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2.6 Evolution of normal and millisecond pulsars

A simplified version of the presently favoured model [37952852Jump To The Next Citation Point] to explain the formation of the various types of systems observed is shown in Figure 7View Image. Starting with a binary star system, a neutron star is formed during the supernova explosion of the initially more massive star. From the virial theorem, in the absence of any other factors, the binary will be disrupted if more than half the total pre-supernova mass is ejected from the system during the (assumed symmetric) explosion [120Jump To The Next Citation Point33Jump To The Next Citation Point]. In practice, the fraction of surviving binaries is also affected by the magnitude and direction of any impulsive “kick” velocity the neutron star receives at birth from a slightly asymmetric explosion [12020]. Binaries that disrupt produce a high-velocity isolated neutron star and an OB runaway star [38]. The high probability of disruption explains qualitatively why so few normal pulsars have companions. There are currently four known normal radio pulsars with massive main sequence companions in eccentric orbits which are examples of binary systems which survived the supernova explosion [140Jump To The Next Citation Point153295Jump To The Next Citation Point296Jump To The Next Citation Point193Jump To The Next Citation Point]. Over the next 107-8 yr after the explosion, the neutron star may be observable as a normal radio pulsar spinning down to a period >~~ several seconds. After this time, the energy output of the star diminishes to a point where it no longer produces significant amounts of radio emission.
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Figure 7: Cartoon showing various evolutionary scenarios involving binary pulsars.
For those few binaries that remain bound, and in which the companion is sufficiently massive to evolve into a giant and overflow its Roche lobe, the old spun-down neutron star can gain a new lease of life as a pulsar by accreting matter and angular momentum at the expense of the orbital angular momentum of the binary system [2Jump To The Next Citation Point]. The term “recycled pulsar” is often used to describe such objects. During this accretion phase, the X-rays produced by the liberation of gravitational energy of the infalling matter onto the neutron star mean that such a system is expected to be visible as an X-ray binary. Two classes of X-ray binaries relevant to binary and millisecond pulsars exist: neutron stars with high-mass or low-mass companions. Detailed reviews of the X-ray binary population, including systems likely to contain black holes, can be found elsewhere [33Jump To The Next Citation Point].
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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 [294Jump To The Next Citation Point]. The solid line shows the median of the predicted relationship between orbital period and eccentricity [249Jump To The Next Citation Point]. Dashed lines show 95% the confidence limit about this relationship. The dotted line shows 2 Pb oc e. Figure provided by Ingrid Stairs [294Jump To The Next Citation Point] using an adaptation of the orbital period-eccentricity relationship tabulated by Fernando Camilo.
In a high-mass X-ray binary, the companion is massive enough that it might also explode as a supernova, producing a second neutron star. If the binary system is lucky enough to survive the explosion, the result is a double neutron star binary. At least five and probably eight such systems are now known, the original example being PSR B1913+16 [129Jump To The Next Citation Point] - a 59 -ms radio pulsar which orbits its companion every 7.75 hr [312Jump To The Next Citation Point313Jump To The Next Citation Point]. In this formation scenario, PSR B1913+16 is an example of the older, first-born, neutron star that has subsequently accreted matter from its companion.

For many years, no clear example was known where the second-born neutron star was observed as a pulsar. The discovery of the double pulsar J0737-3039 [44Jump To The Next Citation Point198Jump To The Next Citation Point], where a 22.7-ms recycled pulsar “A” orbits a 2.77-s normal pulsar “B” every 2.4 hr, has now provided a dramatic confirmation of this evolutionary model in which we identify A and B as the first and second-born neutron stars respectively. Just how many more observable double pulsar systems exist in our Galaxy is not clear. Although the population of double neutron star systems in general is reasonably well understood (see Section 3.4.1), given that the lifetime of the second born pulsar is less than one tenth that of the recycled pulsar, and that its radio beam is likely to be much smaller (see Section 3.2.3), the prospects of ever finding more than a few 0737-like systems are rather low.

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Figure 9: Companion mass versus orbital period 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 [307Jump To The Next Citation Point]. 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 [330Jump To The Next Citation Point].
The companion in a low-mass X-ray binary evolves and transfers matter onto the neutron star on a much longer time-scale, spinning it up to periods as short as a few ms [2]. Tidal forces during the accretion process serve to circularize the orbit. At the end of the spin-up phase, the secondary sheds its outer layers to become a white dwarf in orbit around a rapidly spinning millisecond pulsar. This model has gained strong support in recent years from the discoveries of quasi-periodic kHz oscillations in a number of low-mass X-ray binaries [338], as well as Doppler-shifted 2.49 -ms X-ray pulsations from the transient X-ray burster SAX J1808.4-3658 [34059]. Six other “X-ray millisecond pulsars” are now known with spin rates and orbital periods ranging between 185 -600 Hz and 40 min -4.3 hr respectively [339220144]. Despite intensive searches [43], no radio pulsations have so far been detected in these binaries. This could be a result of free-free absorption of any radio waves by the thick accretion disk, or perhaps quenching the accelerating potential in the neutron star magnetosphere by infalling matter. More sensitive radio observations are ultimately required to place stringent limits on the physical processes responsible for the lack of emission.

Numerous examples of these systems in their post X-ray phase are now seen as the millisecond pulsar-white dwarf binary systems. Presently, 20 of these systems have compelling optical identifications of the white dwarf companion, and upper limits or tentative detections have been found in about 30 others [330Jump To The Next Citation Point]. Comparisons between the cooling ages of the white dwarfs and the millisecond pulsars confirm the age of these systems and suggest that the accretion rate during the spin-up phase was well below the Eddington limit [114].

Further support for the above evolutionary scenarios comes from two correlations in the observed sample of low-mass binary pulsars. Firstly, as seen in Figure 8View Image, there is a strong correlation between orbital period and eccentricity. The data are very good agreement with a theoretical relationship which predicts a relic orbital eccentricity due to convective eddy currents in the accretion process [249]. Secondly, as shown in Panel b of Figure 9View Image, where companion masses have been measured accurately, through radio timing (see Section 4.4) and/or through optical observations [330], they are in good agreement with a relation between companion mass and orbital period predicted by binary evolution theory [307]. A word of caution is required in using these models to make predictions, however. When confronted with a larger ensemble of binary pulsars using statistical arguments to constrain the companion masses (see Panel a of Figure 9View Image), current models have problems in explaining the full range of orbital periods on this diagram [294Jump To The Next Citation Point].

The range of white dwarf masses observed is becoming broader. Since this article originally appeared [179], the number of “intermediate-mass binary pulsars” [49] has grown significantly [54Jump To The Next Citation Point]. These systems are distinct to the millisecond pulsar-white dwarf binaries in several ways:

  1. The spin period of the radio pulsar is generally longer (9- 200 ms).
  2. The mass of the white dwarf is larger (typically >~~ 0.5 Mo .).
  3. The orbit, while still essentially circular, is often significantly more eccentric (e >~~ 10 -3).
  4. They do not necessarily follow the mass-period or eccentricity-period relationships.

It is not presently clear whether these systems originated from low- or high-mass X-ray binaries. It was suggested by van den Heuvel [329] that they have more in common with high-mass systems. More recently, it has been proposed [172] that a thermal-viscous instability in the accretion disk of a low-mass X-ray binary could truncate the accretion phase and produce a more slowly spinning neutron star.

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