Einstein@Home Discovery of a Millisecond Pulsar in an Eccentric Binary Orbit

Einstein@Home Discovery of a PALFA Millisecond Pulsar in an Eccentric Binary Orbit

B. Knispel11affiliation: Leibniz Universität, Hannover, D-30167 Hannover, Germany 22affiliation: Max-Planck-Institut für Gravitationsphysik, Callinstr. 38, D-30167 Hannover, Germany $\dagger$$\dagger$affiliation: Email: benjamin.knispel@aei.mpg.de , A. G. Lyne33affiliation: Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, UK , B. W. Stappers33affiliation: Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, UK , P. C. C. Freire44affiliation: Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany , P. Lazarus44affiliation: Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany , B. Allen22affiliation: Max-Planck-Institut für Gravitationsphysik, Callinstr. 38, D-30167 Hannover, Germany 55affiliation: Physics Department, University of Wisconsin – Milwaukee, Milwaukee WI 53211, USA 11affiliation: Leibniz Universität, Hannover, D-30167 Hannover, Germany , C. Aulbert22affiliation: Max-Planck-Institut für Gravitationsphysik, Callinstr. 38, D-30167 Hannover, Germany , O. Bock22affiliation: Max-Planck-Institut für Gravitationsphysik, Callinstr. 38, D-30167 Hannover, Germany , S. Bogdanov66affiliation: Columbia Astrophysics Laboratory, Columbia University, New York, NY 10027, USA , A. Brazier77affiliation: Department of Astronomy and Center for Radiophysics and Space Research, Cornell University, Ithaca, NY 14853, USA 88affiliation: Cornell Center for Advanced Computing, Rhodes Hall, Cornell, University, Ithaca, NY 14853, USA , F. Camilo66affiliation: Columbia Astrophysics Laboratory, Columbia University, New York, NY 10027, USA , F. Cardoso99affiliation: Department of Physics and Astronomy, West Virginia University, Morgantown, WV 26506, USA , S. Chatterjee77affiliation: Department of Astronomy and Center for Radiophysics and Space Research, Cornell University, Ithaca, NY 14853, USA , J. M. Cordes77affiliation: Department of Astronomy and Center for Radiophysics and Space Research, Cornell University, Ithaca, NY 14853, USA , F. Crawford1010affiliation: Department of Physics and Astronomy, Franklin and Marshall College, Lancaster, PA 17604-3003, USA , J. S. Deneva1111affiliation: National Academies of Science, resident at the Naval Research Laboratory, Washington, DC 20375, USA , H.-B. Eggenstein22affiliation: Max-Planck-Institut für Gravitationsphysik, Callinstr. 38, D-30167 Hannover, Germany , H. Fehrmann22affiliation: Max-Planck-Institut für Gravitationsphysik, Callinstr. 38, D-30167 Hannover, Germany , R. Ferdman1212affiliation: Department of Physics, McGill University, Montreal, QC H3A 2T8, Canada , J. W. T. Hessels1313affiliation: ASTRON, Netherlands Institute for Radio Astronomy, Postbus 2, 7990 AA, Dwingeloo, The Netherlands 1414affiliation: Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands , F. A. Jenet1515affiliation: Center for Gravitational Wave Astronomy, University of Texas at Brownsville, TX 78520, USA , C. Karako-Argaman1212affiliation: Department of Physics, McGill University, Montreal, QC H3A 2T8, Canada , V. M. Kaspi1212affiliation: Department of Physics, McGill University, Montreal, QC H3A 2T8, Canada , J. van Leeuwen1313affiliation: ASTRON, Netherlands Institute for Radio Astronomy, Postbus 2, 7990 AA, Dwingeloo, The Netherlands 1414affiliation: Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands , D. R. Lorimer99affiliation: Department of Physics and Astronomy, West Virginia University, Morgantown, WV 26506, USA , R. Lynch1212affiliation: Department of Physics, McGill University, Montreal, QC H3A 2T8, Canada , B. Machenschalk22affiliation: Max-Planck-Institut für Gravitationsphysik, Callinstr. 38, D-30167 Hannover, Germany , E. Madsen1212affiliation: Department of Physics, McGill University, Montreal, QC H3A 2T8, Canada , M. A. McLaughlin99affiliation: Department of Physics and Astronomy, West Virginia University, Morgantown, WV 26506, USA , C. Patel1212affiliation: Department of Physics, McGill University, Montreal, QC H3A 2T8, Canada , S. M. Ransom1616affiliation: NRAO, Charlottesville, VA 22903, USA , P. Scholz1212affiliation: Department of Physics, McGill University, Montreal, QC H3A 2T8, Canada , X. Siemens55affiliation: Physics Department, University of Wisconsin – Milwaukee, Milwaukee WI 53211, USA , L. G. Spitler44affiliation: Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany , I. H. Stairs1717affiliation: Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road Vancouver, BC V6T 1Z1, Canada , K. Stovall1818affiliation: Department of Physics and Astronomy, University of New Mexico, NM, 87131, USA , J. K. Swiggum99affiliation: Department of Physics and Astronomy, West Virginia University, Morgantown, WV 26506, USA , A. Venkataraman1919affiliation: Arecibo Observatory, HC3 Box 53995, Arecibo, PR 00612, USA , R. S. Wharton77affiliation: Department of Astronomy and Center for Radiophysics and Space Research, Cornell University, Ithaca, NY 14853, USA , W. W. Zhu44affiliation: Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany 1717affiliation: Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road Vancouver, BC V6T 1Z1, Canada

We report the discovery of the millisecond pulsar (MSP) PSR J19502414 ( ms) in a binary system with an eccentric () 22-day orbit in Pulsar ALFA survey observations with the Arecibo telescope. Its companion star has a median mass of 0.3  and is most likely a white dwarf. Fully recycled MSPs like this one are thought to be old neutron stars spun-up by mass transfer from a companion star. This process should circularize the orbit, as is observed for the vast majority of binary MSPs, which predominantly have orbital eccentricities . However, four recently discovered binary MSPs have orbits with ; PSR J19502414 is the fifth such system to be discovered. The upper limits for its intrinsic spin period derivative and inferred surface magnetic field strength are comparable to those of the general MSP population. The large eccentricities are incompatible with the predictions of the standard recycling scenario: something unusual happened during their evolution. Proposed scenarios are a) initial evolution of the pulsar in a triple system which became dynamically unstable, b) origin in an exchange encounter in an environment with high stellar density, c) rotationally delayed accretion-induced collapse of a super-Chandrasekhar white dwarf, and d) dynamical interaction of the binary with a circumbinary disk. We compare the properties of all five known eccentric MSPs with the predictions of these formation channels. Future measurements of the masses and proper motion might allow us to firmly exclude some of the proposed formation scenarios.

