An analysis of the timing irregularities for 366 pulsars

An analysis of the timing irregularities for 366 pulsars

G. Hobbs, A. G. Lyne & M. Kramer
Australia Telescope National Facility, CSIRO, PO Box 76, Epping NSW 1710, Australia
University of Manchester, Jodrell Bank Observatory, Macclesfield, Cheshire SK11 9DL
Abstract

We provide an analysis of timing irregularities observed for 366 pulsars. Observations were obtained using the 76-m Lovell radio telescope at the Jodrell Bank Observatory over the past 36 years. These data sets have allowed us to carry out the first large-scale analysis of pulsar timing noise over time scales of  yr, with multiple observing frequencies and for a large sample of pulsars. Our sample includes both normal and recycled pulsars. The timing residuals for the pulsars with the smallest characteristic ages are shown to be dominated by the recovery from glitch events, whereas the timing irregularities seen for older pulsars are quasi-periodic. We emphasise that previous models that explained timing residuals as a low-frequency noise process are not consistent with observation.

keywords:
pulsars: general

1 Introduction

The Jodrell Bank data archive of pulsar observations contains over 6000 years of pulsar rotational history. The pulsar timing method (for a general overview see Lorimer & Kramer 2005, Lyne & Graham-Smith 2004 or Manchester & Taylor 1977. Details are provided in Edwards et al. 2006) allows the observed pulse times of arrival (TOAs) to be compared with a model of the pulsar’s astrometric, orbital and rotational parameters. The differences between the predicted arrival times and the actual arrival times are known as the pulsar “timing residuals”. For a perfect model the timing residuals would be dominated by measurement errors and have a “white” spectrum. Any features observed in the timing residuals indicate the presence of unmodelled effects which may include calibration errors, orbital companions or spin-down irregularities. There are two main types of irregularity, namely “glitches” which are sudden increases in rotation rate followed by a period of relaxation, and “timing noise”, which consists of low-frequency structures.

A more complete understanding of pulsar timing noise will lead to many important results. For instance, explaining the cause of timing noise and glitches may also allow us to relate these phenomena and hence provide an insight into the interior structure of neutron stars. Pulsar timing array projects are being developed around the world with the aim of detecting gravitational waves by looking for irregularities in the timing of millisecond pulsars (see e.g. Hobbs 2005 and references therein). A stochastic background formed by coalescing supermassive binary black hole systems will induce signatures in the timing residuals with amplitudes of approximately 100 ns. If the intrinsic timing noise for millisecond pulsars is at a higher level then it becomes more difficult to extract the gravitational wave signal from the observations.

In this paper we study the timing noise in the residuals of 366 pulsars that have been regularly observed over the past 10 to 36 years. The basic observational parameters for the pulsars in our sample were provided by Hobbs et al. (2004); hereafter H04. These timing ephemerides included the pulsar positions, rotational frequencies and their first two derivatives, dispersion measures and their derivatives and proper motions. The proper motions were subsequently updated with more recent observations, combined with other measurements of pulsar proper motions available from the literature and analysed by Hobbs et al. (2005). This work allowed us to present a new velocity distribution for the pulsar population.

In order to obtain the precise spin and astrometric parameters presented in H04, it was necessary to remove the low-frequency timing noise. This pre-whitening procedure was undertaken using a simple high-pass filter where harmonically related sinusoids were fitted to the residuals and the lowest frequency waves subtracted. The low-frequency noise was not subsequently studied in the previous papers. In this paper, we address the properties of this timing noise.

Low-frequency structures previously observed in pulsar data sets have been explained by random processes (e.g. Cordes & Helfand 1980, Lyne 1999), unmodelled planetary companions (e.g. Cordes 1993) or free-precession (e.g. Stairs, Lyne & Shemar 2000). However, the physical phenomenon underlying most of the timing noise still has not been explained. Much of the basic theoretical work was described by Boynton et al. (1972) who analysed the arrival times for the Crab pulsar over a two-year period. In their paper, an attempt was made to describe the timing noise as either phase, frequency or slowing-down noise corresponding to random walks in these parameters. Later, Cordes & Helfand (1980) found that out of a sample of 11 pulsars, seven showed timing noise consistent with frequency noise, two from slowing-down noise and two from phase-noise. They concluded that 1) timing noise is widespread in pulsars, 2) it is correlated with period derivative and weakly with period, 3) it is not correlated with height above the Galactic plane, luminosity nor with pulse shape changes. However, the data sets used were small in number, short and small-scale pulse shape variations would have been undetectable. The assumption that timing noise is a red-noise process has continued to date. However, Cordes & Downs (1985) showed that the idealised, random walk model was too simple. They developed a more detailed model where discrete ‘micro-jumps’ in one or more of the timing parameters were superimposed on the random walk process. D’Alessandro et al. (1995) analysed the timing residuals for 45 pulsars with data spanning up to seven years. They observed very weak timing noise for 19 of their pulsars, for seven the activity was attributed to random walk processes comprising a large number of events in one of the rotation variables, a further seven were explained as resolved jumps in the pulse frequency and , its derivative, seven more as resolved jumps on a low-level background and for the remaining five the timing noise could not be explained as a pure random walk process nor resolved jumps.

