aa r X i v : . [ a s t r o - ph . I M ] J u l The Parkes Pulsar Timing Array
G. Hobbs
CSIRO Astronomy and Space Science, PO Box 76, Epping, NSW 1710, AustraliaE-mail: [email protected]
Abstract.
The aims of the Parkes Pulsar Timing Array (PPTA) project are to 1)make a direct detection of gravitational waves, 2) improve the solar system planetaryephemeris and 3) develop a pulsar-based time scale. In this article we describe theproject, explain how the data are collected and processed and describe current research.Our current data sets are able to place an upper bound on the gravitational wavebackground that is the most stringent to date.
1. Introduction
Approximately two thirds of the available observing time with the Parkes radio telescopeis currently dedicated to searching for and studying pulsars. Numerous pulsars areobserved over many years enabling studies of the pulsars themselves, theories of gravity,the interstellar medium and many other phenomena.Traditionally pulsars were analysed individually. The pulsar timing method, inwhich the pulse arrival times are compared with predictions for those arrival times, isused to obtain accurate measurements of each pulsar’s pulse, astrometric and binaryparameters. The resulting post-fit timing residuals indicate unmodelled physical effectsthat affect the pulsar signal. Some of these, such as intrinsic instabilities in the pulsarrotation will be specific to a given pulsar. If the post-fit timing residuals for all pulsarsare identical then the cause must be an Earth-based phenomenon. Processing the datasets with an imprecise knowledge of the solar system planetary masses will affect somepulsars, but not others (depending for instance, on the ecliptic latitude of the pulsar). Asupermassive black hole binary system emitting gravitational waves will induce timingresiduals dependent upon the angle between the pulsar, Earth and gravitational-wavesource. Therefore by identifying the angular distribution of the correlations it is possibleto disentangle many of these phenomena. This leads to the concept of a Pulsar TimingArray (see, e.g., Foster & Backer 1990) in which a large number of millisecond pulsars areobserved, their post-fit timing residuals determined and a search is made for correlatedtiming residuals.Since the year 2005, the Parkes Pulsar Timing Array (PPTA) project team havebeen observing a sample of pulsars in order to form a PTA data set. The major scientificaims of the project are to: he Parkes Pulsar Timing Array § § §
2. History of the Parkes Pulsar Timing Array
A history of the PPTA project has been presented in Hobbs et al. (2012a). Here weprovide a brief summary.The first request for observations with the Parkes telescope for the PPTA wassubmitted in late 2003 and the first high-quality observations were obtained in March2005. At that time the basic concept of a PTA was understood, but the necessarytiming precision and the total data span required to produce scientifically valuable datawas only roughly known. The initial sample of pulsars was based on the analysis ofJenet et al. (2005) who demonstrated that an isotropic, stochastic gravitational wavebackground with the amplitude predicted from the available theoretical calculationscould be detected if ∼
20 pulsars were timed weekly over a period of five years withan rms timing residual of ∼
100 ns. As data were collected, a few pulsars were droppedfrom the sample and, as new discoveries made, new pulsars added.Jenet et al. (2006) published the first major result from the PPTA. That workprovided, at the time, the most stringent upper bound on the existence of a gravitationalwave background, but only made use of a small subset of pulsars. The algorithmdeveloped in 2006 could only be applied to pulsar timing residuals that were “white”.However, “red” (low-frequency) noise was already detectable in many of the data sets.You et al. (2007a,b) showed that much of this red noise could be attributable todispersion measure variations from the interstellar medium and/or the solar wind. Thiswork highlighted the necessity for an observing system that provides sufficient frequencycoverage to enable correction for these dispersion measure variations.The first analysis of the sensitivity of a PTA to individual, continuous sources ofgravitational waves was presented by Yardley et al. (2010) using PPTA data sets. Thisled to a sky-averaged constraint on the merger rate of nearby ( z < .
6) black holebinaries with a chirp mass of 10 M ⊙ of less than one merger every seven years. Inthe year 2010, progress was also made towards the second scientific aim of the PPTAproject. Champion et al. (2010) developed algorithms that allowed errors in the masses he Parkes Pulsar Timing Array Table 1.