Subject headings:
methods: data analysis, stars: neutron, pulsars: general, pulsars: individual (J1950+2414)

1. Introduction

Millisecond pulsars (MSPs; Backer et al., 1982) are thought to be old neutron stars (NS) spun up by mass accretion and transfer of angular momentum from a companion star (Radhakrishnan & Srinivasan, 1982; Alpar et al., 1982). The spin frequencies of these so-called “recycled” pulsars can range up to 716 Hz (Hessels et al., 2006; ATNF pulsar catalog, Manchester et al., 2005). The different evolutionary phases of these pulsars in binary systems and also the transitions between these phases have been recently observed in much more detail, though several major puzzles still remain. The binary system starts off as a low-mass X-ray binary in which a NS accretes matter from a companion star (Smarr & Blandford, 1976; Bildsten et al., 1997). The main emission from these system is X-rays from the hot accretion disk. These system can transition into an accreting X-ray MSP in a binary (Wijnands & van der Klis, 1998), in which matter is funnelled onto the neutron star’s surface and significant X-ray emission modulated by the NS spin is detected. After the accretion dies off, the NS can become “visible” as a radio MSP, powered by the rotation of the neutron star’s magnetic field (Tauris & Savonije, 1999; Stairs, 2004). In some cases, these systems are seen to switch on roughly year-long timescales between states as an LMXB and a radio MSP. For example, Archibald et al. (2009) showed that the radio MSP PSR J10230038 has turned on after a recent (10 yrs) LMXB phase; more recently this system changed back into an LMXB (Archibald et al., 2014; Patruno et al., 2014; Stappers et al., 2014). Similarly, LMXB/radio MSP state transitions have been shown for PSRs J18242452 and J12274853 (Papitto et al., 2013; Bassa et al., 2014; Roy et al., 2015). Together, these observations nicely demonstrate the basic recycling scenario; however, they have also raised new puzzles and shown that the details of the process are quite complex. It is also possible that these three aforementioned transitional MSP systems, all “redback” MSPs (Roberts, 2013), are not representative of the evolution of all types of MSPs and that these systems might not lead to recycled pulsars at all (Chen et al., 2013). As such, much remains to be understood in the formation of radio MSPs.

The recycling pathway results in highly circular orbits of the binary system through tidal forces acting during the year long accretion phase (Phinney & Kulkarni, 1994). Until 2008, this seemed true of all fully recycled MSPs. All binary pulsars with  Hz and  Hz s outside of globular clusters had orbital eccentricities between and (Manchester et al., 2005).These eccentricity limits do not apply to MSPs in globular clusters because their high stellar densities and resultant close stellar encounters can significantly increase the orbital eccentricity of a binary MSP after the end of the accretion phase (Rasio & Heggie, 1995; Heggie & Rasio, 1996) or even in some cases lead to exchange encounters. Indeed, several highly eccentric binary MSPs have been found in the Galactic globular cluster system (e.g., Ransom et al. (2005); see also the online catalog of globular cluster pulsars at http://www.naic.edu/~pfreire/GCpsr.html).

In 2008, the situation changed with the discovery of PSR J19030327. This fast-spinning MSP ( ms) in an eccentric orbit () with a main-sequence star (Champion et al., 2008) cannot have formed through the “normal” binary evolution described above. Rather, it is believed to have originated from a hierarchical triple that became dynamically unstable (Freire et al., 2011; Portegies Zwart et al., 2011; Pijloo et al., 2012).

Soon afterwards, Bailes (2010) reported an “anomalous” orbital eccentricity of 0.027 for PSR J16183921 (Bailes; private communication), a MSP first reported in Edwards & Bailes (2001). More recently, Deneva et al. (2013) and Barr et al. (2013) reported the discovery of two more unusual binary MSP systems PSR J223406 () and PSR J19463417 (). These three systems are fully recycled with spin periods between 3 and 12 ms, orbital periods from 22 to 32 days and median companion masses ; i.e., apart from the large orbital eccentricity all parameters are compatible with the canonical recycling formation channel leading to a MSP with a white dwarf (WD) companion as described above.

These unusual orbital eccentricities require a non-standard formation channel. Like PSR J1903+0327, they could have formed in a triple system which later became unstable and ejected the outer (tertiary) companion. In fact, fully recycled MSPs can form in stable triple systems, as shown by the discovery of PSR J03371715, the first MSP in a stellar triple system with two white dwarf companions (Ransom et al., 2014; Tauris & van den Heuvel, 2014).

However, the chaotic disruption of a triple system would most likely not lead to the formation of MSPs with very similar orbital and spin characteristics as discussed above. These similarities suggest instead a more orderly mechanism with a more predictable outcome.

A possibility for such a mechanism was proposed by Freire & Tauris (2014). They suggest these systems formed through an accretion-induced collapse (AIC) of a super-Chandrasekhar mass oxygen-neon-magnesium white dwarf in a close binary. This star initially avoids AIC due to its rapid rotation. Only after the end of the accretion episode, and after the WD loses sufficient spin angular momentum, does it undergo AIC to directly produce an MSP in an eccentric orbit. A second possibility was suggested by Antoniadis (2014): here the MSPs form through the usual channel, but the orbital eccentricity arises from the dynamical interaction with a circumbinary disk. This disk may form from donor material ejected during hydrogen-shell flash episodes. Antoniadis (2014) shows that even a short-lived disk can produce eccentricities as large as .

Here we present the discovery and initial timing of the binary MSP PSR J19502414 in Pulsar ALFA (PALFA) survey data obtained at 1.4 GHz with the Arecibo telescope. This is the fifth eccentric MSP in the Galactic field to be discovered; its orbital and spin parameters are similar to those of PSR J223406 and PSR J19463417.

First, we will briefly describe the PALFA survey, the Einstein@Home project and its analysis of PALFA survey data, and the discovery of PSR J19502414. We then describe the timing observations, data reduction, and timing solution, followed by a discussion of PSR J19502414. We discuss our discovery in the context of different possible formation channels for MSPs in eccentric binaries. We conclude with an overview of future studies of this pulsar system and how they might allow us to exclude some of the possible formation channels.

1.1. The PALFA Survey

The PALFA Survey (Cordes et al., 2006) was proposed and is managed by the PALFA Consortium. It consists of about 40 researchers (including students) at about ten institutions worldwide111http://www2.naic.edu/alfa/pulsar/.

At Arecibo Observatory, the PALFA Consortium uses the Arecibo L-band Feed Array (ALFA222http://www.naic.edu/alfa/). The output of the seven ALFA beams is fed into the Mock spectrometers333Details of the Mock spectrometers may be found on the following NAIC web page: http://www.naic.edu/~phil/hardware/pdev/pdev.html. The observing band of 322.6 MHz is split into two overlapping bands with bandwidths of 172.0625 MHz each. The two sub-bands are centred at 1300.1680 MHz and 1450.1680 MHz, respectively. A total of 960 frequency channels is used, generated by polyphase filterbanks to enable the correction of radio pulse dispersion in the interstellar medium. Spectra are sampled every 65.4762 s.

