GRAVITATIONAL WAVES FROM KNOWN PULSARS: RESULTS FROM THE INITIAL DETECTOR ERA

The expected quadrupolar gravitational wave signal from a triaxial neutron star ¹⁴⁴ steadily spinning about one of its principal axes of inertia is at twice the rotation frequency, with a strain of

$$\begin{eqnarray} h(t) = &\frac{1}{2}F_+(t, \psi)h_0(1+\cos {}^2\iota)\cos {\phi (t)} \nonumber \\ & + F_{\times }(t, \psi)h_0\cos {\iota }\sin {\phi (t)} \end{eqnarray} \tag{ 1 }$$

in the detector, where

$$\begin{equation} h_0=\frac{16\pi ^2G}{c^4}\frac{I_{zz}\varepsilon f_{\rm rot} ^2}{d} \end{equation} \tag{ 2 }$$

is the dimensionless gravitational wave strain amplitude. h₀ is dependent on I_zz , the fiducial equatorial ellipticity, defined as ε = (I_xx − I_yy )/I_zz in terms of principal moments of inertia, the rotational frequency, f_rot, and the distance to the source d. The signal amplitudes in the two polarizations ("+" and "×") depend on the inclination of the star's rotation axis to the line-of-sight, ι, while the detector antenna pattern responses for the two polarization states, F₊(t, ψ) and F_×(t, ψ), depend on the gravitational wave polarization angle, ψ, as well as the detector location, orientation and source sky position. The gravitational wave phase evolution, ϕ(t), depends on both the intrinsic rotational frequency and frequency derivatives of the pulsar and on Doppler and propagation effects. These extrinsic effects include relativistic modulations caused by the Earth's orbital and rotational motion, the presence of massive bodies in the solar system close to the line-of-sight to the pulsar, the proper motion of the pulsar, and (in the case of a binary system) pulsar orbital motions. We will assume that ϕ(t) is phase-locked to the electromagnetic pulse phase evolution, but with double the value and with an initial phase offset, ϕ₀. Given this phase evolution, the four unknown search parameters are simply h₀, cos ι, ϕ₀ and ψ. The gravitational wave amplitude is related to the star's l = m = 2 mass quadrupole moment via (see, e.g., Owen 2005)

$$\begin{equation} Q_{22} = \sqrt{\frac{15}{8\pi }} I_{zz}\varepsilon = h_0\left(\frac{c^4 d}{16\pi ^2G f_{\rm rot} ^2} \right) \sqrt{\frac{15}{8\pi }}, \end{equation} \tag{ 3 }$$

where Q₂₂ is the slightly non-standard definition of quadrupole moment used in Ushomirsky et al. (2000) and many subsequent papers. This value can be constrained independently of any assumptions about the star's equation of state and moment of inertia.

If we allocate all the spin-down luminosity, $\dot{E}$, to gravitational wave luminosity, $\dot{E}_{\rm gw}$, where

$$\begin{eqnarray} \dot{E}_{\rm gw} =& \frac{2048\pi ^6}{5}\frac{G}{c^5}f_{\rm rot} ^6(I_{zz}\varepsilon)^2, \nonumber \\ =& \frac{8\pi ^2}{5}\frac{c^3}{G}f_{\rm rot} ^2 h_0^2 d^2, \end{eqnarray} \tag{ 4 }$$

then we have the canonical "spin-down limit" on gravitational wave strain ¹⁴⁵

$$\begin{eqnarray} h_0^{\rm sd} = &\left(\frac{5}{2} \frac{G I_{zz} \dot{f}_{\rm rot}}{c^3 d^2 f_{\rm rot}} \right)^{1/2}\nonumber \\ = & \: 8.06\times 10^{-19}\frac{I^{1/2}_{38}}{d_{\rm kpc}}\left(\frac{|\dot{f}_{\rm rot}|}{f_{\rm rot}}\right)^{1/2}, \end{eqnarray} \tag{ 5 }$$

where I₃₈ is the star's moment of inertia in the units of 10³⁸ kg m², and d_kpc is the distance to the pulsar in kiloparsecs. The spin-down limit on the signal amplitude corresponds (via Equation (2)) to an upper limit on the star's fiducial ellipticity ¹⁴⁶

$$\begin{equation} \varepsilon ^{\rm sd} = 0.237\left(\frac{h_0^{\rm sd}}{10^{-24}}\right)f_{\rm rot} ^{-2} I_{38}^{-1} d_{\rm kpc}. \end{equation} \tag{ 6 }$$

Johnson-McDaniel (2013) shows how to relate this to the physical ellipticity of the star's surface for a given equation of state.

A gravitational wave strain upper limit that is below the spin-down limit is an important milestone, as such a measurement is probing uncharted regions of the parameter space. Likewise it directly constrains the fraction of spin-down power that could be due to the emission of gravitational waves, which gives insight into the overall spin-down energy budget.

In this paper we have used calibrated data from the Virgo second (Aasi et al. 2012) and fourth science runs (VSR2 and VSR4) and the LIGO sixth science run (S6). Virgo's third science run (VSR3) was relatively insensitive in comparison with VSR4 and has not been included in this analysis. This was partially because Virgo introduced monolithic mirror suspensions prior to VSR4 which improved sensitivity in the low-frequency range. During S6, the two LIGO 4 km detectors at Hanford, Washington (LHO/H1), and Livingston, Louisiana (LLO/L1), were running in an enhanced configuration (Adhikari et al. 2006) over that from the previous S5 run (Abbott et al. 2009). Table 1 shows dates of the runs, the duty factors and science data lengths for each detector that we analyzed.

The Virgo and LIGO data used in these analyses have been calibrated through different reconstruction procedures, but both based ultimately on the measured response to actuation controls on the positions of the mirrors that define the interferometers. For Virgo VSR2, the calibration uncertainty was about 5.5% in amplitude and ∼50 mrad (3°) in phase over most of the frequency range (Accadia et al. 2011). For VSR4, the uncertainty amounted to about 7.5% in amplitude and to (40 + 50f) mrad in phase, where f is the frequency in kilohertz, for frequencies up to 500 Hz (Mours & Rolland 2011). For LIGO, the S6 calibration uncertainties over the relevant frequency range (50–1500 Hz) were up to ∼19% in amplitude and ∼170 mrad (10°) in phase for L1, and up to ∼16% in amplitude and ∼120 mrad (7°) for H1 (Bartos et al. 2011). These phase errors are well within the range (i.e., less than 30°as applied in Abbott et al. 2007a) that would cause significant loss in signal power due to decoherence between the pulsar signal and the assumed phase evolution.

We used three semi-independent methods (very similar to those used in the Vela pulsar search in Abadie et al. 2011) to search for signals described in Section 1.1. Here, we briefly outline their operation, but for full descriptions we refer the reader to the references below. Two of the search methods work with time domain data that has been heterodyned to remove the signal's phase evolution and then heavily decimated. This leaves a complex data stream in which any signal would only be modulated by the detector's beam pattern. In the first method, this data stream is used to give Bayesian parameter estimates of the unknown signal parameters ¹⁴⁷ (Dupuis & Woan 2005). The second method computes the maximum likelihood $\mathcal {F}$-statistic rather than a Bayesian posterior (or in case where ψ and ι are well constrained, the $\mathcal {G}$-statistic) (Jaranowski & Królak 2010). The third method (Astone et al. 2010) makes use of a Short Fourier Transform Database (SFDB) of each detector's data. After the extraction of a small frequency band around the signal's expected frequency, the Doppler effect, Einstein delay and spin-down are removed in the time domain and the data are down-sampled with a re-sampling technique. Two matched filters on the "+" and "×" signal Fourier components are then computed at the five frequencies at which the signal power is spread due to the signal amplitude and phase modulation; they are used to build a detection statistic and to estimate signal parameters in the case of detection. This 5-vector method has been extended over that used in Abadie et al. (2011) to allow for coherent analysis of data from multiple detectors (Astone et al. 2012). Each of these methods can incorporate prior information on the pulsar's inclination and polarization angle. From here on, we will refer to the first method as the Bayesian method, ¹⁴⁸ the second as the $\mathcal {F}$/$\mathcal {G}$-statistic method and the third as the 5n-vector method, where n refers to the number of datasets coherently combined.

All three methods apply some data cleaning. The procedure used to obtain the heterodyned data removes extreme outliers by running two passes of a scheme that identifies points with absolute values greater than five times the standard deviation of the dataset. The $\mathcal {F}$/$\mathcal {G}$-statistic method performs further cleaning of this data through the Grubbs test (see Abadie et al. 2011). In the 5n-vector method, after an initial time-domain cleaning before the construction of the SFDB, a further cleaning step is applied on the final down-sampled time series in which the largest outliers belonging to the non-Gaussian tail of the data amplitude distribution are removed.