Timing noise analyses with large samples of pulsars have been limited by the relatively short data spans studied. Long data-spans have been analysed in a few papers, but for only a small number of pulsars. For instance, Baykal et al. (1999) analysed four pulsars timed for 14 yr. Shabanova (1995) observed PSR B032954 for 16 yr, Stairs, Lyne & Shemar (2000) reported on 13 yr of PSR B182811 observations and Shabanova, Lyne & Urama (2001) analysed PSR B164203 over a 30 yr data span. More recently, the millisecond pulsar PSR J17130747 was observed for 12 yr (Splaver et al. 2005) and the young pulsar PSR B150958 for 21 yr (Livingstone et al. 2005). Most of the analysis has concentrated on obtaining high quality spectral estimates of the timing residuals or fitting a simple model to the timing residuals of a single pulsar. We note that our sample is 20 times larger than the previous large study of pulsar timing noise (D’Alessandro et al. 1995) in terms of the number of years of rotational history studied.

Glitches are thought to represent a sudden unpinning of superfluid vortices in the interior of the neutron star (Lyne, Shemar & Graham-Smith 2000). The relationship between glitches and timing noise is not understood although Janssen & Stappers (2006) showed that it is possible to model the timing noise in PSR B1951+32 as multiple small glitches. Glitches are discrete events that occur more commonly for young pulsars111We use the terms “young” and “old” throughout referring to a pulsar’s characteristic age which is only an approximation of the pulsar’s true age. (although for two pulsars with similar rotational parameters, one may glitch frequently while the other may never have been observed to glitch) and have a wide range of sizes with fractional frequency increases between and (e.g. Lyne, Shemar & Graham-Smith 2000, Hobbs et al. 2002). No model currently predicts the time between glitches or the size of any given event although pulsars with large glitches tend to show larger intervals between glitches (Lyne et al. 2000). Melatos, Peralta & Wyithe (2008) recently showed that, for most pulsars in their sample, the waiting time between glitch events followed an exponential distribution. This distribution was subsequently modelled by Warszawski & Melatos (2008) using a cellular automaton model of pulsar glitches. However, it is still not clear whether the glitch and timing noise phenomena are related.

In this paper we describe the observing system and present the measured timing residuals (§2), rule out some models of timing noise (§3.1) and highlight various properties of the timing noise (§3.2).

2 Results

Figure 1: Period–period-derivative diagram for the pulsars in our sample.
Figure 2: Histogram of the time-span of our observations.

The timing solutions for the pulsars in our sample have been updated since H04 with more recent data from the Jodrell Bank Observatory. The timing solutions were obtained using standard pulsar timing techniques as described in Paper 1. In brief, the majority of the observations were obtained from the 76-m Lovell radio telescope. The earliest times-of-arrival (TOAs) for 18 pulsars were obtained from observations using the NASA Deep Space Network (Downs & Reichley 1983; Downs & Krause-Polstorff 1986). Observations using the Lovell telescope were carried out predominately at frequencies close to 408, 610, 910, 1410 and 1630 MHz with a few early observations at 235 and 325 MHz. The last observations used in our data set were obtained around MJD 53500. The signals were combined to produce, for every observation, a total intensity profile. TOAs were subsequently determined by convolving, in the time domain, the profile with a template corresponding to the observing frequency. The pulsar timing residuals described in this paper were obtained by fitting a timing model to the TOAs using the tempo2 pulsar timing software (Hobbs, Edwards & Manchester 2006).

For those pulsars in which the residuals are dominated by large glitches it is difficult to obtain phase coherent timing solutions across many years of observation. For example, for PSR B180021 we have data spanning from the year 1985 to the present. However, for this analysis we can only use data between the years 1991 and 1997. We have a similarly short data-span for PSR B172733. Although PSRs B053121, B175823 and B175724 have been regularly observed we cannot obtain a useful data-set for the analysis described in this paper. These pulsars are therefore not included in our sample.

In Table 1 we present the basic parameters for our sample of pulsars. In column order, we first provide the pulsar’s J2000 and B1950 names, spin-frequency, , frequency derivative, and frequency second derivative, . The following three columns give the epoch of the centre of the data span, the number of observations and the time span of the observations. We then provide various measures characterising the amount of timing noise for each data set. We present , the unweighted rms of the residuals after fitting for and , the unweighted rms of the residuals after removal of and its first two derivatives and , the rms after whitening the data set by fitting, and removing, harmonically related sinusoids (as described in H04). The last two columns contain two stability measures ( and ) that are discussed in §3.2.1.