The PALFA survey setup (high observation frequency, large number of filterbank channels, fast-sampling spectrometers) is chosen to maximize the chances of discovering MSPs at large distances within the Galactic plane, where previous surveys have had little to no sensitivity to MSPs. At the same time, the detection of these objects has been difficult because of their high values of dispersion measure (DM), which induce high dispersive smearing per channel. The narrow channels used in the PALFA survey address this issue. Finding many MSPs is the highest priority in this survey because of their wide range of astrophysical applications: testing Einstein’s theory of general relativity and alternative theories of gravity (Antoniadis et al., 2013), measuring NS masses (Demorest et al., 2010), which can strongly constrain the equation of state of dense matter, finding suitable sources for pulsar timing arrays (Hobbs et al., 2010), which will be used for detection of very low-frequency gravitational waves, improved estimates of the Galactic MSP population (Swiggum et al., 2014), and – in the case of PSR J19502414 and similar systems – a better understanding of stellar and NS formation and evolution. PALFA discoveries are proof of the power of the survey to discover MSPs at high DMs (Champion et al., 2008; Knispel et al., 2010, 2011; Crawford et al., 2012; Deneva et al., 2012).

Since its first observations in 2004, the PALFA Consortium has been surveying the part of the sky close to the Galactic plane () that is visible to Arecibo Observatory, i.e., declinations . The complete survey of this sky area will require about 330,000 separate Arecibo beams (equivalent to 47,000 pointings of the seven-beam ALFA receiver).

Data from the PALFA survey are analyzed by the Einstein@Home pipeline briefly described below and also by an independent pipeline operating on a supercomputer at McGill University using the PRESTO software package444https://github.com/scottransom/presto (Lazarus et al., in prep.).

1.2. Einstein@Home

Einstein@Home555http://einsteinathome.org is a distributed volunteer computing project (Anderson et al., 2006). Members of the public donate otherwise unused compute cycles on their home and/or office PCs, and Android devices to the project to enable blind searches for unknown NS.

Einstein@Home is one of the largest distributed computing projects. In the last ten years since its launch, more than 390,000 volunteers have contributed to the project. On average, about 46,000 different volunteers donate computing time each week on roughly 105,000 different hosts666http://einsteinathome.org/server_status.html as of early April 2015. The sustained computing power provided by these volunteers is currently of order 1.75 PFlop s, which is 5% the computing power of the world’s fastest supercomputer

Einstein@Home analyzes data from the LIGO gravitational-wave detectors, the Fermi Gamma-ray Space Telescope, and large radio telescopes such as the Arecibo Observatory and the Parkes Radio Telescope. Observational data are stored and prepared for Einstein@Home processing on the Atlas computer cluster at the Albert Einstein Institute in Hannover, Germany (Aulbert & Fehrmann, 2009). Volunteers’ computers download the data along with scientific software from dedicated servers in Hannover and Milwaukee, and run it automatically. The central coordination and management of the computing is handled by the Berkeley Open Infrastructure for Network Computing (BOINC; Anderson et al. (2006)).

The Einstein@Home PALFA analysis pipeline consists of three main steps. 1) Observational data are de-dispersed at 4,000 trial values to mitigate the radio pulse dispersion from the signal passing through the interstellar medium. Strong burst-like RFI is masked and periodic RFI is identified and replaced by random noise. Step 2) is done on the computers of the general public, attached to the project: each resulting de-dispersed time series is analyzed for periodic radio pulsar signals using Fourier methods. The Einstein@Home pipeline searches for radio pulsars in compact binary systems with orbital periods as short as 11 min. The required orbital demodulation to remove the Doppler effect from binary motion is done in the time domain. The demodulation is repeated for 7,000 different orbital configurations to cover a wide range of possible physical orbital parameters. For each of these, the Fourier analysis is repeated after the time-domain demodulation. The 100 statistically most significant candidates from each de-dispersed time series are stored and sent back to the project servers in Hannover. 3) The resulting 400,000 candidates for each beam are sifted and remaining candidates folded using the raw data and graded by machine learning methods (Zhu et al., 2014). Per-beam overview plots are also visually inspected to identify (of order a few) promising candidates in each beam.

A full description of the Einstein@Home radio pulsar search pipeline employed to discover PSR J19502414 is beyond the scope of this publication and is available in Allen et al. (2013). The sifting techniques used to reduce the number of relevant candidates are described in Knispel (2011); Knispel et al. (2013)

To date, the project has discovered 51 neutron stars through their radio emission. As part of the PALFA collaboration, Einstein@Home has discovered a total of 27 radio pulsars777All discoveries are available online at http://einsteinathome.org/radiopulsar/html/rediscovery_page/rediscoveries.html and http://einsteinathome.org/radiopulsar/html/BRP4_discoveries/, including the fastest spinning disrupted recycled pulsar (i.e., a pulsar ejected from a binary system due to the companion star’s supernova explosion; Knispel et al., 2010), and a relativistic intermediate-mass binary pulsar (Knispel et al., 2011; Lazarus et al., 2014). The Einstein@Home search for radio pulsars in archival data from the Parkes Radio Telescope has found 24 pulsars missed by several previous re-analyses of this data set (Knispel et al., 2013).

Einstein@Home has to date also discovered four gamma-ray pulsars in Fermi data (Pletsch et al., 2013). These ongoing searches use highly efficient data analysis methods initially conceived for gravitational-wave data analysis (Pletsch & Allen, 2009; Pletsch, 2010, 2011; Pletsch et al., 2012).

The detection of continuous gravitational waves from rotating neutron stars in data from ground-based interferometric detectors is the main, long-term goal of Einstein@Home. The project has provided the most stringent upper limits for gravitational waves from rapidly rotating neutron stars in blind searches to date (Abbott et al., 2009a, b; Aasi et al., 2013).

1.3. Discovery of PSR J19502414

PSR J19502414 was discovered by the Einstein@Home PALFA pipeline on 2011 October 4 with a statistical significance (negative decadic logarithm of the false-alarm probability in Gaussian noise) in a PALFA survey observation from 2009 April 4. The pulsar was found at a spin period of  ms and a DM of  pc cm. The signal’s celestial nature was confirmed the same day with a second observation by the Arecibo telescope.

2. Observations and Data Analysis

2.1. Observations

Following its discovery, PSR J19502414 was observed during the PALFA survey observing sessions and with dedicated observations by the 76-m Lovell telescope at Jodrell Bank.

The observations with the Arecibo telescope employed the usual PALFA survey set up as described in Section 1.1, using only the central beam of ALFA. The durations were between 4.5 mins and 15 mins. In total 24 PALFA survey observations of PSR J19502414 were carried out from 2011 October 5 until 2012 May 5.

Between 2012 September 21 and 2012 December 31, nine dedicated timing observations of PSR J19502414 were carried out as part of a PALFA millisecond pulsar timing campaign. Observations used the L-wide receiver and the Puerto-Rican Ultimate Pulsar Processing Instrument (PUPPI) backend. A frequency band of 800 MHz in 2048 channels, centered on a frequency of 1380 MHz was observed in all sessions. The usable bandwidth is limited by the L-wide receiver which delivers an observation bandwidth of 700 MHz from 1.1 GHz to 1.8 GHz. Observation times were 10 mins or 15 mins with a sampling time of 40.96 s.