We have incorporated some limits from the previous LIGO S5 results (Abbott et al. 2010) as priors in the Bayesian analysis. However, the S6/VSR2,4 phase models were produced with updated pulsar ephemerides resulting in an unknown phase offset between them and the S5 results. We have, therefore, simply used the S5 marginalized posterior on h₀ and cos ι, p(h₀, cos ι), as our prior for the new results. In the case of glitching pulsars (see Section 2), we used the same approach and (incoherently) combined the separate coherent analyses produced between glitches. In the case of the $\mathcal {F}$/$\mathcal {G}$-statistic method, the results from different detectors or different inter-glitch periods are combined incoherently by adding the respective statistics. Also, for the 5n-vector method, results from different inter-glitch periods are incoherently combined by summing the corresponding statistics. Our reasons for not coherently combining the data over glitches are twofold. The first is that we do not know how a glitch would effect the relative phase offset between the electromagnetic pulses and the gravitational wave signal. The second reason is a practical consideration based on the timing solutions we have for our pulsars. For three of the four glitching pulsars (all except J0537−6910) in this analysis we have separate timing solutions for each inter-glitch period. These separate timing solutions, as provided by the pulsar timing software TEMPO(2), do not give an epoch defined at a fixed pulse phase (i.e., the epoch is not given as the time of the peak of a particular pulse), so there is some unknown phase offset between the separate solutions. However, if this phase offset were known (e.g., by going back to the original pulsar pulse time of arrival data) the gain in sensitivity would still be minimal: for the Vela pulsar and J1813−1246 the data from VSR4 (which was after the glitches in these pulsars) was much more sensitive, so completely dominates the result; for J1952+3252 the post-glitch data contains the latter part of S6, which was more sensitive and would again dominate the results. For J0537−6910 the epoch for each inter-glitch timing solution is defined (see Appendix), so the electromagnetic phase could be tracked over the glitches, but again our result is dominated by the longest and most sensitive inter-glitch period.

Even without a detection, all three methods can be used to produce upper limits on the gravitational wave amplitude from the pulsars. Here, we will quote 95% confidence upper limits on the amplitude. In the Bayesian method, an upper limit on the h₀ posterior (after marginalization over the orientation parameters) is found by calculating the upper bound, from zero, on the integral over this posterior that encloses 95% of the probability. In the $\mathcal {F}$/$\mathcal {G}$-statistic method, a frequentist upper limit is calculated through Monte-Carlo simulations, which find the value of h₀ for which 95% of trials exceed the maximum likelihood statistic. ¹⁴⁹ The 5n-vector method computes an upper limit on the H₀ posterior, given the actual value of the detection statistic, and the marginalization over the other parameters is implicitly done in the Monte Carlo simulation used to compute the likelihood. The amplitude, H₀, is linked to the classical h₀, given by Equation (2), by the relation $H_0=({h_0}/{2})\sqrt{1+6\cos {}^2\iota +\cos {}^4\iota }$ (see Equation (A5) in Abadie et al. 2011). H₀ is the strain amplitude of a linearly polarized signal with polarization angle ψ = 0. In order to convert an upper limit on H₀ to an upper limit on h₀, we use the previous equation replacing the coefficient on the right hand side with its mean value over the distribution of cos ι used in the upper limit procedure. This is justified by the fact that the posterior distribution of H₀ is not dependent on ι. The three methods have been tested with hardware and software simulated signal injections to check that they can recover the expected signal model (see, e.g., Abadie et al. 2011). In the Bayesian analysis these upper limits are really 95% credibility, or degrees-of-belief, values, whereas for the frequentist analysis these are 95% confidence values. These are both asking different questions and in general should not be expected to produce identical results. A brief discussion of this is given in the first search for a pulsar in LIGO data in Abbott et al. (2004), whilst a more technical discussion of the differences between the upper limits can be found in Röver et al. (2011).

For this analysis, we have obtained ephemerides using radio, X-ray and γ-ray observations. The radio telescope observations have come from a variety of sources: the 12.5-m telescope and Lovell telescope at Jodrell Bank in the UK, the 26-m telescope at Hartebeesthoek in South Africa, the 15-m eXperimental Development Model (XDM) telescope in South Africa, the Giant Metrewave Radio Telescope (GMRT) in India, the Robert C. Byrd Green Bank Radio Telescope in the US, the Parkes radio telescope in Australia, the Nançay Decimetric Radio Telescope in France and the Hobart radio telescope in Australia. High energy X-ray and γ-ray timings have been obtained from the Rossi X-ray Timing Explorer (RXTE) and the Fermi Large Area Telescope (LAT).

In total, for this analysis, we collected timing solutions for 179 pulsars. This selection includes 73 pulsars that have not been previously studied. However, for five of the pulsars targeted in the S3/S4 analysis (Abbott et al. 2007a) and another eleven of the pulsars targeted in the S5 analysis (Abbott et al. 2010), new coherent timing solutions were not available, so these stars ¹⁵² have not been included in this search.

2.1.1. High Interest Targets

As discussed in Abbott et al. (2008), ¹⁵³ due to our ignorance of the correct neutron star equation of state there is a large uncertainty in the moments of inertia for our targets, from 1 to 3 × 10³⁸ kg m². Therefore, the canonical spin-down limit estimates could be increased by a factor of ∼1.7. Also, there are uncertainties in some pulsar distance measurements of up to a factor of two which could further increase or decrease the spin-down limit. We therefore identified all sources that were within a factor of four of the canonical spin-down limit as worthy of special attention. Seven of the pulsars for which we have obtained timing solutions beat, or approach to within a factor of four, this limit. The electromagnetic observation epochs for each pulsar (which include each inter-glitch epoch for pulsars that glitched during the analysis) are given in Table 2.

Table 2. Electromagnetic Observation Epochs for the High Interest Pulsars

MJD and Date
J0534+2200 (Crab pulsar)
54997 (2009 Jun 15) – 55814 (2011 Sep 10)
J0537−6910 (N157B)
54897 (2009 Mar 7) – 55041 (2009 Jul 29)
55045 (2009 Aug 2) – 55182 (2009 Dec 17)
55185 (2009 Dec 20) – 55263 (2010 Mar 8)
55275 (2010 Mar 20) – 55445 (2010 Sep 6)
55458 (2010 Sep 19) – 55503 (2010 Nov 3)
J0835−4510 (Vela pulsar)
54983 (2009 Jun 1) – 55286 (2010 Mar 31)
55713 (2011 Jun 1) – 55827 (2011 Sep 23)
J1813−1246
54693 (2008 Aug 15) – 55094 (2009 Sep 20)
55094 (2009 Sep 20) – 55828 (2011 Sep 24)
J1833−1034 (G21.5−0.9)
55041 (2009 Jul 29) – 55572 (2011 Jan 11)
J1913+1011
54867 (2009 Feb 5) – 55899 (2011 Dec 4)
J1952+3252 (CTB 80)
54589 (2008 May 3) – 55325 (2010 May 9)
55331 (2010 May 15) – 55802 (2011 Aug 29)

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Further details of these observations are given below:

• J0534+2200 (the Crab pulsar). We have used the Jodrell Bank Monthly Ephemeris (Lyne et al. 1993) to track the phase of the Crab pulsar over the period of our runs. This ephemeris has timing solutions using the DE200 solar system ephemeris and the Barycentric Dynamical Time (TDB) time coordinate system. During S6/VSR2,4 the pulsar did not show signs of any timing glitches.
• J0537−6910 (N157B). Long-term X-ray timing has been performed with the RXTE (Middleditch et al. 2006). Recent data covering S6 shows four glitches over the span of our science runs and the ephemerides for each inter-glitch epoch are given in the Appendix. The timing solutions used the DE200 solar system ephemeris (see Marshall et al. 1998) and the TDB time coordinate system. Several more glitches have been observed since the end of our science runs, but we do not report on them here.
• J0835−4510 (the Vela pulsar). Radio observations over the period of VSR2 were taken with the Hobart radio telescope in Tasmania and the Hartebeesthoek 26-m radio telescope in South Africa (Abadie et al. 2011). Radio timing over the VSR4 run was performed with the XDM telescope and the 26-m telescope at Hartebeesthoek. The timing solutions have used the DE405 solar system ephemeris and the Barycentric Coordinate Time (TCB) time coordinate system. Vela was observed to glitch on 2010 July 31 (Buchner 2010), between VSR2 and VSR4, but it has not glitched since then.
• J1813−1246. This pulsar was discovered in a search of gamma-ray data from the Fermi LAT (Abdo et al. 2009), and using the unbinned maximum likelihood methods of Ray et al. (2011) timing measurements were made covering all our runs. It was observed to glitch once during this time on 2009 September 20. Pre-and-post glitch timing solutions have been produced using the DE405 solar system ephemeris and the TDB time coordinate system.
• J1833−1034 (G21.5−0.9). The period from the start of S6/VSR2 until 2011 January is covered by observations made with the GMRT (Roy et al. 2012). During this period, one glitch was observed, with a best fit epoch of 2009 November 6 (MJD 55142±2). To remove its effect, an ephemeris fit was performed on timing data excluding 80 days after the glitch. The timing solution uses the DE405 solar system ephemeris and the TDB time coordinate system.
• J1913+1011. This pulsar was observed at Jodrell Bank and showed no timing anomalies over the science runs. The timing solution uses the DE405 solar system ephemeris and the TDB time coordinate system.
• J1952+3252 (CTB 80). This pulsar was observed over the whole of our science runs at Nançay and Jodrell Bank. It glitched on 2010 May 11 (MJD 55327), between the end of S6/VSR2 and the start of VSR4. Phase incoherent pre- and post-glitch timing solutions have been produced using the DE405 solar system ephemeris and the TCB time ephemeris. The solution include fits to the timing noise using the tempo2 Fitwaves method described in Hobbs et al. (2006).

