The first direct detection of gravitational waves (GWs) would be of great importance to astrophysics and fundamental physics: it would confirm some key predictions of general relativity, and lay the foundation for observational gravitational-wave astronomy. Pulsar Timing Arrays (PTAs) are collaborations which aim to detect low-frequency (10-9-10-8Hz) extragalactic gravitational waves directly, by using a set of Galactic millisecond pulsars as nearly perfect Einstein clocks. The basic idea is to exploit the fact that millisecond pulsars create pulse trains of exceptional regularity. GWs perturb spacetime between the pulsars and the Earth, and this creates detectable deviations from the strict periodicity in the arrival times of the pulses (TOAs). This GWB is expected to be generated by a large number of black-hole binaries located at the centres of galaxies, by relic gravitational waves, or, more speculatively, by oscillating cosmic-string loops.

**Figure 1: View of the Nancay radiotelescope**- credit I.Cognard/Obs Paris

The Nançay radiotelescope (Figure 1) is involved in a high precision pulsar timing campaign and constant efforts are being done to improve the crucial instrumentation needed to properly observe and very precisely time the fastest pulsars. From a ’millisecond’ pulsar, with a period of the order of a few milliseconds, we can derive a Time of Arrival characterized by an uncertainty as low as 30ns ! Presently, the Nançay pulsar timing data is coherently dedispersed (dispersion removed directly on the recorded complex voltages in the Fourier domain) and folded with the BON (Berkeley-Orleans-Nançay) instrumentation built in collaboration with University of California, Berkeley (Astronomy Dept and CASPER). The instrumentation use the powerfull GPUs (Graphical Processing Unit) to perform this real-time data processing (Figure 2).

Figure 2: View of the BON (Berkeley OrlÃ©ans NanÃ§ay) pulsar instrumenation. Based on powefull GPUs (Graphical Processing Unit), the last version of this instrumentation is able to dedisperse a bandwidth of 512MHz in real-time (a filter applied in the frequency domain on a data stream at 16Gb/s)

Timing observations of five radio pulsars, observed with three of the EPTA telescopes, were used for this work. The contributors are the Westerbork Synthesis Radio Telescope (WSRT) with pulsar J1713+0747, the Effelsberg Telescope (EFF) with pulsars J1713+0747 and J1744-1134 and the Nancay Radio Telescope (NRT) with pulsars J0613-0200, J1012+5307, J1744-1134 and J1909-3744 (Figure 3). With four pulsars provided and among them the best one, J1909-3744, NanÃ§ay is the most important contributor to this data set. Click on the image to enlarge it

**Figure 3: Timing residuals of all the pulsars used in the GWB limit calculation as function of the date. Names of the pulsars along with the telescopes used is indicated on the right. A 1 micro second tick is shown on the left of the dashed-dotted line.**

The Bayesian technic consists in building a parametrised model of the timing residuals, forming a probability distribution function as a function of the model parameters, and marginalizing over everything but the GWB contribution. In the examples used by van Haasteren (2009), the model for the systematic errors included only the quadratic contribution to the TOAs from pulsar spindowns and assumed a single telescope used.

The Bayesian technic consists in building a parametrised model of the timing residuals, forming a probability distribution function as a function of the model parameters, and marginalizing over everything but the GWB contribution. In the examples used by van Haasteren (2009), the model for the systematic errors included only the quadratic contribution to the TOAs from pulsar spindowns and assumed a single telescope used. Figure 3: Timing residuals of all the pulsars used in the GWB limit calculation as function of the date. Names of the pulsars along with the telescopes used is indicated on the right. A 1 micro second tick is shown on the left of the dashed-dotted line. Click on the image to enlarge it

In the multi-telescope context of the EPTA, the method now follows two steps : firstly, the contribution of each pulsar dataset is evaluated individually for each telescope in terms of red noise, probing its sensitivity to a GWB, and only the most red noise free ones are kept. In a second step, the time series are mixed and combined together, forming a multi-telescope sample. Then, the correlation matrix is built (dimension 12502) and the posterior probability distribution is marginalised using a mix of analytic integration and Markov Chain Monte Carlo (MCMC). For this first EPTA result, only the datasets for the five best pulsars were kept out of the 20 very stable millisecond pulsars regularly monitored by the consortium. For the expected spectral index for a GWB generated by a large number of supermassive blackhole binaries, alpha = 2/3, a 95% confidence GWB upper limit was fund at amplitude (1yr) < 6 × 10-15 (Figure 4). This is smaller by a factor of 1.8 than the previously published PPTA limit and only a factor of 2 above the predictions ( 2 × 10-16 - 4 × 10-15) made by Sesana et al. (2008) for the characteristic strain spectrum generated by an ensemble of supermassive black holes binaries !

**Figure 4: The marginalised posterior distribution as a function of the GWB amplitude, and spectral index. The contours marked as "van Haasteren et al. (2011)" are the results of this work at the 1-sigma and 2-sigma level, indicating a respective volume inside that region of 68%, and 95%. The vertical dash-dotted line at alpha = 2/3 shows where we expect a GWB generated by supermassive black-hole binaries. The most recent published limits are shown as the three upper limit arrows pointing down, marked as "Jenet et al. (2006)".**

Due to hardware and software upgrades at the EPTA observatories, and due to the ever increasing time baseline of the data, we expect the sensitivity to increase greatly over the next few years. Especially the combination of the EPTA data sets with the data of the other PTA projects seems promising.

Last update on 9 October 2013