EPTA timing of 42 MSPs

High-precision timing of 42 millisecond pulsars with the European Pulsar Timing Array


We report on the high-precision timing of 42 radio millisecond pulsars (MSPs) observed by the European Pulsar Timing Array (EPTA). This EPTA Data Release 1.0 extends up to mid-2014 and baselines range from 7-18 years. It forms the basis for the stochastic gravitational-wave background, anisotropic background, and continuous-wave limits recently presented by the EPTA elsewhere. The Bayesian timing analysis performed with TempoNest yields the detection of several new parameters: seven parallaxes, nine proper motions and, in the case of six binary pulsars, an apparent change of the semi-major axis. We find the NE2001 Galactic electron density model to be a better match to our parallax distances (after correction from the Lutz-Kelker bias) than the M2 and M3 models by Schnitzeler (2012). However, we measure an average uncertainty of 80% (fractional) for NE2001, three times larger than what is typically assumed in the literature. We revisit the transverse velocity distribution for a set of 19 isolated and 57 binary MSPs and find no statistical difference between these two populations. We detect Shapiro delay in the timing residuals of PSRs J16003053 and J19180642, implying pulsar and companion masses , and , , respectively. Finally, we use the measurement of the orbital period derivative to set a stringent constraint on the distance to PSRs J10125307 and J19093744, and set limits on the longitude of ascending node through the search of the annual-orbital parallax for PSRs J16003053 and J19093744.

pulsars:general – stars:distances – proper motions

1 Introduction

Three decades ago Backer et al. (1982) discovered the first millisecond pulsar (MSP), spinning at 642 Hz. Now over 300 MSPs have been found; see the Australia Telescope National Facility (ATNF) pulsar catalog3 (Manchester et al., 2005). MSPs are thought to be neutron stars spun-up to rotation periods (generally) shorter than 30 ms via the transfer of mass and angular momentum from a binary companion (Alpar et al., 1982; Radhakrishnan & Srinivasan, 1982). We know that the vast majority of the MSP population (%) still reside in binary systems and these objects have been shown to be incredible probes for testing physical theories. Their applications range from high-precision tests of general relativity (GR) in the quasi-stationary strong-field regime (Kramer et al., 2006; Freire et al., 2012b) to constraints on the equation of state of matter at supra-nuclear densities (Demorest et al., 2010; Antoniadis et al., 2013). Binary systems with a MSP and a white dwarf in wide orbits offer the most stringent tests of the strong equivalence principle (e.g. Stairs et al., 2005; Freire et al., 2012a; Ransom et al., 2014).

Most of these applications and associated results mentioned above arise from the use of the pulsar timing technique that relies on two properties of the radio MSPs: their extraordinary rotational and average pulse profile stability. The pulsar timing technique tracks the times of arrival (TOAs) of the pulses recorded at the observatory and compares them to the prediction of a best-fit model. This model, which is continuously improved as more observations are made available, initially contains the pulsar’s astrometric parameters, the rotational parameters and the parameters describing the binary orbit, if applicable. With the recent increase in timing precision due to e.g. improved receivers, larger available bandwidth and the use of coherent dedispersion (Hankins & Rickett, 1975), parameters that have a smaller effect on the TOAs have become measurable.

The first binary pulsar found, PSR B1913+16 (Hulse & Taylor, 1975), yielded the first evidence for gravitational waves (GWs) emission. Since then, several ground-based detectors have been built around the globe, e.g. Advanced LIGO (Aasi et al., 2015) and Advanced Virgo (Acernese et al., 2015), to directly detect GWs in the frequency range of 10-7000 Hz. Also a space mission, eLISA (Seoane et al., 2013), is being designed to study GWs in the mHz regime. Pulsars, on the other hand, provide a complementary probe for GWs by opening a new window in the nHz regime (Sazhin, 1978; Detweiler, 1979). Previous limits on the amplitude of the stochastic GW background (GWB) have been set by studying individual MSPs (e.g. Kaspi et al., 1994). However, an ensemble of pulsars spread over the sky (known as Pulsar Timing Array; PTA) is required to ascertain the presence of a GWB and discriminate between possible errors in the Solar System ephemeris or in the reference time standards (Hellings & Downs, 1983; Foster & Backer, 1990).

A decade ago, Jenet et al. (2005) claimed that timing a set of a least 20 MSPs with a precision of 100 ns for five years would allow a direct detection of the GWB. Such high timing precision has not yet been reached (Arzoumanian et al., 2015). Nonetheless, Siemens et al. (2013) recently argued that when a PTA enters a new signal regime where the GWB signal starts to prevail over the low frequency pulsar timing noise, the sensitivity of this PTA depends more strongly on the number of pulsars than the cadence of the observations or the timing precision. Hence, datasets consisting of many pulsars with long observing baselines, even with timing precision of s, constitute an important step towards the detection of the GWB. In addition to the GWB studies, such long and precise datasets allow additional timing parameters, and therefore science, to be extracted from the same data.

Parallax measurements can contribute to the construction of Galactic electron density models (Taylor & Cordes, 1993; Cordes & Lazio, 2002). Once built, these models can provide distance estimates for pulsars along generic lines-of-sight. New parallax measurements hence allow a comparison and improvement of the current free electron distribution models (Schnitzeler, 2012). An accurate distance is also crucial to correct the spin-down rate of the pulsar from the bias introduced by its proper motion (Shklovskii, 1970). This same correction has to be applied to the observed orbital period derivative before any test of GR can be done with this parameter (Damour & Taylor, 1991).

In binary systems, once the Keplerian parameters are known, it may be possible to detect post-Keplerian (PK) parameters. These theory-independent parameters describe the relativistic deformation of a Keplerian orbit as a function of the Keplerian parameters and the a priori unknown pulsar mass (), companion mass () and inclination angle (). Measurement of the Shapiro delay, an extra propagation delay of the radio waves due to the gravitational potential of the companion, gives 2 PK parameters (range and shape ). Other relativistic effects such as the advance of periastron and the orbital decay provide one extra PK parameter each. In GR, any PK parameter can be described by the Keplerian parameters plus the two masses of the system. Measuring three or more PK parameters therefore overconstrains the masses, allowing one to perform tests of GR (Taylor & Weisberg, 1989; Kramer et al., 2006).

The robustness of the detections of these parameters can be hindered by the presence of stochastic influences like dispersion measure (DM) variations and red (low-frequency) spin noise in the timing residuals (Coles et al., 2011; Lentati et al., 2014). Recent work by Keith et al. (2013) and Lee et al. (2014) discussed the modeling of the DM variations while Coles et al. (2011) used Cholesky decomposition of the covariance matrix to properly estimate the parameters in the presence of red noise. Correcting for the DM variations and the effects of red noise has often been done through an iterative process. However, TempoNest, a Bayesian pulsar timing analysis software (Lentati et al., 2014) used in this work allows one to model these stochastic influences simultaneously while performing a non-linear timing analysis.

In this paper we report on the timing solutions of 42 MSPs observed by the European Pulsar Timing Array (EPTA). The EPTA is a collaboration of European research institutes and radio observatories that was established in 2006 (Kramer & Champion, 2013). The EPTA makes use of the five largest (at decimetric wavelengths) radio telescopes in Europe: the Effelsberg Radio Telescope in Germany (EFF), the Lovell Radio Telescope at the Jodrell Bank Observatory (JBO) in England, the Nançay Radio Telescope (NRT) in France, the Westerbork Synthesis Radio Telescope (WSRT) in the Netherlands and the Sardinia Radio Telescope (SRT) in Italy. As the SRT is currently being commissioned, no data from this telescope are included in this paper. The EPTA also operates the Large European Array for Pulsars (LEAP), where data from the EPTA telescopes are coherently combined to form a tied-array telescope with an equivalent diameter of 195 meters, providing a significant improvement in the sensitivity of pulsar timing observations (Bassa et al., 2015).

This collaboration has already led to previous publications. Using multi-telescope data on PSR J10125307, Lazaridis et al. (2009) put a limit on the gravitational dipole radiation and the variation of the gravitational constant . Janssen et al. (2010) presented long-term timing results of four MSPs, two of which are updated in this work. More recently, van Haasteren et al. (2011) set the first EPTA upper limit on the putative GWB. Specifically for a GWB formed by circular, GW-driven supermassive black-hole binaries, they measured the amplitude of the characteristic strain level at a frequency of 1/yr, , using a subset of the EPTA data from only 5 pulsars.

Similar PTA efforts are ongoing around the globe with the Parkes Pulsar Timing Array (PPTA; Manchester et al. (2013)) and the NANOGrav collaboration (McLaughlin, 2013), also setting limits on the GWB (Demorest et al., 2013; Shannon et al., 2013a).

