1. Search for the Gravitational Wave Memory effect with the Parkes Pulsar Timing Array Jingbo Wang 1,2,3, Hobbs George 3, Dick Manchester 3, Na Wang 1,4 1 Xinjiang Astronomical Observatory,, Urumqi, Xinjiang, China,830011; wangjingbo@xao.ac.cn 2 Graduate School, Chinese Academy of Sciences, Beijing 100049, China 3 CSIRO Astronomy and Space Science PO Box 76, Epping, NSW 1710, Australia 4 Key Laboratory of Radio Astronomy, Chinese Academy of Science, Nanjing, China,210008 ABSTRACT. Bursts of gravitational waves produced by supermassive black hole mergers will leave a permanent imprint on space-time. It has been shown that such gravitational wave memory signals are, in principle, detectable by pulsar timing arrays as a glitch event would seem to occur simultaneously for all pulsars. Here, we describe an algorithm that can search for gravitational wave memory signals and limit the maximum size of possible gravitational wave memory event that could remain undetectable in a data set. We apply this algorithm to the Parkes Pulsars Timing Array data set. No significant gravitational wave memory signal is founded in the data set. INTRODUCTION Cordes & Jenet (2012), van Haasteren & Levin (2010), Pshirkov et al. (2009) and Seto (2009) have previously shown that pulsar timing arrays are sensitive to such GW memory events. When such a GW signal passes the Earth or a pulsar, it will lead to a simple frequency jump in the observed pulse frequency of the pulsar. The timing residuals will therefore have the characteristics of a simple glitch event. GW memory events passing a single pulsar will lead to a glitch event in the timing residuals of that pulsar only. GW memory events passing the Earth will lead to a glitch event seen in the timing residuals of all pulsars with the size of the glitch depending upon the source-Earth-pulsar angle. Recently, Cordes & Jenet (2012) have discussed the delectability of the GW burst passing the pulsar. Here, we focus on searching and limiting the size of such GW memory events at the Earth. GWM SIGNAL The pre-fit timing residuals induced by the Earth term at t = t0 can be written as: In the above, amplitude of the GWM signal, t0 is the time the GWM signal reaches the observer on Earth is the angle between the direction from the observer to the pulsar and the direction of GW propagation to the direction of the wave propagation, ϕ is the angle between the wave’s principle polarization and the projection of the pulsar onto the plane perpendicular to the propagation direction Therefore, the GWM signal is characterized by a persistent change of the gravitational wave field which gives rise to a linear increase of the pre-fit residuals with time. OBSERVATIONS We make use of the Parkes Pulsar Timing Array (PPTA) data set which is described in Manchester et al. (2012). These data include regular observations of 20 millisecond pulsars at intervals of 2-3 weeks from 2005. All observations were obtained with the Parkes 64-m radio telescope. The typical integration time for each pulsar is 1 hr. Most of the timing offsets between the different observing systems have been measured and removed. However, some of the arbitrary jumps from the timing model included in the Verbiest et al. (2008, 2009) were retained (Manchester et al. 2012). Variations of dispersion measure were corrected using multifrequency observations. Figure 1. The timing residuals of the PPTA data set. The dashed line indicates zero residual. The pulsar name and the range of the timing residual for a given pulsar are labeled on each subplot. METHOD We have updated the tempo2 pulsar timing model to include the effect of a GWM event. The position of the GW source and pulsars are specified in the equatorial coordinate system by their right ascension and declination (α, δ). The principle polarization of GW is defined in a temporal coordinate system (r g,α g, δg) where the GW is propagate alone the - r g direction (Fig.1 of Hobbs et al. 2009). As we do not know the sky-position of the source we obtain the detection statistic for a large number (defined later) of possible sky positions. At each possible sky position we then search every possible GWM epoch for a detectable event. To account for the unknown polarization angle we carry out two fits, one with PA = 0 and the second with PA = π/4. For each fit we obtain a measurement of hmem (h 1 and h 2 for PA = 0 and PA = π/4, respectively) their corresponding uncertainties (σ 1 and σ 2 for PA = 0 and PA = π/4, respectively). We then form the following detection statistic: Figure 4 The detection statistic value distribution for original PPTA data set on certain epoch. In order to find the appropriate searching grid for epoch and position, we added a small GWM signal into the PPTA data set. Figure.2 shows the detection statistic value as a function of trial epoch, the searching interval was 10 days. The biggest epoch error for 60 days trial epoch intervals is 30 days. The sensitivity loss is smaller than 1 % for 60 days trial interval. Therefore 60 days searching interval is enough. Figure.3 shows the maximum detection significance as a function of the number of spatial grids used for searching. it dose not change much as increased number of trial grids. We used 50 grids for searching the sky- position of the GWM source. Figure 2. The detection significance as a function of trial epoch (left). The maximum detection significance as a function of number of spatial grids used for searching. Figure 3 shows the distribution of the detection significance on the celestial sphere for PPTA data set with GWM signal added. 1000 grids were used for this plot. The PPTA pulsars are marked as five angle star. The open square indicates the maximum significance value. In this case, we detected the GM source with high significance and located the position of the sources. By contrast, set without any gravitational-wave memory signal injected. The detection significance values of the original PPTA data set are shown in Figure 3. Figure 3. The detection statistic value distribution for PPTA data set with gravitational-wave memory signal injected. RESULTS We searched for GWM signal in the PPTA data set by using the algorithm mentioned above. Figure 5 shows the histogram of the detection statistic value. The statistic value ranges from 0 to 20. The ”diagnostic plot” which is often used for searching rotation radio transients are shown in Figure 6. The statistic value are scaled with the size of the circle as a function of RA and time or DEC and time. It is obvious that these statistic value are correlated with each other. This is possibly because we are fitting for the same parameter for the same data set. Figure 5. The histogram of the detection statistic value for PPTA data set. Figure 6. The diagnostic plot for PPTA data set Jingbo WANG: PhD student of Xinjiang Astronomical observatory/CSIRO