2.5 Searching for pulsars2 An Introduction to Pulsar 2.3 The pulsar distance scale

2.4 Normal and millisecond pulsars 

2.4.1 Spin parameters 

The present public-domain catalogue, available on-line at Princeton [196Jump To The Next Citation Point In The Article], contains up-to-date parameters for 706 pulsars. Parameters for many of the new Parkes multibeam pulsar surveys are also available on-line [28, 197Jump To The Next Citation Point In The Article]. Most of these are ``normal'' in the sense that their pulse periods P are of order one second and are observed to increase secularly at rates tex2html_wrap_inline9123 of typically tex2html_wrap_inline9125 . 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 rates of slowdown tex2html_wrap_inline9127 . The first millisecond pulsar discovered, B1937+21 [17Jump To The Next Citation Point In The Article], with tex2html_wrap_inline9129, remains the most rapidly rotating neutron star presently known.


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Figure 7: The ubiquitous P- tex2html_wrap_inline9123 diagram shown for a sample of radio pulsars. Those objects known to be members of binary systems are highlighted by a circle (for low-eccentricity orbits) or an ellipse (for elliptical orbits). Pulsars thought to be associated with supernova remnants are highlighted by the starred symbols.

A very useful means of demonstrating the distinction between these two classes is the `` P - tex2html_wrap_inline9123 diagram'' - a logarithmic scatter plot of the observed pulse period versus the period derivative. As shown in Fig.  7, normal pulsars occupy the majority of the upper right hand part of the diagram, while the millisecond pulsars reside in the lower left hand part of the diagram. The differences in P and tex2html_wrap_inline9123 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_inline9143  [163Jump To The Next Citation Point In The Article]. Lines of constant magnetic field strength are drawn on Fig.  7, together with lines of constant characteristic age (tex2html_wrap_inline9145). Typical inferred magnetic fields and ages are tex2html_wrap_inline9147 and tex2html_wrap_inline9149 for the normal pulsars and tex2html_wrap_inline9151 and tex2html_wrap_inline9153 for the millisecond pulsars.

2.4.2 Binary companions 

As can be inferred from Fig.  1, just under 4% of all known pulsars in the Galactic disk 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. Two notable hybrid systems are the ``planet pulsars'' PSR B1257+12 and B1620-26. B1257+12 is a 6.2-ms pulsar accompanied by at least three Earth-mass bodies [273Jump To The Next Citation Point In The Article, 186Jump To The Next Citation Point In The Article, 272Jump To The Next Citation Point In The Article] while B1620-26, an 11-ms pulsar in the globular cluster M4, is part of a triple system with a white dwarf and a high-mass planet [247Jump To The Next Citation Point In The Article, 15Jump To The Next Citation Point In The Article, 245Jump To The Next Citation Point In The Article].


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Figure 8: Companion mass versus orbital eccentricity for the sample of binary pulsars.

A very important additional difference between normal and millisecond pulsars is the presence of an orbiting companion. Orbital companions are much more commonly observed around millisecond pulsars (tex2html_wrap_inline9155 % of the observed sample) than around the normal pulsars (tex2html_wrap_inline9157 %). Fig.  8 is a scatter plot of orbital eccentricity versus mass of the companion. The dashed line serves merely to guide the eye in this figure. Binary systems lying below the line are those with low-mass companions (tex2html_wrap_inline9159 - predominantly white dwarfs) and essentially circular orbits: tex2html_wrap_inline9161 . Binary pulsars with high-mass companions (tex2html_wrap_inline9163 - neutron stars or main sequence stars) are in eccentric orbits, tex2html_wrap_inline9165, and lie above the line.

2.4.3 Evolutionary scenarios 

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, 77, 218, 2Jump To The Next Citation Point In The Article]. The model is sketched in Fig.  9 and is now qualitatively summarised.

Starting with a binary star system, a 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 [98Jump To The Next Citation Point In The Article, 31Jump To The Next Citation Point In The Article]. In addition, the fraction of surviving binaries is affected by the magnitude and direction of any impulsive ``kick'' velocity the neutron star receives at birth [98, 18]. Those binary systems that disrupt produce a high-velocity isolated neutron star and an OB runaway star [35]. The high binary disruption probability during the explosion explains, qualitatively at least, why so few normal pulsars have companions. Over the next tex2html_wrap_inline9167 yr or so after the explosion, the neutron star may be observable as a normal radio pulsar spinning down to a period tex2html_wrap_inline9169 several seconds. After this time, the energy output of the star diminuishes to a point where it no longer produces significant radio emission.

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 therefore angular momentum at the expense of the orbital angular momentum of the binary system [2Jump 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 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 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 [31Jump To The Next Citation Point In The Article].


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Figure 9: Cartoon showing various evolutionary scenarios involving binary pulsars.

The high-mass companions are massive enough to explode 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 [102Jump To The Next Citation Point In The Article], a 59-ms radio pulsar with a characteristic age of tex2html_wrap_inline9171 yr which orbits its companion every 7.75 hr [239Jump To The Next Citation Point In The Article, 240Jump To The Next Citation Point In The Article]. 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. So far there are no clear examples of systems where the second-born neutron star is observed as a radio pulsar. In the case of {PSR B1820-11 [155Jump To The Next Citation Point In The Article], which may be an example, the mass of the companion is not well determined, so either a main-sequence [193Jump To The Next Citation Point In The Article] or a white dwarf companion [194] are plausible alternatives. This lack of observation of second-born neutron stars as radio pulsars is probably reasonable when one realises that the observable lifetimes of recycled pulsars are much larger than those of normal pulsars. As discussed in §  3.4.1, double neutron star binary systems are very rare in the Galaxy - another indication that the majority of binary systems get disrupted when one of the components explodes as a supernova. Systems disrupted after the supernova of the secondary form a mildly-recycled isolated pulsar and a young pulsar formed during the explosion of the secondary.