A period–period-derivative diagram222Note: we have attempted to be consistent in our use of pulse frequency and its derivatives. However, in order to make a direct comparison with earlier publications we sometimes use the pulse period and its derivatives where , . for the pulsars in our sample is shown in Figure 1 to indicate the range of pulsar parameters included in our sample. The diagram includes dotted lines representing various characteristic ages and dashed lines for representative surface magnetic field strengths  G. A histogram indicating the time-spans of our observations is shown in Figure 2. The mean and median time spans are 18.5 and 18.3 yr respectively. For the recycled pulsars, the unweighted rms of the residuals after subtracting a cubic polynomial ranges from 8 s for PSR J17441134 to s for PSR B191316333Our sample includes 31 recycled pulsars defined with spin-periods  s and spin-down rates . We note that lower rms values have been published for some of our pulsars. For instance, Splaver et al. (2005) obtained TOA timing precisions  ns and as small as  ns for PSR J17130747 (compared with for our data). In contrast to the high precision timing experiments that often use coherent de-dispersion systems and long observing durations the data presented here have been obtained with a stable observing system over many years and the large sample has necessitated short observations and hence poorer TOA precision.. For the ordinary pulsars the rms ranges up to 948 ms for PSR B170616, a pulsar with a 653 ms spin-period444For a large number of pulsars the timing residuals deviate by more than one pulse period. In these cases phase jumps of at least one period need to be added to keep track of the pulsar spin-down..