The EPTA dataset introduced here, referred to as the EPTA Data Release 1.0, serves as the reference dataset for the following studies: an analysis of the DM variations (Janssen et al., in prep.), a modeling of the red noise in each pulsar (Caballero et al., 2015), a limit on the stochastic GWB (Lentati et al., 2015b) and the anisotropic background (Taylor et al., 2015) as well as a search for continuous GWs originating from single sources (Babak et al., 2016). The organization of this paper is as follows. The instruments and methods to extract the TOAs at each observatory are described in Section 2. The combination and timing procedures are detailed in Section 3. The timing results and new parameters are presented in Section 4 and discussed in Section  5. Finally, we summarize and present some prospects about the EPTA in Section 6.

2 Observations and data processing

This paper presents the EPTA dataset, up to mid-2014, that was gathered from the ‘historical’ pulsar instrumentations at EFF, JBO, NRT and WSRT with, respectively, the EBPP (Effelsberg-Berkeley Pulsar Processor), DFB (Digital FilterBank), BON (Berkeley-Orléans-Nançay) and PuMa (Pulsar Machine) backends. The data recorded with the newest generation of instrumentations, e.g. PSRIX at EFF (Lazarus et al., 2016) and PuMaII at WSRT (Karuppusamy et al., 2008), will be part of a future EPTA data release.

Compared to the dataset presented in van Haasteren et al. (2011), in which timing of only five pulsars was presented, this release includes 42 MSPs (listed in Table 1 with their distribution on the sky shown in Fig. 1). Among those 42 MSPs, 32 are members of binary systems. The timing solutions presented here span at least seven years, and for 16 of the MSPs the baseline extends back years. For the five pulsars included in van Haasteren et al. (2011), the baseline is extended by a factor 1.7-4. When comparing our set of pulsars with the NANOGrav Nine-year Data Set (Arzoumanian et al., 2015) (consisting of 37 MSPs) and the PPTA dataset (Manchester et al., 2013; Reardon et al., 2016) (consisting of 20 MSPs), we find an overlap of 21 and 12 pulsars, respectively. However, we note that the NANOGrav dataset contains data for 7 MSPs with a baseline less than two years.

In this paper, we define an observing system as a specific combination of observatory, backend and frequency band. The radio telescopes and pulsar backends used for the observations are described below.

Figure 1: Distribution of the 42 MSPs, represented with a star, in Galactic coordinates (longitude and latitude ). The center of the plot is oriented towards the Galactic Center. The hatched area is the part of the sky (declination ) that is not accessible to the EPTA.

2.1 Effelsberg Radio Telescope

The data from the 100-m Effelsberg Radio Telescope presented in this paper were acquired using the EBPP, an online coherent dedispersion backend described in detail by Backer et al. (1997). This instrument can process a bandwidth (BW) up to 112 MHz depending on the DM value. The signals from the two circular polarizations are split into 32 channels each and sent to the dedisperser boards. After the dedispersion takes place, the output signals are folded (i.e. individual pulses are phase-aligned and summed) using the topocentric pulse period.

EPTA timing observations at Effelsberg were made at a central frequency of 1410 MHz until April 2009 then moved to 1360 MHz afterwards due to a change in the receiver. Additional observations at S-Band (2639 MHz) began in November 2005 with observations at both frequencies taken during the same two-day observing run. Typically, the observations occur on a monthly basis with an integration time per source of about 30 minutes. The subintegration times range from 8 to 12 mins before 2009 and 2 mins thereafter. For 4 pulsars, namely PSRs J00300451, J10240719, J17302304 and J23171439, there is a gap in the data from 1999 to 2005 as these sources were temporarily removed from the observing list. Data reduction was performed with the PSRCHIVE package (Hotan et al., 2004). The profiles were cleaned of radio frequency interference (RFI) using the PSRCHIVE paz tool but also examined and excised manually with the pazi tool. No standard polarization calibration using a pulsed and linearly polarized noise diode was performed. However the EBPP automatically adjusts the power levels of both polarizations prior to each observation. The TOAs were calculated by cross-correlating the time-integrated, frequency-scrunched, total intensity profile, with an analytic and noise free template. This template was generated using the paas tool to fit a set of von Mises functions to a profile formed from high signal-to-noise ratio (S/N) observations. In general, we used the standard ‘Fourier phase gradient’ algorithm (Taylor, 1992) implemented in PSRCHIVE to estimate the TOAs and their uncertainties. We used a different template for each observing frequency, including different templates for the 1410 and 1360 MHz observations. Local time is kept by the on-site H-maser clock, which is corrected to Coordinated Universal Time (UTC) using recorded offsets between the maser and the Global Positioning System (GPS) satellites.

2.2 Lovell Radio Telescope

At Jodrell bank, the 76-m Lovell telescope is used in a regular monitoring program to observe most of the pulsars presented in this paper. All TOAs used here were generated by using the DFB, a clone of the Parkes Digital FilterBank. Each pulsar was observed with a typical cadence of once every 10 days for 30 mins with a subintegration time of 10 s. The DFB came into operation in January 2009 observing at a central frequency of 1400 MHz with a BW of 128 MHz split into 512 channels. From September 2009, the center frequency was changed to 1520 MHz and the BW increased to 512 MHz (split into 1024 channels) of which approximately 380 MHz was usable, depending on RFI conditions. As this is a significant change, and to account for possible profile evolution with observing frequency, both setups are considered as distinct observing systems and different templates were used. Data cleaning and TOA generation were done in a similar way to the Effelsberg data. There is no standard polarization calibration (through observations of a noise diode) applied to the DFB data. However the power levels of both polarizations are regularly and manually adjusted via a set of attenuators. Local time is kept by the on-site H-maser clock, which is corrected to UTC using recorded offsets between the maser and the GPS satellites.

2.3 Nançay Radio Telescope

The Nançay Radio Telescope is a meridian telescope with a collecting area equivalent to a 94-m dish. The moving focal carriage that allows an observing time of about one hour per source hosts the Low Frequency (LF) and High Frequency (HF) receivers covering 1.1 to 1.8 GHz and 1.7 to 3.5 GHz, respectively. A large timing program of MSPs started in late 2004 with the commissioning of the BON instrumentation, a member of the ASP-GASP coherent dedispersion backend family (Demorest, 2007). A 128 MHz BW is split into 32 channels by a CASPER4 Serendip V board and then sent to servers to be coherently dedispersed and folded to form 2-min subintegrations.

From 2004 to 2008 the BW was limited to 64 MHz and then extended to 128 MHz. At the same time, the NRT started to regularly observe a pulsed noise diode prior to each observation in order to properly correct for the difference in gain and phase between the two polarizations. In August 2011, the L-Band central frequency of the BON backend shifted from 1.4 GHz to 1.6 GHz to accommodate the new wide-band NUPPI dedispersion backend (Liu et al., 2014). Due to known instrumental issues between November 2012 and April 2013 (i.e. loss of one of the polarization channels, mirroring of the spectrum), these data have not been included in the analysis.

The flux density values at 1.4 GHz reported in Table 1 are derived from observations recorded with the NUPPI instrument between MJD 55900 and 56700. The quasar 3C48 was chosen to be the reference source for the absolute flux calibration. These flux density values have been corrected for the declination-dependent illumination of the mirrors of the NRT. Although the NUPPI timing data are not included in this work, we used these observations to estimate the median flux densities as no other EPTA data were flux-calibrated. The NUPPI timing data will be part of a future EPTA data release along with the data from other telescopes recorded with new-generation instrumentations.

The data were reduced with the PSRCHIVE package and automatically cleaned for RFI. Except for pulsars with short orbital periods, all daily observations are fully scrunched in time and frequency to form one single profile. For PSRs J06102100, J07511807, J17380333, J18022124 the data were integrated to form 6, 12, 16 and 8 min profiles respectively. The templates for the three observing frequencies are constructed by phase-aligning the 10% profiles with the best S/N. The resulting integrated profiles are made noise free with the same wavelet noise removal program as in Demorest et al. (2013). As stated above, we used the standard ‘Fourier phase gradient’ from PSRCHIVE to estimate the TOAs and their uncertainties. However, we noticed that in the case of very low S/N profiles, the reported uncertainties were underestimated. Arzoumanian et al. (2015) also observed that TOAs extracted from low S/N profiles deviate from a Gaussian distribution and therefore excluded all TOAs where S/N <8 (see Appendix B of their paper for more details). Here, we made use of the Fourier domain Markov Chain Monte Carlo TOA estimator (hereafter FDM) to properly estimate the error bars in this low S/N regime. We applied the FDM method to PSRs J00340534, J02184232, J14553330, J20192425, J20331734. All the BON data are time-stamped with a GPS-disciplined clock.

For PSR J19392134, archival data from 1990 to 1999 recorded with a swept-frequency local oscillator (hereafter referred to as DDS) at a frequency of 1410 MHz (Cognard et al., 1995) were added to the dataset. These data are time-stamped with an on-site Rubidium clock, which is corrected to UTC using recorded offsets between the Rubidium clock and the Paris Observatory Universal Time.

