A very useful means of demonstrating the distinction between these two classes is the `` '' 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 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 . Lines of constant magnetic field strength are drawn on Fig. 5, together with lines of constant characteristic age (). From these, one infers typical magnetic fields and ages of G and yr for the normal pulsars and G and 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 Earth-mass bodies [168, 2]. Orbital companions are much more commonly observed around millisecond pulsars ( % 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 ( -- predominantly white dwarfs) and essentially circular orbits: . The binary pulsars with high-mass companions ( -- neutron stars or main sequence stars) are in much more eccentric orbits: 0.2 > e > 0.9 and lie above the line.
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, 14] 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 . Over the next 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 . 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 .
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 , a 59 ms radio pulsar with a characteristic age of yr which orbits its companion every 7.75 hr [151, 152]. Other examples include PSR B2303+46, a 1 s pulsar with a characteristic age of yr in a 12 day orbit . 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 M -- exactly that expected for a neutron star . 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 . This model has recently gained strong support from the discoveries of kHz quasi-periodic oscillations in a number of low-mass X-ray binaries , 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 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 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 .
|Binary and Millisecond Pulsars
D. R. Lorimer (email@example.com)
© Max-Planck-Gesellschaft. ISSN 1433-8351
Problems/Comments to firstname.lastname@example.org