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## Pulsar, Gravitational wave, Gravitational wave polarization

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**Pulsar, Gravitational wave, Gravitational wave polarization**K.J.Lee Jul. 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, geometry of spacetime**• Gravity theory must be a geometrical theory, even from Newton times.**Gravitational wave**Gravitation = Geometry Gravitational wave = Geometrical wave**A little bit math**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 Ae Ab Al 1972, Eardley et al.**G-wave is G-wave**y x y x**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**2 1 3 4**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....**The optical theory in curved space time**Geometric optic**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....)**Single pulsar response function**Longitudinal?!! To understand this back to geodesic equation**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?**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?**GR**B Longitudinal Shear Mode dependent polarization Lee et al. 2009a**Celestial object**Detection procedure Receiver TEMPO . . . . . Compare**The Probability**Intrusion No intrusion Alarm √ X False alarm rate (pf) No Alarm X Missing rate (Pm) √ The ability to discriminate them Neyman-Person type detection Example: Radar detect enemy’s intrusion 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 5 yr 20 yr 10 yr 5 yr 30ns 100ns L S B L S B**The ability to discriminate them 2**20 yr 10 yr 5 yr 20 yr 10 yr 5 yr 30ns 100ns L S B L S B**The ability to discriminate them 3**20 yr 10 yr 5 yr 20 yr 10 yr 5 yr 30ns 100ns 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~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.