2.4 Westerbork Synthesis Radio Telescope

The Westerbork Synthesis Radio Telescope is an East-West array consisting of fourteen 25-m dishes, adding up to the equivalent size of a 94-m dish when combined as a tied-array. From 1999 to 2010, an increasing number of MSPs were observed once a month using the PuMa pulsar machine (a digital filterbank) at WSRT (Voûte et al., 2002). In each observing session, the pulsars were observed for 25 minutes each at one or more frequencies centered at 350 MHz (10 MHz BW), 840 MHz (80 MHz BW) and 1380 MHz (80 MHz spread across a total of 160 MHz BW). Up to 512 channels were used to split the BW for the observations at 350 MHz. At 840 MHz and 1380 MHz, 64 channels were used per 10 MHz subband. For a more detailed description of this instrumentation, see e.g. Janssen et al. (2008). Since 2007, the 840 MHz band was no longer used for regular timing observations, however, an additional observing frequency centered at 2273 MHz using 160 MHz BW was used for a selected set of the observed pulsars. The data were dedispersed and folded offline using custom software, and then integrated over frequency and time to obtain a single profile for each observation. Gain and phase difference between the two polarizations are adjusted during the phased-array calibration of the dishes. To generate the TOAs, a high-S/N template based on the observations was used for each observing frequency separately. Local time is kept by the on-site H-maser clock, which is corrected to UTC using recorded offsets between the maser and the GPS satellites.

3 Data combination and timing

The topocentric TOAs recorded at each observatory are first converted to the Solar System barycenter (SSB) using the DE421 planetary ephemeris (Folkner et al., 2009) with reference to the latest Terrestrial Time standard from the Bureau International des Poids et Mesures (BIPM) (Petit, 2010). The DE421 model is a major improvement on the DE200 ephemeris that was used for older published ephemerides and later found to suffer from inaccurate values of planetary masses (Splaver et al., 2005; Hotan et al., 2006; Verbiest et al., 2008).

We used TempoNest (Lentati et al., 2014), a Bayesian analysis software that uses the Tempo2 pulsar timing package (Hobbs et al., 2006; Edwards et al., 2006) and MULTINEST (Feroz et al., 2009), a Bayesian inference tool, to evaluate and explore the parameter space of the non-linear pulsar timing model. All pulsar timing parameters are sampled in TempoNest with uniform priors. The timing model includes the astrometric (right ascension, , declination, , proper motion in and , and ) and rotational parameters (period and period derivative ). If the pulsar is part of a binary system, five additional parameters are incorporated to describe the Keplerian binary motion: the orbital period , the projected semi-major axis of the pulsar orbit, the longitude of periastron , the epoch of the periastron passage and the eccentricity . For some pulsars in our set, we require theory-independent PK parameters (Damour & Deruelle, 1985, 1986) to account for deviations from a Keplerian motion, or parameters to describe changes in the viewing geometry of the systems. The parameters we used include the precession of periastron , the orbital period derivative , the Shapiro delay (‘range’ and ‘shape’ ; has a uniform prior in space) and the apparent derivative of the projected semi-major axis . These parameters are implemented in Tempo2 under the ‘DD’ binary model. In the case of quasi-circular orbits, the ‘ELL1’ model is preferred and replaces , and with the two Laplace-Lagrange parameters and and the time of ascending node (Lange et al., 2001). For the description of the Shapiro delay in PSRs J07511807, J16003053 and J19180642 we adopted the orthometric parametrization of the Shapiro delay introduced by Freire & Wex (2010) with the amplitude of the third harmonic of the Shapiro delay and the ratio of successives harmonics .

To combine the TOAs coming from the different observing systems described in Section 2, we first corrected them for the phase difference between the templates by cross-correlation of the reference template with the other templates. We then fit for the arbitrary time offsets, known as JUMPs, between the reference observing system and the remaining systems. These JUMPs encompass, among other things: the difference in instrumental delays, the use of different templates and the choice for the fiducial point on the template. The JUMPs are analytically marginalized over during the TempoNest Bayesian analysis. In order to properly weight the TOAs from each system, the timing model includes a further two ad hoc white noise parameters per observing system. These parameters known as the error factor ‘EFAC’, , and the error added in quadrature ‘EQUAD’, (in units of seconds), relate to a TOA with uncertainty in seconds as:


Note that this definition of EFAC and EQUAD in TempoNest is different from the definition employed in Tempo2 and the earlier timing software Tempo, where was added in quadrature to before applying . The and parameters are set with uniform priors in the logarithmic space (log-uniform priors) in the -range , respectively. These prior ranges are chosen to be wide enough to include any value of EFAC and EQUAD seen in our dataset.

Each pulsar timing model also includes two stochastic models to describe the DM variations and an additional achromatic red noise process. Both processes are modeled as stationary, stochastic signals with a power-law spectrum of the form , where , , and are the power spectral density as function of frequency , the amplitude and the spectral index, respectively. The power laws have a cutoff frequency at the lowest frequency, equal to the inverse of the data span, which is mathematically necessary for the subsequent calculation of the covariance matrix (van Haasteren et al., 2009). It has been shown that this cutoff rises naturally for the achromatic red noise power law in pulsar timing data because any low-frequency signal’s power below the cutoff frequency is absorbed by the fitting of the pulsar’s rotational frequency and frequency derivative (van Haasteren et al., 2009; Lee et al., 2012). It is possible to do the same for the DM variations model, by fitting a first and a second DM derivative (parameters DM1 and DM2) in the timing model (Lee et al., 2014). Implementation of the models is made using the time-frequency method of Lentati et al. (2013). Details on this process and applications can be found in Lentati et al. (2015b) and Caballero et al. (2015). In brief, denoting matrices with boldface letters, the red noise process time-domain signal, is expressed as a Fourier series, , where is the sum of sines and cosines with coefficients given by the matrix a. Fourier frequencies are sampled with integer multiples of the lowest frequency, and are sampled up to  days. The Fourier coefficients are free parameters.

The DM variations component is modeled similarly, with the only difference being that the time-domain signal is dependent on the observing frequency. According to the dispersion law from interstellar plasma, the delay in the arrival time of the pulse depends on the inverse square of the observing frequency, see e.g. Lyne & Graham-Smith (2012). As such, the Fourier transform components are , where the i,j indices denote the residual index number, , and  Hzcmpc s, is the dispersion constant. This stochastic DM variations component is additional to the deterministic linear and quadratic components implemented as part of the Tempo2 timing model. In addition, we used the standard electron density model for the solar wind included in Tempo2 with a value of 4 cm at 1 AU. This solar wind model can be covariant with the measured astrometric parameters of the pulsar.

The covariance matrix of each of these two components is then calculated with a function of the form (Lentati et al., 2015b):


The equation is valid for both the DM variations and achromatic red noise process, by using the corresponding Fourier transform F and covariance matrix of the Fourier coefficients . The term is the white noise covariance matrix and is a diagonal matrix with the main diagonal formed by the residual uncertainties squared. The superscript T denotes the transpose of the matrix.

The power-law parameterization of the DM variations and red noise spectra means that the parameters we need to sample are the amplitudes and spectral indices of the power law. We do so by using uniform priors in the range for the spectral index and log-uniform priors for the amplitudes, in the -range . For discussion on the impact of our prior type selection, see Lentati et al. (2014) and Caballero et al. (2015). Here, we have used the least informative priors on the noise parameters. This means that the Bayesian inference will assign equal probability to these parameters if the data are insufficient to break the degeneracy between them. This approach is adequate to derive a total noise covariance matrix (addition of white noise, red noise and DM variations covariance matrices) that allows robust estimation of the timing parameters. The prior ranges are set to be wide enough to encompass any DM or red noise signal seen in the data. The lower bound on the spectral index of the red noise process is set to zero as we assume there is no blue process in the data. Together with the EFAC and EQUAD values, the DM and red noise spectral indices and amplitudes are used by the timing software to form the timing residuals.

3.1 Criterion for Shapiro delay detectability

To assess the potential detectability of Shapiro delay, we used the following criterion. With the orthometric parametrization of Shapiro delay, we can compute the amplitude (in seconds) in the timing residuals (Freire & Wex, 2010),


Here, is the speed of light, s is the mass of the Sun in units of time. By assuming a median companion mass, , given by the mass function with M and an inclination angle , we can predict an observable . We can then compare this value to the expected precision given by where is the median uncertainty of the TOAs and the number of TOAs in the dataset. The criterion associated with a non detection of Shapiro delay would likely mean an unfavorable inclination angle, i.e. .

4 Timing results

In this section we summarize the timing results of the 42 MSPs obtained from TempoNest. Among these sources, six pulsars, namely PSRs J06130200, J1012+5307, J16003053, J1713+0747, J17441134 and J19093744, have been selected by Babak et al. (2016) to form the basis of the work presented by Lentati et al. (2015b); Taylor et al. (2015); Babak et al. (2016). The quoted uncertainties represent the Bayesian credible interval of the one-dimensional marginalized posterior distribution of each parameter. The timing models are shown in Tables 2 to 12. These models, including the stochastic parameters, are made publicly available on the EPTA website5. The reference profiles at L-Band can be found in Fig. 14 and 15. Throughout the paper, we refer to RMS as the weighted Root Mean Square timing residuals. The details on the data sets used in this paper can be found in Table 18.