PSR J PSR B Epoch N
(s) () () (MJD) (yr) (ms) (ms) (ms)
J00144746 B001147 0.806 0.367 49285.0 365 22.8 4.26 4.23 4.23 ¡1.14 10.91
J00340534 532.713 1.409 51096.0 402 12.8 0.06 0.06 0.06 ¡3.04 12.44
J00340721 B003107 1.061 0.459 47051.0 772 35.0 3.84 3.47 3.38 1.44 10.79
J00405716 B003756 0.894 2.302 50091.0 426 18.5 0.62 0.62 0.62 ¡1.79 11.65
J00483412 B004533 0.822 1.589 50083.0 201 18.4 2.17 2.15 2.15 ¡1.21 11.06
J00555117 B005251 0.473 2.132 50092.0 417 18.5 1.51 1.08 1.08 ¡1.63 11.03
J00564756 B005347 2.118 14.938 50103.0 252 18.2 6.09 5.82 2.29 ¡1.36 10.24
J01026537 B005965 0.596 2.113 50091.0 339 18.5 65.23 2.66 1.37 ¡1.34 9.91
J01086608 B010565 0.779 7.918 50482.0 427 16.2 157.09 148.26 3.51 0.16 8.70
J01086905 B010568 0.934 0.042 50091.0 336 18.5 2.63 2.62 2.62 ¡1.36 11.21
J01081431 1.238 0.118 51251.0 332 12.1 4.49 4.47 4.47 ¡1.45 10.84
J01175914 B011458 9.858 568.596 50083.0 314 18.4 165.07 25.71 0.34 1.55 9.21
J01342937 7.301 4.178 51251.0 298 12.1 0.19 0.19 0.19 ¡2.59 12.53
J01395814 B013657 3.670 144.309 49706.0 684 20.6 56.33 52.63 0.20 0.95 9.27
J01416009 B013859 0.818 0.261 49495.0 451 19.4 1.09 1.06 1.06 ¡2.24 11.51
J01475922 B014459 5.094 6.661 50080.0 430 18.2 2.72 1.16 0.16 2.56 10.62
J01521637 B014916 1.201 1.874 48651.0 455 26.4 5.79 1.39 0.59 ¡2.07 11.10
J01563949 B015339 0.552 0.046 50104.0 81 18.1 9.88 9.88 9.88 0.31 10.46
J01576212 B015461 0.425 34.160 50126.0 463 18.3 26.74 20.09 2.18 1.49 9.73
J02156218 1.822 2.198 51788.0 327 10.5 1.46 0.98 0.43 2.29 10.62
J02184232 430.461 14.340 51268.0 387 11.9 0.05 0.05 0.05 ¡3.26 13.04
J02317026 B022670 0.682 1.445 50088.0 305 18.5 1.83 1.81 1.81 ¡1.36 10.98
J03041932 B030119 0.721 0.673 49141.0 498 23.7 4.26 1.76 1.00 ¡1.39 10.54
J03233944 B032039 0.330 0.069 49229.0 520 23.2 2.25 2.24 2.24 ¡1.71 11.35
J03325434 B032954 1.400 4.012 46775.0 1170 36.5 7.46 6.76 0.46 1.86 10.38
J03354555 B033145 3.715 0.101 50081.0 483 18.4 0.33 0.33 0.33 ¡2.33 12.19
J03435312 B033953 0.517 3.587 49557.0 325 22.9 4.64 4.13 4.13 ¡1.24 10.42
J03575236 B035352 5.075 12.277 50081.0 412 18.4 0.98 0.63 0.18 ¡2.39 10.79
J04066138 B040261 1.682 15.773 50428.0 406 16.7 13.77 8.43 0.43 1.57 9.69
J04156954 B041069 2.559 0.502 50092.0 375 18.5 0.51 0.41 0.36 ¡2.17 11.32
J04210345 0.463 0.249 50847.0 226 13.3 1.27 1.13 1.13 ¡1.71 10.84
J04482749 2.220 0.731 51427.0 332 11.2 0.88 0.85 0.85 ¡2.03 11.43
J04501248 B044712 2.283 0.535 49751.0 527 20.2 1.68 1.64 1.64 ¡2.00 11.29
J04521759 B045018 1.822 19.092 49295.0 576 22.9 8.21 5.15 0.29 1.97 10.16
J04545543 B045055 2.935 20.441 50336.0 335 17.2 29.42 10.56 0.33 1.70 9.51
J04590210 0.883 1.089 51269.0 238 12.0 1.34 1.34 1.34 ¡1.50 11.53
J05024654 B045846 1.566 13.690 49129.0 497 23.6 7.35 2.19 0.54 1.98 10.69
J05202553 4.138 0.515 51657.0 181 10.2 0.42 0.41 0.41 ¡1.98 11.46
J05251115 B052311 2.821 0.586 48663.0 643 26.3 0.32 0.28 0.26 ¡2.46 11.78
J05282200 B052521 0.267 2.854 46909.0 954 35.8 20.34 15.25 1.39 ¡1.38 10.01
J05382817 6.985 179.088 51821.0 353 10.1 21.28 0.34 0.18 1.91 9.48
J05432329 B054023 4.065 254.898 49294.0 691 22.9 46.67 7.89 0.16 2.09 10.03
J06123721 B060937 3.356 0.670 50092.0 456 18.5 2.07 0.80 0.35 ¡2.38 10.81
J06130200 326.601 1.019 51240.0 656 12.1 0.04 0.04 0.04 ¡3.47 12.89
J06142229 B061122 2.985 529.522 50164.0 973 18.1 1735.68 514.15 1.82 0.14 7.97
J06211002 34.657 0.057 51145.0 685 10.8 0.03 0.03 0.03 3.41 12.79
J06240424 B062104 0.962 0.769 50302.0 459 17.4 0.87 0.87 0.87 ¡1.77 11.63
J06292415 B062624 2.098 8.785 49846.0 541 19.7 5.75 5.53 0.41 1.96 10.30
J06302834 B062828 0.804 4.601 47013.0 807 35.2 131.89 91.99 1.52 1.84 9.71
J06538051 B064380 0.823 2.576 49141.0 283 23.7 1.23 0.83 0.70 ¡1.84 11.01