The observations with the 76-m Lovell telescope used a cryogenically-cooled dual-polarization receiver at a central frequency of about 1520 MHz. A 512-MHz band was sampled at 8-bits resolution and processed using a digital filter bank into 2048 0.25-MHz frequency channels. After radio frequency interference excision, approximately 384 MHz of usable bandwidth remained. The data were folded into 1024 pulse phase bins and were de-dispersed, generating an average profile for each 10-second sub-integration. Observations of mostly 30 mins duration were made approximately every 10 days and the data set includes 61 TOAs from the MJD period 55851 to 56272.

2.2. Data reduction

Observational data were processed offline for radio frequency interference (RFI) mitigation, and to obtain times-of-arrival (TOAs).

The separate sub-band data files obtained with the PALFA Mock spectrometers were merged into one file in PSRFITS format for each observation. PUPPI data were written in separate PSRFITS files, each covering adjacent observation time stretches.

For RFI mitigation, the rfifind program from the PRESTO pulsar processing suite was used to generate an RFI mask for each observation.

Each observation was folded at the appropriate dispersion measure and topocentric spin period with the prepfold program from PRESTO. Folded data files were used to create summed pulse profiles from all ALFA/Mock spectrometer observations and all L-wide/PUPPI observations, respectively. Fig. 1 shows these pulse profiles, averaged over 25 observations with the Mock spectrometers and over ten observations with the PUPPI backend, respectively. The full width at half maximum duty cycle is 8%. This corresponds to a width of the pulse of  ms. The dispersive delay across a single frequency channel is 0.18 ms for the given DM, frequency resolution and central frequency. An exponential scattering tail is apparent in the folded pulse profile. Centered on a rotational phase of 0.65 a small additional pulse component appears in both the ALFA/Mock and L-wide/PUPPI observations.

Figure 1.— The averaged radio flux density pulse profiles from the data collected with Arecibo Observatory using the Mock spectrometers and the ALFA receiver (dark-grey line) and with the PUPPI backend and the L-wide receiver (black line), respectively. The averaged radio flux density pulse profile from observations at the Lovell Telescope in Jodrell Bank is shown (light-grey line). The spin period of the pulsar is  ms. These profiles were used to obtain the TOAs. All pulse profiles have been normalized and aligned at their maximum. The period-averaged flux density at 1.4 GHz is Jy.

We calibrate the profile using the radiometer equation (e.g., Lorimer & Kramer, 2012)


to predict the observing system’s noise level . We assume a system equivalent flux density  Jy for the L-wide receiver 888Table 3 in http://www.naic.edu/~astro/guide/guide.pdf. The combined observation bandwidth of L-wide with the PUPPI backend is  MHz. We used a pulse profile summed from nine individual observations, six of which with 9.8 mins duration and three with 14.9 mins duration. The summed pulse profile was folded into bins; then the expected off-pulse noise standard deviation used for calibration is 9.2 Jy. Scaling the off-pulse noise level of the observations (between pulse phases 0.73 and 1.07 in Fig. 1), the resulting estimated period-averaged flux density of the pulsar at 1.4 GHz is Jy.

The get_TOAs.py routine from PRESTO was used to extract TOAs by employing the sums of pulse profiles as templates. A single TOA was extracted for each ALFA/Mock spectrometer and L-wide/PUPPI observation, respectively. A total of 33 TOAs was extracted from the data obtained with the Arecibo telescope, 24 of which with the Mock spectrometer, the remaining 9 with the PUPPI backend.

The PSRCHIVE999http://psrchive.sourceforge.net package by Hotan et al. (2004) was used for the data inspection, interference removal and arrival time determination in the Lovell Telescope data. A single TOA was generated for each of the observations using a high signal-to-noise template formed from the observations.

The timing analysis used the TEMPO2 software (Hobbs et al., 2006). Our timing solution uses the BT orbital model (Blandford & Teukolsky, 1976; Edwards et al., 2006). The coherent solution fits 94 TOAs obtained between MJDs 55839 and 56293, covering a baseline of 454 days. As visible in Fig. 2, the timing model accurately predicts TOAs. There are no clear trends in the TOA residuals as a function of time, nor as a function of binary orbital phase. Constant time offsets between the three TOA data sets have been fitted with TEMPO2.

The weighted RMS of the timing residuals is 4.7 s when including TOAs from both observatories with all receivers and backends. The most precise TOAs are obtained with the PUPPI backend and the L-wide receiver at Arecibo. For an observation time of 15 mins, the TOAs have an average precision of 1.3 s. This makes PSR J19502414 an interesting pulsar to be used in Pulsar Timing Arrays (Hobbs et al., 2010).

Figure 2.— The TOA residuals of our timing model as a function of MJD (upper panel) and binary orbital phase (lower panel). Light-grey squares show TOA residuals from observations with the 76-m Lovell telescope, dark-gray circles residuals from observations with the Arecibo telescope using the ALFA receiver and the Mock spectrometers, and black triangles observations with the Arecibo telescope using the L-wide receiver and the PUPPI backend. The TOA residual distribution does not exhibit any clear trends.

3. Timing Results

Astrometric, spin, and binary parameters, including the relativistic periastron advance, were determined from the timing analysis of the TOAs described in the previous section. Table 1 shows the parameters of our timing solution obtained with TEMPO2.

Parameter Value
General Information
MJD Range 55839.0—56292.7
Number of TOAs 94
Weighted RMS of Timing Residuals (s) 4.7
Reduced- value 1.2
MJD of Period Determination 55839
Binary Model Used BT
Fitted Parameters
R.A., (J2000) 19:50:45.06390(10)
Dec., (J2000) +24:14:56.9638(11)
MJD of Position Determination 55839
Spin Frequency, (Hz) 232.30014862462(14)
Spin Frequency Derivative, ( Hz s) 1.020(6)
Dispersion Measure, DM (pc cm) 142.089(18)
MJD of DM Determination 55839
Projected Semi-Major Axis, (lt-s) 14.2199738(11)
Orbital Period, (days) 22.1913727(10)
Epoch of periastron, (MJD) 55846.0226219(15)
Longitude of periastron, (deg) 274.4155(3)
Periastron advance, (deg yr) 0.0020(3)
Orbital eccentricity, 0.07981158(12)
Derived Parameters
Spin Period, (ms) 4.304775549739(2)
Spin Period Derivative, () 1.8900(10)
Intrinsic , () 2.1166(10)
Galactic longitude, (deg) 61.10
Galactic latitude, (deg) 1.17
Distance, (NE2001, kpc) 5.5
Mass Function, () 0.00626918(2)
Minimum companion mass () 0.253
Total Mass, () 2.3(4)
Characteristic Age, (Gyr) 3.2
Surface Magnetic Field Strength, ( G) 3.1
Spin-down Luminosity, ( ergs/s) 1.0

The numbers in parentheses are the 1-, TEMPO2-reported uncertainties on the last digit(s). Uncertainties in the pulsar distance inferred from NE2001 are assuming a 20% uncertainty in DM to account for model uncertainties.
The solution here is based on single-frequency TOAs per Arecibo and Jodrell Bank observations, respectively. Fitting the DM is therefore degenerate with fitting the JUMPs between the data sets. The DM and its uncertainty were therefore fitted from TOAs obtained in two sub-bands for the Arecibo data combined with the Jodrell Bank TOAs, and kept fixed for the solution presented here.
The observed period derivative has been corrected for Galactic acceleration. We cannot correct for the Shklovskii effect, and therefore the value of is an upper limit, see Section 3. Its reported uncertainty here does not include the uncertainty from the Galactic model. , , and have been inferred from .

