Discovery of gamma and X-ray pulsations from the young and energetic PSR J13576429 with Fermi and XMM-Newton
Key Words.:pulsar, pulsar wind nebula, PSR J13576429
Context:Since the launch of the Fermi satellite, the number of known gamma-ray pulsars has increased tenfold. Most gamma-ray detected pulsars are young and energetic, and many are associated with TeV sources. PSR J13576429 is a high spin-down power pulsar ( erg/s), discovered during the Parkes multibeam survey of the Galactic plane, with significant timing noise typical of very young pulsars. In the very-high-energy domain (E 100 GeV), H.E.S.S. has reported the detection of the extended source HESS J1356645 (intrinsic Gaussian width of 12’) whose centroid lies 7’ from PSR J13576429.
Aims:We search for gamma and X-ray pulsations from this pulsar, characterize the neutron star emission and explore the environment of PSR J13576429.
Methods:Using a rotational ephemeris obtained with 74 observations made with the Parkes telescope at 1.4 GHz, we phase-fold more than two years of gamma-ray data acquired by the Large Area Telescope aboard Fermi as well as those collected with XMM-Newton, and perform gamma-ray spectral modeling.
Results:Significant gamma and X-ray pulsations are detected from PSR J13576429. The light curve in both bands shows one broad peak. Gamma-ray spectral analysis of the pulsed emission suggests that it is well described by a simple power-law of index with an exponential cut-off at GeV and an integral photon flux above 100 MeV of () cm s. The X-ray spectra obtained from the new data provide results consistent with those reported by Zavlin (2007). Upper limits on the gamma-ray emission from its potential pulsar wind nebula (PWN) are also reported.
Conclusions:Assuming a distance of 2.4 kpc, the Fermi LAT energy flux yields a gamma-ray luminosity for PSR J13576429 of erg s, consistent with an relationship. The Fermi non-detection of the pulsar wind nebula associated with HESS J1356645 provides new constraints on the electron population responsible for the extended TeV emission.
Since the launch of the Fermi Gamma-ray Space Telescope, the number of known gamma-ray pulsars has increased dramatically. The first Fermi Large Area Telescope (LAT) catalog of pulsars (Abdo et al., 2010a) also marks the birth of new classes of gamma-ray pulsars, such as millisecond (Abdo et al., 2009a) and radio-faint gamma-ray pulsars (Abdo et al., 2009b). The rest are young pulsars, discovered via an efficient collaboration among gamma-ray, radio and X-ray astronomers. Interestingly, many of the detected pulsars are found to be powering pulsar wind nebulae (PWN), and some are associated with TeV sources.
PSR J13576429 is a very young, energetic pulsar discovered during the Parkes multibeam survey of the Galactic plane, as reported in Camilo et al. (2004). From its dispersion measure of () , the NE2001 model of the Galactic electron distribution (Cordes & Lazio, 2002) assigns PSR J13576429 a distance of kpc. With a spin period of ms and a period derivative of , the characteristic age is yr.
No EGRET source is coincident with PSR J13576429. Recently, Very Large Telescope data were used to search for optical emission from PSR J13576429 (Mignani et al., 2011). No counterpart was found, and an upper limit of V was determined. Using X-ray Chandra data collected in 2005, Zavlin (2007) reported a hint of pulsed emission using an accurate, contemporaneous radio rotation ephemeris. While of low significance (2–3), it is nevertheless more compelling than the non-detection of pulsations reported by Esposito et al. (2007), who folded the same data with an older ephemeris as a starting point to scan for a rotation period for which X-ray pulsations might appear. This pulsar’s timing noise imposes a large number of period trials, which in turn diminishes the significance of what was, at best, a weak signal. In this article, we confirm the detection using new XMM-Newton data from 2009.
