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PTA and GW detection --- Lecture. K. J. Lee ( 李柯伽 ) Max-Planck Institute for Radio astronomy kjlee007@gmail.com Aug. 2013. Outline. Pulsar timing array Basic physics about GW Pulsar timing response to GW Detect GW background Detect single source Practical aspects of pulsar timing array

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## PTA and GW detection --- Lecture

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**PTA and GW detection--- Lecture**K. J. Lee (李柯伽) Max-Planck Institute for Radio astronomy kjlee007@gmail.com Aug. 2013**Outline**Pulsar timing array Basic physics about GW Pulsar timing response to GW Detect GW background Detect single source Practical aspects of pulsar timing array Current status of PTA projects IPTA data challenge Outlook**Example of PTA data**Millisecond pulsar are stable. Pulsar timing data are 1. Two parts: TOA and parameter 2. Non-stationary 3. systematics affected 2011RvMP…83….1H 2009MNRAS.400..951V**Pulsar timing residual**Count the pulse Model the frequency with polynomial Residual describe how data deviates from the pulsar rotation model. Residual includes GW signal, clock noise and other interesting signals.**Pulsar timing array and pulsar timing**– review Pulsar timing array is the observation and data analysis projects involving multiple pulsars. It is not a telescope array!**PTA philosophy**• Each pulsar's noise is not spatially correlated. • Interesting signal are spatially correlated. • Check the correlation, we can detect these interesting signals!**GWs**Gws are ripples of space-time. Because they are usually weak, we treat them as the perturbation of Mankowski background:where**Gws**Filed equation: Weak field approximation, neglect anything like h^2 Choose a gauge condition Re-parameterize In vacuum**Solutions of vacuum field equation**Null wave vector Transverse wave Extra degree of freedom comes from gauge transformation Traceless**Generation of GW**R In GW astronomy, we are detecting h~1/R. Increasing sensitivity by a factor of 10, the number of source is 1000 times. For other detector, they depend on energy flux, which goes as 1/R^2, number of source increase as 100 times. a**In history**• For GR, only two polarization modes exist. Einstein derive the wave equation soon after formulated the GR. However, in 1916, he made mistake and state that there are three polarization modes. The mistake was corrected in 1918.**Effects of GW on photon propagation**Photon's geodesic: Time components Q P**Effects to pulsar timing**D T Perfect pulses: With perturbation This is THE equation we can use To calculate the effect of GW on pulsar timing.**Big picture of GW detection**CMB...**Description of stochastic background**Independent polarization assumption Power Spectra**Spatial cross correlation of timing signal**Gravitational wave propagate from inside of the screen to the outside. + + q - 0 90 180 1983ApJ…265L..39H**Detection algorithm**Gravitational wave detection is to extract the statistics of GW signal from the pulsar timing signals. In simple way, we can check the correlation of pulsar timing signal to get the GW data. Maximal likelihood approach Van haasteren et al. 2010 Freqnentist approach Jenet et al. 2006**We are not far from detection!**h=1e-15, 20 pulsar 5 year ----> detect GW!!! 2005ApJ…625L.123J**How the timing data looks like?**h<6e-15 2011MNRAS.414.3117V**Astrophysical consequence**2011MNRAS.411.1467K Current uplimit EPTA A<6E-15 (2011MNRAS.414.3117V) NANOGrav A<7.2E-15 (2013ApJ...762...94D) PPTA A<2.4E-15 (Shannon et al. In prep.)**“See” the SMBH**The size make big difference L < l L > l See Hear**PTA as a short-wave detector**L>> l q~l/L**Detectable population**SMBH is detectable given: 1. amplitude large enough 2. frequency is in band Due to the fact that we have both the pulsar and earth term, We can see the evolution of GW sources over several thousand years. 2011MNRAS.414.3251L**We can see more clearly**2011MNRAS.414.3251L**Performances and sub-Lyr distance ladder**We can determine the GW source position with great precision! 2011MNRAS.414.3251L**Beyond Newtonian motion**2012PhRvL.109h1104M Also see Tong's talk later for the elliptic orbit.**Test gravity in radiative regime**By far, general relativity is still the most success theory to describe the gravitational processes in the low energy regime. It is beautiful, but we had a singularity at the center of black hole. We know it must be the effective theory to THE theory. Can we see any evidence of deviation? M/R<<1 v<<1 M/R<<1 v~1 GW tests Solar system test M/R~1 v~1 M/R~1 v<<1 Post Newtonian tests Blackhole merger, Blackhole perturbation**Polarization of GW**Such tests are independent of GW source properties!! Edward, et al. 73 2008ApJ...685.1304L**Single pulsar response function**To understand this back to geodesic equation**Another interesting thing** 0 180 are NOT symmetrical? Propagation breaks symmetry! 90 is NOT the most negative correlation**Dispersion / graviton mass**GR case Lee et al. 09**Current international efforts**And many more...**International pulsar timing array**http://www.ipta4gw.org/**IPTA**Aim: detect GW Share resources, 30+ MSPs are observed. 200+ persons, stuffs+students ~10 largest radio telescope involves Observers+ data analysts+ astrophysicists Sensitivity improves by nearly an order of magnitude in last 10 years In the SKA era, the pulsar timing community may collaborate as the IPTA.**IPTA data challenge**Web site: http://www.ipta4gw.org/?page_id=89 We simulate fake data, you do the analysis and report your results. Good test data for all types of detection algorithm. The challenge is nearly once per year. We will soon have the second data challenge.**Current**∑Paper published =786 ∑GW detection events ≈ 0**Summary**In this lecture, we covered the basics of GW physics We studied the effects of GW on pulsar timing signal We discussed the detection method We may detect gravitational wave in the near future using PTA and after the detection, we can Study gravity theories Polarization and graviton mass Study the astrophysics BH merger processes, mass function, cosmic structural formation Locate the GW source and do other type of follow ups Multi-messenger astronomy**Thanks.**If there is any questions or suggestions, please do not hesitate to contact me via kjlee007@gmail.com

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