2.5 Pulsar Velocities2 The Pulsar Phenomenon2.3 The Pulsar Distance Scale

2.4 Normal and Millisecond Pulsars 

The present public-domain catalogue, available on-line at Princeton [4Jump To The Next Citation Point In The Article], contains up-to-date parameters for some 706 pulsars. Most of these are ``normal'' in the sense that their pulse periods are of order one second and, with few exceptions, are observed to increase secularly at rates of typically tex2html_wrap_inline1859 s/s. A growing fraction of the observed sample are the so-called ``millisecond pulsars'', which have spin periods primarily in the range 1.5 and 30 ms and have rates of slowdown tex2html_wrap_inline1865 s/s. The first millisecond pulsar discovered, PSR B1937+21 [20Jump To The Next Citation Point In The Article], with a period of 1.5578 ms, remains the most rapidly rotating neutron star presently known to man.


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Figure 5: Pulse periods plotted against period derivatives for a sample of 639 pulsars. Filled red stars denote those pulsars known to be associated with supernova remnants. The blinking blue circles highlight those pulsars which are members of binary systems.

A very useful means of demonstrating the distinction between these two classes is the `` tex2html_wrap_inline1866 '' diagram - a logarithmic scatter plot of the observed pulse period versus the period derivative. This is shown in Fig.  5, in which normal pulsars occupy the majority of the upper right hand part of the diagram, whilst the millisecond pulsars reside in the lower left hand part of the diagram.

The differences in P and tex2html_wrap_inline1869 imply different ages and surface magnetic field strengths. By treating the pulsar as a rotating magnetic dipole, one may show that the surface magnetic field strength is proportional to tex2html_wrap_inline1875 [113Jump To The Next Citation Point In The Article]. Lines of constant magnetic field strength are drawn on Fig.  5, together with lines of constant characteristic age (tex2html_wrap_inline1877). From these, one infers typical magnetic fields and ages of tex2html_wrap_inline1879 G and tex2html_wrap_inline1881 yr for the normal pulsars and tex2html_wrap_inline1883 G and tex2html_wrap_inline1885 yr for the millisecond pulsars respectively.

A very important additional difference between normal and millisecond pulsars is the presence of an orbiting companion. Presently, about 7% of all known pulsars are members of binary systems. Timing measurements (§ 4) place useful constraints on the masses of the companions which, supplemented by observations at other wavelengths, tell us a great deal about their nature. The present sample of orbiting companions are either white dwarfs, main sequence stars, or other neutron stars. A notable additional hybrid system is the so-called ``planets pulsar'' PSR B1257+12 -- a 6.2 ms pulsar accompanied by at least two tex2html_wrap_inline1855 Earth-mass bodies [168Jump To The Next Citation Point In The Article, 2Jump To The Next Citation Point In The Article]. Orbital companions are much more commonly observed around millisecond pulsars (tex2html_wrap_inline1889 % of the observed sample) than the normal pulsars (< 1%). The sample of binary pulsars is delineated in Fig.  6 as orbital eccentricity against mass of the companion. The dashed line serves merely to guide the eye in this figure. From this we note that the binary systems below the line are those with low-mass companions (tex2html_wrap_inline1893 -- predominantly white dwarfs) and essentially circular orbits: tex2html_wrap_inline1895 . The binary pulsars with high-mass companions (tex2html_wrap_inline1897 -- neutron stars or main sequence stars) are in much more eccentric orbits: 0.2 > e > 0.9 and lie above the line.


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Figure 6: Companion mass versus orbital eccentricity for the sample of binary pulsars.