Parameters of the current observing systems for the Parkes Pulsar TimingArray
Parameter ValueTelescope diameter 64 m10 cm observing band 2588 – 3612 MHz20 cm observing band 1241 – 1497 MHz50 cm observing band 700 – 764 MHz10 cm system equivalent flux density 50 Jy20 cm system equivalent flux density 36 Jy50 cm system equivalent flux density 62 JyIncoherent digital filter bank systems PDFB3, PDFB4Coherent de-dispersion systems APSR, CASPSRTypical observing time 1 hrof known solar system planets to be identified and this work led to the most precisepublished estimate for the mass of the Jovian system of 9 . × − M ⊙ .Yardley et al. (2011) attempted to make a detection of gravitational waves withthe PPTA data sets. His algorithms were able to detect simulated gravitational waves,but his work showed that our observations were consistent with the hypothesis that nogravitational wave background is present in the data. However, his algorithm is noteffective in the presence of significant red noise in the pulsar timing residuals. This ledto Coles et al. (2011) which described how pulsar data sets should be analysed whenaffected by red noise.The third of our major project aims was achieved by Hobbs et al. (2012b) whodeveloped the first pulsar-based time scale that had a precision comparable to terrestrialtime standards. This work demonstrated that, for existing data sets, the atomictimescales were sufficient for our purposes, but with improved data sets it is expectedthat pulsar-based time scales will become more important.Even after the work of You et al. (2007a), the effects of dispersion measurevariations were still not fully dealt with. Keith et al. (2012) developed a new algorithmfor the measurement and removal of dispersion measure variations and this is now beingroutinely applied in our data analysis.Ravi et al. (2012) improved our prediction of the expected amplitude of agravitational wave background. Interestingly, his predictions (based on the Millenniumsimulation) are ruled out by a new PPTA upper bound on the gravitational wavebackground (Shannon et al., submitted). The ramifications of the Shannon et al. limiton the predictions of the expected gravitational wave signal are still being considered. he Parkes Pulsar Timing Array
3. The telescope and details of observations
All observations are obtained using the 64-m Parkes radio telescope situated in NewSouth Wales, Australia. Since the year 2005, observations have been made in sessionsat 2-3 week intervals. In each observing session each pulsar is observed at least once inthe 20 cm observing band and once with a dual-frequency 10/50 cm receiver. It is oftenpossible within an observing session to obtain more than one observation of each pulsar(particularly for pulsars such as PSR J0437 −
4. Forming pulse arrival times and timing residuals
The “raw” data as obtained from the observing system are available for download fromthe Parkes pulsar data archive (http://data.csiro.au; Hobbs et al. 2011). An automatedpipeline based on the PSRCHIVE software suite (Hotan et al. 2004) runs the followingroutines on the raw data (details are provided in Manchester et al. 2013): • The edges of the observing band are removed along with any identified radio-frequency interference • The best available timing model for the pulsar is installed into the data file • Polarisation and flux calibration routines are applied • The data are averaged in time, frequency and polarisation to produce a single profilefor each observation. ‡ ‡ For PSR J0437 − he Parkes Pulsar Timing Array Table 2.
Parkes Pulsar Timing Array pulsar sample and summary of data sets sinceJan. 1 2012.PSR J P DM P b
10 cm 20 cm 50 cmN pts σ min σ med . N pts σ min σ med . N pts σ min σ med . (ms) (cm − pc) (days) ( µ s) ( µ s) ( µ s) ( µ s) ( µ s) ( µ s)J0437 − − − − − − − − − − − − − − − − − The pulse arrival time is then calculated by cross-correlating, in the frequencydomain, a noise-free, analytic template with the calibrated observation.Timing residuals are formed using the tempo2 (Hobbs, Edwards & Manchester2006) software package. Each arrival time is referred to Terrestrial Time as realised bythe Bureau International des Poids et Mesures (BIPM2012) § and we make use of theJet Propulsion Laboratory (JPL) DE421 planetary ephemeris k . The pulsar models arebased on those of Verbiest et al. (2009) and we correct the dispersion measure variationsas described by Keith et al. (2012).In order to produce data sets with the longest possible data spans we have, wherepossible, combined the PPTA data (which starts in the year 2005) with earlier Parkesobservations of the same pulsars. These earlier data sets have been described by Verbiestet al. (2008, 2009). These extra data allow us to expand our data sets backwards to1995. The earlier data have poorer observing cadence and timing precision than the § k http://tmo.jpl.nasa.gov/progress_report/42-178/178C.pdf he Parkes Pulsar Timing Array Figure 1.
Average median timing residuals per year for PSR J0437 − − more recent data, but the most significant problem is that the data were only obtainedin the 20 cm observing band. This restricts the precision with which the dispersionmeasure variations can be measured and corrected.Over time our data sets have been improving as new systems (both front-endreceivers and back-end instruments) have been commissioned. To demonstrate thisimprovement we show, in Figure 1, the median ToA uncertainty for data obtained ina given year for PSRs J0437 − − he Parkes Pulsar Timing Array Table 3.