PSR J13576429 was highlighted by Abdo et al. (2010a) because of the absence of gamma-ray pulsations, and might have become a candidate “gamma-faint” pulsar (Romani et al., 2011). Nearby, with a high spin-down power erg s, it has that is 1% of Vela’s, a threshold above which the LAT detects most pulsars. Here we show that the previous non-detection was due not to beaming or emission physics, but rather because the timing noise typical of very young pulsars made it difficult to construct an accurate rotation ephemeris after a large glitch early in the Fermi epoch. Once enough post-glitch radio observations had been obtained to build a phase-connected timing model, the gamma-ray pulsations became immediately apparent. We note that Pellizzoni et al. (2009) reported a weak detection with AGILE.
Very often, young and energetic pulsars are embedded in compact nebulae powered by relativistic pulsar winds.
Short X-ray observations were performed in 2005 with XMM-Newton and Chandra to search for X-ray emission from a PWN (Esposito et al., 2007; Zavlin, 2007). Using the XMM-Newton data, Esposito et al. (2007) found
marginal evidence of diffuse emission in the 2–4 keV energy band consisting of a faint elongated structure starting from PSR J13576429.
They also set a 3
upper limit on the luminosity of in the 2–10 keV range
on putative diffuse emission
using the Chandra data.
On the other hand, Zavlin (2007) reported the detection of tail-like emission associated with the pulsar with a 0.5–10 keV luminosity of
. In the very high energy domain (E 100 GeV), the H.E.S.S. data show significantly
extended emission (intrinsic Gaussian width of ) lying close to PSR J13576429 (Abramowski et al., 2011).
In this article, a GeV upper limit is derived on the emission from the possible PWN observed in the TeV band, providing new constraints on the leptonic population responsible for the very high energy emission.
2 LAT description and observations
The LAT is a gamma-ray telescope that detects photons by conversion into electron-positron pairs in the energy range between 20 MeV to more than 300 GeV, as described by Atwood et al. (2009). It is made of a high-resolution converter/tracker (for direction measurement of the incident gamma rays), a CsI(Tl) crystal calorimeter (for energy measurement) and an anti-coincidence detector to identify the background of charged particles. Compared to EGRET, the LAT has a larger effective area ( 8000 cm on-axis above 1 GeV), a broader field of view ( 2.4 sr) and superior angular resolution ( 0.6 68 containment at 1 GeV for events converting in the front section of the tracker). The on-orbit calibration is described in Abdo et al. (2009c).
The analysis used 29 months of data collected starting August 4, 2008, and extending until January 15, 2011. We selected events with energies greater than 0.1 GeV but excluded those with zenith angles larger than 100, to minimize contamination from secondary gamma-rays from the Earth’s atmosphere (Abdo et al., 2009d). We selected events in the Source class, as described in Atwood et al. (2009). Source events optimize the trade-off between gamma-ray detection efficiency and residual charged-particle contamination in a manner well-suited to localized, persistent sources, as distinct from the Transient or Diffuse classes. We used the most recent analysis version, called “Pass 7”, documented at the Fermi Science Support Center 111FSSC: http://fermi.gsfc.nasa.gov/ssc/data/.
3 Radio timing observations
As part of the space- and ground-based pulsar timing campaign supporting Fermi (Smith et al., 2008), the pulsar PSR J13576429 is being observed at the 64-m Parkes radio telescope (Weltevrede et al., 2010). A total of 74 observations spanning MJDs 54220 to 55575 were made in a band centred at MHz. In this band, the pulsar has a flux density of Jy (Camilo et al., 2004). Observations were made using the central beam of the 20 cm Multibeam Receiver (Staveley-Smith et al., 1996) and recorded using one of the digital filterbanks (DFBs) built by the Australia Telescope National Facility. The DFBs employed real time pulse phase folding to average data into second sub-integrations using MHz of total bandwidth. After calibration, pulse profiles for minute observations were cross correlated with a template to obtain times-of-arrival. The TEMPO2 timing package (Hobbs et al., 2006) was then used to build the timing solution, taking into account a significant glitch at MJD 54786 and strong timing noise prevalent in young pulsars. The glitch was modeled by including jumps in spin phase, spin frequency, and spin frequency derivative at the glitch epoch. Higher order spin frequency derivatives and harmonically related sinusoids (Hobbs et al 2004) were used to model the timing noise. The post-fit rms is 1.4 ms, or 0.8 % of a pulsar rotation. This timing solution will be made available through the FSSC.
