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Review
, 11 (1), 8

Binary and Millisecond Pulsars

Affiliations
Review

Binary and Millisecond Pulsars

Duncan R Lorimer. Living Rev Relativ.

Abstract

We review the main properties, demographics and applications of binary and millisecond radio pulsars. Our knowledge of these exciting objects has greatly increased in recent years, mainly due to successful surveys which have brought the known pulsar population to over 1800. There are now 83 binary and millisecond pulsars associated with the disk of our Galaxy, and a further 140 pulsars in 26 of the Galactic globular clusters. Recent highlights include the discovery of the young relativistic binary system PSR J1906+0746, a rejuvination in globular cluster pulsar research including growing numbers of pulsars with masses in excess of 1.5 M, a precise measurement of relativistic spin precession in the double pulsar system and a Galactic millisecond pulsar in an eccentric (e = 0.44) orbit around an unevolved companion.

Electronic supplementary material: Supplementary material is available for this article at 10.12942/lrr-2008-8.

Figures

Figure 1
Figure 1
Venn diagram showing the numbers and locations of the various types of radio pulsars known as of September 2008. The large and small Magellanic clouds are denoted by LMC and SMC.
Figure 2
Figure 2
gif-Movie (861 KB) Still from a movie showing The rotating neutron star (or “lighthouse”) model for pulsar emission. Animation designed by Michael Kramer. (For video see appendix)
Figure 3
Figure 3
The P−Ṗ diagram showing the current sample of radio pulsars. Binary pulsars are highlighted by open circles. Lines of constant magnetic field (dashed), characteristic age (dash-dotted) and spin-down energy loss rate (dotted) are also shown.
Figure 4
Figure 4
A variety of integrated pulse profiles taken from the available literature. References: Panels a, b, d, f [124], Panel c [23], Panels e, g, i [203], Panel h [31]. Each profile represents 360 degrees of rotational phase. These profiles are freely available from an online database [378].
Figure 5
Figure 5
A recent phenomenological model for pulse shape morphology. The neutron star is depicted by the grey sphere and only a single magnetic pole is shown for clarity. Left: a young pulsar with emission from a patchy conal ring at high altitudes from the surface of the neutron star. Right: an older pulsar in which emission emanates from a series of patchy rings over a range of altitudes. Centre: schematic representation of the change in emission height with pulsar age. Figure designed by Aris Karastergiou and Simon Johnston [179].
Figure 6
Figure 6
Pulse dispersion shown in this Parkes observation of the 128 ms pulsar B1356–60. The dispersion measure is 295 cm−3 pc. The quadratic frequency dependence of the dispersion delay is clearly visible. Figure provided by Andrew Lyne.
Figure 7
Figure 7
Cartoon showing various evolutionary scenarios involving binary pulsars.
Figure 8
Figure 8
Eccentricity versus orbital period for a sample of 21 low-mass binary pulsars which are not in globular clusters, with the triangles denoting three recently discovered systems [347]. The solid line shows the median of the predicted relationship between orbital period and eccentricity [298]. Dashed lines show 95% the confidence limit about this relationship. The dotted line shows Pbe2. Figure provided by Ingrid Stairs [347] using an adaptation of the orbital period-eccentricity relationship tabulated by Fernando Camilo.
Figure 9
Figure 9
Orbital period versus companion mass for binary pulsars showing the whole sample where, in the absence of mass determinations, statistical arguments based on a random distribution of orbital inclination angles (see Section 4.4) have been used to constrain the masses as shown (Panel a), and only those with well determined companion masses (Panel b). The dashed lines show the uncertainties in the predicted relation [361]. This relationship indicates that as these systems finished a period of stable mass transfer due to Roche-lobe overflow, the size and hence period of the orbit was determined by the mass of the evolved secondary star. Figure provided by Marten van Kerkwijk [384].
Figure 10
Figure 10
gif-Movie (213 KB) Still from a movie showing A simulation following the motion of 100 pulsars in a model gravitational potential of our Galaxy for 200 Myr. The view is edge-on, i.e. the horizontal axis represents the Galactic plane (30 kpc across) while the vertical axis represents ±10 kpc from the plane. This snapshot shows the initial configuration of young neutron stars. (For video see appendix)
Figure 11
Figure 11
Left panel: The current sample of all known radio pulsars projected onto the Galactic plane. The Galactic centre is at the origin and the Sun is at (0, 8.5) kpc. Note the spiral-arm structure seen in the distribution which is now required by the most recent Galactic electron density model [84, 85]. Right panel: Cumulative number of pulsars as a function of projected distance from the Sun. The solid line shows the observed sample while the dotted line shows a model population free from selection effects.
Figure 12
Figure 12
Left panel: Pulse scattering caused by irregularities in the interstellar medium. The different path lengths and travel times of the scattered rays result in a “scattering tail” in the observed pulse profile which lowers its signal-to-noise ratio. Right panel: A simulation showing the percentage of Galactic pulsars that are likely to be undetectable due to scattering as a function of observing frequency. Low-frequency (≲ 1 GHz) surveys clearly miss a large percentage of the population due to this effect.
Figure 13
Figure 13
Left panel: A 22.5-min Arecibo observation of the binary pulsar B1913+16. The assumption that the pulsar has a constant period during this time is clearly inappropriate given the quadratic drifting in phase of the pulse during the observation (linear grey scale plot). Right panel: The same observation after applying an acceleration search. This shows the effective recovery of the pulse shape and a significant improvement in the signal-to-noise ratio.
Figure 14