The extended Parkes Pulsar Timing Array data sets. σ is the weightedrms timing residual in the 20 cm observing band. PSR J First obs. Last obs. T span N obs σ (MJD) (MJD) (yr) ( µ s)J0437 − − − − − − − − − − − − − − − − − −
5. Current research
Members of the PPTA team are working on all aspects of the project - from improvingthe instrumentation at Parkes to developing the algorithms required for us to achievethe main aims of the project. Here we first describe improvements being made in theobserving system. We then highlight current research related to the three main projectgoals. he Parkes Pulsar Timing Array Figure 2.
Extended 20 cm PPTA data sets. Each panel, representing each pulsar inthe PPTA sample, is scaled independently. The value listed under the pulsar’s nameindicates the residual range (i.e., the highest residual minus the lowest).
Figure 3. (left panel) Timing residuals for PSR J1022+1001 in the 20 cm observingband. Two observations separated by two days are indicated by the labels (A) and(B). (right panel) the profiles for the observations indicated. he Parkes Pulsar Timing Array Figure 4. (left panel) A sample of 20 cm data sets that have been corrected fordispersion measure variations, but are still significantly affected by low frequency noise.(right panel) The timing residuals in the 50 cm band for PSR J1603 − The initial intention for the PPTA project was to obtain timing residuals for around 20pulsars with rms timing residuals of ∼
100 ns. This has not been achieved. Many of thepulsars are relatively weak and with the available observation times and receiver systemswe are only able to achieve timing precisions between ∼
500 ns and ∼ µs . However, someof our data sets are affected by unexplained white- and red-noise processes. Removingthe cause of such excess noise would significantly improve these data sets. In this sectionwe describe the current status of current research to study such excess noise.Oslowski et al. (2011) analysed 25 hours of observations of PSR J0437 − µ s.The timing residuals show no excess red-noise and yet the weighted rms timing residualis 1.2 µ s and the unweighted rms is 2.4 µ s (Figure 3). In the figure two observations arelabelled as (A) and (B). They are separated in time by only two days, but the residualsare ∼ µ s apart. The reason for this is shown in the right hand panel of Figure 3. The he Parkes Pulsar Timing Array ν measurement. The most extreme cases are shown in Figure 4 wherewe show the timing residuals after correction for dispersion measure variations. If thisred noise has similar properties to the timing noise studied by Lyne et al. (2010) thenit may be possible to correct this timing noise by searching for correlations with pulseshape variations. To date, we have not been successful in our attempts to do this.The timing residuals for PSR J1603 − ∼ × − cm − pc possibly caused by an extreme scattering event.Improving our calibration procedures and attempting to correct for red timingnoise will significantly improve our current data sets. However, it is also necessary tocontinue to improve our hardware systems. We are currently proposing a wide-bandreceiver system that will cover the band from 0.7 to 4 GHz. The entire band will bedirectly digitised in the focus cabin and processed by a GPU-based processor. It ishoped that such a system will be commissioned within two years. New theoretical calculations are suggesting that the detectable gravitational wave signalis unlikely to be an isotropic, stochastic gravitational wave background (see, for instance,Ravi et al. 2012). We therefore require gravitational-wave detection algorithms that aresensitive to backgrounds, individual continuous wave sources, evolving sources, burstevents or memory events. We have recently attempted to simplify the search for thesevarious types of wave, by noting that the pulsars in the PPTA act as individual elementsof a giant gravitational wave telescope. By suitably weighting the timing residuals fromeach pulsar we can “point” this gravitational wave telescope to a particular directionin the sky and hence obtain the functional form of the gravitational wave signal fromthat direction. We have recently updated the tempo2 software package to producetime series for the two gravitational wave polarisation states ( A + ( t ) and A × ( t )) from aspecified sky direction. Separate algorithms can then be applied to search the time seriescorresponding to different sky positions for the signatures of burst events, individualsources or memory events.As an example we show, in the left-hand panel of Figure 5, five simulated datasets that contain a unrealistic, but instructional, gravitational wave burst event. In theright-hand panel of Figure 5 we show the resulting A + ( t ) and A × ( t ) time series (data he Parkes Pulsar Timing Array Figure 5.