For several of these pulsars potential constraints on their orientations (the inclination ι and polarization angle ψ ¹⁵⁴ ) are available from observations of their pulsar wind nebulae (Ng & Romani 2004, 2008). These are listed in Table 3 where the uncertainties used are estimated from the systematic and statistical values given in Ng & Romani (2004, 2008), and the mean angle value is used if multiple fits are given (e.g., fits to the inner and outer tori of the Crab pulsar wind nebula). We briefly discussed how these constraints are used in the analyses in Section 1.3.

Table 3. Implied Orientations of Pulsars from their Pulsar Wind Nebulae Observations (Ng & Romani 2004, 2008)

Pulsar	ι	ψ
J0534+2200 (Crab pulsar)	622 ± 19	352 ± 15
J0537−6910	928 ± 09	410 ± 22
J0835−4510 (Vela pulsar)	636 ± 06	406 ± 01
J1833−1034	854 ± 03	45° ± 1°
J1952+3252 a	⋅⋅⋅	−115 ± 86

Note. ^a The polarization angle is not taken from a fit to the pulsar wind nebula, but instead is the average of the angle calculated from proper motion measurements and Hα observations of a bow shock (Ng & Romani 2004).

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For J0534+2200 and J0537−6910, the Bayesian method also makes use of results from the LIGO S5 run (Abbott et al. 2010) as a prior on the h₀ and cos ι parameters. During S5, both of these pulsars glitched, and the data for each inter-glitch period was analyzed independently. Results were also produced assuming that the data could be analyzed coherently over the glitches. To avoid the assumptions about coherence over the glitches, we have used the independent inter-glitch results that gave the lowest h₀ as the prior for the current analysis (see Table 3 of Abbott et al. 2010).

As discussed in Section 2.1, for a few pulsars the electromagnetic observations did not always span the S6/VSR2,4 runs completely, and some pulsars glitched during the runs. As a result, we deal with these instances separately. In most cases, we can use all the data coherently, but, in other cases, sections of data must be combined incoherently. The relative sensitivities of the detectors at the pulsar frequencies also dictate whether we have used Virgo-only, LIGO-only or Virgo and LIGO data (see Figure 1). For J0537−6910, only the LIGO data has been used because of its better sensitivity at the corresponding frequency, and results from each inter-glitch period have been combined incoherently. For J0835−4510 (the Vela pulsar), a glitch occurred just prior to VSR4 and we had no phase-connected timing solution between VSR2 (Abadie et al. 2011) and VSR4 epochs. The VSR2 results and VSR4 data have therefore been incoherently combined. For J1813−1246, the results from the pre- and post-glitch periods using all data from S6 and VSR2,4 have been combined incoherently. For J1833−1034, only VSR2 data up to the time of the observed glitch has been used.

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The parameters and results (from the three different analyses discussed in Section 1.3) for the seven pulsars highlighted in Section 2.1 are given in Tables 4 and 5, respectively. Table 5 gives the 95% upper limit on the gravitational wave amplitude, $h_0^{95\%}$, the equivalent limits (via Equation (3)) on the stars fiducial ellipticity, ε, and mass quadrupole moment, Q₂₂, the ratio of the limit to the spin-down limit, $h_0^{95\%}/h_0^{\rm sd}$, and the limit on the gravitational wave luminosity compared to the total spin-down luminosity. This final value is given in the form of the percentage of the spin-down luminosity required to produce a gravitational wave at the amplitude limit (it can be seen from Equation (4) that this is just the square of the ratio $h_0^{95\%}/h_0^{\rm sd}$). For those pulsars with constrained orientations (see Table 3) the results with and without the constraints are also given in Table 5. Despite the very tight constraints given in Table 3 it should be noted that these results would only show minor differences if the angle (ι and ψ) errors were expanded to several times the given values. This is because the recovered posterior probability distributions on these parameters are slowly and smoothly varying over their parameter ranges. A brief discussion of the differences between the upper limits from the different methods is given in Section 1.3.

Table 4. The Properties of the Pulsars of High Interest

Pulsar	α	δ	frot	fgw	$\dot{f}_{\rm rot}$	d	$\dot{E}$ a	hsd a
			(Hz)	(Hz)	(Hz s−1)	(kpc)	(W)
J0534+2200 (Crab)	05h34m3197	22°00'5207	29.72	59.44	−3.7 × 10−10	2.0 b	4.6 × 1031	1.4 × 10−24
J0537−6910 (N157B)	05h37m4736	−69°10'2040	61.97	123.94	−2.0 × 10−10	50.0 c	4.9 × 1031	3.0 × 10−26
J0835−4510 (Vela)	08h35m2061	−45°10'3488	11.19	22.39	−1.6 × 10−11	0.29 d	6.9 × 1029	3.3 × 10−24
J1813−1246	18h13m2374	−12°46'0086	20.80	41.60	−7.6 × 10−12	1.9 e	6.2 × 1029	2.6 × 10−25
J1833−1034 (G21.5−0.9)	18h33m3361	−10°34'1661	16.16	32.33	−5.3 × 10−11	4.8 f	3.4 × 1030	3.0 × 10−25
J1913+1011	19h13m2034	10°11'2311	27.85	55.70	−2.6 × 10−12	4.5 g	2.8 × 1029	2.3 × 10−25
J1952+3252 (CTB 80)	19h52m5811	32°52'4124	25.30	50.59	−3.7 × 10−12	3.0 g	3.7 × 1029	1.0 × 10−25

Notes. ^aThe spin-down luminosity, $\dot{E}$, and spin-down gravitational wave amplitude limit, h^sd, both assume a canonical moment of inertia of I_zz = 10³⁸ kg m². ^bSee Appendix of Kaplan et al. (2008). ^cPietrzyński et al. (2013). ^dDodson et al. (2003). ^eThis distance is the average of the two estimates from Wang (2011), which allow a distance between ∼0.9–3.5 kpc. ^fTian & Leahy (2008). ^gThe distance is taken from the ATNF pulsar catalog (Manchester et al. 2005).

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Table 5. Upper Limits for the High Interest Pulsars ^a