PSR JName Observatories RMS S References
(yr) () () (ms) (d) (mJy)
J00300451 EFF, JBO, NRT 907 15.1 3.79 4.1 4.9 0.8 Abdo et al. (2009); A15
J00340534 NRT, WSRT 276 13.5 8.51 4.0 1.9 1.59 0.01 Hobbs et al. (2004b); Abdo et al. (2010)
J02184232 EFF, JBO, NRT, WSRT 1196 17.6 10.51 7.4 2.3 2.03 0.6 Hobbs et al. (2004b)
J06102100 JBO, NRT 1034 6.9 8.14 4.9 3.9 0.29 0.4 Burgay et al. (2006)
J06130200 EFF, JBO, NRT, WSRT 1369 16.1 2.57 1.8 3.1 1.20 1.7 V09; A15; R16
J06211002 EFF, JBO, NRT, WSRT 673 11.8 9.43 15.6 28.9 8.32 1.3 Splaver et al. (2002); Nice et al. (2008)
J07511807 EFF, JBO, NRT, WSRT 1491 17.6 4.33 3.0 3.5 0.26 1.1 Nice et al. (2005); Nice et al. (2008)
J09003144 JBO, NRT 875 6.9 4.27 3.1 11.1 18.74 3.2 Burgay et al. (2006)
J10125307 EFF, JBO, NRT, WSRT 1459 16.8 2.73 1.6 5.3 0.60 3.0 Lazaridis et al. (2009); A15
J10221001 EFF, JBO, NRT, WSRT 908 17.5 4.02 2.5 16.5 7.81 2.9 V09; R16
J10240719 EFF, JBO, NRT, WSRT 561 17.3 3.42 8.3 5.2 1.3 V09;Espinoza et al. (2013); A15; R16
J14553330 JBO, NRT 524 9.2 7.07 2.7 8.0 76.17 0.4 Hobbs et al. (2004b); A15
J16003053 JBO, NRT 531 7.7 0.55 0.46 3.6 14.35 2.0 V09; A15; R16
J16402224 EFF, JBO, NRT, WSRT 595 17.3 4.48 1.8 3.2 175.46 0.4 Löhmer et al. (2005); A15
J16431224 EFF, JBO, NRT, WSRT 759 17.3 2.53 1.7 4.6 147.02 3.9 V09; A15; R16
J17130747 EFF, JBO, NRT, WSRT 1188 17.7 0.59 0.68 4.6 67.83 4.9 V09;Zhu et al. (2015); A15; R16
J17212457 NRT, WSRT 150 12.8 24.28 11.7 3.5 1.0 Janssen et al. (2010)
J17302304 EFF, JBO, NRT 285 16.7 4.17 1.6 8.1 2.7 V09; R16
J17380333 JBO, NRT 318 7.3 5.95 3.0 5.9 0.35 0.3 Freire et al. (2012b); A15
J17441134 EFF, JBO, NRT, WSRT 536 17.3 1.21 0.86 4.1 1.6 V09; A15; R16
J17512857 JBO, NRT 144 8.3 3.52 3.0 3.9 110.75 0.4 Stairs et al. (2005)
J18011417 JBO, NRT 126 7.1 3.81 2.6 3.6 1.1 Lorimer et al. (2006)
J18022124 JBO, NRT 522 7.2 3.38 2.7 12.6 0.70 0.9 Ferdman et al. (2010)
J18042717 JBO, NRT 116 8.4 7.23 3.1 9.3 11.13 1.0 Hobbs et al. (2004b)
J18431113 JBO, NRT, WSRT 224 10.1 2.48 0.71 1.8 0.5 Hobbs et al. (2004a)
J18531303 JBO, NRT 101 8.4 3.58 1.6 4.1 115.65 0.5 Gonzalez et al. (2011); A15
J18570943 EFF, JBO, NRT, WSRT 444 17.3 2.57 1.7 5.4 12.33 3.3 V09; A15; R16
J19093744 NRT 425 9.4 0.26 0.13 2.9 1.53 1.1 V09; A15; R16
J19101256 JBO, NRT 112 8.5 3.39 1.9 5.0 58.47 0.5 Gonzalez et al. (2011); A15
J19111347 JBO, NRT 140 7.5 1.78 1.4 4.6 0.6 Lorimer et al. (2006)
J19111114 JBO, NRT 130 8.8 8.82 4.8 3.6 2.72 0.5 Toscano et al. (1999a)
J19180642 JBO, NRT, WSRT 278 12.8 3.18 3.0 7.6 10.91 1.2 Janssen et al. (2010); A15
J19392134 EFF, JBO, NRT, WSRT 3174 24.1 0.49 34.5 1.6 8.3 V09; A15; R16
J19552908 JBO, NRT 157 8.1 14.92 6.5 6.1 117.35 0.5 Gonzalez et al. (2011); A15
J20101323 JBO, NRT 390 7.4 2.89 1.9 5.2 0.5 Jacoby et al. (2007); A15
J20192425 JBO, NRT 130 9.1 26.86 9.6 3.9 76.51 0.1 Nice et al. (2001)
J20331734 JBO, NRT 194 7.9 18.24 12.7 5.9 56.31 0.1 Splaver (2004)
J21243358 JBO, NRT 544 9.4 5.57 3.2 4.9 2.7 V09; R16
J21450750 EFF, JBO, NRT, WSRT 800 17.5 2.64 1.8 16.1 6.84 4.0 V09; A15; R16
J22292643 EFF, JBO, NRT 316 8.2 11.18 4.2 3.0 93.02 0.1 Wolszczan et al. (2000)
J23171439 EFF, JBO, NRT, WSRT 555 17.3 7.78 2.4 3.4 2.46 0.3 Camilo et al. (1996); A15
J23222057 JBO, NRT 229 7.9 12.47 5.9 4.8 0.03 Nice & Taylor (1995)
Table 1: Summary of the 42-pulsar data set. The columns present the pulsar name in the J2000 coordinate system, the observatories that contributed to the dataset, the number of TOAs, the time span of the dataset, the median TOA uncertainty () taking into account the white noise parameters ‘EFAC’ and ‘EQUAD’, the RMS timing residual, the spin period, the orbital period and the median flux density of the pulsar at 1400 MHz (see Section 2.3 for more details about the flux measurements). The last column gives the reference for the last published timing solution where V09, A15, R16 relate to Verbiest et al. (2009), Arzoumanian et al. (2015), Reardon et al. (2016), respectively. The pulsars indicated by are also named following the B1950 coordinate system, with the names B185509, B193721 and B195329 respectively. The quoted RMS values are obtained from keeping the noise parameters, DM and red noise models at the maximum likelihood value while subtracting the DM signal from the residuals. Because of the degeneracy between the DM and red noise models, especially where no multifrequency data are available, the resulting RMS quoted here can be biased towards smaller values (when the removed DM signal absorbed part of the red noise signal).

4.1 Psr J00300451

A timing ephemeris for this isolated pulsar has been published by Abdo et al. (2009) with a joint analysis of gamma-ray data from the Fermi Gamma-ray Space Telescope. Because the authors used the older DE200 version of the Solar System ephemeris model, we report here updated astrometric measurements. While our measured proper motion is consistent with the Abdo et al. (2009) value, we get a significantly lower parallax value mas that we attribute partly to the errors in the DE200 ephemeris. Indeed reverting back to the DE200 in our analysis yields an increased value of the parallax by 0.3 mas but still below the parallax mas determined by Abdo et al. (2009).

4.2 Psr J00340534

PSR J00340534 is a very faint MSP when observed at L-Band with a flux density mJy leading to profiles with very low S/N compared to most other MSPs considered here. Helped by the better timing precision at 350 MHz, we were able to improve on the previously published composite proper motion mas yr by Hobbs et al. (2005) to mas yr. We also measure the eccentricity of this system for the first time. Even with our improved timing precision characterized by a timing residuals RMS of 4 s, the detection of the parallax signature (at most 2.4 s according to Abdo et al. (2010)) is still out of reach.