Table 1Fitted and derived parameters for PSR J19502414.

The pulsar’s mass function is given by


where is the pulsar’s projected orbital semi-major axis in light-seconds, s is the solar mass in time units, is the orbital period, and and are the masses of the pulsar and the companion in units of solar masses, respectively. We find , which indicates a low-mass companion with a minimum mass , which is obtained for and a pulsar mass . The median companion mass, assuming , is . Therefore, the binary companion is most likely a helium WD.

Considering the system’s mass function, its high spin frequency  Hz and small spin period derivative, PSR J19502414 is very similar to the majority of comparable binary pulsar systems in the Galactic field. The most probable nature for the system would therefore be a fully recycled millisecond pulsar with a WD companion. In this case, mass transfer from the WD progenitor to the MSP in the system’s past would have circularized the binary orbit, spun up the pulsar, and damped its magnetic field, as described in Section 1.

However, the orbital eccentricity of PSR J19502414 is larger (by roughly two orders of magnitude or more) than that of all millisecond pulsars with helium WD companions in the Galactic field with the exception of the three recently discovered similar systems (see Sections 1 and 4).

The theory of general relativity predicts an advance of the longitude of periastron, depending on the total mass of the system, its eccentricity and orbital period (Weisberg & Taylor, 1981), given by


where , , and are defined as above and is the orbital eccentricity.

Our observations of PSR J19502414 significantly detect the system’s periastron advance  deg yr. This corresponds to an inferred total mass of , where the uncertainty is dominated by the uncertainty in . This measurement is suggestive of a NS significantly more massive than 1.35 , however, it is currently not precise enough to infer the individual masses of the pulsar and/or the companion star. We expect our ongoing observation campaign to significantly improve the measurement of and therefore the estimate of the total mass.

Ongoing timing observations might also help to constrain or measure the Shapiro delay in the binary system. Combined measurements of the Shapiro delay and the periastron advance can be used to infer the separate masses of both components (Freire & Wex, 2010).

The observed spin period derivative has been corrected for Galactic acceleration (Nice & Taylor, 1995), to obtain a value of the spin period derivative of . This takes into account a Galactic acceleration model that uses the radial velocity curve published in Reid et al. (2014). However, since the proper motion currently cannot be measured with useful accuracy, we cannot correct for the contribution to the period derivative from the Shklovskii effect (Shklovskii, 1970), and therefore we can only estimate an upper limit for the intrinsic .

Both the intrinsic and the Shklovskii effect contribution are always positive and fulfill . Therefore, assuming , we obtain an upper limit to the intrinsic spin period derviative of . On the other hand, assuming we can constrain the total proper motion to  mas/yr.

From  s s we infer a lower limit for the characteristic age of  Gyr and upper limits for the the surface magnetic field strength  G and spin-down luminosity  ergs/s. These parameters are very similar to those of the general MSP population.

3.1. Counterparts at other Wavelengths

Let us now consider whether PSR J19502414 is observable at X-ray and -ray wavelengths and whether the nature of its companion can be established by way of optical/IR observations.

The field around PSR J19502414 has not been previously targeted in a pointed observation by any former or current X-ray mission. A 581-s exposure from the ROSAT all-sky survey is too shallow to yield any useful constrains on the X-ray flux from the pulsar. Based on its , PSR J19502414 likely has a soft, thermal X-ray spectrum due to heating of its magnetic polar caps, with erg s, as typically seen in non-eclipsing MSPs (Zavlin, 2006; Bogdanov et al., 2006). At a distance of 5.5 kpc and assuming an absorbing column of  cm (based on the empirical DM- relation from He et al., 2013) a detection of the pulsar with Chandra or XMM-Newton would require impractically long exposures.

There is no Fermi LAT Third Point Source Catalog (3FGL; The Fermi-LAT Collaboration, 2015) object in the vicinity of PSR J19502414’s position. A visual inspection of the Fermi LAT data from the beginning of the mission up to 2015 January 19 shows no excess emission at the pulsar position. This is expected given that at the Galactic latitude of PSR J19502414 (), the diffuse -ray background is overwhelming. In addition, the commonly used -ray “detectability” metric for pulsars, is erg s kpc for PSR J19502414, substantially lower compared to MSPs detected by Fermi LAT (see, e.g., Figure 15 in Abdo et al., 2013) so it is not expected to be a bright -ray source.

In principle, the nature of the companion of PSR J19502414 can be established by way of optical/IR observations. If the secondary is a main sequence star – in this case PSR J19502414 would belong to the same class as of systems as PSR J19030327 – it is likely to be a M3.5 red dwarf based on the mass measurement from radio timing (0.25 M). Data from the Digitized Sky Survey reveal no optical counterpart at the radio position of the MSP, likely because it is too distant and extincted. Indeed, using the relations by Predehl & Schmitt (1995) and He et al. (2013) combined with the pulsar’s dispersion measure, we estimate the visual extinction to the target to be . Taking the absolute magnitude of a M3.5V star, (Henry et al., 2002), and scaling with the dispersion measure derived distance (5.5 kpc) yields an expected apparent magnitude of including extinction.

If we consider the intrinsic colors of an M3.5V star based on 2MASS data (Lépine & Gaidos, 2011), and scale the extinction with wavelength (based on Cardelli et al., 1989), we obtain apparent magnitudes in the near-IR of , and, . Based on this, it is evident that near-IR imaging observations provide the better means of establishing the nature of the companion, which in turn helps constrain the evolutionary history of PSR J19502414. Existing near-IR data from the 2MASS all-sky survey (Skrutskie et al., 2006) show no counterpart at the pulsar position, although this provides no meaningful constraints on the PSR J19502414 companion since the limiting magnitude is only 16. Thus, deeper near-IR observations are required.

If the companion star is a He WD, its absolute magnitude is (Kaler, 2006). The extinction given above and the DM-inferred pulsar distance yield an apparent magnitude of . Detection in the visual band in imaging observations with 8-meter class telescopes requires apparent magnitudes of (Bates et al., 2015). Therefore, a detection or spectroscopic identification of an He WD companion in the optical band is currently impossible.

4. Discussion

PSR J19502414 has an unusual combination of small pulsar spin period and high orbital eccentricity. The small spin period and small spin period derivative (and inferred surface magnetic field) point to a long recycling episode in the system’s past, in which matter from the companion star accreted onto the pulsar, spun it up and reduced its magnetic field. Yet, the high orbital eccentricity appears at odds with this picture because long recycling episodes are believed to circularize the binary orbits to eccentricities in the range (Phinney, 1992).

Thus, these systems must form through different channels and/or experience some mechanism that increases the orbital eccentricity after the pulsar is recycled. We will discuss four proposed channels: 1) Formation in a hierarchical triple system which became unstable and ejected one of its members; 2) Perturbations in regions with high stellar density (globular clusters); 3) The rotationally delayed accretion-induced collapse of a super-Chandrasekhar white dwarf; 4) Dynamical interaction of the binary with a circumbinary disk.