Analysis	$h_0^{95\%}$	ε	Q22 (kg m2)	$h_0^{95\%}/h_0^{\rm sd}$	$\dot{E}_{\rm gw}/\dot{E}$ %
J0534+2200 (Crab)
Bayesian	1.6 (1.4) × 10−25	8.6 (7.5) × 10−5	6.6 (5.8) × 1033	0.11 (0.10)	1.2 (1.0)
$\mathcal {F}$/$\mathcal {G}$-statistic	2.3 (1.8) × 10−25	12.3 (9.6) × 10−5	11.6 (7.4) × 1033	0.16 (0.13)	2.6 (1.7)
5n-vector	1.8 (1.6) × 10−25	9.7 (8.6) × 10−5	7.4 (6.6) × 1033	0.12 (0.11)	1.4 (1.2)
J0537−6910
Bayesian	3.8 (4.4) × 10−26	1.2 (1.4) × 10−4	0.9 (1.0) × 1034	1.4 (1.7)	200 (290)
$\mathcal {F}$/$\mathcal {G}$-statistic	1.1 (1.0) × 10−25	3.4 (3.1) × 10−4	2.6 (2.4) × 1034	4.1 (3.9)	1700 (1500)
5n-vector	4.5 (6.7) × 10−26	1.4 (2.1) × 10−4	1.1 (1.6) × 1034	1.6 (2.4)	260 (580)
J0835−4510 (Vela)
Bayesian	1.1 (1.0) × 10−24	6.0 (5.5) × 10−4	4.7 (4.2) × 1034	0.33 (0.30)	11 (9.0)
$\mathcal {F}$/$\mathcal {G}$-statistic	4.2 (9.0) × 10−25	2.3 (4.9) × 10−4	1.8 (3.8) × 1034	0.13 (0.27)	1.7 (7.3)
5n-vector	1.1 (1.1) × 10−24	6.0 (6.0) × 10−4	4.7 (4.7) × 1034	0.33 (0.33)	11 (11)
J1813−1246
Bayesian	3.4 × 10−25	3.5 × 10−4	2.7 × 1034	1.3	170
$\mathcal {F}$/$\mathcal {G}$-statistic	7.1 × 10−25	7.4 × 10−4	5.7 × 1034	2.7	730
5n-vector	4.8 × 10−25	4.9 × 10−4	3.8 × 1034	1.8	320
J1833−1034
Bayesian	1.3 (1.4) × 10−24	5.7 (6.1) × 10−3	4.4 (4.7) × 1035	4.3 (4.6)	1800 (2100)
$\mathcal {F}$/$\mathcal {G}$-statistic	1.2 (1.2) × 10−24	5.2 (5.2) × 10−3	4.0 (4.0) × 1035	3.9 (3.9)	1500 (1500)
5n-vector	1.4 (2.0) × 10−24	6.1 (8.7) × 10−3	4.7 (6.7) × 1035	4.6 (6.6)	2100 (4400)
J1913+1011
Bayesian	1.6 × 10−25	2.2 × 10−4	1.7 × 1034	2.9	840
$\mathcal {F}$/$\mathcal {G}$-statistic	2.9 × 10−25	4.1 × 10−4	3.1 × 1034	5.3	2800
5n-vector	2.5 × 10−25	3.4 × 10−4	2.7 × 1034	4.5	2000
J1952+3252
Bayesian	2.7 (2.5) × 10−25	3.0 (2.8) × 10−4	2.3 (2.1) × 1034	2.6 (2.5)	680 (630)
$\mathcal {F}$/$\mathcal {G}$-statistic	6.0 × 10−25	6.7 × 10−4	5.1 × 1034	5.8	3400
5n-vector	3.1 (3.2) × 10−25	3.4 (3.5) × 10−4	2.6 (2.7) × 1034	3.0 (3.1)	900 (960)

Notes. Limits with constrained orientations are given in parentheses. ^aDetector calibration errors mean that for pulsars with f_gw below and above 50 Hz (see Table 4) there are ∼6% and ∼20% uncertainties respectively on these limits.

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One of the new targets, J1824−2452I (which is an interesting pulsar that is seen to switch between being accretion and rotation powered; Papitto et al. 2013), had a coherent timing solution that covered 2006, so S5 data from the LIGO detectors has been reanalyzed for this result. For all other pulsars, we have used only the VSR2 and VSR4 data if f_gw < 40 Hz, and have coherently combined VSR2, VSR4 and S6 data from H1 and L1 for pulsars with f_gw > 40 Hz. All the available science mode data (i.e., when the detectors were operating in a stable state) has been used, with details given in Table 1.

For the 19 pulsars with f_gw < 40 Hz the results can be found in Table 6. Because of their low frequencies, none of these pulsars had been targeted before.

Table 6. Limits on the Gravitational Wave Amplitude for Known Pulsars with f_gw < 40 Hz Using VSR2,4 Data

Pulsar	frot	fgw	$\dot{f}_{\rm rot}$	d	$h_0^{\rm sd}$	$h_0^{95\%}$	ε	Q22	$h_0^{95\%}/h_0^{\rm sd}$
	(Hz)	(Hz)	(Hz s−1)	(kpc)				(kg m2)
J0106+4855	12.03	24.05	−6.2 × 10−14	7.3	7.9 × 10−27	7.4 × 10−25	8.9 × 10−3	6.9 × 1035	94
J0609+2130	17.95	35.91	−7.6 × 10−17	1.8	9.1 × 10−28	4.4 × 10−25	5.9 × 10−4	4.6 × 1034	490
J1528−3146	16.44	32.88	−6.7 × 10−17	1.0	1.6 × 10−27	6.0 × 10−25	5.2 × 10−4	4.0 × 1034	360
J1718−3825	13.39	26.78	−2.4 × 10−12	4.2	8.0 × 10−26	7.6 × 10−25	4.2 × 10−3	3.3 × 1035	9.5
J1747−2958	10.12	20.24	−6.3 × 10−12	2.5	2.6 × 10−25	1.8 × 10−24	1.0 × 10−2	7.9 × 1035	7.0
J1748−2446J	12.45	24.89	−2.0 × 10−16	5.5	5.8 × 10−28 a	1.3 × 10−24	1.1 × 10−2	8.3 × 1035	2200
J1753−1914	15.88	31.77	−4.9 × 10−16	2.8	1.6 × 10−27	5.5 × 10−25	1.4 × 10−3	1.1 × 1035	340
J1753−2240	10.51	21.02	−6.9 × 10−17	3.5	6.0 × 10−28	2.2 × 10−24	1.6 × 10−2	1.3 × 1036	3700
J1809−1917	12.08	24.17	−3.7 × 10−12	3.7	1.2 × 10−25	1.2 × 10−24	7.2 × 10−3	5.6 × 1035	9.9
J1828−1101	13.88	27.76	−2.9 × 10−12	7.3	5.0 × 10−26	1.0 × 10−24	9.2 × 10−3	7.1 × 1035	20
J1831−0952	14.87	29.73	−1.8 × 10−12	4.3	6.5 × 10−26	5.7 × 10−25	2.6 × 10−3	2.0 × 1035	8.7
J1833−0827	11.72	23.45	−1.3 × 10−12	4.5	5.9 × 10−26 b	1.6 × 10−24	1.2 × 10−2	9.6 × 1035	27
J1856+0245	12.36	24.72	−9.5 × 10−12	10.3	6.9 × 10−26	10.0 × 10−25	1.6 × 10−2	1.2 × 1036	15
J1904+0412	14.07	28.13	−2.8 × 10−17	4.0	2.8 × 10−28	9.2 × 10−25	4.4 × 10−3	3.4 × 1035	3300
J1915+1606	16.94	33.88	−2.5 × 10−15	7.1	1.4 × 10−27 b	3.9 × 10−25	2.3 × 10−3	1.7 × 1035	280
J1928+1746	14.55	29.10	−2.8 × 10−12	8.1	4.3 × 10−26	6.8 × 10−25	6.2 × 10−3	4.8 × 1035	16
J1954+2836	10.79	21.57	−2.5 × 10−12	1.6	2.4 × 10−25	1.2 × 10−24	4.0 × 10−3	3.1 × 1035	5.1
J2043+2740	10.40	20.80	−1.3 × 10−13	1.1	8.1 × 10−26	1.7 × 10−24	4.1 × 10−3	3.2 × 1035	21
J2235+1506	16.73	33.46	−2.9 × 10−17	1.1	9.2 × 10−28 b	4.2 × 10−25	4.0 × 10−4	3.1 × 1034	450

Notes. Detector calibration errors mean that for these pulsars there are ∼6% uncertainties on these limits. ^aThe pulsar's spin-down is calculated using a characteristic spin-down age of 10⁹ yr. ^bThe pulsar's spin-down is corrected for proper motion effects.

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Results for pulsars with f_gw > 40 Hz using S6 and VSR2,4 are shown in Table 7. Distances to pulsars in Terzan 5 (with designations J1748−2446) are assumed to be 5.5 kpc (Ortolani et al. 2007) rather than the value of 8.7 kpc given in the ATNF catalog, and distances to the pulsars in M28 (with designations J1824−2452) are assumed to be 5.5 kpc (Harris 1996) rather than the distance of 4.9 kpc given in Abbott et al. (2010). Unless otherwise specified in the table for all other pulsars we use the distance values given by the DIST value in the ATNF catalog (Manchester et al. 2005), which generally are dispersion measure calculations from the electron density distribution model of Taylor & Cordes (1993). For the 16 pulsars where new timing solutions were not available during the most recent runs (see Section 2.1), we include the results from the LIGO S3/S4 (Abbott et al. 2007a) and S5 analysis (Abbott et al. 2010).

