gravitational wave and pulsar timing xiaopeng you, jinlin han, dick manchester national astronomical...
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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