Gravitational Wave and Pulsar Timing

Xiaopeng You, Jinlin Han, Dick Manchester

National Astronomical Observatories, Chinese Academy of Sciences

Outline• Gravitational Wave Wave

– Physics of gravitational waves– Gravitational wave detection– Gravitational wave sources

• Detecting G-wave by Pulsar Timing– Introduction to pulsar timing– PPTA project– Directly detecting gravitational wave

• Effect of ISM on Pulsar Timing– Dispersion measure change– Scintillation

Gravitational Wave: Ripples in

Spacetime!• Einstein field equation

• Weak field approximation

• Gravitational wave equation

TG 8

, 1g h h

1, where

2

16

h h h h h

h T

Properties of G-wave• Quadrupole moment• Two polarization states “+”

“×”

• Generation of G-waves

2

2,

3ij ij R

G dh t q t

R dtx

G-wave Detection

• Interferometer detector– Basic formula: – LIGO: h~10-22, L=4 km, L~10-17cm– LISA: h~10-21, L=5×106 km, L~10-10cm

• Pulsar timing as G-wave detector– See pulsar timing part

1

2yx

LLh

L L

G-wave Sources• High frequency (10 ~ 104 Hz, LIGO Band)

– Inspiraling compact binaries (NS and BH, MBH103M )

– Spinning neutron star

– Supernovae

– Gamma ray bursts

– Stochastic background

• Low frequency (10-4 ~ 1 Hz, LISA Band)– Galactic binaries

– Massive BH binary merger (104M MBH109M )

– MBH capture of compact object

– Collapse of super massive star

– Stochastic background

G-wave Sources• Very low frequency (10-9 ~ 10-7 Hz, pulsar

timing)– Processes in the very early universe

• Big bang• Topological defects, cosmic strings• First-order phase transitions

– Inspiral of super-massive BH (MBH>1010M )

• Extremely low frequency (10-18 ~ 10-15 Hz)– Primordial gravitational fluctuations amplified

by the inflation of the universe– Method: imprint on the polarization of CMB

radiation

Pulsar Timing• Pulsars are excellent celestial clocks, especially MSP

• Basic pulsar timing observation

• The timing model, inertial observer

• Correct observed TOA to SSB

• Series TOAs corrected to SSB: ti

• Least squares fit time residual

2SSB obs corr R S E R S E/t t t D f

2

i 0 0 i 0 0 i 0

2 3

i 0 0 i 0 0 i 0 0 i 0

1

21 1

2 6

t t t t t

N t N t t t t t t

i i2

ii

N t n

Modeling Timing Residual and Timing “Noise”

From Hobbs et al. (2005)

Source of Timing Noise• Receiver noise• Clock noise• Intrinsic noise• Perturbations of pulsar motion

– G-wave background– Globular cluster accelerations– Orbital perturbations

• Propagation effects– Wind from binary companion– Variants in interstellar dispersion– Scintillation effects

• Perturbations of Earth’s motion– G-wave background– Errors in the Solar-system ephemeris

Indirect evidence of G-wavePSR B1913+16• First observational

evidence of G-wave

Nobel Prize for

Taylor & Hulse

in 1993 !From Weisberg & Taylor (2003)

Detect G-wave by pulsar timing

• Observation one pulsar, only put limit on strength of G-wave background

• New limits on G-wave radiation (Lommen, 2002)

9 20

c

2 10 h

Photon Path

Pulsar EarthG-w

ave

Direct detection of G-wave

• Observation of many pulsars

• Effect of G-wave background– Uncorrelated on individual pulsars – But correlated on the Earth

• Method: two point correlation

• Sensitive wave frequency 10-8 Hz

PPTA project• Goal: detect G-wave & establish PSR timescale • Timing, 20 MSPs, 2-3 week interval, 5 years• 3 frequencies: 700 MHz, 1400 MHz and 3100 MHz• TOA precision: 100 ns > 10 pulsars, 1 s for others

Detect G-wave background

Simulation using PPTA pulsars with G-wave background from SMBH

(Jenet et al.)

Detect G-wave background

From Jenet et al. (2005)

14 15 2/32A , = , A=10 to 10 yr

3ch f G-wave from SMBH

A) Simple correlation, B) Pre-whiten

20 psrs, 100 ns, 250 obs, 5 years

Low-pass filtering

10 psrs, 100 ns, 250 obs, 5 years

10 psrs, 100ns, 10 psrs, 500 ns, 250 obs, 5 years

20 psrs, 100 ns, 250 obs, 5 years

20 psrs, 100 ns, 500 obs, 10 years

ISM Effect on Pulsar Timing1. Dispersion measure variation

PSR B0458+46

From Hobbs et al. (2004)

What we will do: Calculate DM change for PPTA pulsars, improve the accuracy of pulsar timing

Method: Obtain DM from simultaneous multi-frequency observation

22 3 -1

1 2

1 1, MHz cm s pc

2

et K DM K

f f mc

DMdt

DMd0002.0

)(

ISM Effect on Pulsar Timing2. Scintillation effect

• Scintillation affects precision of pulsar timing

• Second dynamic spectrum can deduce the time delay

PSR B1737+13

From Stinebring & Hemberger (2005)

What we will do:Study scintillation effect on PPTA pulsars, improve the accuracy of pulsar timing

Summary

• Gravitational wave detection is a major goal for current astronomy

• PPTA project has a chance for directly detecting gravitational wave

• Lots of works still need to be done to improve the accuracy of pulsar timing