Table 7. Limits on the Gravitational Wave Amplitude for Known Pulsars with f_gw > 40 Hz

Pulsar	frot	fgw	$\dot{f}_{\rm rot}$	d	$h_0^{\rm sd}$	Prior $h_0^{95\%}$	S6/VSR2,4 $h_0^{95\%}$	ε	Q22	$h_0^{95\%}/h_0^{\rm sd}$
	(Hz)	(Hz)	(Hz s−1)	(kpc)					(kg m2)
J0023+0923	327.85	655.69	−1.3 × 10−15	0.9	1.7 × 10−27	⋅⋅⋅	6.9 × 10−26	1.5 × 10−7	1.1 × 1031	41
J0024−7204C	173.71	347.42	1.6 × 10−15	4.0	6.1 × 10−28 a	5.8 × 10−25	1.7 × 10−25	5.5 × 10−6	4.2 × 1032	290
J0024−7204D	186.65	373.30	1.6 × 10−16	4.0	1.8 × 10−28 a	4.5 × 10−26	2.9 × 10−26	7.8 × 10−7	6.1 × 1031	160
J0024−7204E	282.78	565.56	−7.8 × 10−15	4.0	1.1 × 10−27 a	9.9 × 10−26	9.7 × 10−26	1.1 × 10−6	8.9 × 1031	92
J0024−7204F	381.16	762.32	−9.3 × 10−15	4.0	9.9 × 10−28 a	8.8 × 10−26	6.7 × 10−26	4.4 × 10−7	3.4 × 1031	67
J0024−7204G	247.50	495.00	2.6 × 10−15	4.0	6.6 × 10−28 a	9.9 × 10−26	8.2 × 10−26	1.3 × 10−6	9.8 × 1031	120
J0024−7204H	311.49	622.99	3.0 × 10−16	4.0	2.0 × 10−28 a	6.5 × 10−26	5.2 × 10−26	5.1 × 10−7	3.9 × 1031	260
J0024−7204I	286.94	573.89	3.9 × 10−15	4.0	7.4 × 10−28 a	5.2 × 10−26	5.8 × 10−26	6.7 × 10−7	5.2 × 1031	79
J0024−7204J	476.05	952.09	2.4 × 10−15	4.0	4.5 × 10−28 a	1.0 × 10−25	6.6 × 10−26	2.8 × 10−7	2.1 × 1031	150
J0024−7204L	230.09	460.18	−3.6 × 10−15	4.0	8.0 × 10−28 b	5.8 × 10−26	4.2 × 10−26	7.4 × 10−7	5.7 × 1031	52
J0024−7204M	271.99	543.97	−4.3 × 10−15	4.0	8.0 × 10−28 b	6.2 × 10−26	7.0 × 10−26	9.0 × 10−7	7.0 × 1031	88
J0024−7204N	327.44	654.89	2.5 × 10−15	4.0	5.6 × 10−28 a	8.4 × 10−26	5.1 × 10−26	4.5 × 10−7	3.5 × 1031	91
J0024−7204O	378.31	756.62	−4.2 × 10−15	4.0	6.7 × 10−28 a	9.3 × 10−26	5.8 × 10−26	3.8 × 10−7	3.0 × 1031	86
J0024−7204Q	247.94	495.89	−3.9 × 10−15	4.0	8.0 × 10−28 b	5.8 × 10−26	5.1 × 10−26	7.9 × 10−7	6.1 × 1031	64
J0024−7204R	287.32	574.64	−4.6 × 10−15	4.0	8.0 × 10−28 b	5.6 × 10−26	3.6 × 10−26	4.1 × 10−7	3.2 × 1031	45
J0024−7204S	353.31	706.61	−5.6 × 10−15	4.0	8.0 × 10−28 b	6.9 × 10−26	6.1 × 10−26	4.6 × 10−7	3.6 × 1031	76
J0024−7204T	131.78	263.56	−2.1 × 10−15	4.0	8.0 × 10−28 b	3.3 × 10−26	3.8 × 10−26	2.0 × 10−6	1.6 × 1032	47
J0024−7204U	230.26	460.53	−4.9 × 10−15	4.0	9.3 × 10−28 a	5.7 × 10−26	4.1 × 10−26	7.2 × 10−7	5.6 × 1031	43
J0024−7204Y	455.24	910.47	−7.2 × 10−15	4.0	8.0 × 10−28 b	9.4 × 10−26	7.2 × 10−26	3.3 × 10−7	2.6 × 1031	90
J0030+0451	205.53	411.06	−4.3 × 10−16	0.3	4.1 × 10−27 a	⋅⋅⋅	7.2 × 10−26	1.1 × 10−7	8.7 × 1030	17
J0034−0534	532.71	1065.43	−1.5 × 10−16	1.0	4.4 × 10−28 a	⋅⋅⋅	1.8 × 10−25	1.5 × 10−7	1.1 × 1031	410
J0218+4232	430.46	860.92	−1.4 × 10−14	5.8	7.9 × 10−28 a	1.5 × 10−25	8.7 × 10−26	6.5 × 10−7	5.0 × 1031	110
J0307+7443	316.85	633.70	−1.7 × 10−15	0.6 c	3.3 × 10−27	⋅⋅⋅	8.6 × 10−26	1.1 × 10−7	8.9 × 1030	26
J0340+41	303.09	606.18	−6.5 × 10−16	2.7	4.4 × 10−28	⋅⋅⋅	5.6 × 10−26	3.8 × 10−7	3.0 × 1031	130
J0407+1607	38.91	77.82	−1.2 × 10−16	4.1	3.5 × 10−28	6.2 × 10−26	5.1 × 10−26	3.2 × 10−5	2.5 × 1033	140
J0437−4715	173.69	347.38	−4.1 × 10−16	0.2	7.8 × 10−27 a	5.7 × 10−25	1.2 × 10−25	1.6 × 10−7	1.2 × 1031	16
J0605+3757 d	366.58	733.15	−6.5 × 10−16	0.7 c	1.6 × 10−27	⋅⋅⋅	9.3 × 10−26	1.1 × 10−7	8.6 × 1030	59
J0610−2100	258.98	517.96	−2.3 × 10−16	5.6	1.3 × 10−28 a	⋅⋅⋅	7.9 × 10−26	1.6 × 10−6	1.2 × 1032	590
J0613−0200	326.60	653.20	−9.4 × 10−16	0.9	1.5 × 10−27 a	1.1 × 10−25	5.6 × 10−26	1.1 × 10−7	8.6 × 1030	37
J0614−3329	317.59	635.19	−1.7 × 10−15	3.0	6.4 × 10−28	⋅⋅⋅	8.5 × 10−26	5.9 × 10−7	4.5 × 1031	130
J0621+1002	34.66	69.31	−5.5 × 10−17	1.9	5.4 × 10−28 a	1.5 × 10−25	9.6 × 10−26	3.6 × 10−5	2.7 × 1033	180
J0711−6830	182.12	364.23	−2.9 × 10−16	1.0	9.8 × 10−28 a	5.0 × 10−26	3.4 × 10−26	2.5 × 10−7	2.0 × 1031	35
J0737−3039A	44.05	88.11	−3.4 × 10−15	1.1	6.5 × 10−27 a	7.8 × 10−26	6.0 × 10−26	8.0 × 10−6	6.2 × 1032	9.2
J0751+1807	287.46	574.92	−6.3 × 10−16	0.4	3.0 × 10−27 a	1.6 × 10−25	1.1 × 10−25	1.2 × 10−7	9.6 × 1030	36
J0900−3144	90.01	180.02	−4.0 × 10−16	0.8	2.1 × 10−27	⋅⋅⋅	1.8 × 10−25	4.3 × 10−6	3.3 × 1032	88
J1012+5307	190.27	380.54	−4.1 × 10−16	0.7	1.7 × 10−27 a	6.9 × 10−26	4.6 × 10−26	2.1 × 10−7	1.6 × 1031	27
J1017−7156	427.62	855.24	−3.1 × 10−16	8.1	8.5 × 10−29	⋅⋅⋅	1.0 × 10−25	1.1 × 10−6	8.3 × 1031	1200
J1022+1001	60.78	121.56	−1.6 × 10−16	0.5	2.5 × 10−27	4.5 × 10−26	4.8 × 10−26	1.6 × 10−6	1.2 × 1032	19
J1024−0719	193.72	387.43	1.3 × 10−16	0.5	1.3 × 10−27 a	5.0 × 10−26	4.6 × 10−26	1.4 × 10−7	1.1 × 1031	35
J1038+0032	34.66	69.32	−7.8 × 10−17	2.4	5.1 × 10−28	⋅⋅⋅	1.2 × 10−25	5.5 × 10−5	4.3 × 1033	230
J1045−4509	133.79	267.59	−3.1 × 10−16	0.2	5.3 × 10−27 a	4.3 × 10−26	3.0 × 10−26	9.3 × 10−8	7.2 × 1030	5.7
J1231−1411	271.45	542.91	1.6 × 10−15	0.5	4.3 × 10−27 a	⋅⋅⋅	7.5 × 10−26	1.1 × 10−7	8.4 × 1030	17