PSR J19030327 2.1 ms 95.2 days 0.44 0.1 kpc
PSR J223406 3.6 ms 32 days 0.13 0.4 kpc
PSR J19463417 3.2 ms 27 days 0.14 0.5 kpc
PSR J16183921 12.0 ms 22.8 days 0.027 0.6 kpc
PSR J19502414 4.3 ms 22.2 days 0.30  0.08 0.1 kpc
Table 2Physical parameters of the five known eccentric MSPs. PSR J19030327 (Champion et al., 2008) was most likely formed from a triple system. PSR J16183921 (data reproduced from Edwards & Bailes, 2001, Bailes, 2010, and Bailes – private communication), two recently discovered MSPs (data from Freire & Tauris, 2014; Barr et al., 2013; Deneva et al., 2013) and PSR J19502414 (from this publication) have very similar orbital and spin characteristics, suggesting a common formation channel. The height above the Galactic plane, , was calculated from the DM-inferred distance and the Galactic latitude.

Table 2 compares our discovery with the four known eccentric MSPs in the Galactic field.

The similarity of the spin and orbital parameters of PSR J19502414 to those of PSR J223406 and PSR J19463417 (and also, to a lesser extent, to PSR J16183921) is striking, and is further evidence for the existence of a common formation mechanism that is clearly distinct from that of PSR J1903+0327 (which, as mentioned before, likely resulted from the chaotic disruption of a triple system, as indicated by its more massive main-sequence companion, much larger eccentricity and orbital period). PSR J16183921 differs from the aforementioned pulsars by a longer spin period and less eccentric orbit, however the orbital period is similar to that of PSR J19502414, supporting the idea that something anomalous happens within this range of orbital periods.

All pulsars in Table 2 have small distances from the Galactic plane  kpc. If the systems were produced by 2) exchange interactions in globular clusters, their distances to the Galactic plane are expected to be large, similar to the values for the globular cluster population (Harris, 1996). Therefore, it is unlikely that any of the pulsars originated in a globular cluster. Future observations of PSR J19502414 might be used to constrain its proper motion and further elucidate the issue.

As described in Section 1, Freire & Tauris (2014) recently have proposed the formation mechanism 3) for fully recycled MSPs in eccentric orbits. Since PSR J19502414 is such a system, let us now consider whether it could have also formed by the same mechanism.

At the center of their model is an accretion-induced collapse of a super-Chandrasekhar mass white dwarf in a close binary. The WD only collapses after the end of the accretion episode, and after it has lost sufficient spin angular momentum, directly producing an MSP in an eccentric orbit. Based on their simulations, Freire & Tauris (2014) provide a list of predictions for MSP systems formed through the rotationally delayed AIC channel. At the current time, PSR J19502414 is consistent with these predictions as detailed in the following.

From Fig. 3 in Freire & Tauris (2014), and assuming a range of pre-AIC WD masses between 1.37 and 1.48 , isotropically directed kicks, and initial orbital periods between 15 and 30 days, the kick velocity must be around 2 km s to yield orbital eccentricities between 0.09 and 0.14. The orbital eccentricity of PSR J19502414 is just outside the lower end of that range (and that certainly is the case for PSR J16183921). This might suggest a slightly larger kick magnitude and a slightly wider range of eccentricities to be observed in these systems in the future, or a slightly smaller NS binding energy than that assumed in that simulation.

The companion should be a He WD with a mass in the range , as predicted by the - relation from Fig. 5 in Tauris & Savonije (1999) for this orbital period of 22 days. Although we cannot currently determine the nature of the companion of PSR J19502414, its median companion mass of 0.30  is certainly compatible with this expectation.

Freire & Tauris (2014) predict a pulsar mass of typically . Currently, we have not measured the total mass of the system to a sufficiently high precision to test this prediction.

The system has low Galactic height, as expected from systems that formed with very small kick velocity ( km/s) in an AIC event. Indeed, the low Galactic heights of the MSPs in eccentric orbits discovered to date suggests small peculiar space velocities compared to the general MSP population. This assumption might be further tested with a future measurement of the proper motion of the system.

The characteristics of PSR J19502414 are also consistent with dynamical interaction with a circumbinary disk (Antoniadis, 2014). The circumbinary disk model makes two predictions which could be tested for PSR J19502414 with further observations: 1) As in Freire & Tauris (2014), the companions should also be He WDs with masses given by Tauris & Savonije (1999), which as we have seen agrees with our current mass constraint for the companion of PSR J19502414. 2) The masses of the MSP and the peculiar space velocities should closely resemble those of circular binary MSPs, unlike the small velocities ( km/s) predicted by the AIC model. With our current timing data, we cannot constrain the proper motion and can therefore neither confirm nor falsify this prediction.

Whatever the formation scenario for systems like PSR J19502414 is, it has in this case produced an object with an inferred surface magnetic field comparable to the general MSP population. This does not falsify any of the models discussed above, but might be useful constraint on other possible formation scenarios.

The fact that the characteristic age ( Gyr) is very similar to that of the general MSP population can be used to formulate a first rough estimate of the occurrence of these systems. It suggests that the relative frequency of occurrence of PSR J19502414-like MSPs in the population is comparable to the fraction of the currently known systems in the currently known population. Assuming that PSRs J16183921, J19463417, J19502414, and J223406 all formed through the same mechanism and all have similar , the relative frequency of these systems is of order 4 of a total of 230 known MSPs101010http://astro.phys.wvu.edu/GalacticMSPs/GalacticMSPs.txt not associated with a globular cluster, roughly 2% of the population.

5. Conclusions and Future Work

We have presented the discovery and initial timing of the fully-recycled ( ms) MSP PSR J19502414 in an eccentric () orbit ( days) with a median companion mass of 0.3 . PSR J19502414 is only the fifth system with a large eccentricity to be discovered. Its spin and orbital parameters are similar to those of three previously known systems with orbital periods in the range of  days, spin periods between 2 ms and 12 ms, large orbital eccentricities (), and companions with masses .

This combination of parameters cannot be explained in the standard pulsar recycling scenario. The existence of now four known similar systems which probably have a helium WD companion suggests the existence of a common formation channel leading to these unusual MSP systems. The upper limit on the intrinsic spin period and the inferred surface magnetic field are comparable to those of the general MSP population.

We compared the properties of PSR J19502414 with the predictions of four proposed formation channels. The initial evolution of the pulsar in a hierarchical triple and the origin in an exchange encounter in an high stellar density environment (e.g., globular cluster) are unlikely. Although we cannot conclusively rule out or confirm formation through a rotationally-delayed AIC event or interaction with a circumbinary disk with the measurements presented here, future observations might allow us to test a variety of predictions made by the different possible formation models.