4 X-ray observations and data reduction
XMM-Newton observed PSR J13576429 on October 14–15, 2009 with the EPIC-pn instrument operated in Small Window mode and two EPIC-MOS detectors in Full Window mode (for 55.5 and 78.1 ks effective exposures, respectively). The data were reprocessed and reduced with the XMM-Newton Science Analysis Software (SAS v. 11.0).
The pulsar was also observed on October 8–9, 2009 with the Chandra ACIS-I instrument operated in Timed Exposure (Very Faint) mode for a 59.2 ks effective exposure. The Chandra Interactive Analysis of Observations software (CIAO v. 4.3; the calibration database CALDB v. 4.4.3) was used to generate the “level 2” event file for this observation.
5 Analysis and results
5.1 Gamma- and X-ray Light Curves
PSR J13576429 is located below the Galactic plane where the diffuse gamma radiation is still intense. For the timing analysis, we took photons within a radius of with respect to the radio pulsar position (, ) using an energy-dependent cone of radius . This choice takes into account the instrument performance and maximizes the signal-to-noise ratio over a broad energy range (Atwood et al., 2009). The arrival times of events were corrected to the Solar System Barycenter using the JPL DE405 Solar System ephemeris (Standish, 1998), and the events were folded using the radio ephemeris from Parkes, using the TEMPO2 fermi plugin.
A total of 8707 gamma rays remain above 100 MeV in our energy-dependent circular region, and among them pulsed photons after background subtraction. We estimated the background level represented by the dashed horizontal line in Figure 1 (top panel) using two circular regions 1.5 from PSR J13576429 and at the same Galactic latitude. Nearby sources were avoided, and we normalized to the solid angle of the source region. An H-test value of 89.6 is obtained above 100 MeV, corresponding to a pulsed detection significance of 8 (de Jager & Büsching, 2010). Figure 1 shows the 25 bin gamma-ray light curve (top panel) as well as the 1.4 GHz radio profile (bottom panel) derived from observations with the Parkes radio telescope (Weltevrede et al., 2010). The gamma-ray peak is offset from the radio pulse by according to a Lorentzian fit with a full width at half maximum (FWHM) of . The first phase uncertainty arises from the gamma-ray fit. The uncertainty in DM of 0.5 pc cm causes an uncertainty in the extrapolation of the radio pulse time-of-arrival to infinite frequency of 0.01 in phase. There is no significant evolution of the gamma-ray peak with energy as can be seen from Figure 1 (middle panels). We defined the ‘off-pulse interval’ as the pulse minimum between 0.8 and 1.1 in phase.
Figure 1 also shows the pulse profile obtained from the XMM-Newton EPIC-pn data with 6 ms time resolution. For the timing analysis, 1543 events were extracted
(with 270 background counts) from a -radius circle centered at the pulsar position in the 0.5-2 keV range to maximize the signal-to-noise ratio. The
photons_plug.html TEMPO2 package was used to assign a phase to each selected photon. This allowed us to use the full complexity of the ephemeris parameters including those for the glitch mentioned in Section 3 in the timing model. Performing an unbinned maximum likelihood fit of the phases to a constant plus single Gaussian we obtained an intrinsic pulsed fraction of (accounting for the contribution of the diffuse emission surrounding the pulsar; see Section 5.2), with a Gaussian of width centered at phase . The H-test yields a value of corresponding to the probability of a chance occurrence in a single trial , or a 6.7 detection significance. The main contribution to the value comes from the fundamental and first harmonics, in accordance with the shape of the X-ray light curve with a single broad pulse. Such a pulse profile can be produced by a thermal radiation emitted from the neutron star surface (see Section 5.2). This result unambiguously confirms the previous evidence of pulsations found by Zavlin (2007) in the Chandra data taken in 2005.