J1300+1240	160.81	321.62	−7.9 × 10−16	0.6	3.0 × 10−27 a	⋅⋅⋅	4.9 × 10−26	2.7 × 10−7	2.1 × 1031	16
J1301+0833	542.38	1084.76	−3.1 × 10−15	0.9	2.1 × 10−27	⋅⋅⋅	1.1 × 10−25	7.9 × 10−8	6.1 × 1030	51
J1435−6100 e	106.98	213.95	−2.8 × 10−16	3.3	4.0 × 10−28	2.7 × 10−25	⋅⋅⋅	1.8 × 10−5	1.4 × 1033	670
J1453+1902	172.64	345.29	−3.2 × 10−16	0.9	1.2 × 10−27 a	⋅⋅⋅	1.4 × 10−25	1.0 × 10−6	8.0 × 1031	120
J1455−3330	125.20	250.40	−2.5 × 10−16	0.7	1.5 × 10−27 a	5.1 × 10−26	3.6 × 10−26	4.1 × 10−7	3.1 × 1031	24
J1518+0204A	180.06	360.13	−2.9 × 10−15	8.0	4.0 × 10−28 b	⋅⋅⋅	7.8 × 10−26	4.6 × 10−6	3.5 × 1032	190
J1518+4904	24.43	48.86	−1.3 × 10−17	0.7	8.5 × 10−28 a	⋅⋅⋅	2.9 × 10−25	8.1 × 10−5	6.2 × 1033	340
J1537+1155	26.38	52.76	−1.6 × 10−15	1.0	6.3 × 10−27 a	⋅⋅⋅	2.4 × 10−25	8.4 × 10−5	6.5 × 1033	39
J1600−3053	277.94	555.88	−6.5 × 10−16	2.4	5.1 × 10−28 a	5.6 × 10−26	6.7 × 10−26	4.9 × 10−7	3.8 × 1031	130
J1603−7202	67.38	134.75	−5.4 × 10−17	1.6	4.4 × 10−28 a	2.3 × 10−26	2.3 × 10−26	1.9 × 10−6	1.5 × 1032	51
J1614−2230	317.38	634.76	3.9 × 10−16	1.8	5.0 × 10−28 a	⋅⋅⋅	6.4 × 10−26	2.7 × 10−7	2.1 × 1031	130
J1623−2631	90.29	180.57	−5.1 × 10−15	2.2	2.7 × 10−27 a	5.7 × 10−26	5.1 × 10−26	3.3 × 10−6	2.5 × 1032	19
J1629−6902 e	166.65	333.30	−2.8 × 10−16	1.4	7.7 × 10−28	3.2 × 10−25	⋅⋅⋅	3.8 × 10−6	2.9 × 1032	420
J1630+3734 d	301.38	602.75	−8.9 × 10−16	0.9 c	1.5 × 10−27	⋅⋅⋅	9.0 × 10−26	2.2 × 10−7	1.7 × 1031	60
J1640+2224	316.12	632.25	−1.6 × 10−16	1.2	4.9 × 10−28 a	6.7 × 10−26	5.1 × 10−26	1.4 × 10−7	1.1 × 1031	110
J1641+3627A	96.36	192.72	−1.5 × 10−15	7.5	4.3 × 10−28 b	⋅⋅⋅	5.0 × 10−26	9.5 × 10−6	7.3 × 1032	120
J1643−1224	216.37	432.75	−8.5 × 10−16	0.4	3.8 × 10−27 a	4.4 × 10−26	3.6 × 10−26	7.6 × 10−8	5.9 × 1030	9.4
J1701−3006A	190.78	381.57	−3.0 × 10−15	6.9	4.7 × 10−28 b	5.8 × 10−26	3.6 × 10−26	1.6 × 10−6	1.3 × 1032	78
J1701−3006B f	278.25	556.50	2.7 × 10−14	6.9	4.7 × 10−28 b	7.6 × 10−26	⋅⋅⋅	1.6 × 10−6	1.2 × 1032	160
J1701−3006C f	131.36	262.72	1.1 × 10−15	6.9	4.7 × 10−28 b	3.5 × 10−26	⋅⋅⋅	3.3 × 10−6	2.6 × 1032	76
J1709+2313	215.93	431.85	−6.9 × 10−17	1.8	2.5 × 10−28 a	⋅⋅⋅	9.3 × 10−26	8.6 × 10−7	6.7 × 1031	370
J1713+0747	218.81	437.62	−3.9 × 10−16	1.1	1.0 × 10−27 a	4.5 × 10−26	3.5 × 10−26	1.8 × 10−7	1.4 × 1031	34
J1719−1438	172.71	345.41	−2.3 × 10−16	1.6	5.8 × 10−28	⋅⋅⋅	1.6 × 10−25	2.0 × 10−6	1.6 × 1032	270
J1721−2457	285.99	571.98	−2.4 × 10−16	1.6	4.7 × 10−28 a	⋅⋅⋅	5.5 × 10−26	2.5 × 10−7	1.9 × 1031	120
J1730−2304	123.11	246.22	−3.1 × 10−16	0.5	2.5 × 10−27	5.8 × 10−26	4.5 × 10−26	3.6 × 10−7	2.8 × 1031	18
J1731−1847	426.52	853.04	−4.6 × 10−15	4.0	6.6 × 10−28	⋅⋅⋅	1.3 × 10−25	6.6 × 10−7	5.1 × 1031	190
J1732−5049	188.23	376.47	−5.0 × 10−16	1.8	7.3 × 10−28	5.3 × 10−26	4.6 × 10−26	5.6 × 10−7	4.3 × 1031	63
J1738+0333	170.94	341.87	−6.7 × 10−16	2.0	8.1 × 10−28 a	⋅⋅⋅	1.1 × 10−25	1.8 × 10−6	1.4 × 1032	140
J1741+1351	266.87	533.74	−2.2 × 10−15	1.4	1.6 × 10−27	⋅⋅⋅	1.1 × 10−25	5.1 × 10−7	3.9 × 1031	67
J1744−1134	245.43	490.85	−4.3 × 10−16	0.4	2.5 × 10−27 a	1.1 × 10−25	6.3 × 10−26	1.0 × 10−7	8.0 × 1030	25
J1745−0952	51.61	103.22	−7.6 × 10−17	2.4	4.1 × 10−28 a	⋅⋅⋅	6.0 × 10−26	1.3 × 10−5	9.8 × 1032	150
J1748−2446A	86.48	172.96	−1.4 × 10−15	5.5	5.8 × 10−28 b	3.9 × 10−26	3.2 × 10−26	5.6 × 10−6	4.3 × 1032	55
J1748−2446C	118.54	237.08	−1.9 × 10−15	5.5	5.8 × 10−28 b	5.0 × 10−26	3.8 × 10−26	3.5 × 10−6	2.7 × 1032	65
J1748−2446D	212.14	424.27	−3.4 × 10−15	5.5	5.8 × 10−28 b	6.8 × 10−26	5.3 × 10−26	1.5 × 10−6	1.2 × 1032	91
J1748−2446E	455.00	910.00	−7.2 × 10−15	5.5	5.8 × 10−28 b	9.0 × 10−26	7.3 × 10−26	4.6 × 10−7	3.6 × 1031	130
J1748−2446F	180.50	361.00	−2.9 × 10−15	5.5	5.8 × 10−28 b	8.3 × 10−26	7.4 × 10−26	3.0 × 10−6	2.3 × 1032	130
J1748−2446G	46.14	92.29	−7.3 × 10−16	5.5	5.8 × 10−28 b	5.9 × 10−26	4.5 × 10−26	2.8 × 10−5	2.1 × 1033	78
J1748−2446H	203.01	406.02	−3.2 × 10−15	5.5	5.8 × 10−28 b	7.8 × 10−26	5.8 × 10−26	1.8 × 10−6	1.4 × 1032	99
J1748−2446I	104.49	208.98	−1.7 × 10−15	5.5	5.8 × 10−28 b	3.6 × 10−26	3.7 × 10−26	4.5 × 10−6	3.4 × 1032	64
J1748−2446K	336.74	673.48	−5.3 × 10−15	5.5	5.8 × 10−28 b	6.8 × 10−26	5.9 × 10−26	6.8 × 10−7	5.3 × 1031	100
J1748−2446L	445.49	890.99	−7.1 × 10−15	5.5	5.8 × 10−28 b	1.4 × 10−25	1.1 × 10−25	7.5 × 10−7	5.8 × 1031	200
J1748−2446M	280.15	560.29	−4.4 × 10−15	5.5	5.8 × 10−28 b	1.0 × 10−25	9.5 × 10−26	1.6 × 10−6	1.2 × 1032	160
J1748−2446N	115.38	230.76	−1.8 × 10−15	5.5	5.8 × 10−28 b	5.8 × 10−26	6.4 × 10−26	6.3 × 10−6	4.8 × 1032	110
J1748−2446O	596.44	1192.87	−9.4 × 10−15	5.5	5.8 × 10−28 b	2.6 × 10−25	2.6 × 10−25	9.6 × 10−7	7.4 × 1031	450
J1748−2446P f	578.50	1157.00	−8.7 × 10−14	5.5	5.8 × 10−28 b	1.6 × 10−25	⋅⋅⋅	6.1 × 10−7	4.8 × 1031	267