The pulsar is currently being observed with Arecibo Observatory, and this will allow us to better constrain the pulsar and companion masses, which is of highest importance to discriminate between the AIC model and the circumbinary-disk model. The individual masses of the pulsar and the companion can be obtained from combining observations of the relativistic periastron advance with observations of the Shapiro delay. Using the orthometric parametrization of the Shapiro delay from Freire & Wex (2010) should provide the most precise estimates of the individual masses. The uncertainties of the periastron advance and the Shapiro delay in this parametrization are less degenerate than in the standard parametrization. Therefore, even if the measurement of the Shapiro delay has larger errors, a precise measurement of the relativistic periastron advance will allow for well-defined pulsar mass determination, see, e.g., Lynch et al. (2012). The ongoing observations will improve the relativistic periastron advance measurement and might also lead to a detection of the Shapiro delay.

Radio observations with longer time baselines will provide upper limits on or a measurement of the proper motion of the pulsar, and therefore of its peculiar space velocity. The AIC model predicts small values ( km/s), while the circumbinary-disk model predicts larger values. Measuring the proper motion could therefore permit discrimination between the two models.

Further information about the nature of the companion might be obtained from observations at optical or infrared wavelengths, as detailed in Section 3.1. Near-IR imaging observations provide the best means of establishing the nature of the companion, which in turn helps constrain the evolutionary history of PSR J19502414.

Modern pulsar surveys like PALFA are probing the Galactic disk to unprecedented depths and are likely to find other such systems. Having a larger sample size will allow discriminating between the different proposed models with greater confidence than is possible now.


We thank all Einstein@Home volunteers, especially those whose computers found PSR J19502414 with the highest statistical significance111111Where the real name is unknown or must remain confidential we give the Einstein@Home user name and display it in single quotes.: David Miller, Cheltenham, Gloucestershire, UK and ‘georges01’.

The authors would like to thank the anonymous referee for the advice and comments that helped to improve this manuscript.

This work was supported by the Max-Planck-Gesellschaft and by NSF grants 1104902, 1105572, and 1148523.

The Arecibo Observatory is operated by SRI International under a cooperative agreement with the National Science Foundation (AST-1100968), and in alliance with Ana G. Méndez-Universidad Metropolitana, and the Universities Space Research Association.

I.H.S. and W.Z. acknowledge support from an NSERC Discovery Grant and Discovery Accelerator Supplement and from CIfAR.

J.S.D. was supported by the Chief of Naval Research.

J.W.T.H. acknowledges funding from an NWO Vidi fellowship and ERC Starting Grant “DRAGNET” (337062).

P.C.C.F. and L.G.S. gratefully acknowledge financial support by the European Research Council for the ERC Starting Grant BEACON under contract no. 279702.

V.M.K. acknowledges support from an NSERC Discovery Grant and Accelerator Supplement, the FQRNT Centre de Recherche en Astrophysique du Québec, an R. Howard Webster Foundation Fellowship from the Canadian Institute for Advanced Research (CIFAR), the Canada Research Chairs Program and the Lorne Trottier Chair in Astrophysics and Cosmology.


