Search for the gravitational wave memory effect with the Parkes Pulsar Timing Array

1. Search for the gravitational wave memory effect with the Parkes Pulsar Timing Array Jingbo Wang, George Hobbs, Dick Manchester, Na Wang Xinjiang Astronomical Observatory/CSIRO Orange Meeting, 2012, University of Melbourne

2. Contents • Gravitational wave memory effect • Search for Gravitational wave memory effect by PTAs • Algorithm for searching and limiting a glitch in a data set • Future plan

3. Gravitational wave memory effect • The Gravitational wave memoryis a step change, non-oscillatorycontribution to the gravitational potential • Gravitational waves with memory will leave a permanent imprint on space-time • Gravitational waves with memory can be produced by merger of binary black holes • It increases rapidly during the merger phase of binary black holes We can treat it as a discontinuous jump propagating through space

4. Search for gravitational wave with memory by PTAs • A gravitational wave will distort space-time between theEarth and the pulsar. This affects the distancetravelled by each pulse • The pulse times-of-arrivalwill be different from those predicted by timing model,so it will induce timing residuals • There will be a discontinuous metric memory jump propagating through space • the memory jump would causea pair of pulse frequency jumps of equalmagnitude and the oppositesign The timing residuals See vanHasteren & Levin2010,MNRAS

5. Algorithm for searching and limiting a glitch • Simulating timing residuals only contain white noise, regular samping, same error bars ,100ns rms, 5 years • Fitting for a glitch at different times in the data sets and calculating a statistic, find the maxium value S=|GLF0/GLF0_err| • Repeat it 100 times Distribution of S at different epochs Distribution of S_max for 100 iterations

6. Algorithm for searching and limiting a glitch • Add a glitch at the middle of the observations into the white timing residuals • Calculating the statistic at different glitch epoch, find the maxium value • Repeat it 100 times • Try different glitch sizes Distribution of S at different epochs Distribution of S_max for glitch size of 5e-12 Hz

7. Algorithm for searching and limiting a glitch • Significance distribution plot for a fixed epoch, 100 different white noises

8. Algorithm for searching and limiting a glitch • The smallest glitch size we can dectect for 5 years observations, 100ns noise level is ~1.5e-12 Hz if we put a glitch in the middle of the observation into our data Distribution of S_max for glitch size of 1.5e-12 Hz,100 iterations Distribution of S_max for glitch size of 1e-12 Hz, 100 iterations

9. Algorithm for searching and limiting a glitch • Simulate a white data set, pretend it is "real" data, caculate the statistic S_real • Add a glitch of a given size at a random position in the data set, get the statistic, S_i repeat it 100 times • Change the glitch size, find the glitch size which make 95% percents S_i > S_real, record it as A_95 • Try different white noise levels

10. Future plan • Add red noise into the simulated timing residuals • Modelling the red noise with the Cholesky method • Fitting for a glitch simultaneously for many pulsars • Apply the algorithm to PPTA data sets • Detect gravitational wave memory effect or place a upper limit on the number of supermassive black hole mergers with the algorithm • Search for glitches in young pulsars from PPTA or Nanshan data sets by using the algorithm Thank you!