J1748−2446Q	355.64	711.29	−5.6 × 10−15	5.5	5.8 × 10−28 b	8.8 × 10−26	9.4 × 10−26	9.7 × 10−7	7.5 × 1031	160
J1748−2446R	198.86	397.73	−3.2 × 10−15	5.5	5.8 × 10−28 b	8.1 × 10−26	5.1 × 10−26	1.7 × 10−6	1.3 × 1032	87
J1748−2446S	163.49	326.98	−2.6 × 10−15	5.5	5.8 × 10−28 b	4.5 × 10−26	5.3 × 10−26	2.6 × 10−6	2.0 × 1032	91
J1748−2446T	141.15	282.29	−2.2 × 10−15	5.5	5.8 × 10−28 b	5.1 × 10−26	3.0 × 10−26	2.0 × 10−6	1.5 × 1032	52
J1748−2446U	304.03	608.06	−4.8 × 10−15	5.5	5.8 × 10−28 b	⋅⋅⋅	1.4 × 10−25	1.9 × 10−6	1.5 × 1032	230
J1748−2446V	482.51	965.02	−7.6 × 10−15	5.5	5.8 × 10−28 b	1.3 × 10−25	1.3 × 10−25	7.2 × 10−7	5.6 × 1031	220
J1748−2446W	237.80	475.60	−3.8 × 10−15	5.5	5.8 × 10−28 b	9.4 × 10−26	9.5 × 10−26	2.2 × 10−6	1.7 × 1032	160
J1748−2446X	333.42	666.83	−5.3 × 10−15	5.5	5.8 × 10−28 b	8.3 × 10−26	4.8 × 10−26	5.7 × 10−7	4.4 × 1031	83
J1748−2446Y	488.24	976.49	−7.7 × 10−15	5.5	5.8 × 10−28 b	2.1 × 10−25	2.1 × 10−25	1.2 × 10−6	9.0 × 1031	370
J1748−2446Z	406.08	812.15	−6.4 × 10−15	5.5	5.8 × 10−28 b	8.5 × 10−26	8.6 × 10−26	6.8 × 10−7	5.2 × 1031	150
J1748−2446aa	172.77	345.54	−2.7 × 10−15	5.5	5.8 × 10−28 b	2.3 × 10−25	1.5 × 10−25	6.6 × 10−6	5.1 × 1032	260
J1748−2446ab	195.32	390.65	−3.1 × 10−15	5.5	5.8 × 10−28 b	4.7 × 10−26	4.0 × 10−26	1.4 × 10−6	1.1 × 1032	69
J1748−2446ac	196.58	393.17	−3.1 × 10−15	5.5	5.8 × 10−28 b	7.2 × 10−26	5.6 × 10−26	1.9 × 10−6	1.5 × 1032	97
J1748−2446ad f	716.36	1432.70	1.7 × 10−14	5.5	5.8 × 10−28 b	1.8 × 10−25	⋅⋅⋅	4.5 × 10−7	3.5 × 1031	300
J1748−2446ae	273.33	546.66	−4.3 × 10−15	5.5	5.8 × 10−28 b	6.6 × 10−26	6.8 × 10−26	1.2 × 10−6	9.2 × 1031	120
J1748−2446af	302.63	605.26	−4.8 × 10−15	5.5	5.8 × 10−28 b	1.1 × 10−25	6.0 × 10−26	8.5 × 10−7	6.5 × 1031	100
J1748−2446ag	224.82	449.64	−3.6 × 10−15	5.5	5.8 × 10−28 b	9.4 × 10−26	5.1 × 10−26	1.3 × 10−6	1.0 × 1032	87
J1748−2446ah	201.40	402.81	−3.2 × 10−15	5.5	5.8 × 10−28 b	5.5 × 10−26	4.0 × 10−26	1.3 × 10−6	10.0 × 1031	69
J1748−2446ai	47.11	94.21	−7.5 × 10−16	5.5	5.8 × 10−28 b	⋅⋅⋅	1.6 × 10−25	9.2 × 10−5	7.1 × 1033	270
J1751−2857	255.44	510.87	−7.3 × 10−16	1.4	9.5 × 10−28	⋅⋅⋅	6.8 × 10−26	3.6 × 10−7	2.8 × 1031	72
J1756−2251	35.14	70.27	−1.3 × 10−15	2.9	1.7 × 10−27	9.7 × 10−26	7.4 × 10−26	4.1 × 10−5	3.2 × 1033	45
J1757−5322 e	112.74	225.48	−3.3 × 10−16	1.4	1.0 × 10−27	3.7 × 10−25	⋅⋅⋅	9.4 × 10−6	7.3 × 1032	360
J1801−1417	275.85	551.71	3.1 × 10−16	1.8	4.8 × 10−28 a	6.2 × 10−26	7.3 × 10−26	4.1 × 10−7	3.1 × 1031	150
J1801−3210	134.16	268.33	1.8 × 10−17	5.0	5.8 × 10−29	⋅⋅⋅	3.5 × 10−26	2.3 × 10−6	1.8 × 1032	610
J1802−2124	79.07	158.13	−4.4 × 10−16	3.3	5.7 × 10−28 a	⋅⋅⋅	4.7 × 10−26	6.0 × 10−6	4.6 × 1032	83
J1803−30	140.82	281.63	−2.2 × 10−15	7.8	4.1 × 10−28 b	5.5 × 10−26	4.1 × 10−26	3.8 × 10−6	3.0 × 1032	100
J1804−0735	43.29	86.58	−6.9 × 10−16	8.4	3.8 × 10−28 b	8.4 × 10−26	8.8 × 10−26	9.4 × 10−5	7.2 × 1033	230
J1804−2717	107.03	214.06	−4.7 × 10−16	1.2	1.4 × 10−27	2.4 × 10−26	2.2 × 10−26	5.3 × 10−7	4.1 × 1031	15
J1807−2459A	326.86	653.71	−5.2 × 10−15	2.7	1.2 × 10−27 b	1.5 × 10−25	9.6 × 10−26	5.8 × 10−7	4.5 × 1031	81
J1810+1744	601.41	1202.82	−1.6 × 10−15	2.5	5.3 × 10−28	⋅⋅⋅	1.8 × 10−25	2.9 × 10−7	2.3 × 1031	340
J1810−2005	30.47	60.93	−5.0 × 10−17	4.0	2.6 × 10−28 a	2.2 × 10−25	1.6 × 10−25	1.6 × 10−4	1.3 × 1034	630
J1811−2405	375.86	751.71	−1.9 × 10−15	1.7	1.1 × 10−27	⋅⋅⋅	8.5 × 10−26	2.4 × 10−7	1.9 × 1031	80
J1823−3021A	183.82	367.65	−2.9 × 10−15	7.9	4.1 × 10−28 b	4.0 × 10−26	3.5 × 10−26	1.9 × 10−6	1.5 × 1032	86
J1824−2452A	327.41	654.81	−1.7 × 10−13	5.5	3.4 × 10−27 a	7.9 × 10−26	5.5 × 10−26	6.7 × 10−7	5.2 × 1031	16
J1824−2452B f	152.75	305.50	5.6 × 10−15	5.5	5.8 × 10−28 b	4.2 × 10−26	⋅⋅⋅	2.3 × 10−6	1.8 × 1032	72
J1824−2452C f	240.48	480.96	−9.8 × 10−15	5.5	5.8 × 10−28 b	6.6 × 10−26	⋅⋅⋅	1.5 × 10−6	1.2 × 1032	110
J1824−2452E f	184.53	369.06	3.7 × 10−15	5.5	5.8 × 10−28 b	7.5 × 10−26	⋅⋅⋅	2.9 × 10−6	2.2 × 1032	130
J1824−2452F f	407.97	815.94	−1.6 × 10−15	5.5	5.8 × 10−28 b	9.8 × 10−26	⋅⋅⋅	7.6 × 10−7	5.9 × 1031	170
J1824−2452G f	169.23	338.46	−5.2 × 10−15	5.5	5.8 × 10−28 b	7.3 × 10−26	⋅⋅⋅	3.3 × 10−6	2.6 × 1032	130
J1824−2452H f	216.01	432.02	−3.6 × 10−15	5.5	5.8 × 10−28 b	8.2 × 10−26	⋅⋅⋅	2.3 × 10−6	1.8 × 1032	140
J1824−2452I g	254.33	508.67	−5.4 × 10−15	5.5	5.8 × 10−28 b	2.2 × 10−25	⋅⋅⋅	4.4 × 10−6	3.4 × 1032	370
J1824−2452J f	247.54	495.08	4.7 × 10−15	5.5	5.8 × 10−28 b	1.1 × 10−25	⋅⋅⋅	2.3 × 10−6	1.7 × 1032	180
J1841+0130	33.59	67.18	−9.2 × 10−15	3.2	4.2 × 10−27	1.6 × 10−25	1.3 × 10−25	8.7 × 10−5	6.7 × 1033	31
J1843−1113	541.81	1083.62	−2.8 × 10−15	2.0	9.3 × 10−28	1.6 × 10−25	1.1 × 10−25	1.8 × 10−7	1.4 × 1031	120
J1853+1303	244.39	488.78	−5.1 × 10−16	1.6	7.3 × 10−28 a	⋅⋅⋅	8.5 × 10−26	5.4 × 10−7	4.2 × 1031	120