5.2 Spatial and spectral analysis of the X-ray data
We used the XMM-Newton data from 2009 to derive the spectrum of PSR J13576429. Photons were extracted from a -radius circle centered at the pulsar position in the EPIC-pn and MOS data. Background was evaluted from similar regions in the vicinity of the pulsar. The estimated numbers of source counts are , and for the EPIC-pn, MOS1 and MOS2 data sets (respectively). The instrumental responses were generated with the SAS rmfgen and arfgen tools. The purely non-thermal interpretation of the pulsar’s X-ray emission can be most likely ruled out since the single power-law (PL) fit to the obtained spectra results in a best estimate of the hydrogen column density, cm, significantly lower than the value suggested by the pulsar dispersion measure, cm (see Zavlin (2007) for details). Adding a thermal component, blackbody (BB) or neutron star magnetized atmosphere model (NSA; see Zavlin (2009) for a review) yields reasonable values of and provides good fit quality (with –1; see Figure 2). Generally, the results derived with the two-component model fits to the new data are consistent with those reported in Zavlin (2007). For example, the NSA-plus-PL fit gives the estimate on the neutron star effective temperature K (assuming the standard star mass and radius km, and the distance kpc). The non-thermal component is well described by the PL model with a photon index and (unabsorbed) flux ergs cm s in 0.5–10 keV (this range is used for the estimates on all non-thermal fluxes below), whereas the hydrogen column density is = cm.
In addition to the results yielded by the new XMM-Newton observation, the Chandra ACIS-I data of 2009 reveal diffuse emission both surrounding PSR J13576429 and extending – from the pulsar in the north-east direction (see Figure 3). Despite the small number of counts () estimated in the elongated and bent feature (outlined with the dashed contour in Figure 3), its detection is significant at a 6.1 level. The spectrum of this feature, extracted with the CIAO tool specextract that yields both the spectra and instrumental responses, is fitted with a PL model of and unabsorbed flux ergs cm s. This confirms the earlier detection of a potential PWN reported by Zavlin (2007). The diffuse emission surrounding the pulsar (denoted with the elliptical contour in Figure 3, with the estimated number of source counts), is characterized by a PL spectrum of and ergs cm s. A detailed analysis of the detected nebula is outside the scope of this paper but see Chang et al. (2011) for more results on the X-ray PWN.
But it should be noted the diffuse emission is included in the extraction region used to derive the X-ray spectra from the XMM-Newton EPIC instruments. Therefore, a fraction of the non-thermal flux measured from the EPIC data is contributed by the PWN. This is clearly seen in Figure 4, showing the pulsar’s spectrum extracted from the -radius circle centered at its radio position in the Chandra ACIS-I data ( source counts; see Figure 3). While the thermal component (and the hydrogen column density) is well described by the NSA model yielded by the XMM-Newton data, the non-thermal component is fitted with a PL model of photon index and unabsorbed X-ray flux ergs cm s (with ; Figure 4). We note that the sum of the non-thermal fluxes estimated in the Chandra data for the pulsar, the surrounding emission and the elongated tail match well that derived from the XMM-Newton spectra.
Another interesting point to mention is that the elongation of the detected X-ray PWN, about to North-East, may indicate the direction of the pulsar’s proper motion (see also Mignani et al., 2011).
5.3 Fermi LAT spectra and phase-averaged flux
The phase-averaged spectrum of PSR J13576429 was obtained using gtlike, a maximum likelihood spectral analysis (Mattox et al., 1996) implemented in the Fermi Science Tools. This tool fits a source model to the data. The model includes the object under study as well as other gamma-ray sources in a region extending well beyond the LAT’s angular resolution. Sources near PSR J13576429 exceeding the background with statistical significance larger than are extracted from the Fermi LAT 2FGL catalog (Abdo et al., 2011). Galactic diffuse emission is modeled using the ring-hybrid model ring_2year_P76_v0.fits. The instrumental background and the extragalactic radiation are described by a single isotropic component with the spectral shape in the tabulated model isotrop_2year_P76_source_v0.txt. The likelihood tool gtlike further requires tables of the Instrument Response Functions (IRFs), which are the energy and direction dependent angular resolution, effective area, and energy resolution. We used the P7_V6 IRFs. These new models and their detailed description will be available through the FSSC.