The presently favoured model to explain the formation of the various types of systems has been developed over the years by a number of authors [34, 59, 143, 14Jump To The Next Citation Point In The Article] and can be qualitatively summarised as follows: Starting with a binary star system, the neutron star is formed during the supernova explosion of the initially more massive star which has an inherently shorter main sequence lifetime. From the virial theorem, it follows that the binary system gets disrupted if more than half the total pre-supernova mass is ejected from the system during the explosion. In addition, the fraction of surviving binaries is affected by the magnitude and direction of the impulsive ``kick'' velocity the neutron star receives at birth [76, 21]. Those binary systems that disrupt produce a high velocity isolated neutron star and an OB runaway star [35]. Over the next tex2html_wrap_inline1881 yr or so after the explosion, the neutron star may be observable as a normal radio pulsar spinning down to periods of several seconds or longer. The high disruption probability explains why so few normal pulsars have companions.

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 on life as a pulsar by accreting matter and therefore angular momentum from its companion [14Jump To The Next Citation Point In The Article]. The term ``recycled pulsar'' is often used to describe such objects. During this accretion phase, the X-rays liberated by heating the infalling material onto the neutron star mean that such a system is expected to be visible as an X-ray binary system. Two classes of X-ray binaries relevant to binary and millisecond pulsars exist, viz: neutron stars with high-mass or low-mass companions. For a detailed review of the X-ray binary population, including systems likely to contain black holes rather than neutron stars, the interested reader is referred to [32Jump To The Next Citation Point In The Article].

The high-mass companions are massive enough to explode themselves as a supernova, producing a second neutron star. If the binary system is lucky enough to survive this explosion, it ends up as a double neutron star binary. The classic example is PSR B1913+16 [78Jump To The Next Citation Point In The Article], a 59 ms radio pulsar with a characteristic age of tex2html_wrap_inline1903 yr which orbits its companion every 7.75 hr [151Jump To The Next Citation Point In The Article, 152Jump To The Next Citation Point In The Article]. Other examples include PSR B2303+46, a 1 s pulsar with a characteristic age of tex2html_wrap_inline1905 yr in a 12 day orbit [146]. Within the framework of this formation scenario, PSR B1913+16 is an example of the older, first-born, neutron star that has subsequently accreted matter from its companion. PSR B2303+46 is, on the other hand, likely to be the younger, second-born neutron star in its binary system. As we shall see (§ 3.4), double neutron star binary systems are very rare in the Galaxy, a direct indication that the majority of binary systems get disrupted by the exploding star.

Although no such system has yet been found in which both neutron stars are visible as radio pulsars, timing measurements (§ 4.3) show that the companion masses are tex2html_wrap_inline1907 M tex2html_wrap_inline1827 -- exactly that expected for a neutron star [140]. In addition, no optical counterparts are seen. Thus, we conclude that these unseen companions are neutron stars that are either too weak to be seen/no longer active as radio pulsars or their emission beams do not intersect our line of sight. The two known radio pulsars with main sequence companions may well represent the ``missing link'' between high-mass X-ray binaries and double neutron star systems [83, 86].

By definition, the companions in the low-mass X-ray binaries evolve and transfer matter onto the neutron star on a much longer time-scale, spinning it up to periods as short as a few ms [14]. This model has recently gained strong support from the discoveries of kHz quasi-periodic oscillations in a number of low-mass X-ray binaries [164], as well as Doppler-shifted 2.49 ms X-ray pulsations from the transient X-ray burster SAX J1808.4-3658 [165, 42].

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. Presently tex2html_wrap_inline1911 of these systems have compelling optical identifications of the white dwarf companion [27, 29, 101, 100]. Perhaps the best example is the white dwarf companion to the 5.25 ms pulsar J1012+5307 [119, 97]. This tex2html_wrap_inline1913 magnitude white dwarf is bright enough to allow precise measurements of its surface gravity, as well as the Doppler shifts of its spectral lines as it moves in its orbit [161].

2.5 Pulsar Velocities2 The Pulsar Phenomenon2.3 The Pulsar Distance Scale

image Binary and Millisecond Pulsars
D. R. Lorimer (dunc@mpifr-bonn.mpg.de)
© Max-Planck-Gesellschaft. ISSN 1433-8351
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