J06591414 B065614 2.598 371.288 49721.0 772 16.1 120.42 7.27 1.49 1.26 9.09
J07006418 B065564 5.111 0.018 49138.0 402 23.7 0.64 0.64 0.64 ¡2.06 11.48
J07251635 2.357 0.515 50884.0 277 13.3 0.57 0.54 0.54 ¡2.00 11.24
J07291836 B072718 1.960 72.832 50126.0 635 18.3 76.04 40.15 0.55 0.55 9.05
J07422822 B074028 5.997 604.876 49696.0 1009 20.6 165.35 145.16 0.40 0.84 8.92
J07511807 287.458 0.643 51389.0 531 11.3 0.04 0.04 0.04 ¡3.67 13.55
J07543231 B075132 0.693 0.519 49763.0 492 20.3 1.54 1.28 1.21 ¡1.79 11.04
J08147429 B080974 0.774 0.101 49369.0 474 22.4 1.07 1.06 1.06 ¡1.59 11.47
J08201350 B081813 0.808 1.373 49299.0 631 22.7 0.55 0.55 0.26 ¡2.24 11.62
J08230159 B082002 1.156 0.140 49144.0 573 23.7 1.10 0.88 0.84 2.00 11.08
J08262637 B082326 1.884 6.069 46857.0 979 36.1 110.89 90.82 0.29 1.63 9.49
J08283417 B082634 0.541 0.292 48508.0 146 25.9 19.16 16.03 14.04 ¡0.16 9.88
J08370610 B083406 0.785 4.191 49138.0 604 23.7 0.36 0.34 0.34 ¡1.91 11.73
J08463533 B084435 0.896 1.285 49145.0 119 23.7 1.95 1.52 1.52 ¡0.95 10.98
J08498028 B084180 0.624 0.174 50419.0 90 16.6 4.80 4.79 4.79 ¡0.42 10.70
J08553331 B085333 0.789 3.934 49735.5 435 17.2 1.63 1.60 1.60 ¡1.66 11.07
J09081739 B090617 2.490 4.151 49140.0 639 23.7 0.75 0.43 0.29 2.49 11.23
J09216254 B091763 0.638 1.468 49687.0 156 16.3 0.86 0.85 0.85 ¡1.58 11.18
J09220638 B091906 2.322 73.982 48518.0 766 27.0 99.33 22.52 0.35 1.07 9.36
J09431631 B094016 0.920 0.077 49143.0 443 23.7 4.04 4.04 4.04 ¡1.03 11.24
J09441354 B094213 1.754 0.139 49764.0 533 20.3 0.41 0.40 0.40 ¡2.62 11.83
J09460951 B094310 0.911 2.902 49352.0 117 22.3 47.86 10.29 10.29 0.28 9.79
J09530755 B095008 3.952 3.588 46777.0 953 36.5 11.22 9.53 0.12 2.31 10.53
J10125307 190.268 0.620 51331.0 521 11.6 0.02 0.02 0.02 ¡3.91 13.30
J10122337 B101023 0.397 0.139 49127.0 137 23.6 4.66 4.56 4.56 ¡0.25 10.70
J10181642 B101616 0.554 0.535 50093.0 243 18.5 2.79 2.78 2.78 ¡1.12 11.78
J10221001 60.779 0.160 51638.0 625 11.2 0.02 0.02 0.02 ¡3.99 13.56
J10240719 193.716 0.695 51422.0 366 11.0 0.06 0.06 0.06 ¡3.32 13.22
J10343224 0.869 0.174 51123.0 225 12.9 1.83 1.82 1.82 ¡1.37 11.89
J10411942 B103919 0.721 0.492 49143.0 477 23.7 1.31 1.30 1.30 ¡1.78 11.63
J10473032 3.027 0.559 51445.0 264 11.1 1.84 1.84 1.84 ¡1.81 11.24
J11155030 B111250 0.604 0.909 49753.0 491 20.2 1.28 1.28 1.28 ¡1.90 11.60
J11361551 B113316 0.842 2.646 46407.0 900 36.4 15.22 13.76 0.24 ¡2.07 10.92
J11413107 1.857 6.880 51271.0 179 12.1 71.87 37.79 2.94 0.30 8.91
J11413322 6.862 10.921 51446.0 328 11.1 6.64 4.22 0.51 ¡2.15 9.88
Table 1: Basic parameters for the pulsars in our sample. is the rms residual after removing a quadratic term, , the rms value after removing a cubic term and the value after whitening the data.
PSR J PSR B Epoch N
(s) () () (MJD) (yr) (ms) (ms) (ms)
J123821 B123821 0.894 1.155 51822.0 82 10.1 1.81 1.80 1.80 ¡1.35 11.23
J12392453 B123725 0.723 0.502 46942.0 1026 35.6 3.15 2.12 0.57 ¡2.11 11.17
J12571027 B125410 1.620 0.952 49348.2 475 18.4 1.12 1.12 1.09 ¡1.96 11.46
J13001240 B125712 160.810 2.957 50788.0 360 14.5 0.08 0.07 0.07 ¡3.09 13.10
J13111228 B130912 2.235 0.753 50094.0 433 18.5 0.65 0.56 0.49 ¡2.11 11.16
J13218323 B132283 1.492 1.262 49282.0 289 22.8 3.97 2.30 2.30 ¡1.41 10.58
J13323032 1.537 1.322 51447.0 192 11.1 9.62 9.52 9.52 ¡0.96 10.46
J14553330 125.200 0.381 51190.0 269 12.4 0.07 0.07 0.07 ¡2.94 12.46
J15095531 B150855 1.352 9.144 49294.0 471 22.9 63.60 22.20 0.52 1.52 9.87
J15184904 24.429 0.016 51619.0 309 10.0 0.03 0.03 0.03 ¡3.48 13.21
J15322745 B153027 0.889 0.616 50096.0 414 18.5 3.37 3.03 1.62 ¡1.64 10.55