Assuming a power-law with an exponential cut-off spectral shape, the best fit result is obtained for a spectral index of 1.5 0.3 0.3 with a cut-off at GeV and an integral photon flux above 100 MeV of (6.5 1.6 2.3) cm s. The integral energy flux is (1.9 0.2 0.8) MeV cm s. The first error is statistical, while the second represents our estimate of systematic effects as discussed below. To check the assumption of a cut-off energy in the spectrum, we have also fit the same dataset with a simple power-law. The spectral model using an exponential cut-off is better constrained with a difference between the log likelihoods of , disfavoring the power-law hypothesis. Figure 5 shows the spectral energy distribution of PSR J13576429 as seen by Fermi. The Fermi LAT spectral points were obtained by dividing the 100 MeV – 100 GeV range into 9 logarithmically-spaced energy bins and performing a maximum likelihood spectral analysis in each interval, assuming a power-law shape for the source. These points are overlaid with the exponentially cut off power law fit over the total energy range.
Two main systematic uncertainties can affect the LAT flux estimation for a point source: uncertainties on the Galactic diffuse background and on the effective area. The dominant uncertainty at low energy comes from the Galactic diffuse emission since PSR J13576429 is located only from the Galactic plane. By changing the normalization of the Galactic diffuse model artificially by % as done in Abdo et al. (2010c), we estimate the systematic error on the integrated flux of the pulsar to be 50% below 500 MeV, 20% between 500 MeV and 1 GeV, and 7% above 1 GeV. The second systematic is estimated by using modified IRFs whose effective areas bracket those of our nominal IRF. These ‘biased’ IRFs are defined by envelopes above and below the nominal energy dependence of the effective area by linearly connecting differences of (10%, 5%, 20%) at log(E) of (2, 2.75, 4), respectively. We combine the errors in quadrature to obtain our best estimate of the total systematic uncertainty at each energy, and propagate through to the fit model parameters.
As can be seen from Figure 5, no significant emission is detected above 4.5 GeV at the position of PSR J13576429. In very high energy gamma rays, the H.E.S.S. experiment has detected significant emission close to the pulsar and significantly extended with an intrinsic Gaussian width of . As a first search for unpulsed emission from the TeV source HESS J1356645, we fitted a Gaussian of to the data in the energy band 4.5 – 100 GeV where no pulsed emission is detected. No significant signal could be observed and we derived 95% Confidence Level (CL) upper limits on the flux in the 4 logarithmically-spaced energy bins between 4.5 and 100 GeV assuming a power-law shape for the source with fixed spectral index of . In a second step, we used the off-pulse data selecting photons in the 0.8 1.1 phase interval and fit the same Gaussian of to data in the whole energy band 100 MeV – 100 GeV. Again, no significant emission could be detected and we derived 95% CL upper limits on the flux in the 9 logarithmically-spaced energy bins (assuming the same spectral index). These upper limits are presented in Figure 5.
Johnston & Weisberg (2006) measured the polarization profiles for 14 young pulsars at Parkes. For PSR J13576429 the polarization position angle increases with a constant slope of across the radio pulse. In the simplest RVM scenario (Rotating Vector Model, Radhakrishnan & Cooke, 1969), , hence the angle between the magnetic axis and the line-of-sight is small, . The lack of an inflection in vs and the narrow range of the pulse make a full RVM fit unconstraining.
PSR J13576429’s gamma-ray profile resembles that of PSR J2229+6114 (Abdo et al., 2009e), PSR J0248+5832 (Theureau et al., 2011), and PSR J17183825 (Weltevrede et al., 2010) in having a single, wide peak offset from the radio pulse by a bit less than a half-rotation. The “Atlas” update by Romani & Watters (2010) provides gamma-ray profiles calculated for different emission models, over a coarse grid of inclination angles and , and for 4 gap widths approximated by the efficiency, . We find erg s and above 100 MeV, with the beaming correction factor as defined by Romani & Watters (2010). Two profiles therein resemble the data. They are for , , and and (adjacent plots in the coarse grid). This is consistent with small suggested by the RVM. For these geometries, the Atlas predicts , that is, a small correction to . This luminosity is within the distance-dominated scatter of the rule shown by Abdo et al. (2010a), with in units of erg s.