Figure 14
Dynamic power spectra showing two recent pulsar discoveries in the globular cluster M62 showing fluctuation frequency as a function of time. Figure provided by Adam Chandler.
Figure 15
Figure 15
Small-number bias of the scale factor estimates derived from a synthetic population of sources where the true number of sources is known. Left panel: An edge-on view of a model Galactic source population. Right panel: The thick line shows NG, the true number of objects in the model Galaxy, plotted against Nobserved, the number detected by a flux-limited survey. The thin solid line shows Nest, the median sum of the scale factors, as a function of Nobs from a large number of Monte Carlo trials. Dashed lines show 25 and 75% percentiles of the Nest distribution.
Figure 16
Figure 16
Beaming fraction plotted against pulse period for four different beaming models: Narayan & Vivekanand 1983 (NV83) [269], Lyne & Manchester 1988 (LM88) [243], Biggs 1990 (JDB90) [37] and Tauris & Manchester 1998 (TM98) [360].
Figure 17
Figure 17
Left panel: The corrected luminosity distribution (solid histogram with error bars) for normal pulsars. The corrected distribution before the beaming model has been applied is shown by the dot-dashed line. Right panel: The corresponding distribution for millisecond pulsars. In both cases, the observed distribution is shown by the dashed line and the thick solid line is a power law with a slope of −1. The difference between the observed and corrected distributions highlights the severe under-sampling of low-luminosity pulsars.
Figure 18
Figure 18
The relativistic binary merging plane. Top: Orbital eccentricity versus period for eccentric binary systems involving neutron stars. Bottom: Orbital period distribution for the massive white dwarf-pulsar binaries. Isocrones show coalescence times assuming neutron stars of 1.4M and white dwarfs of 0.3 M.
Figure 19
Figure 19
The current best empirical estimates of the coalescence rates of relativistic binaries involving neutron stars. The individual contributions from each known binary system are shown as dashed lines, while the solid line shows the total probability density function on a logarithmic and (inset) linear scale. The left panel shows the most recent analysis for DNS binaries [189], while the right panel shows the equivalent results for NS-WD binaries [191]. Figures provided by Chunglee Kim.
Figure 20
Figure 20
Schematic showing the main stages involved in pulsar timing observations.
Figure 21
Figure 21
A 120 µs window centred on a coherently-dedispersed giant pulse from the Crab pulsar showing high-intensity nanosecond bursts. Figure provided by Tim Hankins [130].
Figure 22
Figure 22
Timing model residuals for PSR B1133+16. Panel a: Residuals obtained from the best-fitting model which includes period, period derivative, position and proper motion. Panel b: Residuals obtained when the period derivative term is set to zero. Panel c: Residuals showing the effect of a 1-arcmin position error. Panel d: Residuals obtained neglecting the proper motion. The lines in Panels b–d show the expected behaviour in the timing residuals for each effect. Data provided by Andrew Lyne.
Figure 23
Figure 23
Examples of timing residuals for a number of normal pulsars. Note the varying scale on the ordinate axis, the pulsars being ranked in increasing order of timing “activity”. Data taken from the Jodrell Bank timing program [335, 146]. Figure provided by Andrew Lyne.
Figure 24
Figure 24
The fractional stability of three millisecond pulsars compared to an atomic clock. Both PSRs B1855+09 and B1937+21 are comparable, or just slightly worse than, the atomic clock behaviour over timescales of a few years [254]. More recent timing of the millisecond pulsar J0437−4715 [388] indicates that it is inherently a very stable clock. Data for the latter pulsar provided by Joris Verbiest.
Figure 25
Figure 25
Panel a: Keplerian orbital fit to the 669-day binary pulsar J0407+1607 [233]. Panel b: Orbital fit in the period-acceleration plane for the globular cluster pulsar 47 Tuc S [115].
Figure 26
Figure 26
Orbital decay in the binary pulsar B1913+16 system demonstrated as an increasing orbital phase shift for periastron passages with time. The GR prediction due entirely to the emission of gravitational radiation is shown by the parabola. Figure provided by Joel Weisberg.
Figure 27
Figure 27
‘Mass—mass’ diagram showing the observational constraints on the masses of the neutron stars in the double pulsar system J0737−3039. Inset is an enlarged view of the small square encompassing the intersection of the tightest constraints. Figure provided by René Breton [44].
Figure 28
Figure 28
Distribution of neutron star masses as inferred from timing observations of binary pulsars and X-ray binary systems. Figure adapted from an original version provided by Ingrid stairs. Additional information on globular cluster pulsar mass constraints provided by Paulo Freire. Error bars show one-sigma uncertainties on each mass determination.
Figure 29
Figure 29
Pulsar mass versus companion mass diagram showing mass constraints for the eccentric binary millisecond pulsar B1516+02B [118]. The allowed parameter space is bounded by the dashed lines which show the uncertainty on the total mass from the measurement of the relativistic advance of periastron. Masses within the hatched region are disallowed by the Keplerian mass function and the constraint that sin i < 1. Assuming a random distribution of orbital inclination angles allows the probability density functions of the pulsar and companion mass to be derived, as shown by the top and right hand panels. Figure provided by Paulo Freire.
Figure 30
Figure 30
Top panel: Observed timing residuals for PSR B1855+09. Bottom panel: Simulated timing residuals induced from a putative black hole binary in 3C66B. Figure provided by Rick Jenet [161].
Figure 31
Figure 31
Summary of the gravitational wave spectrum showing the location in phase space of the pulsar timing array (PTA) and its extension with the Square Kilometre Array (SKA). Figure updated by Michael Kramer [198] from an original design by Richard Battye.

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