Although no system has so far been found in which both neutron stars are visible as radio pulsars, timing measurements of three systems show that the companion masses are tex2html_wrap_inline9057 - as expected for neutron stars [215]. In addition, no optical counterparts are seen. Thus, we conclude that these unseen companions are neutron stars that are either too weak to be detected, no longer active as radio pulsars, or their emission beams do not intersect our line of sight. The two known young radio pulsars with main sequence companions massive enough to explode as a supernova probably represent the intermediate phase between high-mass X-ray binaries and double neutron star systems [110Jump To The Next Citation Point In The Article, 115].

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 [2]. 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 [266], as well as Doppler-shifted 2.49-ms X-ray pulsations from the transient X-ray burster SAX J1808.4-3658 [267, 53]. 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_inline9177 of these systems have compelling optical identifications of the white dwarf companion [25, 27, 139, 138]. Perhaps the best example is the white dwarf companion to the 5.25-ms pulsar J1012+5307 [177Jump To The Next Citation Point In The Article, 133]. This 19th magnitude white dwarf is bright enough to allow measurements of its surface gravity and orbital velocity [257].

The range of white dwarf masses observed is becoming broader. Since this article originally appeared in 1998, the number of ``intermediate-mass binary pulsars'' [43] has grown significantly [49Jump To The Next Citation Point In The Article]. These systems are distinct to the ``classical'' millisecond pulsar-white dwarf binaries like PSR J1012+5307 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 close to tex2html_wrap_inline9179); (3) the orbital eccentricity, while still essentially circular, is often significantly larger (tex2html_wrap_inline9181). It is not presently clear whether these systems originated from either low- or high-mass X-ray binaries. It was suggested by van den Heuvel [254] that they have more in common with high-mass systems, the difference being that the secondary star was not sufficiently massive to explode as a supernova. Instead it formed a white dwarf. Detailed studies of this sub-population of binary pulsars are required for further understanding in this area.

Another relatively poorly understood area is the existence of solitary millisecond pulsars in the Galactic disk (which comprise just under 20% of all Galactic millisecond pulsars). Although it has been proposed that the millisecond pulsars have got rid of their companion by ablation, as appears to be happening in the PSR B1957+20 system [83Jump To The Next Citation Point In The Article], it is not clear whether the time-scales for this process are feasible. There is some observational evidence that suggests that solitary millisecond pulsars are less luminous than binary millisecond pulsars [20Jump To The Next Citation Point In The Article, 122Jump To The Next Citation Point In The Article]. If confirmed by future discoveries, this would need to be explained by any viable evolutionary model.

2.4.4 Space velocities 

Pulsars have long been known to have space velocities at least an order of magnitude larger than those of their main sequence progenitors, which have typical values between 10 and 50  tex2html_wrap_inline9183 . The first direct evidence for large velocities came from optical observations of the Crab pulsar in 1968 [251], showing that the neutron star has a velocity in excess of 100  tex2html_wrap_inline9183 . Proper motions for about 100 pulsars have subsequently been measured largely by radio interferometric techniques [142, 21, 78, 92]. These data imply a broad velocity spectrum ranging from 0 to over 1000  tex2html_wrap_inline9183  [148Jump To The Next Citation Point In The Article].


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Figure 10: 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 tex2html_wrap_inline8985 10 kpc from the plane. This snapshot shows the initial configuration of young neutron stars. Click here to see the movie in action.

Such large velocities are perhaps not surprising, given the violent conditions under which neutron stars are formed. Shklovskii [217] demonstrated that, if the explosion is only slightly asymmetric, an impulsive ``kick'' velocity of up to 1000  tex2html_wrap_inline9183 is imparted to the neutron star. In addition, if the neutron star progenitor was a member of a binary system prior to the explosion, the pre-supernova orbital velocity will also contribute to the resulting speed of the newly-formed pulsar. High-velocity pulsars born close to the Galactic plane quickly migrate to higher Galactic latitudes. This migration is seen in Fig.  10, a dynamical simulation of the orbits of 100 neutron stars in a model of the Galactic gravitational potential. Given such a broad velocity spectrum, as much as half of all pulsars will eventually escape the gravitational potential of the Galaxy and end up in intergalactic space [148Jump To The Next Citation Point In The Article, 58Jump To The Next Citation Point In The Article].

Based on the proper motion data, recent studies have demonstrated that the mean birth velocity of normal pulsars is tex2html_wrap_inline9095 450  tex2html_wrap_inline9183 ([148, 132, 58, 84]; see, however, also [93, 91]). This is significantly larger than the velocities of millisecond and binary pulsars. Recent studies suggest that their mean birth velocity is likely to be in the range tex2html_wrap_inline9197  [129, 57, 152Jump To The Next Citation Point In The Article]. The main reason for this difference surely lies in the fact that about 80% of the millisecond pulsars are members of binary systems (§  2.4) which could not have survived had the neutron star received a substantial kick velocity.

2.5 Searching for pulsars2 An Introduction to Pulsar 2.3 The pulsar distance scale

image Binary and Millisecond Pulsars at the New Millennium
Duncan R. Lorimer
© Max-Planck-Gesellschaft. ISSN 1433-8351
Problems/Comments to livrev@aei-potsdam.mpg.de