PSR Name J00300451 J00340534 J02184232 J06102100
MJD range 51275 — 56779 51770 — 56705 50370 — 56786 54270 — 56791
Number of TOAs 907 276 1196 1034
RMS timing residual () 4.1 4.0 7.4 4.9
Reference epoch (MJD) 55000 55000 55000 55000
Measured parameters
Right ascension, 00:30:27.42836(6) 00:34:21.83422(8) 02:18:06.357299(19) 06:10:13.595462(17)
Declination, 04:51:39.707(3) 05:34:36.722(3) 42:32:17.3821(4) 21:00:27.9313(4)
Proper motion in (mas yr) 5.9(5) 7.9(3) 5.31(7) 9.0(1)
Proper motion in (mas yr) 0.2(11) 9.2(6) 3.15(13) 16.78(12)
Period, (ms) 4.86545328635201(19) 1.87718188583171(10) 2.32309053151224(8) 3.861324766195(3)
Period derivative, () 1.0172(3) 0.49784(13) 7.73955(7) 1.2298(19)
Parallax, (mas) 2.79(23)
DM (cmpc) 4.329(6) 13.7658(19) 61.2488(17) 60.67(3)
DM1 (cmpc yr) 0.0007(5) 0.0001(1) 0.0003(2) 0.014(8)
DM2 (cmpc yr) 0.0001(1) 0.000030(17) 0.000056(20) 0.002(1)
Orbital period, (d) 1.58928182532(14) 2.02884611561(9) 0.2860160068(6)
Epoch of periastron, (MJD) 48766.98(4) 49150.883(16) 52814.303(13)
Projected semi-major axis, (lt-s) 1.4377662(5) 1.9844344(4) 0.0734891(4)
Longitude of periastron, (deg) 313(9) 49(3) 67(16)
Orbital eccentricity, 4.3(7) 6.8(4) 2.9(8)
3.1(7) 5.1(4) 2.7(8)
3.0(6) 4.5(4) 1.2(8)
Time of asc. node (MJD) 48765.5995019(5) 49150.6089170(3) 52814.249581(3)
Derived parameters
Gal. longitude, (deg) 113.1 111.5 139.5 227.7
Gal. latitude, (deg) 57.6 68.1 17.5 18.2
LK Px Distance, (pc)
Composite PM, (mas yr) 5.9(5) 12.1(5) 6.18(9) 19.05(11)
0.015(3) 0.036 0.057 1.2
0.078(7) 0.056 0.034 0.082
0.0030(3) 0.00086 0.013 0.011
1.084(6) 0.518 7.7 0.0955
Characteristic age, (Gyr) 7.1 5.7 0.48 64.0
Surface magnetic field, ( G) 2.3 1.0 4.3 0.6
Min. companion mass (M) 0.13 0.16 0.02
Table 2: Timing model parameters for PSRs J00300451, J00340534, J02184232 and J06102100. Figures in parentheses represent the confidence uncertainties in the last digit quoted and come from the one-dimensional marginalized posterior distribution of each parameter. The measured timing parameters are introduced in Section 3. The derived parameters show the Galactic longitude () and latitude (), the parallax distance corrected from the Lutz-Kelker bias (), the composite proper motion (). The position, spin period and DM are given for the reference epoch of MJD 55000. The three kinematic contributions (, and ) to the intrinsic period derivative () are introduced in Section 5.3. For binary pulsars, the minimum companion mass, assuming a pulsar mass of 1.2 M, is also indicated on the last line.

4.3 Psr J02184232

The broad shape of the pulse profile of this pulsar (with a duty cycle of about 50%, see Figure 14) and its low flux density limit our timing precision to about 7 s and, therefore, its use for GWB detection. Du et al. (2014) recently published the pulsar composite proper motion mas yr from very long baseline interferometry (VLBI). With EPTA data, we find mas yr. This value is in disagreement with the VLBI result. A possible explanation for this discrepancy is that Du et al. (2014) overfitted their model with five parameters for five observing epochs. Du et al. (2014) also reported a distance kpc from VLBI parallax measurement. Verbiest & Lorimer (2014) later argued that the Du et al. (2014) parallax suffers from the Lutz-Kelker bias and corrected the distance to be kpc. This distance is consistent with the 2.5 to 4 kpc range estimated from the properties of the white dwarf companion to PSR J0218+4232 (Bassa et al., 2003). Even with the Verbiest & Lorimer (2014) lowest distance estimate, the parallax would induce a signature on the timing residuals of less than 800 ns (Lorimer & Kramer, 2004), which is far from our current timing precision. We therefore cannot further constrain the distance with our current dataset. Our measurement of the system’s eccentricity is significantly lower than the previously reported value by Hobbs et al. (2004b).

4.4 Psr J06102100

With a very low-mass companion (), PSR J06102100 is a member of the ‘black widow’ family, which are a group of (often) eclipsing binary MSPs believed to be ablating their companions. Here we report on a newly measured eccentricity, , and an improved proper motion ( mas yr and mas yr) compared to the previous values ( mas yr and mas yr) from Burgay et al. (2006) derived with slightly more than two years of data. It is interesting to note that, in contrast to another well studied black widow pulsar, PSR J20510827 (Lazaridis et al., 2011), no secular variations of the orbital parameters are detected in this system. There is also no evidence for eclipses of the radio signal in our data.

We checked our data for possible orbital-phase dependent DM-variation that could account for the new measurement of the eccentricity. We found no evidence for this within our DM precision. We also obtained consistent results for the eccentricity and longitude of periastron after removing TOAs for given orbital phase ranges.

4.5 Psr J06130200

For PSR J06130200, we measure a parallax mas that is consistent with the value published in Verbiest et al. (2009) ( mas). In addition, we report on the first detection of the orbital period derivative thanks to our 16-yr baseline. This result will be discussed further in Section 5.3. Finally, we improve on the precision of the proper motion with mas yr and mas yr.

4.6 Psr J06211002

Despite being the slowest rotating MSP of this dataset with a period of almost 30 ms, PSR J06211002 has a profile with a narrow peak feature of width s. We are able to measure the precession of the periastron deg yr and find it to be within 1 of the value reported by Nice et al. (2008) using Arecibo data. We also find a similar value of the proper motion to Splaver et al. (2002).

4.7 Psr J07511807

PSR J07511807 is a 3.5-ms pulsar in an approximately 6-h orbit. Nice et al. (2005) originally reported a parallax  mas and a measurement of the orbital period derivative . Together with their detection of the Shapiro delay, they initially derived a large pulsar mass . Nice et al. (2008) later corrected the orbital period derivative measurement to , giving a much lower pulsar mass . Here we report on a parallax mas and that is similar to the value in Nice et al. (2008). However, we measured a precise composite proper motion of mas yr, inconsistent with the result ( mas yr) from Nice et al. (2005). Nice et al. (2008) explained the issue found with the timing solution presented in Nice et al. (2005) but did not provide an update of the proper motion for comparison with our value. We are also able to measure an apparent change in the semi-major axis . Finally, we applied the orthometric parametrization of the Shapiro delay to get and . The interpretation of these results will be discussed in Section 5.4.

4.8 Psr J09003144

With about seven years of timing data available for PSR J09003144 (discovered by (Burgay et al., 2006)) we detect the proper motion for the first time, revealing it to be one of the lowest composite proper-motion objects among our data set with mas yr. We also uncover a marginal signature of the parallax mas. However, we do not detect the signature of the Shapiro delay despite the improvement in timing precision compared to Burgay et al. (2006). Following the criterion introduced in Section 3.1, we get s. With s and N, we find  s. Hence, given , we argue for to explain the lack of Shapiro delay detection in this system.

PSR Name J06130200 J06211002 J07511807 J09003144
MJD range 50931 — 56795 52482 — 56780 50363 — 56793 54286 — 56793
Number of TOAs 1369 673 1491 875
RMS timing residual () 1.8 15.6 3.0 3.1
Reference epoch (MJD) 55000 55000 55000 55000
Measured parameters
Right ascension, 06:13:43.975672(2) 06:21:22.11436(3) 07:51:09.155331(13) 09:00:43.953088(8)
Declination, 02:00:47.22533(7) 10:02:38.7352(15) 18:07:38.4864(10) 31:44:30.89520(13)
Proper motion in (mas yr) 1.822(8) 3.23(12) 2.73(5) 1.01(5)
Proper motion in (mas yr) 10.355(17) 0.5(5) 13.4(3) 2.02(7)
Period, (ms) 3.061844088094608(15) 28.8538611940574(16) 3.47877083927942(4) 11.1096493380938(6)
Period derivative, () 0.959013(14) 4.730(5) 0.77874(5) 4.8880(11)
Parallax, (mas) 1.25(13) 0.82(17) 0.77(44)
DM (cmpc) 38.7746(14) 36.47(3) 30.246(6) 75.707(8)
DM1 (cmpc yr) 0.00002(7) 0.0094(3) 0.0000(2) 0.0009(7)
DM2 (cmpc yr) 0.000002(7) 0.0011(2) 0.00004(4) 0.0002(3)
Orbital period, (d) 1.198512575184(13) 8.3186812(3) 0.263144270792(7) 18.7376360594(9)
Epoch of periastron, (MJD) 53113.953(4) 49746.86675(19) 51800.283(7) 52682.295(5)
Projected semi-major axis, (lt-s) 1.09144409(6) 12.0320732(4) 0.3966158(3) 17.24881126(15)
Longitude of periastron, (deg) 47.2(11) 188.774(9) 92(9) 70.41(10)
Orbital eccentricity, 5.40(10) 0.00245724(7) 3.3(5) 1.0490(17)
3.96(10) 3.3(5) 9.883(17)
3.67(11) 3.8(50) 3.517(17)
Time of asc. node (MJD) 53113.796354200(16) 51800.21586826(4) 52678.63028819(13)
Orbital period derivative, 4.8(11) 3.50(25)
First derivative of , 4.9(9)
Periastron advance, (deg/yr) 0.0113(6)
Third harmonic of Shapiro, () 0.30(6)
Ratio of harmonics amplitude, 0.81(17)
Derived parameters
Gal. longitude, (deg) 210.4 200.6 202.7 256.2
Gal. latitude, (deg) 9.3 2.0 21.1 9.5
LK Px Distance, (pc)
Composite PM, (mas yr) 10.514(17) 3.27(14) 13.7(3) 2.26(7)
0.064(7) 0.1 0.16(3) 0.011(5)
0.0039(4) 0.0016 0.015(2) 0.012(4)
0.010(1) 0.24 0.018(4) 0.06(3)
0.889(8) 4.39 0.62(3) 4.95(3)
Characteristic age, (Gyr) 5.5 10.4 8.9 3.6
Surface magnetic field, ( G) 1.7 11.4 1.5 7.5
Min. companion mass (M) 0.12 0.41 0.12 0.33
Table 3: Timing model parameters for PSRs J06130200, J06211002, J07511807 and J09003144. See caption of Table 2 for a description of this table.