J15371155 B153412 26.382 1.686 50300.0 400 13.8 0.04 0.04 0.04 ¡3.14 12.88
J15430929 B154109 1.336 0.772 49141.0 452 23.7 10.61 6.46 3.27 ¡1.28 10.03
J15430620 B154006 1.410 1.749 49839.0 503 19.7 7.06 3.02 0.36 1.36 10.36
J15552341 B155223 1.878 2.447 50301.0 346 17.3 6.42 1.40 0.88 ¡1.90 10.23
J15553134 B155231 1.930 0.232 50299.0 289 17.3 0.69 0.69 0.69 ¡1.92 11.58
J16032531 3.533 19.875 51121.0 192 12.8 9.21 8.47 0.15 1.72 9.85
J16032712 B160027 1.285 4.968 50302.0 199 17.3 1.61 1.36 0.67 ¡1.91 10.72
J16070032 B160400 2.371 1.720 47386.0 729 33.2 3.53 0.47 0.44 ¡2.38 11.30
J16101322 B160713 0.982 0.222 50094.0 213 18.5 4.77 4.75 4.75 ¡1.02 10.81
J16140737 B161207 0.829 1.620 49897.0 160 15.1 1.19 1.12 1.12 ¡1.78 11.24
J16152940 B161229 0.404 0.258 49026.0 99 23.1 4.91 4.89 4.89 0.18 10.58
J16230908 B162009 0.783 1.584 49142.0 394 23.7 0.85 0.75 0.75 ¡1.08 11.30
J16232631 B162026 90.287 2.953 50292.0 768 17.5 103.55 3.06 0.15 1.35 9.22
J16352418 B163324 2.039 0.496 49130.0 149 23.6 1.23 1.18 1.18 ¡1.28 11.23
J16431224 216.373 0.865 51251.0 433 12.0 0.03 0.03 0.03 ¡3.30 13.10
J16450317 B164203 2.579 11.846 46930.0 957 35.7 21.63 20.68 0.22 0.99 9.66
J16483256 1.390 6.815 51276.0 149 12.0 4.54 4.50 0.76 1.39 10.26
J16501654 0.572 1.046 51272.0 172 12.1 3.07 2.95 2.95 1.06 10.72
J16511709 B164817 1.027 3.205 50430.0 168 16.7 1.56 1.53 1.31 ¡1.30 11.06
J16522404 B164923 0.587 1.088 49132.0 348 23.6 3.36 1.70 1.60 ¡1.61 10.91
J16542713 1.263 0.268 51414.0 154 11.1 2.39 2.38 2.38 ¡1.19 11.04
J16591305 B165713 1.560 1.503 50094.0 147 18.5 10.86 2.66 2.66 ¡1.02 10.12
J17003312 0.736 2.555 51276.0 250 12.0 3.96 1.87 1.41 ¡1.42 10.28
J17031846 B170018 1.243 2.676 50314.0 209 17.3 0.56 0.56 0.56 ¡1.98 12.02
J17033241 B170032 0.825 0.449 50427.0 159 16.6 0.78 0.51 0.51 ¡1.58 11.08
J17051906 B170219 3.345 46.284 50497.0 410 16.3 1.28 1.24 0.25 ¡2.36 11.11
J17053423 3.915 16.484 51256.0 152 11.9 4.72 2.85 1.01 1.55 9.96
J17083426 1.445 8.775 51276.0 124 12.0 2.42 2.05 2.05 ¡1.12 10.62
J17091640 B170616 1.531 14.783 47389.0 498 33.2 948.18 63.69 0.43 1.14 9.07
J17111509 B170915 1.151 1.461 50094.0 197 18.5 3.78 1.72 0.67 ¡1.71 10.65
J17130747 218.812 0.409 51318.0 345 11.5 0.01 0.01 0.01 3.94 13.51
J17173425 B171434 1.524 22.761 50673.0 139 15.2 17.88 17.35 0.82 0.74 9.51
J17200212 B171802 2.093 0.363 49853.0 320 19.8 3.44 3.44 3.44 ¡1.53 12.20
J17201633 B171716 0.639 2.366 50084.0 214 18.4 8.95 8.95 1.57 1.20 10.06
J17202933 B171729 1.612 1.938 50290.0 164 17.2 3.88 0.87 0.69 ¡1.58 10.62
J17211936 B171819 0.996 1.609 50840.0 288 14.4 67.75 54.68 2.99 0.83 8.89
J17213532 B171835 3.566 320.260 51505.0 139 10.7 20.82 20.24 0.90 0.98 10.71
J17223207 B171832 2.096 2.838 50495.0 180 16.3 1.72 1.70 0.16 2.12 10.84
J17280007 B172600 2.591 7.535 50513.0 152 16.1 2.88 1.28 0.93 ¡1.64 10.81
J17302304 123.110 0.306 51240.0 444 12.0 0.03 0.03 0.03 ¡3.49 12.73
J17303350 B172733 7.170 4355.079 51419.0 220 8.1 408.75 30.19 0.70 0.28 7.21
J17321930 2.067 0.776 51644.0 100 10.1 1.40 1.38 1.38 ¡1.42 11.03
J17332228 B173022 1.147 0.056 49140.0 395 23.7 1.40 1.40 1.40 ¡1.27 11.50
J17340212 B173202 1.191 0.597 50117.0 127 18.3 3.53 3.36 3.36 ¡0.88 10.59
J17350724 B173207 2.385 6.908 50312.0 342 17.3 1.22 1.18 0.25 2.08 10.85
J17383211 B173532 1.301 1.346 50018.0 365 18.9 1.34 1.32 1.29 ¡1.90 11.37
J17392903 B173629 3.097 75.578 49872.0 394 19.7 28.59 12.75 0.85 1.52 9.54
J17393131 B173631 1.889 66.269 49884.0 244 18.1 326.94 174.40 0.90 0.11 8.49
J17401311 B173713 1.245 2.250 48669.0 442 26.3 24.89 3.58 0.55 ¡1.94 10.30
J17412758 0.735 0.994 51750.0 104 10.4 2.48 2.34 2.34 ¡1.21 11.48
J17410840 B173808 0.489 0.545 50306.0 297 17.2 1.38 1.37 1.37 ¡1.53 11.42
