rriv

al

0 0.5 1 1.5 2 2.5 3 3.5

x 108

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 0.5 1 1.5 2 2.5 3 3.5

x 108

-6

-5

-4

-3

-2

-1

0

1x 10

-6

0 0.5 1 1.5 2 2.5 3 3.5

x 108

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1x 10

-7

1 2

3 4

20

1Earth motion+Solar motion+gravitational redshift+plasma effects+noise

2t t pn pn

In reality...

In fact TOA is more complex than I have illustrated....

We have so many accurate clock

• 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

TaaTb 0

dd

12hij

,0kikj 0

12

g

kgikpi gpkikjhijqhijp

Timing formula

Rt dt

G12Pi Pj Hij

1 PgkPk

Rt Ag

GTPsr TEar

The First Possibility

• As

• 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....)

Rt Ag

GTPsr TEar

Single pulsar response function

To understand this back to geodesic equation

Longitudinal?!!

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 non-Einsteinian modes.

Lee et al. 2009 b

2nd Possibility

• Correlation function– Correlate the two R(t)– Define C=<R(t,P1) R(t,P2)>

• Why?

Rt Ag

GTPsr TEar RtRtAg2 GP1TPsr TEarP1Gp1TPsr TEarP2 Ag2 GP1 Gp1TEar

2 Cor

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 B

ShearLongitudinal

Lee et al. 2009a

Detection procedure

.

.

.

.

. Compare

Receiver

TEMPO

Celestial object

The detection significance

The ability to discriminate them

Neyman-Person type detectionExample: Radar detect enemy’s intrusion

√X Missing rate (Pm)

No Alarm

X False alarm rate (pf) √Alarm

No intrusionIntrusionThe Probability

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

L S B L S B

30ns

100ns

20 yr

10 yr

5 yr

20 yr

10 yr

5 yr

The ability to discriminate them 2

L S B L S B

20 yr

10 yr

5 yr

20 yr

10 yr

5 yr

100ns

30ns

The ability to discriminate them 3

L S B

20 yr

10 yr

5 yr

20 yr

10 yr

5 yr

30ns

100ns

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~1e-

14, 1e-14 for GR and B modes; With 60 pulsars, shear and longitudinal modes stronger than hc~1e-16 and 3e-17 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 G-wave 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.