4.9 Psr J10125307

Lazaridis et al. (2009) previously presented a timing solution using a subset of these EPTA data to perform a test on gravitational dipole radiation and variation of the gravitational constant, . The and parameters we present here are consistent with the values from Lazaridis et al. (2009) but we improve on the uncertainties of these parameters by factors of two and three, respectively. Nonetheless, we note that our value for the parallax mas differs by less than 2 from the value measured by Lazaridis et al. (2009) using the DE405 ephemeris.

4.10 Psr J10221001

As recently pointed out by van Straten (2013), this source requires a high level of polarimetric calibration in order to reach the best timing precision. Indeed, by carefully calibrating their data, van Straten (2013) greatly improved on the timing model of Verbiest et al. (2009) and successfully unveiled the precession of the periastron deg yr, the presence of Shapiro delay and the secular variation of . Here we find similar results with deg yr and a 2- consistent with a completely independent dataset. Nonetheless, we can not confirm the measurement of Shapiro delay with our dataset. For this pulsar, we get s. With s, our constraint implies that the inclination angle , in agreement with the result presented by van Straten (2013).

4.11 Psr J10240719

Hotan et al. (2006) were the first to announce a parallax mas for this nearby and isolated MSP that shows a large amount of red noise (Caballero et al., 2015). More recently, Espinoza et al. (2013) used a subset of this EPTA dataset to produce an ephemeris and detected gamma-ray pulsations from this pulsar. The authors assumed the LK bias corrected distance (Verbiest et al., 2012) from the Hotan et al. (2006) parallax value to estimate its gamma-ray efficiency. However, it should be noted that Verbiest et al. (2009) did not report on the measurement of the parallax using an extended version of the Hotan et al. (2006) dataset. With this independent dataset we detect a parallax mas, a value inconsistent with the early measurement reported by Hotan et al. (2006). A possible explanation for this discrepancy could be that Hotan et al. (2006) did not include a red noise model in their analysis.

4.12 Psr J14553330

The last timing solution for this pulsar was published by Hobbs et al. (2004b) and characterized by an RMS of 67 s. Thanks to our 9 years of data with an RMS of less than 3 s, we successfully detect the signature of the proper motion mas yr and mas yr, the parallax mas and the secular variation of the semi-major axis, for the first time.

4.13 Psr J16003053

This 3.6-ms pulsar can be timed at very high precision thanks to the s wide peak on the right edge of its profile (see Fig. 14). We present here a precise measurement of the parallax mas, a value marginally consistent with the mas from Verbiest et al. (2009). We also show a large improvement on the Shapiro delay detection through the use of the orthometric parametrization (Freire & Wex, 2010) with and . The resulting mass measurement of this system is discussed in Section 5.4.

PSR Name J10125307 J10221001 J10240719 J14553330
MJD range 50647 — 56794 50361 — 56767 50460 — 56764 53375 — 56752
Number of TOAs 1459 908 561 524
RMS timing residual () 1.6 2.5 8.3 2.7
Reference epoch (MJD) 55000 55000 55000 55000
Measured parameters
Right ascension, 10:12:33.437521(5) 10:22:57.9992(15) 10:24:38.675378(5) 14:55:47.969869(14)
Declination, 53:07:02.29999(6) 10:01:52.78(6) 07:19:19.43395(15) 33:30:46.3801(4)
Proper motion in (mas yr) 2.609(8) 18.2(64) 35.28(3) 7.88(8)
Proper motion in (mas yr) 25.482(11) 3(16) 48.18(7) 2.23(19)
Period, (ms) 5.255749101970103(19) 16.45292995606771(11) 5.1622046403157(3) 7.987204929333(3)
Period derivative, () 1.712730(17) 4.3322(4) 1.8553(4) 2.428(4)
Parallax, (mas) 0.71(17) 0.72(20) 0.80(17) 1.04(35)
DM (cmpc) 9.0172(14) 10.250(4) 6.485(10) 13.563(7)
DM1 (cmpc yr) 0.00016(2) 0.0004(1) 0.0025(8) 0.002(4)
DM2 (cmpc yr) 0.000016(2) 0.00026(5) 0.0007(2) 0.001(1)
Orbital period, (d) 0.604672722901(13) 7.8051348(11) 76.174568631(9)
Epoch of periastron, (MJD) 50700.229(13) 50246.7166(7) 48980.1330(10)
Projected semi-major axis, (lt-s) 0.58181703(12) 16.7654104(5) 32.362222(3)
Longitude of periastron, (deg) 88(8) 97.68(3) 223.460(5)
Orbital eccentricity, 1.30(16) 9.7229(14) 1.69636(12)
Time of asc. node (MJD) 50700.08174604(3)
Orbital period derivative, 6.1(4)
First derivative of , 2.0(4) 1.79(12) 1.7(4)
Periastron advance, (deg/yr) 0.0097(23)
Derived parameters
Gal. longitude, (deg) 160.3 242.4 251.7 330.7
Gal. latitude, (deg) 50.9 43.7 40.5 22.6
LK Px Distance, (pc)
Composite PM, (mas yr) 25.615(11) 19(9) 59.72(6) 8.19(9)
1.0(2) 1.6(1.4) 4.8(10) 0.10(4)
0.077(7) 0.24(2) 0.057(5) 0.035(7)
0.016(3) 0.010(2) 0.021(4) 0.03(1)
0.8(2) 3.0(1.4) -2.9(10) 2.33(4)
Characteristic age, (Gyr) 10.3 8.7 5.4
Surface magnetic field, ( G) 2.1 7.1 4.4
Min. companion mass (M) 0.10 0.66 0.23
Table 4: Timing model parameters for PSRs J10125307, J10221001, J10240719 and J14553330. See caption of Table 2 for a description of this table. For the observer, we report here the values from the analysis in the ecliptic coordinate system, longitude , latitude , proper motion in , mas yr and proper motion in , mas yr. The reason for the negative intrinsic period derivative of PSR J10240719 is explained in Section 5.3.

4.14 Psr J16402224

Löhmer et al. (2005) used early Arecibo and Effelsberg data to report on the tentative detection of Shapiro delay for this wide binary system in a 6-month orbit. From this measurement they deduced the orientation of the system to be nearly edge-on () and a companion mass for the white dwarf . We cannot constrain the Shapiro delay with the current EPTA data, even though our data comprise almost twice the number of TOAs with a similar overall timing precision. The parallax signature in the residuals also remains undetected (based on Bayesian evidence6) but we find a significant , consistent with the upper limit set by Löhmer et al. (2005).

4.15 Psr J16431224

Using PPTA data, Verbiest et al. (2009) previously announced a parallax value mas that is marginally consistent with our value of mas. We get a similar proper motion and , albeit measured with a greater precision.

4.16 Psr J17130747

PSR J17130747 is one of the most precisely timed pulsars over two decades (Verbiest et al., 2009; Zhu et al., 2015). Our proper motion and parallax values are consistent with the ones from Verbiest et al. (2009) and Zhu et al. (2015). Nonetheless we can not detect any hint of the orbital period derivative . The measurement of the Shapiro delay yields the following masses of the system, and , in very good agreement with Zhu et al. (2015).

When inspecting the residuals of PSR J17130747 we noticed successive TOAs towards the end of 2008 that arrived significantly earlier ( s) than predicted by our ephemeris (see top panel of Figure 2). After inspection of the original archives and comparison with other high precision datasets like those on PSRs J17441134 and J19093744, we ruled out any instrumental or clock issue as an explanation for this shift. We therefore attribute this effect to a deficiency of the electron content towards the line of sight of the pulsar. This event has also been observed by the other PTAs (Zhu et al., 2015; Coles et al., 2015) and interpreted as possibly a kinetic shell propagating through the interstellar medium (Coles et al., 2015) followed by a rarefaction of the electron content.