J17430339 B174003 2.249 7.873 50199.0 139 16.6 111.71 76.44 1.71 0.44 8.72
J17431351 B174013 2.467 2.910 50095.0 184 18.5 19.27 8.52 1.13 ¡1.49 9.88
J17433150 B174031 0.414 20.716 50674.0 284 15.3 17.60 8.73 2.76 ¡1.22 9.67
J17441134 245.426 0.539 51490.0 282 10.7 0.01 0.01 0.01 ¡4.19 12.95
J17453040 B174230 2.722 79.021 50311.0 393 17.3 10.69 4.96 0.18 2.04 10.01
J17481300 B174512 2.537 7.808 50315.0 289 17.3 5.91 1.86 0.26 2.10 10.34
J17482021 B174520 3.465 4.803 50677.0 362 15.3 14.84 13.67 13.67 ¡0.75 9.96
J17482444 2.258 0.568 50917.0 190 14.2 1.82 1.80 1.73 ¡1.62 11.02
J17493002 B174630 1.640 21.163 50653.0 193 15.2 11.54 5.34 1.96 ¡1.33 9.93
J17503157 B174731 1.098 0.237 50674.0 213 15.3 1.37 1.36 1.36 ¡1.55 11.45
J17503503 1.462 0.079 51426.0 131 11.2 15.89 15.65 15.65 ¡0.62 10.00
J17522806 B174928 1.778 25.687 46889.0 655 35.8 67.62 63.41 0.44 1.15 9.45
J17532501 B175024 1.893 50.565 49883.0 216 19.6 22.35 21.63 3.82 ¡1.22 9.78
J17545201 B175352 0.418 0.274 50095.0 296 18.5 5.08 5.06 5.06 ¡0.97 10.82
J17562435 B175324 1.491 0.633 49848.0 232 18.8 0.75 0.75 0.75 ¡1.80 11.67
J17572421 B175424 4.272 235.755 49121.0 397 22.8 92.18 29.55 0.76 1.04 9.55
J17592205 B175622 2.169 51.171 50126.0 388 18.3 49.92 11.50 0.31 1.73 9.41
J17592922 1.741 14.028 51256.0 133 11.9 0.96 0.95 0.95 ¡1.46 11.17
J18010357 B175803 1.085 3.897 50084.0 201 18.4 22.82 16.73 0.67 ¡1.36 9.71
J18012920 B175829 0.924 2.814 51417.0 229 11.0 1.58 1.49 0.59 1.81 10.63
J18032137 B180021 7.484 7511.371 49527.0 352 6.7 2375.83 1.87 0.99 0.73 6.74
J18032712 B180027 2.990 0.153 50661.0 151 15.1 1.18 1.17 1.17 ¡1.06 11.19
J18040735 B180207 43.288 0.875 50709.0 433 15.0 0.28 0.28 0.28 ¡2.45 12.05
Table 1: …continued
PSR J PSR B Epoch N
(s) () () (MJD) (yr) (ms) (ms) (ms)
J18042717 107.032 0.468 51440.0 261 10.9 0.07 0.07 0.07 ¡3.17 12.45
J18050306 B180203 4.572 20.892 50331.0 198 16.9 3.85 1.83 0.26 ¡1.76 10.48
J18061154 B180412 1.913 5.157 51096.0 180 12.8 3.01 1.06 0.75 ¡1.59 10.50
J18070847 B180408 6.108 1.074 48671.0 456 26.3 1.13 0.54 0.09 ¡3.00 11.39
J18072715 B180427 1.208 17.768 50291.0 233 17.2 27.64 3.29 0.76 ¡1.66 9.57
J18080813 1.141 1.616 51271.0 154 12.0 0.99 0.90 0.90 ¡1.63 10.88
J18082057 B180520 1.089 20.243 49937.0 188 18.8 48.80 4.60 0.97 0.92 9.72
J18092109 B180621 1.424 7.747 49995.0 227 18.8 4.93 3.09 0.34 1.91 10.54
J18120226 B181002 1.260 5.711 50336.0 244 17.1 1.32 1.28 1.28 ¡1.59 11.00
J18121718 B1809173 0.830 13.128 49887.0 234 19.6 84.15 48.55 1.03 1.20 8.83
J18121733 B1809176 1.858 3.390 50688.0 191 15.2 3.81 2.99 2.99 ¡1.33 10.42
J18134013 B181140 1.074 2.939 50300.0 266 17.2 5.10 1.16 0.85 ¡1.64 10.50
J18161729 B181317 1.278 11.873 49887.0 238 19.6 106.40 18.59 0.63 1.46 9.24
J18162650 B181326 1.687 0.189 49573.9 261 23.6 2.04 1.88 1.88 ¡1.12 11.18
J18181422 B181514 3.431 23.995 49993.0 218 18.8 8.75 8.32 0.28 1.61 9.90
J18200427 B181804 1.672 17.700 47020.0 690 35.1 93.58 45.77 0.66 1.01 9.19
J18201346 B181713 1.085 5.294 50018.0 218 18.9 8.06 2.03 1.18 ¡1.64 10.26
J18201818 B181718 3.227 0.975 50663.0 170 15.1 0.71 0.58 0.58 1.69 11.23
J18211715 B182117 0.732 0.466 51819.0 112 10.2 2.41 2.39 2.39 ¡1.08 11.33
J18220705 0.734 0.941 51748.0 102 10.6 1.24 1.15 1.15 ¡1.36 11.05
J18221400 B182014 4.656 19.666 50042.0 208 18.8 16.84 10.36 0.86 1.32 9.79
J18222256 B181922 0.534 0.385 49120.0 164 16.0 1.10 1.10 1.10 ¡1.46 11.44
J18230550 B182105 1.328 0.400 49844.0 365 19.8 1.02 0.60 0.36 ¡2.13 11.08
J18230154 1.316 1.960 51276.0 157 12.0 1.36 0.71 0.54 ¡1.68 10.51
J18231115 B182011 3.574 17.612 49993.0 469 18.8 26.54 11.44 2.88 1.63 9.82