The new X-ray data collected from PSR J13576429 with XMM-Newton and Chandra in 2009 strongly suggest that the bulk of the pulsar flux at soft X-ray energies (below about 1.5 keV) is of thermal origin, making this pulsar the second youngest neutron star with a detected thermal component known at this time (see Zavlin (2007) for details). As the X-ray pulsed flux shown in Figure 1 is extracted in the 0.5-2 keV range, it mostly comes from thermal radiation. It explains the sine-like shape of the light curve with the single broad pulse that is characteristic of the majority of X-ray pulse profiles observed from pulsars with dominating thermal emission. It is also consistent with the phase shift between the pulses in the gamma-ray and X-ray fluxes — the pulses originate at different sites. The thermal component is emitted from the neutron star surface, whereas the high-energy radiation is generated far from the surface (e. g., in the pulsar magnetosphere). Yet the origin of the thermal component remains unclear. It may be emitted from a small hot area (polar caps) of a radius of 1–2 km on the pulsar’s surface,
as suggested by the interpretation involving the BB model, or from the entire surface as indicated by the fits with the NSA models. To discriminate between these two interpretations, one should model the pulsed flux, as has been done for X-rays detected from a number of millisecond pulsars (e.g., Zavlin & Pavlov, 1998; Bogdanov et al., 2008). This modeling should take into account the effects of the neutron star geometry (orientation of the pulsar spin and magnetic axes with respect the line of view), surface magnetic and temperature distributions, intrinsic properties (anisotropy) of the thermal emission, and the gravitational bending of photon trajectories near the star surface. If future X-ray observations provide much better photon statistics, such an analysis can be supported by phase-resolved spectroscopy and energy-resolved pulse modeling. At present, we can only speculate that the detected thermal flux is intrinsically anisotropic, as predicted by the atmosphere models, otherwise the effect of the gravitational bending would strongly suppress the pulsations.
PSR J13576429 also lies within the extended TeV source HESS J1356645, proposed as its associated PWN (Abramowski et al., 2011). No significant signal is detected using Fermi LAT data above 4.5 GeV, nor in the off-pulse interval below 4.5 GeV. In the context of the leptonic model proposed by Abramowski et al. (2011), our upper limits constrain the spectrum of the electron population responsible for the extended TeV emission. The best model reproducing both the radio, X-ray and TeV data as well as the non-detection by Fermi is obtained for a magnetic field of 4 G (similar to what is seen in other evolved TeV PWNe) and an electron spectrum characterized with a spectral index of 2.4, a minimum energy of 10 GeV, a cut-off energy of 100 TeV and a total energy of erg (Abramowski et al., 2011). This energy is only 10% of the total kinetic energy since birth of PSR J13576429, assuming an initial period of 80 ms.
Acknowledgements.The Fermi LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the LAT as well as scientific data analysis. These include the National Aeronautics and Space Administration and the Department of Energy in the United States, the Commissariat à l’Energie Atomique and the Centre National de la Recherche Scientifique / Institut National de Physique Nucléaire et de Physique des Particules in France, the Agenzia Spaziale Italiana, the Istituto Nazionale di Fisica Nucleare, and the Istituto Nazionale di Astrofisica in Italy, the Ministry of Education, Culture, Sports, Science and Technology (MEXT), High Energy Accelerator Research Organization (KEK) and Japan Aerospace Exploration Agency (JAXA) in Japan, and the K. A. Wallenberg Foundation and the Swedish National Space Board in Sweden. Additional support for science analysis during the operations phase from the following agencies is also gratefully acknowledged: the Instituto Nazionale di Astrofisica in Italy and the Centre National d’Études Spatiales in France.