J1857+0943	186.49	372.99	−6.1 × 10−16	0.9	1.6 × 10−27 a	7.3 × 10−26	5.7 × 10−26	3.5 × 10−7	2.7 × 1031	35
J1903+0327	465.14	930.27	−3.8 × 10−15	6.5	3.6 × 10−28 a	⋅⋅⋅	1.6 × 10−25	1.1 × 10−6	8.8 × 1031	450
J1905+0400	264.24	528.48	−2.8 × 10−16	1.3	6.3 × 10−28 a	7.4 × 10−26	5.0 × 10−26	2.3 × 10−7	1.8 × 1031	80
J1909−3744	339.32	678.63	−1.9 × 10−16	1.3	4.7 × 10−28 a	8.2 × 10−26	5.9 × 10−26	1.5 × 10−7	1.2 × 1031	120
J1910+1256	200.66	401.32	−3.4 × 10−16	1.9	5.4 × 10−28 a	⋅⋅⋅	7.7 × 10−26	8.8 × 10−7	6.8 × 1031	140
J1910−5959A	306.17	612.33	−1.9 × 10−16	4.5	1.4 × 10−28 a	7.7 × 10−26	5.5 × 10−26	6.2 × 10−7	4.8 × 1031	390
J1910−5959B	119.65	239.30	−1.9 × 10−15	4.5	7.1 × 10−28 b	3.8 × 10−26	2.5 × 10−26	1.9 × 10−6	1.4 × 1032	35
J1910−5959C	189.49	378.98	1.1 × 10−18	4.5	1.4 × 10−29 a	4.4 × 10−26	3.2 × 10−26	9.5 × 10−7	7.4 × 1031	2300
J1910−5959D	110.68	221.35	−1.8 × 10−15	4.5	7.1 × 10−28 b	3.1 × 10−26	2.1 × 10−26	1.8 × 10−6	1.4 × 1032	29
J1910−5959E	218.73	437.47	−3.5 × 10−15	4.5	7.1 × 10−28 b	4.8 × 10−26	3.6 × 10−26	8.0 × 10−7	6.1 × 1031	50
J1911+0101A e	276.36	552.71	5.0 × 10−16	7.4	4.3 × 10−28 b	6.0 × 10−25	⋅⋅⋅	1.4 × 10−5	1.1 × 1033	1400
J1911+0101B e	185.72	371.45	6.9 × 10−17	7.4	4.3 × 10−28 b	7.4 × 10−25	⋅⋅⋅	3.8 × 10−5	2.9 × 1033	1700
J1911+1347	216.17	432.34	−7.9 × 10−16	1.6	9.6 × 10−28	7.0 × 10−26	4.8 × 10−26	3.9 × 10−7	3.0 × 1031	50
J1911−1114	275.81	551.61	−4.7 × 10−16	1.6	6.7 × 10−28 a	5.7 × 10−26	6.3 × 10−26	3.1 × 10−7	2.4 × 1031	94
J1918−0642	130.79	261.58	−4.0 × 10−16	1.4	1.0 × 10−27 a	⋅⋅⋅	4.0 × 10−26	7.7 × 10−7	6.0 × 1031	39
J1939+2134	641.93	1283.86	−4.3 × 10−14	5.0	1.3 × 10−27 a	1.8 × 10−25	1.3 × 10−25	3.6 × 10−7	2.8 × 1031	96
J1944+0907	192.86	385.71	−3.6 × 10−16	1.3	8.6 × 10−28 a	⋅⋅⋅	5.5 × 10−26	4.4 × 10−7	3.4 × 1031	64
J1955+2908	163.05	326.10	−7.5 × 10−16	5.4	3.2 × 10−28 a	7.0 × 10−26	5.4 × 10−26	2.6 × 10−6	2.0 × 1032	170
J1959+2048	622.12	1244.24	−4.4 × 10−15	1.5	1.4 × 10−27 a	⋅⋅⋅	1.5 × 10−25	1.4 × 10−7	1.1 × 1031	110
J2007+2722	40.82	81.64	−1.6 × 10−15	6.8	7.4 × 10−28	⋅⋅⋅	7.1 × 10−26	6.9 × 10−5	5.3 × 1033	96
J2010−1323	191.45	382.90	−1.8 × 10−16	1.3	6.0 × 10−28	⋅⋅⋅	6.3 × 10−26	5.2 × 10−7	4.0 × 1031	100
J2017+0603	345.28	690.56	−9.6 × 10−16	1.3	1.0 × 10−27	⋅⋅⋅	1.3 × 10−25	3.4 × 10−7	2.6 × 1031	130
J2019+2425	254.16	508.32	−1.7 × 10−16	0.9	7.2 × 10−28 a	9.2 × 10−26	5.6 × 10−26	1.9 × 10−7	1.4 × 1031	79
J2033+17	168.10	336.19	−2.3 × 10−16	1.4	6.8 × 10−28 a	7.5 × 10−26	8.0 × 10−26	9.2 × 10−7	7.1 × 1031	120
J2043+1711	420.19	840.38	−7.3 × 10−16	1.1	9.4 × 10−28 a	⋅⋅⋅	7.3 × 10−26	1.1 × 10−7	8.5 × 1030	78
J2051−0827	221.80	443.59	−6.1 × 10−16	1.3	1.0 × 10−27 a	7.5 × 10−26	5.3 × 10−26	3.3 × 10−7	2.5 × 1031	51
J2124−3358	202.79	405.59	−4.4 × 10−16	0.3	4.0 × 10−27 a	4.9 × 10−26	3.9 × 10−26	6.7 × 10−8	5.2 × 1030	9.9
J2129−5721	268.36	536.72	−1.5 × 10−15	0.4	4.7 × 10−27 a	6.2 × 10−26	5.2 × 10−26	6.8 × 10−8	5.3 × 1030	11
J2140−2310A	90.75	181.50	−1.4 × 10−15	9.2	3.5 × 10−28 b	⋅⋅⋅	5.9 × 10−26	1.6 × 10−5	1.2 × 1033	170
J2145−0750	62.30	124.59	−1.0 × 10−16	0.6	1.8 × 10−27 a	3.8 × 10−26	2.9 × 10−26	1.0 × 10−6	7.9 × 1031	16
J2214+3000	320.59	641.18	−1.5 × 10−15	1.3	1.3 × 10−27	⋅⋅⋅	7.2 × 10−26	2.2 × 10−7	1.7 × 1031	54
J2215+5135	383.20	766.40	−4.1 × 10−15	3.3	8.0 × 10−28	⋅⋅⋅	1.6 × 10−25	8.7 × 10−7	6.7 × 1031	200
J2229+2643	335.82	671.63	1.7 × 10−16	1.4	4.1 × 10−28 a	9.9 × 10−26	6.5 × 10−26	2.0 × 10−7	1.5 × 1031	160
J2241−5236	457.31	914.62	−1.4 × 10−15	0.7	2.1 × 10−27	⋅⋅⋅	8.9 × 10−26	6.9 × 10−8	5.3 × 1030	42
J2302+4442	192.59	385.18	−5.1 × 10−16	0.8	1.8 × 10−27	⋅⋅⋅	4.5 × 10−26	2.2 × 10−7	1.7 × 1031	26
J2317+1439	290.25	580.51	−1.3 × 10−16	1.9	2.8 × 10−28 a	8.8 × 10−26	5.6 × 10−26	3.0 × 10−7	2.3 × 1031	200
J2322+2057	207.97	415.94	−1.8 × 10−16	0.8	9.6 × 10−28 a	1.1 × 10−25	5.4 × 10−26	2.3 × 10−7	1.8 × 1031	57

Notes. Detector calibration errors mean that for pulsars with f_gw below and above 50 Hz there are ∼6% and ∼20% uncertainties on these limits respectively. ^aThe pulsar's spin-down is corrected for proper motion effects. ^bThe pulsar's spin-down is calculated using a characteristic spin-down age of 10⁹ yr. ^cThe pulsar's distance is calculated using the NE2001 model of Cordes & Lazio (2002). ^dRecently discovered pulsar with timing solution from after the end of S6 or VSR4. As this is an MSP the timing solution should extrapolate back well over the search period and it is unlikely that any glitches occurred. ^eResults from S3/S4 (Abbott et al. 2007a). ^fResults from S5 (Abbott et al. 2010). ^gNew result from S5 using data covering 2006.

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