The left-hand panel shows the simulated timing residuals for five pulsarsthat are affected by a gravitational wave burst. The functional form of the burst in thetwo polarisation states A + and A × is shown as the solid lines in the right hand panel.The tempo2 fit for A + ( t ) and A × ( t ) is shown in the right-hand panel with error bars. points with errors) that clearly recover the simulated burst (solid lines). The resultingfit is not perfect as it is impossible to measure the linear or quadratic component of aburst event that lasts longer than the data span. This is because the pulsars’ intrinsicpulse periods and time derivatives are unknown. The A + ( t ) and A × ( t ) time series aretherefore constrained within the fit not to include a quadratic polynomial.The method described above can be used to search for individual sources ofgravitational waves. However, this method is not suitable for a gravitational wavebackground. We are therefore improving the algorithm described by Yardley et al.(2011). Our algorithm is still being developed, but is based on forming cross-powerspectra for each pair of pulsars using the Cholesky method for dealing with steep, rednoise (Coles et al. 2011). These cross-power spectra are used to form the covariancebetween two data sets. The correlations between pairs of pulsars as a function of theangle between the pulsars are expected to follow the prediction of Hellings & Downs(1983). Our algorithm is still work-in-progress, but we have successfully applied ourmethod to the International Pulsar Timing Array data challenge ¶ . Champion et al. (2010) searched for the signatures of incorrect mass estimates of theplanetary systems in our solar system. This method relies on knowledge of the relative ¶ he Parkes Pulsar Timing Array Figure 6.
Left-hand panel shows the induced timing residuals due to an incorrectmass of Jupiter of ∆ M J = 10 − M ⊙ . The right-hand panel displays the offset in theobservatory-SSB position in X, Y and Z as a function of time. positions as a function of time of the planetary system, the Earth and the solar systembarycentre (SSB). This method is therefore not applicable to searching for unknownmasses in the solar system. We have therefore updated the tempo2 software to measureoffsets in the estimate of the Earth’s position with respect to the SSB using a PTA dataset. The initial estimate of the Earth’s position with respect to the SSB is obtainedfrom a planetary ephemeris. Any error, or omission, in that ephemeris will thereforelead to an incorrect estimate of the Earth-SSB vector. Inspection of time series ofthe error in the three components of the Earth-SSB vector allows unknown masses tobe identified. As an example we simulate data sets that include an error in the massof the Jovian system of ∆ M J = 10 − M ⊙ . This mass error could easily be measuredusing the Champion et al. (2010) approach, but here we make no assumption aboutthe nature of the error in the planetary ephemeris. We assume that five pulsars havebeen observed since 1990. The output of the tempo2 global fit provides the offset ofthe Earth-SSB vector from the planetary ephemeris prediction (Figure 6). These offsetscould subsequently be searched to identify the orbital period of the unknown mass andthe orbital angle with respect to the ecliptic plane, thereby determining the positionand orbit of the unknown objects.This procedure can be generalised and used to determine the position of anytelescope at any position in the solar system. We have recently used PPTA data toshow how this method can be used to navigate a space craft through the solar system(Deng et al. submitted). he Parkes Pulsar Timing Array In Hobbs et al. (2012b) we describe new updates to tempo2 that allow the signalcommon to all pulsars to be identified given a PTA data set. This method was appliedto the PPTA data sets and we recovered the known offsets between the world’s best timestandards: International Atomic Time and Terrestrial Time as realised by the BureauInternational des Poids et Mesures (BIPM). One major issue with our method is thatwe assume that the noise in the data sets has the same statistical form throughoutthe observations. However, as described in Manchester et al. (2013), we are unable tocorrect our earliest data sets for dispersion measure variations. The timing residuals formost pulsars are therefore affected, for the earliest observations, by dispersion measurevariations and, for the most recent observations, by other noise processes such as intrinsicpulsar timing noise. We are currently enhancing the Coles et al. (2011) Choleskyroutines to account for non-stationary noise processes and will use the new routines toimprove our pulsar-based time standard.
6. Outreach
Some of the PPTA observations are carried out by high school students as part of thePULSE@Parkes education program (Hobbs et al. 2009). This program provides highschool students with two hours of observing per month. So far more than 1000 studentsfrom Australia, Japan, the USA, the Netherlands, England and Wales have been partof the program.
7. Conclusion
The Parkes Pulsar Timing Array is continuing to obtain high quality pulsar timingobservations of ∼
20 millisecond pulsars. These data sets are leading to exciting newresearch on topics as diverse as studying the solar wind to searching for bursts ofgravitational waves to navigating space craft through the solar system. The data setsare also being combined with observations from Europe and North America to form theInternational Pulsar Timing Array data sets. With further development to the hardwaresystems at Parkes it is likely that these observations will continue to contribute to timingarray data sets into the Square Kilometre Array era.
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