To model this DM event we used shapelet basis functions. A thorough description of the shapelet formalism can be found in Refregier (2003), with astronomical uses being described in e.g., Refregier & Bacon (2003); Kelly & McKay (2004); Lentati et al. (2015a). Shapelets are a complete ortho-normal set of basis functions that allow us to recreate the effect of non-time-stationary DM variations in a statistically robust manner, simultaneously with the rest of the analysis. We used the Bayesian evidence to determine the number of shapelet coefficients to include in the model (only one coefficient was necessary in this study, i.e. the shapelet is given by a Gaussian). Our priors on the location of the event span the entire dataset, while we assume an event width of between five days and one year. The maximum likelihood results indicate an event centered around MJD 54761 with a width of 10 days. The resulting DM signal (including the shapelet functions) and the residuals corrected from it are plotted in the middle and bottom panels of Fig. 2 respectively. The DM model hence predicts a drop of pc cm.

Figure 2: Top panel: zoom-in on the PSR J17130747 residuals (black dots and red triangles are L-Band and S-Band data respectively). Middle panel: DM signal from the maximum likelihood DM model incorporating the shapelet basis functions (see Section 4.16 for details). The bottom panel shows the residuals after subtraction of the DM signal. The uncertainties on the DM signal come directly from the 1- uncertainties on the shapelet amplitudes used to model the event, obtained from the full Bayesian analysis.
PSR Name J16003053 J16402224 J16431224 J1713+0747
MJD range 53998 — 56795 50459 — 56761 50459 — 56778 50360 — 56810
Number of TOAs 531 595 759 1188
RMS timing residual () 0.46 1.8 1.7 0.68
Reference epoch (MJD) 55000 55000 55000 55000
Measured parameters
Right ascension, 16:00:51.903338(4) 16:40:16.744834(7) 16:43:38.161498(8) 17:13:49.5331754(5)
Declination, 30:53:49.37542(18) 22:24:08.84121(13) 12:24:58.6735(6) 07:47:37.492536(16)
Proper motion in (mas yr) 0.940(19) 2.087(20) 6.04(4) 4.923(3)
Proper motion in (mas yr) 6.94(7) 11.29(4) 4.07(15) 3.909(5)
Period, (ms) 3.59792851006493(3) 3.16331586776034(5) 4.62164152573380(10) 4.570136598154477(12)
Period derivative, () 0.95014(6) 0.28161(11) 1.8461(3) 0.852919(13)
Parallax, (mas) 0.64(7) 1.17(26) 0.90(3)
DM (cmpc) 52.3245(16) 18.422(10) 62.411(5) 15.9930(3)
DM1 (cmpc yr) 0.0003(1) 0.0000(2) 0.0013(3) 0.00006(3)
DM2 (cmpc yr) 0.000012(47) 0.00006(8) 0.0000(1) 0.000006(5)
Orbital period, (d) 14.34845777290(15) 175.460664603(11) 147.017397756(17) 67.8251309745(14)
Epoch of periastron, (MJD) 52506.3739(4) 51626.1804(3) 49283.9337(5) 48741.9737(3)
Projected semi-major axis, (lt-s) 8.8016546(5) 55.3297223(5) 25.0726144(7) 32.34241956(15)
Longitude of periastron, (deg) 181.835(9) 50.7343(5) 321.8488(10) 176.1989(15)
Orbital eccentricity, 1.73723(8) 7.97299(8) 5.05746(9) 7.49421(7)
First derivative of , 2.8(5) 1.07(16) 4.79(15)
Inclination angle, (deg) 71.8(6)
Longitude of ascending node, (deg) 89.9(17)
Companion mass, () 0.290(12)
Third harmonic of Shapiro, () 0.33(2)
Ratio of harmonics amplitude, 0.68(5)
Derived parameters
Gal. longitude, (deg) 344.1 41.1 5.7 28.8
Gal. latitude, (deg) 16.5 38.3 21.2 25.2
LK Px Distance, (pc)
Composite PM, (mas yr) 7.00(7) 11.49(4) 7.28(9) 6.286(4)
0.064(8) 0.12 0.05(1) 0.049(2)
0.0137(9) 0.033 0.018(3) 0.0277(4)
0.043(7) 0.0013 0.029(8) 0.020(2)
0.86(1) 0.196 1.79(2) 0.812(2)
Characteristic age, (Gyr) 6.7 25.6 4.1 8.9
Surface magnetic field, ( G) 1.8 0.8 2.9 1.9
Min. companion mass (M) 0.19 0.23 0.11 0.26
Table 5: Timing model parameters for PSRs J16003053, J16402224, J16431224 and J1713+0747. See caption of Table 2 for a description of this table.

4.17 Psr J17212457

Thanks to an additional five years of data compared to Janssen et al. (2010), the proper motion of this isolated MSP is now better constrained. Our current timing precision is most likely limited by the pulsar’s large duty cycle (see Fig. 14) and the apparent absence of sharp features in the profile. The flux density of this pulsar is also quite low with a value of 1 mJy at 1400MHz.

4.18 Psr J17302304

This low-DM and isolated MSP has a profile with multiple pulse components (see Fig. 14). As this pulsar lies very near to the ecliptic plane (), we are unable to constrain its proper motion in declination, similar to the previous study (Verbiest et al., 2009). Assuming the NE2001 distance, the expected parallax timing signature would be as large as 2.3 s. We report here on a tentative detection of the parallax, mas.

4.19 Psr J17380333

After the determination of the masses in this system from optical observations (Antoniadis et al., 2012), Freire et al. (2012b) used the precise measurements of the proper motion, parallax and in this binary system to put constraints on scalar-tensor theories of gravity. Our measured proper motion remains consistent with their measurements. With a longer baseline and more observations recorded with the sensitive Arecibo Telescope, Freire et al. (2012b) were able to detect the parallax and the orbital period derivative of the system. However, we do not yet reach the sensitivity to detect these two parameters with our dataset.

4.20 Psr J17441134

This isolated MSP was thought to show long-term timing noise by Hotan et al. (2006) even with a dataset shorter than 3 years. In our data set we detect a (red) timing noise component (see Caballero et al., 2015). The RMS of the time-domain noise signal is s, but has a peak-to-peak variation of s. The higher latter value, however, is due to a bump which appears localized in time (MJD 54000 to 56000). As discussed in Caballero et al. (2015), non-stationary noise from instrumental instabilities may cause such effects, but data with better multi-telescope coverage are necessary to verify such a possibility. This is further investigated in Lentati et al. (submitted) using a more extended dataset from the International Pulsar Timing Array (IPTA) (Verbiest et al., 2016).

PSR Name J17212457 J17302304 J17380333 J17441134
MJD range 52076 — 56737 50734 — 56830 54103 — 56780 50460 — 56761
Number of TOAs 150 268 318 536
RMS timing residual () 11.7 1.6 3.0 0.86
Reference epoch (MJD) 55000 55000 55000 55000
Measured parameters
Right ascension, 17:21:05.4979(3) 17:30:21.66835(13) 17:38:53.966375(11) 17:44:29.4075373(14)
Declination, 24:57:06.17(5) 23:04:31.16(4) 03:33:10.8720(4) 11:34:54.69437(11)
Proper motion in (mas yr) 1.9(12) 20.7(7) 7.08(6) 18.810(6)
Proper motion in (mas yr) 25(16) 9(12) 4.97(19) 9.36(3)
Period, (ms) 3.496633783466(6) 8.1227980469486(7) 5.850095860612(5) 4.074545941825154(15)
Period derivative, () 0.556(7) 2.0196(11) 2.410(4) 0.89347(4)
Parallax, (mas) 0.86(32) 2.38(8)
DM (cmpc) 48.33(15) 9.622(9) 33.798(18) 3.1312(17)
DM1 (cmpc yr) 0.00(2) 0.001(1) 0.01(1) 0.01(1)
DM2 (cmpc yr) 0.002(4) 0.0004(3) 0.000(2) 0.000(2)
Orbital period, (d) 0.35479073990(3)
Epoch of periastron, (MJD) 52500.25(3)
Projected semi-major axis, (lt-s) 0.3434304(4)
Longitude of periastron, (deg) 52(27)
Orbital eccentricity, 3.6(18)
Time of asc. node (MJD) 52500.1940106(3)
Derived parameters
Gal. longitude, (deg) 0.4 3.1 27.7 14.8
Gal. latitude, (deg) 6.8 6.0 17.7 9.2
LK Px Distance, (pc)
Composite PM, (mas yr) 26(16) 23(5) 8.65(12) 21.009(15)
0.7(9) 0.9(5) 0.15 0.183(6)
0.00298(5) 0.004(1) 0.024 0.00248(6)
0.047(4) 0.07(3) 0.039 0.013(1)
0.0(7) 1.0(6) 2.24 0.699(7)
Characteristic age, (Gyr) 12.3 4.1 9.2
Surface magnetic field, ( G) 2.9 3.7 1.7
Min. companion mass (M) 0.08
Table 6: Timing model parameters for PSRs J17212457, J17302304, J17380333 and J17441134. See caption of Table 2 for a description of this table.