J18233021A B182030A 183.823 114.336 50719.0 302 15.0 0.85 0.09 0.09 2.95 11.06
J18233021B B182030B 2.641 0.225 50700.0 303 14.9 0.79 0.72 0.61 ¡2.00 11.11
J18233106 B182031 3.520 36.277 50315.0 238 17.3 17.68 8.26 0.20 1.73 9.67
J18241118 B182111 2.295 18.716 49874.0 233 19.6 26.36 20.37 0.86 1.35 9.57
J18241945 B182119 5.282 145.939 50101.0 351 18.2 37.37 33.81 0.24 1.19 9.31
J18242452 B182124 327.406 173.519 50238.0 163 17.4 0.13 0.11 0.09 ¡2.56 12.06
J18250004 B182200 1.284 1.445 50336.0 240 17.1 3.29 2.21 0.61 ¡1.54 10.46
J18250935 B182209 1.300 88.369 49831.0 506 19.7 855.97 172.69 1.21 0.44 8.15
J18251446 B182214 3.582 290.947 49862.0 234 19.5 41.52 9.05 0.77 1.38 9.62
J18261131 B182311 0.478 1.121 49867.0 340 19.7 7.12 3.17 2.36 ¡1.42 10.55
J18261334 B182313 9.856 7293.991 50639.9 591 11.8 2267.62 123.04 0.58 0.37 7.28
J18270958 B182410 4.069 16.597 49883.0 253 19.6 7.28 3.63 1.73 ¡1.60 10.18
J18291751 B182617 3.256 58.852 50101.0 363 18.2 10.66 7.31 0.44 0.68 9.65
J18301059 B182811 2.469 365.843 50031.0 755 18.7 217.18 16.82 0.47 0.80 8.68
J18320827 B182908 1.545 152.462 49868.0 359 19.7 40.85 28.31 0.41 1.63 9.82
J18321021 B182910 3.027 38.493 49883.0 372 19.6 52.02 10.37 0.52 1.57 9.55
J18330338 B183103 1.456 88.139 50123.0 499 18.3 45.86 30.84 0.50 0.66 9.18
J18330827 B183008 11.725 1260.890 50740.0 351 14.7 37.77 3.72 0.24 1.49 9.41
J18340010 B183100 1.920 0.039 49123.0 148 12.8 5.45 5.40 5.40 ¡0.97 10.98
J18340426 B183104 3.447 0.854 50165.0 250 18.1 3.22 1.24 0.46 1.90 10.45
J18350643 B183206 3.270 432.507 49993.0 256 18.8 164.18 27.53 1.84 1.37 9.04
J18351106 6.027 748.776 51289.0 243 12.1 357.22 263.09 0.53 0.39 8.11
J18360436 B183404 2.823 13.239 49957.0 246 19.2 18.22 7.52 0.33 1.67 9.95
J18361008 B183410 1.777 37.278 50123.0 279 17.8 37.79 36.84 0.32 0.70 9.04
J18370045 1.621 4.424 51400.0 193 11.0 1.40 1.38 1.38 ¡1.52 11.18
J18370653 B183406 0.525 0.213 50014.0 242 18.9 3.10 3.10 3.10 ¡1.22 11.38
J18405640 B183956 0.605 0.547 49129.0 385 23.6 2.13 1.14 1.07 1.72 10.94
J18410912 B183909 2.622 7.496 48854.0 374 25.3 28.65 12.80 0.50 1.23 9.90
J18410425 B183804 5.372 184.443 49849.0 319 18.6 22.54 21.58 0.21 1.28 9.82
J18420359 B183904 0.543 0.150 49848.0 303 19.6 2.94 2.68 2.68 ¡1.39 10.92
J18441454 B184214 2.663 13.281 49766.0 388 20.3 42.12 40.40 0.40 1.30 9.41
J18440244 B184202 1.970 64.936 49884.0 243 19.2 36.09 25.99 2.18 1.14 9.52
J18440433 B184104 1.009 3.986 50032.0 349 18.8 1.41 1.22 0.70 ¡1.86 10.84
J18440538 B184105 3.911 148.445 49867.0 295 19.2 20.26 17.26 0.34 1.59 9.83
J18450434 B184204 6.163 143.413 49610.0 211 16.7 87.29 31.31 0.71 0.74 9.27
J18470402 B184404 1.673 144.702 49142.0 422 23.7 62.88 2.87 0.39 1.40 9.90
J18480123 B184501 1.516 12.075 50407.0 289 16.5 20.01 17.64 0.31 1.71 9.61
J18481414 3.358 0.158 51269.0 142 12.0 1.12 1.12 1.12 ¡1.55 11.78
J18481952 B184519 0.232 1.254 50515.0 180 16.2 4.19 4.12 4.12 ¡1.18 10.78
J18490636 B184606 0.689 21.953 49142.0 344 23.7 16.65 5.64 0.50 1.59 10.16
J18501335 B184813 2.894 12.497 50128.0 214 18.3 1.97 0.39 0.26 ¡2.11 10.81
J18510418 B184804 3.513 13.431 50113.0 254 18.2 29.56 4.36 1.31 ¡1.22 9.99
J18511259 0.830 7.924 50106.0 195 18.4 135.61 41.86 1.00 1.29 9.11
J18520031 B184900 0.459 20.398 49995.0 232 18.8 33.11 28.91 21.44 ¡0.62 9.50
J18522610 2.973 0.775 51249.0 125 11.9 0.90 0.29 0.29 ¡1.95 10.78
J18541050 B185210 1.745 1.938 50869.0 266 14.2 11.43 11.30 11.30 ¡0.82 10.16
J18541421 B185114 0.872 3.166 50313.0 193 17.3 11.56 4.41 0.69 ¡1.83 10.06
J18560113 B185301 3.739 2911.552 50523.0 344 16.3 3040.36 145.15 1.12 0.57 7.56
J18570057 B185400 2.802 0.429 50097.0 136 18.5 2.56 2.44 2.44 ¡1.18 10.69
J18570212 B185502 2.405 232.901