  • Aasi et al. (2013) Aasi, J., Abadie, J., Abbott, B. P., et al. 2013, Phys. Rev. D, 87, 042001
  • Abbott et al. (2009a) Abbott, B., Abbott, R., Adhikari, R., et al. 2009a, Phys. Rev. D, 79, 022001
  • Abbott et al. (2009b) Abbott, B. P., Abbott, R., Adhikari, R., et al. 2009b, Phys. Rev. D, 80, 042003
  • Abdo et al. (2013) Abdo, A. A., Ajello, M., Allafort, A., et al. 2013, ApJS, 208, 17
  • Allen et al. (2013) Allen, B., Knispel, B., Cordes, J. M., et al. 2013, ApJ, 773, 91
  • Alpar et al. (1982) Alpar, M. A., Cheng, A. F., Ruderman, M. A., & Shaham, J. 1982, Nature, 300, 728
  • Anderson et al. (2006) Anderson, D. P., Christensen, C., & Allen, B. 2006, in Proceedings of the 2006 ACM/IEEE conference on Supercomputing, SC ’06 (New York, NY, USA: ACM)
  • Antoniadis (2014) Antoniadis, J. 2014, ApJ, 797, L24
  • Antoniadis et al. (2013) Antoniadis, J., Freire, P. C. C., Wex, N., et al. 2013, Science, 340, 448
  • Archibald et al. (2009) Archibald, A. M., Stairs, I. H., Ransom, S. M., et al. 2009, Science, 324, 1411
  • Archibald et al. (2014) Archibald, A. M., Bogdanov, S., Patruno, A., et al. 2014, ArXiv e-prints, arXiv:1412.1306 [astro-ph.HE]
  • Aulbert & Fehrmann (2009) Aulbert, C., & Fehrmann, H. 2009, Max-Planck-Gesellschaft Jahrbuch 2009
  • Backer et al. (1982) Backer, D. C., Kulkarni, S. R., Heiles, C., Davis, M. M., & Goss, W. M. 1982, Nature, 300, 615
  • Bailes (2010) Bailes, M. 2010, New Astronomy Reviews, 54, 80
  • Barr et al. (2013) Barr, E. D., Champion, D. J., Kramer, M., et al. 2013, MNRAS, 435, 2234
  • Bassa et al. (2014) Bassa, C. G., Patruno, A., Hessels, J. W. T., et al. 2014, MNRAS, 441, 1825
  • Bates et al. (2015) Bates, S. D., Thornton, D., Bailes, M., et al. 2015, MNRAS, 446, 4019
  • Bildsten et al. (1997) Bildsten, L., Chakrabarty, D., Chiu, J., et al. 1997, ApJS, 113, 367
  • Blandford & Teukolsky (1976) Blandford, R., & Teukolsky, S. A. 1976, ApJ, 205, 580
  • Bogdanov et al. (2006) Bogdanov, S., Grindlay, J. E., Heinke, C. O., et al. 2006, ApJ, 646, 1104
  • Cardelli et al. (1989) Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, ApJ, 345, 245
  • Champion et al. (2008) Champion, D. J., Ransom, S. M., Lazarus, P., et al. 2008, Science, 320, 1309
  • Chen et al. (2013) Chen, H.-L., Chen, X., Tauris, T. M., & Han, Z. 2013, ApJ, 775, 27
  • Cordes et al. (2006) Cordes, J. M., Freire, P. C. C., Lorimer, D. R., et al. 2006, ApJ, 637, 446
  • Crawford et al. (2012) Crawford, F., Stovall, K., Lyne, A. G., et al. 2012, ApJ, 757, 90
  • Demorest et al. (2010) Demorest, P. B., Pennucci, T., Ransom, S. M., Roberts, M. S. E., & Hessels, J. W. T. 2010, Nature, 467, 1081
  • Deneva et al. (2013) Deneva, J. S., Stovall, K., McLaughlin, M. A., et al. 2013, ApJ, 775, 51
  • Deneva et al. (2012) Deneva, J. S., Freire, P. C. C., Cordes, J. M., et al. 2012, ApJ, 757, 89
  • Edwards & Bailes (2001) Edwards, R. T., & Bailes, M. 2001, ApJ, 553, 801
  • Edwards et al. (2006) Edwards, R. T., Hobbs, G. B., & Manchester, R. N. 2006, MNRAS, 372, 1549
  • Freire & Tauris (2014) Freire, P. C. C., & Tauris, T. M. 2014, MNRAS, 438, L86
  • Freire & Wex (2010) Freire, P. C. C., & Wex, N. 2010, MNRAS, 409, 199
  • Freire et al. (2011) Freire, P. C. C., Bassa, C. G., Wex, N., et al. 2011, MNRAS, 412, 2763
  • Harris (1996) Harris, W. E. 1996, AJ, 112, 1487
  • He et al. (2013) He, C., Ng, C.-Y., & Kaspi, V. M. 2013, ApJ, 768, 64
  • Heggie & Rasio (1996) Heggie, D. C., & Rasio, F. A. 1996, MNRAS, 282, 1064
  • Henry et al. (2002) Henry, T. J., Walkowicz, L. M., Barto, T. C., & Golimowski, D. A. 2002, AJ, 123, 2002
  • Hessels et al. (2006) Hessels, J. W. T., Ransom, S. M., Stairs, I. H., et al. 2006, Science, 311, 1901
  • Hobbs et al. (2010) Hobbs, G., Archibald, A., Arzoumanian, Z., et al. 2010, Classical and Quantum Gravity, 27, 084013
  • Hobbs et al. (2006) Hobbs, G. B., Edwards, R. T., & Manchester, R. N. 2006, MNRAS, 369, 655
  • Hotan et al. (2004) Hotan, A. W., van Straten, W., & Manchester, R. N. 2004, Publications of the Astronomical Society of Australia, 21, 302
  • Kaler (2006) Kaler, J. B. 2006, The Cambridge Encyclopedia of Stars
  • Knispel (2011) Knispel, B. 2011, PhD thesis, Leibniz Universität Hannover
  • Knispel et al. (2010) Knispel, B., Allen, B., Cordes, J. M., et al. 2010, Science, 329, 1305
  • Knispel et al. (2011) Knispel, B., Lazarus, P., Allen, B., et al. 2011, ApJ, 732, L1
  • Knispel et al. (2013) Knispel, B., Eatough, R. P., Kim, H., et al. 2013, ApJ, 774, 93
  • Lazarus et al. (2014) Lazarus, P., Tauris, T. M., Knispel, B., et al. 2014, MNRAS, 437, 1485
  • Lépine & Gaidos (2011) Lépine, S., & Gaidos, E. 2011, AJ, 142, 138
  • Lorimer & Kramer (2012) Lorimer, D. R., & Kramer, M. 2012, Handbook of Pulsar Astronomy
  • Lynch et al. (2012) Lynch, R. S., Freire, P. C. C., Ransom, S. M., & Jacoby, B. A. 2012, ApJ, 745, 109
  • Manchester et al. (2005) Manchester, R. N., Hobbs, G. B., Teoh, A., & Hobbs, M. 2005, AJ, 129, 1993
  • Nice & Taylor (1995) Nice, D. J., & Taylor, J. H. 1995, ApJ, 441, 429
  • Papitto et al. (2013) Papitto, A., Ferrigno, C., Bozzo, E., et al. 2013, Nature, 501, 517
  • Patruno et al. (2014) Patruno, A., Archibald, A. M., Hessels, J. W. T., et al. 2014, ApJ, 781, L3
  • Phinney (1992) Phinney, E. S. 1992, Royal Society of London Philosophical Transactions Series A, 341, 39
  • Phinney & Kulkarni (1994) Phinney, E. S., & Kulkarni, S. R. 1994, ARA&A, 32, 591
  • Pijloo et al. (2012) Pijloo, J. T., Caputo, D. P., & Portegies Zwart, S. F. 2012, MNRAS, 424, 2914
  • Pletsch (2010) Pletsch, H. J. 2010, Phys. Rev. D, 82, 042002
  • Pletsch (2011) —. 2011, Phys. Rev. D, 83, 122003
  • Pletsch & Allen (2009) Pletsch, H. J., & Allen, B. 2009, Physical Review Letters, 103, 181102
  • Pletsch et al. (2012) Pletsch, H. J., Guillemot, L., Allen, B., et al. 2012, ApJ, 744, 105
  • Pletsch et al. (2013) —. 2013, ApJ, 779, L11
  • Portegies Zwart et al. (2011) Portegies Zwart, S., van den Heuvel, E. P. J., van Leeuwen, J., & Nelemans, G. 2011, ApJ, 734, 55
  • Predehl & Schmitt (1995) Predehl, P., & Schmitt, J. H. M. M. 1995, A&A, 293, 889
  • Radhakrishnan & Srinivasan (1982) Radhakrishnan, V., & Srinivasan, G. 1982, Current Science, 51, 1096
  • Ransom et al. (2005) Ransom, S. M., Hessels, J. W. T., Stairs, I. H., et al. 2005, Science, 307, 892
  • Ransom et al. (2014) Ransom, S. M., Stairs, I. H., Archibald, A. M., et al. 2014, Nature, 505, 520
  • Rasio & Heggie (1995) Rasio, F. A., & Heggie, D. C. 1995, ApJ, 445, L133
  • Reid et al. (2014) Reid, M. J., Menten, K. M., Brunthaler, A., et al. 2014, ApJ, 783, 130
  • Roberts (2013) Roberts, M. S. E. 2013, in IAU Symposium, Vol. 291, IAU Symposium, ed. J. van Leeuwen, 127
  • Roy et al. (2015) Roy, J., Ray, P. S., Bhattacharyya, B., et al. 2015, ApJ, 800, L12
  • Shklovskii (1970) Shklovskii, I. S. 1970, Soviet Ast., 13, 562
  • Skrutskie et al. (2006) Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163
  • Smarr & Blandford (1976) Smarr, L. L., & Blandford, R. 1976, ApJ, 207, 574
  • Stairs (2004) Stairs, I. H. 2004, Science, 304, 547
  • Stappers et al. (2014) Stappers, B. W., Archibald, A. M., Hessels, J. W. T., et al. 2014, ApJ, 790, 39
  • Swiggum et al. (2014) Swiggum, J. K., Lorimer, D. R., McLaughlin, M. A., et al. 2014, ApJ, 787, 137
  • Tauris & Savonije (1999) Tauris, T. M., & Savonije, G. J. 1999, A&A, 350, 928
  • Tauris & van den Heuvel (2014) Tauris, T. M., & van den Heuvel, E. P. J. 2014, ApJ, 781, L13
  • The Fermi-LAT Collaboration (2015) The Fermi-LAT Collaboration. 2015, ArXiv e-prints, arXiv:1501.02003 [astro-ph.HE]
  • Weisberg & Taylor (1981) Weisberg, J. M., & Taylor, J. H. 1981, General Relativity and Gravitation, 13, 1
  • Wijnands & van der Klis (1998) Wijnands, R., & van der Klis, M. 1998, Nature, 394, 344
  • Zavlin (2006) Zavlin, V. E. 2006, ApJ, 638, 951
  • Zhu et al. (2014) Zhu, W. W., Berndsen, A., Madsen, E. C., et al. 2014, ApJ, 781, 117
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