The Parkes radio telescope is part of the Australia Telescope which is funded by the Commonwealth Government for operation as a National Facility managed by CSIRO. We thank our colleagues for their assistance with the radio timing observations.
VEZ is grateful to Nataliya Ivanova for discussions and support.
- Abdo et al. (2011) Abdo, A. A. et al., 2011, in prep. (2FGL catalog)
- Abdo et al. (2010a) Abdo, A. A. et al., 2010a, ApJS, 187, 460
- Abdo et al. (2010b) Abdo, A. A. et al., 2010b, ApJS, 188, 405
- Abdo et al. (2010c) Abdo, A. A. et al., 2010c, ApJ, 722, 1303
- Abdo et al. (2009a) Abdo, A. A. et al., 2009a, Science, 325, 848
- Abdo et al. (2009b) Abdo, A. A. et al., 2009b, Science, 325, 840
- Abdo et al. (2009c) Abdo, A. A. et al., 2009c, ApJ, 696, 1084
- Abdo et al. (2009d) Abdo, A. A. et al., 2009d, Phys. Rev. D, 80, 122004
- Abdo et al. (2009e) Abdo, A. A. et al., 2009e, ApJ, 706, 1331
- Abramowski et al. (2011) Abramowski, A., et al., A&A submitted (Detection of HESS J1356-645)
- Atwood et al. (2009) Atwood, W.B. et al., 2009, ApJ, 697, 1071
- Bogdanov et al. (2008) Bogdanov, S. et al., 2008, ApJ, 689, 407
- Camilo et al. (2004) Camilo, F. et al. 2004, ApJ, 611, L25
- Chang et al. (2011) Chang, C., Pavlov, G., Kargaltsev, O. ApJ submitted (arXiv:1107.1819)
- Cordes & Lazio (2002) Cordes, J. M. & Lazio, T. J. W., 2002, ArXiv e-prints, (arXiv:astro-ph/0207156)
- de Jager & Büsching (2010) de Jager, O. C. & Büsching, I., 2010, A&A, 517, L9
- Esposito et al. (2007) Esposito, P. et al. 2007, A&A, 467, L45
- Hobbs et al. (2006) Hobbs, G. B. et al., 2006, MNRAS, 369, 655
- Johnston & Weisberg (2006) Johnston, S. & Weisberg, J. M., 2006, MNRAS, 368, 1856
- Mattox et al. (1996) Mattox, J.R. et al., 1996, ApJ, 461, 396
- Mignani et al. (2011) Mignani et al 2011, A&A submitted
- Pellizzoni et al. (2009) Pellizzoni, A. et al. 2009, ApJ, 695, L115
- Radhakrishnan & Cooke (1969) Radhakrishnan, V. & Cooke, D. J. 1969, Astrophys. Lett., 3, 225
- Romani & Watters (2010) Romani, R. W. & Watters, K. P., 2010, ApJ, 714, 810
- Romani et al. (2011) Romani R., et al. 2011, ApJ, accepted (arXiv:1106.5762)
- Smith et al. (2008) Smith, D. A., et al. 2008, A&A, 492, 923
- Standish (1998) Standish, E. M., JPL Planetary and Lunar Ephemerides, DE405/LE405, Memo IOM 312.F-98-048 (1998)
- Staveley-Smith et al. (1996) Staveley-Smith, L., et al. 1996, PASA, 13, 243
- Theureau et al. (2011) Theureau, G. et al. 2011, A&A, 525, A94 ApJ, 695, 1289
- Weltevrede et al. (2010) Weltevrede, P. et al. 2010, ApJ, 708, 1426
- Weltevrede et al. (2010) Weltevrede, P. et al., 2010, PASA, 27, 64
- Zavlin & Pavlov (1998) Zavlin, V. E. & Pavlov, G.G., 1998, A&A, 329, 583
- Zavlin (2007) Zavlin, V. E. 2007, ApJ, 665, L143
- Zavlin (2009) Zavlin, V. E., 2009, in Neutron Stars and Pulsars, Astrophysics and Space Science Library (Springer), v. 357, p. 181