4.21 Psr J17512857

Stairs et al. (2005) announced this wide ( days) binary MSP after timing it for 4 years with an RMS of 28 without a detection of the proper motion. With 6 years of data at a much lower RMS, we are able to constrain its proper motion ( mas yr and mas yr) and detect .

4.22 Psr J18011417

This isolated MSP was discovered by Lorimer et al. (2006). With increased timing precision, we measure a new composite proper motion mas yr. As our dataset for this pulsar does not include multifrequency information; we can not rule out DM variations.

4.23 Psr J18022124

Ferdman et al. (2010) recently reported on the mass measurement of this system by combining TOAs from the Green Bank, Parkes and Nançay radio telescopes. Therefore, our dataset shows no improvement in the determination of the system parameters but gives consistent results to Ferdman et al. (2010).

4.24 Psr J18042717

With an RMS timing residual improved by a factor 25 compared to the last results published by Hobbs et al. (2004b), we obtain a reliable measurement of the proper motion of this system. Assuming the distance based on the NE2001 model pc, the parallax timing signature can amount to 1.5 s, still below our current timing precision.

PSR Name J17512857 J18011417 J18022124 J18042717
MJD range 53746 — 56782 54206 — 56782 54188 — 56831 53766 — 56827
Number of TOAs 144 126 522 116
RMS timing residual () 3.0 2.6 2.7 3.1
Reference epoch (MJD) 55000 55000 55000 55000
Measured parameters
Right ascension, 17:51:32.693197(17) 18:01:51.073331(19) 18:02:05.33522(2) 18:04:21.133087(19)
Declination, 28:57:46.520(3) 14:17:34.526(2) 21:24:03.653(8) 27:17:31.335(4)
Proper motion in (mas yr) 7.4(1) 10.89(12) 1.13(12) 2.56(15)
Proper motion in (mas yr) 4.3(12) 3.0(10) 3(4) 17(3)
Period, (ms) 3.914873259435(3) 3.6250967171671(17) 12.6475937923794(16) 9.343030844543(4)
Period derivative, () 1.121(3) 0.530(3) 7.291(3) 4.085(5)
Parallax, (mas) 1.24(57)
DM (cmpc) 42.84(3) 57.26(4) 149.614(9) 24.74(4)
DM1 (cmpc yr) 0.01(1) 0.004(7) 0.002(2) 0.005(6)
DM2 (cmpc yr) 0.001(2) 0.000(2) 0.0005(6) 0.000(1)
Orbital period, (d) 110.74646080(4) 0.698889254216(9) 11.128711967(3)
Epoch of periastron, (MJD) 52491.574(4) 52595.851(14) 49615.080(9)
Projected semi-major axis, (lt-s) 32.5282215(20) 3.718853(3) 7.2814525(7)
Longitude of periastron, (deg) 45.508(11) 29(7) 158.7(3)
Orbital eccentricity, 1.2795(3) 2.9(3) 3.406(16)
Time of asc. node (MJD) 52595.79522502(4)
First derivative of , 4.6(8) -3(5)
Sine of inclination angle, 0.971(13)
Companion mass, () 0.83(19)
Derived parameters
Gal. longitude, (deg) 0.6 14.5 8.4 3.5
Gal. latitude, (deg) 1.1 4.2 0.6 2.7
LK Px Distance, (pc)
Composite PM, (mas yr) 8.5(6) 11.3(3) 3(4) 17(3)
0.077 0.17 0.02(5) 0.53
0.0002 0.0012 0.000083(4) 0.0014
0.045 0.05 0.07(6) 0.071
0.999 0.31 7.19(8) 3.49
Characteristic age, (Gyr) 6.2 18.5 2.8 4.2
Surface magnetic field, ( G) 2. 1.1 9.7 5.8
Min. companion mass (M) 0.18 0.76 0.19
Table 7: Timing model parameters for PSRs J17512857, J18011417, J18022124 and J18042717. See caption of Table 2 for a description of this table.

4.25 Psr J18431113

This isolated pulsar discovered by Hobbs et al. (2004a) is the second fastest-spinning MSP in our dataset. Its mean flux density (S mJy) is among the lowest, limiting our current timing precision to 1 s. For the first time, we report the detection of the proper motion mas yr and mas yr and still low-precision parallax mas.

4.26 Psr J18531303

Our values of proper motion and semi-major axis change are consistent with the recent work by Gonzalez et al. (2011) using high-sensitivity Arecibo and Parkes data, though there is no evidence for the signature of the parallax in our data , most likely due to our less precise dataset.

4.27 Psr J18570943 (B1855+09)

Our measured parallax mas is lower than, but still compatible with, the value reported by Verbiest et al. (2009). We also report a marginal detection of . Our measurement of the Shapiro delay is also similar to the previous result from Verbiest et al. (2009).

4.28 Psr J19093744

PSR J19093744 (Jacoby et al., 2003) is the most precisely timed source with a RMS timing residual of about 100 ns. As these authors pointed out, this pulsar’s profile has a narrow peak with a pulse duty cycle of 1.5% (43s) at FWHM (see Fig. 15). Unfortunately its declination makes it only visible with the NRT but it will be part of the SRT timing campaign. We improved the precision of the measurement of the orbital period derivative by a factor of six compared to Verbiest et al. (2009) and our constraint on is consistent with their tentative detection.

4.29 Psr J19101256

We get similar results as recently published by Gonzalez et al. (2011) with Arecibo and Parkes data. In addition, we uncover a marginal signature of the parallax mas, consistent with the upper limit set by Gonzalez et al. (2011).

PSR Name J18431113 J18531303 J18570943 J19093744
MJD range 53156 — 56829 53763 — 56829 50458 — 56781 53368 — 56794
Number of TOAs 224 101 444 425
RMS timing residual () 0.71 1.6 1.7 0.13
Reference epoch (MJD) 55000 55000 55000 55000
Measured parameters
Right ascension, 18:43:41.261917(12) 18:53:57.318765(12) 18:57:36.390605(4) 19:09:47.4335737(7)
Declination, 11:13:31.0686(7) 13:03:44.0693(4) 09:43:17.20714(10) 37:44:14.51561(3)
Proper motion in (mas yr) 1.91(7) 1.61(9) 2.649(17) 9.519(3)
Proper motion in (mas yr) 3.2(3) 2.79(17) 5.41(3) 35.775(10)
Period, (ms) 1.8456663232093(6) 4.0917974456530(10) 5.36210054870034(9) 2.947108069766629(7)
Period derivative, () 0.9554(7) 0.8724(14) 1.78447(17) 1.402518(14)
Parallax, (mas) 0.69(33) 0.70(26) 0.87(2)
DM (cmpc) 59.964(8) 30.576(20) 13.303(4) 10.3925(4)
DM1 (cmpc yr) 0.002(4) 0.002(4) 0.0017(2) 0.00032(3)
DM2 (cmpc yr) 0.0005(9) 0.0005(8) 0.00018(8) 0.00004(1)
Orbital period, (d) 115.65378824(3) 12.3271713831(3) 1.533449474329(13)
Epoch of periastron, (MJD) 52890.256(18) 46432.781(3) 53114.72(4)
Projected semi-major axis, (lt-s) 40.7695169(14) 9.2307819(9) 1.89799099(6)
Longitude of periastron, (deg) 346.65(6) 276.47(7) 180(9)
Orbital eccentricity, 2.368(3) 2.170(4) 1.22(11)
Time of asc. node (MJD) 53113.950741990(10)
Orbital period derivative, 5.03(5)
First derivative of , 2.4(7) 2.7(11)
Sine of inclination angle, 0.9987(6) 0.99771(13)
Companion mass, () 0.27(3) 0.213(3)
Derived parameters
Gal. longitude, (deg) 22.1 44.9 42.3 359.7
Gal. latitude, (deg) 3.4 5.4 3.1 19.6
LK Px Distance, (pc)
Composite PM, (mas yr) 3.8(3) 3.22(15) 6.03(3) 37.020(10)
0.007(4) 0.0091 0.05(2) 1.12(3)
0.0004(3) 0.0016 0.0010(3) 0.0242(6)
0.014(9) 0.0028 0.0002(30) 0.031(3)
0.94(1) 0.868 1.73(2) 0.27(3)
Characteristic age, (Gyr) 3.1 7.5 4.9 17.4
Surface magnetic field, ( G) 1.3 1.9 3.1 0.9
Min. companion mass (M) 0.22 0.22 0.18
Table 8: Timing model parameters for PSRs J18431113, J18531303, J18570943 and J19093744. See caption of Table 2 for a description of this table.

4.30 Psr J19111347

With a pulse width at 50% of the main peak amplitude (see Fig. 15), s (only twice the width of J19093744), this isolated MSP is potentially a good candidate for PTAs. Unfortunately it has so far been observed at the JBO and NRT observatories only and no multifrequency observations are available. Based on this work, this pulsar has now been included in the observing list at the other EPTA telescopes. Despite the good timing precision we did not detect the parallax but we did measure the proper motion for the first time with mas yr and